JP4701090B2 - Program and crew route planning device - Google Patents

Description

  The present invention relates to a program or the like for causing a computer to determine a crew route plan by combining a crew member's course constituted by unit crew transitions, which are units of crew sections that can be crewed, based on a train schedule.

  When train schedules are revised in the railway, the assignment of crew members such as drivers and conductors must be planned. This plan is called a crew route plan, and it is necessary to determine a crew route (hereinafter, simply referred to as a “route”) that indicates in which order the crew is to travel from which station to which station.

  FIG. 57 is a diagram illustrating an example of a train diagram, and FIG. 58 is a diagram illustrating an example of a crew route plan for the train diagram of FIG. 57 and 58, the horizontal axis indicates time, and the vertical axis indicates a station and a ward. In FIG. 57, “train stripes” representing train operations are indicated by inclined lines, and the corresponding train numbers are indicated on each train stripe. Further, in FIG. 58, “the road” is indicated by a thick solid line, and “stool riding” is indicated by a thick broken line. However, “pick-up” means that a crew member moves on a train on which another crew member is on board.

  The crew route plan of FIG. 58 is configured by three routes. For example, the first route is a route that starts by riding one train at the B station and finally returns to the B station again at the 13th train and ends. . In this plan, four crew members will be on board every day. There are four crew members, a crew member who takes the first, second and third routes, and a crew member who takes the second day of the same route for the third route the previous day.

  This crew route plan is actually carried out manually over a long period of time and labor every time the train schedule is revised, and recently there has been a strong demand for computer-aided route planning. It is coming.

As a plan performed separately from the crew route plan, there is a vehicle operation plan that determines allocation of vehicles for each train based on a train schedule, and a method for obtaining this vehicle operation plan is disclosed in Patent Document 1, for example. .
JP 2005-259052 A

  By the way, as disclosed in Patent Document 1, in the vehicle operation plan, it is necessary to consider the constraint conditions such as the vehicle alternation inspection and the work inspection, but in the crew route plan, this constraint condition is more severe. Become.

  Because the crew route plan is for crew, (1) work hours are close to the standard value, (2) wasteful waiting time is small, (3) meal time and sleep time are secured appropriately This is because there is a specific problem that the vehicle does not have such as (4) whether work start / end time is appropriate. The severity of such constraints is one of the factors that make it difficult to obtain a crew route plan with a computer.

  In addition, the number of routes that can be considered for one train schedule is enormous, and the combination of the enormous number of routes is an astronomical number, so consider each combination of routes to be used for the crew route plan. This was extremely difficult and was a major barrier to computerization.

  The present invention has been made in view of such problems, and an object of the present invention is to realize an apparatus or the like capable of obtaining an appropriate crew route plan.

The first invention for solving the above problems is:
Dividing all train streaks included in a given train schedule into unit crews, which are units of crew sections where crew members can ride, and configuring the crew's route by combining transitions between the unit crews, A program (for example, the first crew route planning program 501 in FIG. 37) for requesting a crew route plan by combining the configured crewmember routes,
Network generating means (for example, step A3 in FIG. 38) for generating the crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
Cost setting means (for example, step A5 in FIG. 38) for setting a cost for each arc of the generated crew route network based on a predetermined evaluation criterion regarding transition between the unit crews,
A crew route network data storage means (for example, the crew route network data 601 in FIG. 37) for storing the generated crew route network and the set cost,
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. Matching calculation means (e.g., step A7 of FIG. 38),
A route for extracting, as a route plan, a predetermined number of routes having a relatively small sum of the irreducible costs for the arc included in the route among the routes of the crew members represented by the combination of the node-to-node connections according to the arc. Plan extraction means (for example, step A9 in FIG. 38),
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means (for example, step A11 in FIG. 38) that uses the combination as the optimum crew route plan.
As a program for causing the computer to function.

In addition, the sixth invention,
All train streaks included in a given train schedule are divided into unit crews, which are units of crew sections that can be used by the crew, and the crew's course is constructed by combining the transitions between the unit crews. A crew route planning device (for example, the crew route planning device 10 in FIG. 37) that obtains a crew route plan by combining the crew's routes,
Network generating means (for example, CPU 100 of FIG. 37; step A3 of FIG. 38) for generating a crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
Cost setting means (for example, CPU 100 in FIG. 37; step A5 in FIG. 38) that sets a cost for each arc of the generated crew route network based on a predetermined evaluation standard regarding transition between the unit crews;
A crew route network data storage unit (for example, crew route network data 601 in FIG. 37) for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. And; matching calculation means (step A7 in FIG. 38 for example, CPU 100 of FIG. 37)
A route for extracting, as a route plan, a predetermined number of routes having a relatively small sum of the irreducible costs for the arc included in the route among the routes of the crew members represented by the combination of the node-to-node connections according to the arc. Plan extraction means (for example, CPU 100 in FIG. 37; step A9 in FIG. 38);
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means (for example, CPU 100 in FIG. 37; step A11 in FIG. 38) that makes the combination an optimal crew route plan;
It is a crew course planning device provided with.

According to the first or sixth invention, a crew route network in which nodes of transitionable unit crews are connected by arcs is generated, and each arc of the crew route network has a cost based on a predetermined evaluation criterion. Is set. Further, based on the set cost, the value of each arc in the entire crew route network is calculated as an irreducible cost, and a complete matching of nodes is calculated. Of the path of crew represented by the combination between the nodes according to the arc connection, irreducible cost sum is relatively small given number of path of the arc included in the path are extracted as path proposal, the A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and a combination of route plans that minimizes the sum of the costs for the arc to be used among the combinations of the searched route plans. Is considered to be the optimal crew route plan.

  The irreducible cost is not the evaluation value of each arc when viewed from the connection between individual nodes (ie, local evaluation value), but the evaluation value of each arc when viewed from the entire crew route network (ie, global Therefore, a route plan with a small sum of irreducible costs is likely to be a route plan necessary for a crew route plan. Therefore, an appropriate crew route plan is obtained by searching for a combination of route plans from the extracted route plans.

In addition, the second invention,
Dividing all train streaks included in a given train schedule into unit crews, which are units of crew sections where crew members can ride, and configuring the crew's route by combining transitions between the unit crews, A program (for example, the second crew route planning program 521 in FIG. 51) for obtaining a crew route plan by combining the configured crew crew routes,
Network generating means (for example, step D3 in FIG. 53) for generating a crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
Cost setting means (for example, step D5 in FIG. 53) for setting a cost for each arc of the generated crew route network based on a predetermined evaluation criterion regarding transition between the unit crews,
A crew route network data storage unit (for example, the crew route network data 601 in FIG. 52) for storing the generated crew route network and the set cost,
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. Matching calculation means (e.g., step D7 in Fig. 53),
Clique extraction means (for example, step D9 in FIG. 53) for extracting, as a clique, a set of nodes that cannot be included in the same route in the flight of the crew member represented by the combination of node-to-node connections according to the arc.
Of the paths that do not include the nodes belonging to the extracted clique, the paths that do not include the nodes that belong to the extracted clique with respect to the total of the irreducible costs of the path that has the smallest total irreducible cost for the arc included in the path. First relative cost calculation means (for example, step D11 in FIG. 53, step F3 in FIG. 55) for calculating a relative cost of the sum of irreducible costs with respect to arcs included in each of the paths;
For each node belonging to the extracted clique, among the paths including the node, each path including the node with respect to the total irreducible cost of the path with the smallest total irreducible cost for the arc included in the path. Second relative cost calculation means (for example, step D11 in FIG. 53, step F11 in FIG. 55) for calculating the relative cost of the sum of the irreducible costs with respect to the included arc;
A route plan extracting means for extracting a predetermined number of routes having a relatively low relative cost as a route plan from among the crew members' routes represented by the combination of the node-to-node connections according to the arc (for example, step of FIG. 53). D13),
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. Riding route plan calculation means (for example, step D15 in FIG. 53) that makes the combination an optimal riding route plan.
As a program for causing the computer to function.

In addition, the seventh invention,
All train streaks included in a given train schedule are divided into unit crews, which are units of crew sections that can be used by the crew, and the crew's course is constructed by combining the transitions between the unit crews. A crew route planning device (for example, the crew route planning device 20) that obtains a crew route plan by combining the crew's routes,
Network generating means (for example, CPU 120; step D3 in FIG. 53) for generating a crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
Cost setting means (for example, CPU 120; step D5 in FIG. 53) for setting a cost for each arc of the generated crew route network based on a predetermined evaluation criterion regarding transition between the unit crews;
A crew route network data storage means (for example, crew route network data 601 in FIG. 52) for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. And; matching calculation means (step D7 of FIG. 53 for example, CPU 120)
Clique extraction means (for example, CPU 120; step D9 in FIG. 53) that extracts a set of nodes that cannot be included in the same route in the crew's route represented by the combination of node-to-node connections according to the arc. )When,
Of the paths that do not include the nodes belonging to the extracted clique, the paths that do not include the nodes that belong to the extracted clique with respect to the total of the irreducible costs of the path that has the smallest total irreducible cost for the arc included in the path. First relative cost calculation means (for example, CPU 120; step D11 in FIG. 53, step F3 in FIG. 55) for calculating the relative cost of the sum of the irreducible costs for the arcs included in each of the paths;
For each node belonging to the extracted clique, among the paths including the node, each path including the node with respect to the total irreducible cost of the path with the smallest total irreducible cost for the arc included in the path. Second relative cost calculation means (for example, CPU 120; step D11 in FIG. 53, step F11 in FIG. 55) for calculating the relative cost of the sum of the irreducible costs for the included arcs;
A route plan extraction means (for example, CPU 120; FIG. 53) extracts a predetermined number of routes having a relatively low relative cost as a route plan from among crew members' routes represented by the combination of node-to-node connections according to the arc. Step D13),
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means (for example, CPU 120; step D15 in FIG. 53) that makes the combination an optimal crew route plan;
It is a crew course planning device provided with.

According to the second or seventh invention, a crew route network in which nodes of transitionable unit crews are connected by arcs is generated, and each arc of the crew route network has a cost based on a predetermined evaluation criterion. Is set. Further, based on the set cost, the value of each arc in the entire crew route network is calculated as an irreducible cost, and a complete matching of nodes is calculated. Then, a node that becomes a clique is extracted from the crew's routes represented by the combination of node-to-node connections according to the arc, and each of the route that does not include the node that belongs to the clique and the route that includes the node that belongs to the clique The relative cost is calculated based on the irreducible cost. Of the path of crew represented by the combination between the nodes according to the arc connecting the relative cost is relatively small predetermined number of path are extracted as the path plan, flight path from among the extracted path proposal A combination of route plans that can be established as a plan is searched, and a combination of route plans that minimizes the sum of the costs with respect to the arc to be used is determined as the optimum crew route plan.

  Since nodes belonging to the clique cannot be included in the same route, the route plan including each node must be included in the route plan combination, but the relative cost is an evaluation of each route as viewed from the entire route. Because it is not a value (in other words, an absolute evaluation value) but an evaluation value (in other words, a relative evaluation value) that looks at each route for each node belonging to the clique, the route plan is extracted based on the relative cost. Thus, routes including nodes belonging to the clique are not deleted intensively. In addition, since the relative cost is an evaluation value calculated based on the irreducible cost, a route plan with a small relative cost is highly likely to be a route plan necessary for a crew route plan. Therefore, an appropriate crew route plan is obtained by searching for a combination of route plans from the extracted route plans.

The third invention is the program of the second invention,
The clique extraction means is a program for causing the computer to function so as to extract, as the clique, a set of nodes representing unit crews at one time when unit crews are densely packed.

  According to the third aspect of the invention, a set of nodes representing unit crews at one time when unit crews are densely extracted is extracted as a clique.

The fourth invention is a program according to any one of the first to third inventions,
The route plan extraction means is a program for causing the computer to function so as to screen and extract a route plan on condition that each of the nodes appears a predetermined number of times or more.

  According to the fourth aspect, the route plans are screened so that each node appears a predetermined number of times or more. If each node appears more than a predetermined number of times, the occurrence of a situation where only the number of route plans including a specific node is extremely reduced is prevented, so there are combinations of route plans that can be established as a crew route plan. It becomes easy.

The fifth invention is a program according to any one of the first to fourth inventions,
The perfect matching calculation means determines whether or not a part of the path represented by the obtained perfect matching includes a combination of connections between nodes satisfying a predetermined violation condition (for example, FIG. 38 Step A7, step B7 in FIG. 39), and when it is determined that the determination means includes, delete one arc constituting the combination of the connection between the nodes , complete matching and irreducible cost Is a program for causing the computer to function so as to calculate again (for example, Step B7 in FIG. 39; Yes → Step B9 → Step B3).

According to the fifth aspect of the present invention, when a part of a path represented by perfect matching includes a combination of connections between nodes satisfying a predetermined violation condition, one arc constituting the combination of connections between nodes Are deleted, and perfect matching and irreducible costs are calculated again.

  According to the present invention, the irreducible cost of each arc included in the crew route network is calculated, and the total irreducible cost of the arc is relative among the crew's routes represented by combinations of node-to-node connections according to the arc. A predetermined number of routes is extracted as a route plan. Then, a combination of route plans that can be established as a crew route plan is searched from the extracted route plans so as to minimize the total cost of arcs to be used, and is set as the crew route plan.

  The irreducible cost is not the evaluation value of each arc when viewed from the connection between individual nodes (ie, local evaluation value), but the evaluation value of each arc when viewed from the entire crew route network (ie, global Therefore, a route plan with a small sum of irreducible costs is likely to be a route plan necessary for a crew route plan. Therefore, an appropriate crew route plan is obtained by searching for a combination of route plans from the extracted route plans.

1. 1. First embodiment 1-1. Principle First, the principle of crew route planning in the first embodiment will be described.
FIG. 1 is a flowchart showing the flow of the first crew route plan.
The first crew route plan includes crew route network generation (step S1), basic cost setting for each arc (step S3), minimum cost perfect matching calculation processing (step S5), and first route plan extraction processing (step S3). This is realized by five steps of step S7) and set-partition solution search (step S9). Hereinafter, these five steps will be described in detail.

1-1-1. Crew Route Network Generation First, all train lines of a given train schedule are divided between stations where crew members can change, and each section is defined as a “unit crew”. For example, in the train diagram shown in FIG. 57, when one train heading from A station to C station is considered, the crew can change between A station, B station and C station, so the section from A station to B station And the section from B station to C station is a unit crew. Here, however, it is assumed that the crew cannot be on a single train from the ward.

  Next, each unit crew is represented by a point called “node”, and a “crew route network” is generated in which the nodes of the transitionable unit crews are connected by a line called “arc”. Here, the fact that the unit crews are capable of transitioning means that the arrival station of the unit crew of the transition source is the same as the departure station of the unit crew of the transition destination. For example, it is possible to transition from a unit crew representing A station to B station to a unit crew representing B station to C station, but from a unit crew representing A station to B station, a unit representing C station to A station. Transition to crew is impossible. In the crew route network, each arc is represented by an arrow, which indicates that the unit crew can transition only in the direction of the arrow.

1-1-2. Basic cost setting for each arc After the crew route network is generated, an evaluation value called a basic cost is set for each arc included in the crew route network based on a predetermined evaluation criterion. The basic cost is set such that the higher the evaluation, the smaller the value. For example, when the time required for transition from one unit crew to another unit crew (that is, the waiting time of a crew member) is used as an evaluation criterion, it can be said that the time required for transition is shorter from the viewpoint of work efficiency. . Therefore, the basic cost is set smaller for arcs with shorter transition times. Note that the evaluation criteria for setting the basic cost are not limited to those described above, and may be, for example, securing meal time or sleep time, and can be changed as appropriate. Further, the basic cost may be set based on a plurality of evaluation criteria.

  FIG. 2 is a diagram illustrating an example of a crew route network in which a basic cost is set for each arc. In the figure, nodes represented by “a” to “f” each represent a unit crew. The nodes represented by “X” and “Y” represent the start and end of crew, respectively, and are special nodes (hereinafter referred to as “dummy nodes”) used for convenience. In the following description, it is assumed that the crew always starts from the dummy node “X” and ends at the dummy node “Y”. Further, a combination (path) between the nodes from the dummy node “X” to the dummy node “Y” is referred to as “path”. For example, “X” → “a” → “f” → “Y” The route is represented by the route “XafY”.

  Moreover, in FIG. 2, the numerical value attached | subjected to each arc has shown the set basic cost. For example, the basic cost of an arc connecting node “a” and node “f” is “30”, which is a very large value compared to other arcs. It can be said that the transition from the crew to the unit crew representing the node “f” is a transition with a low evaluation.

  The crew route plan is realized by searching for a combination in which each node excluding the dummy node appears once from among the combinations of the routes described above (hereinafter, this combination is referred to as a “set partitioning solution”). Is done. This is because if all nodes appear once, crew members are assigned to all unit crews.

  However, in general, since the number of possible routes is enormous, it is extremely difficult to search for a combination of all the routes, which may exceed the processing capability of the computer. Therefore, it was considered to screen the routes so that only the routes with high necessity in the crew route plan remain.

  In this case, it is necessary to determine the necessity in the crew route planning of each route based on some evaluation criteria. Therefore, focusing on the basic cost set for each arc, the basic cost is an evaluation value focusing only on the connection between the individual nodes, but it is suitable for evaluating the necessity in the crew route planning of each route. It cannot be generally said that it is an evaluation value. This is because, for example, if the routes are screened so that only the routes where the total arc basic cost is small remain, only the routes that include a specific node will remain, and the set-partition solution This is because there is a risk that will disappear.

  Therefore, in order to evaluate the necessity of crew route planning for each route, we decided to introduce a concept called “irreducible cost” that represents the value of each arc when viewed in the entire crew route network. The irreducible cost is an evaluation value indicating that the smaller the value is, the higher the evaluation is, like the basic cost. This irreducible cost is that each node except the dummy node always has one arc going to any other node, and one arc has always entered from any other node. By calculating the “minimum cost perfect matching”, which is a perfect matching that minimizes the sum of the basic costs (hereinafter referred to as “perfect matching”). Can be sought.

1-1-3. Minimum Cost Perfect Matching Calculation Processing Next, a method for calculating the minimum cost perfect matching will be described in detail with reference to FIGS. Here, the case where the minimum cost perfect matching for the crew route network of FIG. 2 is calculated will be described as an example.

  First, a “transition normalization diagram” in which the crew route network of FIG. 2 is rewritten is generated. Specifically, the nodes “a” to “f” are arranged in a row as nodes representing the unit crew of the transition source, and the nodes “a” to “f” are arranged in a row as nodes representing the unit crew of the transition destination at the opposite electrode. To place. That is, for the nodes “a” to “f”, the transition source and the transition destination are distinguished and two nodes are arranged. Hereinafter, a node representing a transition source unit crew is referred to as a “transition source node”, and a node representing a transition destination unit crew is referred to as a “transition destination node”.

  Further, dummy nodes “X” and “Y” are arranged at an intermediate position between the transition source node and the transition destination node. Then, an arc having a basic cost is connected from the transition source node to the transition destination node or the dummy node, and from the dummy node to the transition destination node so as to be equivalent to the crew route network of FIG. The generated transition normalization diagram is shown in FIG.

However, in FIG. 3, in order to distinguish the transition source node and the transition destination node, the transition source node is represented by “a ₁ ” to “f ₁ ”, and the transition destination node is represented by “a ₂ ” to “f ₂ ”. ing. In order to make the figure easy to see, the dummy nodes “X” and “Y” are collectively represented by the dummy node “X / Y”, the order of the transition source nodes “a ₁ ” to “f ₁ ”, and the transition destination The arrangement order of the nodes “a ₂ ” to “f ₂ ” is reversed.

  The basic cost set for each arc is updated as necessary as “irreducible cost” in the process of calculating the minimum cost perfect matching. That is, the basic cost is the initial value of the irreducible cost.

  In addition, “distance label” and “node potential” are set for all nodes. The distance label is the sum of the irreducible costs currently known for the arc connecting from the starting node to the node when a certain node is the starting point (hereinafter referred to as “starting node”). The distance label is set to “∞ (infinity)” as an initial value, and is updated with the newly calculated value when the newly calculated value is smaller than the already set value. Hereinafter, the distance label of the node “i” is represented by d (i).

  The node potential is an intrinsic energy of each node and functions as a work variable for calculating an irreducible cost. The node potential is set to “0” as an initial value, and the value is updated only for a node whose distance label is determined.

Specifically, when the node potential at the node “i” is represented by “π (i)”, π (i) is updated according to the equation (1).
π (i) ← π (i) −d (i) + d (R) (1)
However, d (R) is the sum of the irreducible costs of arcs connecting from the departure node to the node finally reached (hereinafter referred to as “final arrival node”). That is, the distance label of the final destination node is d (R).

  According to Equation (1), the node potential is determined by the relative relationship between the distance label of the target node and the distance label of the final destination node, and the larger the difference between the two distance labels, the more the updated amount is. growing.

The irreducible cost of each arc is updated by updating the node potential of one or both of the two nodes connected by the arc. Specifically, when the irreducible cost of the arc connected from the node “i” to the node “j” is represented by “w (ij)”, w (ij) is updated according to the equation (2). The
w (ij) ← w (ij) −π (i) + π (j) (2)

  According to Equation (2), the irreducible cost is determined by the relative relationship between the node potentials of the two nodes connected by the target arc, and the amount of renewal increases as the difference between the two node potentials increases. .

  After setting the distance label and the node potential, a search is made for a transition destination node that can be reached with a minimum irreducible cost, with each transition source node as a starting node. Then, the searched transition destination node is determined as the final destination node, and the node potential and the irreducible cost are updated according to the equations (1) and (2).

  In the following, the method for searching for the final destination node will be described. The processing for each departure node is sequentially performed, the processing for each departure node is called “turn”, and the distance label whose value is determined in this one turn. In the figure, the node potential and the irreducible cost are expressed in gray. In addition, an arc up to a node whose distance label is currently determined is represented by a thick arrow.

(A) When the transition source node “a ₁ ” is the departure node First, when the transition source node “a ₁ ” is the departure node, the irreducible cost until the transition source node “a ₁ ” reaches itself is “ Since it is “0”, the distance label of the transition source node “a ₁ ” is updated from “∞” to “0”. Since the distance label of the transition source node “a ₁ ” never becomes smaller than this, the distance label of the transition source node “a ₁ ” is fixed to “0” (see FIG. 4).

Next, the transition destination node that can be reached from the transition source node “a ₁ ” is the transition destination node “f ₂ ” or the transition destination node “c ₂ ”, but the existing node until the transition destination node “f ₂ ” is reached. The approximately cost is “30”, and the irreducible cost until the transition destination node “c ₂ ” is reached is “1”.

In this case, the distance label of the transition destination node “f ₂ ” is updated to “30” and the distance label of the transition destination node “c ₂ ” is updated to “1”, but the transition destination node “c ₂ ” It is possible to reach the irreducible cost smaller than the previous node “f ₂ ”. Therefore, the distance label of the transition destination node “c ₂ ” is fixed to “1”. A node can reach the other from transition destination node "c _2" are due to the absence, determined transition destination node "c _2" in the ultimate node (see Figure 5).

By the procedure so far, the distance labels of the transition source node “a ₁ ” and the transition destination node “c ₂ ” are determined. Thus, a transition source node "a _1" node potential "[pi (a _1)" of the node potential of the transition destination node "c _2" "[pi (c _2)" and is updated according to Equation (1).

Specifically, for the node potential “π (a ₁ )”, the current value is “π (a ₁ ) = 0”, and the distance label of the transition source node “a ₁ ” is “d (a ₁ ) = 0”. Since the distance label of the final destination node is “d (R) = d (c ₂ ) = 1”, it is updated to “π (a ₁ ) −d (a ₁ ) + d (R) = 1”. Similarly, for the node potential “π (c ₂ )”, the current value is “π (c ₂ ) = 0”, the distance label of the transition destination node “c ₂ ” is “d (c ₂ ) = 1”, and the final Since the distance label of the destination node is “d (R) = d (c ₂ ) = 1”, it is updated to “π (c ₂ ) −d (c ₂ ) + d (R) = 0”.

Further, since the node potentials “π (a ₁ )” and “π (c ₂ )” are updated, the irreducible cost w (a ₁ f) of the arc from the transition source node “a ₁ ” to the transition destination node “f ₂ ”. ₂ ) and the irreducible cost w (a ₁ c ₂ ) of the arc from the transition source node “a ₁ ” to the transition destination node “c ₂ ” are updated according to equation (2).

Specifically, the irreducible cost “w (a ₁ f ₂ )” is the current value “w (a ₁ f ₂ ) = 30”, and the node potential of the transition source node “a ₁ ” is “π (a ₁ ) = 1 ”and the node potential of the transition destination node“ f ₂ ”is“ π (f ₂ ) = 0 ”, so that“ w (a ₁ f ₂ ) −π (a ₁ ) + π (f ₂ ) = 29 ". Similarly, the irreducible cost “w (a ₁ c ₂ )” is the current value “w (a ₁ c ₂ ) = 1”, and the node potential of the transition source node “a ₁ ” is “π (a ₁ )”. = 1 ”and the node potential of the transition destination node“ c ₂ ”is“ π (c ₂ ) = 0 ”, so“ w (a ₁ c ₂ ) −π (a ₁ ) + π (c ₂ ) = 0 ” Update to

Up to this point, the turn when the transition source node “a ₁ ” is the departure node ends, but the transition source node “a ₁ ” means that the transition destination node “c ₂ ” has been finalized. The direction of the arc heading from “ ₁ ” to “destination node“ c ₂ ”is reversed (see FIG. 6). It is difficult to understand because the irreducible cost of the arc from the transition source node “a ₁ ” to the transition destination node “c ₂ ” is “0”, but the sign of the irreducible cost is also reversed by reversing the arc direction. To do.

(B) When transition source node “b ₁ ” is the departure node Next, transition source node “b ₁ ” is the departure node. First, the distance labels of all nodes are initialized to “∞”.
Thereafter, since the irreducible cost until the transition source node “b ₁ ” reaches itself is “0”, the distance label of the transition source node “b ₁ ” is updated from “∞” to “0” and confirmed. (See FIG. 7).

Next, the transition destination node that can be reached from the transition source node “b ₁ ” is the transition destination node “e ₂ ” or the transition destination node “c ₂ ”, but the existing node until the transition destination node “e ₂ ” is reached. The approximately cost is “10”, and the irreducible cost until the transition destination node “c ₂ ” is reached is “5”.

In this case, the distance label of the transition destination node “e ₂ ” is updated to “10”, and the distance label of the transition destination node “c ₂ ” is updated to “5”, but the transition destination node “c ₂ ” It is possible to reach the irreducible cost smaller than the previous node “e ₂ ”. Therefore, the distance label of the transition destination node “c ₂ ” is fixed to “5” (see FIG. 8).

Since the transition destination node “c ₂ ” is determined as the final destination node of the transition source node “a ₁ ”, the transition destination node “c ₂ ” is determined as the final destination node of the transition source node “b ₁ ”. I can't. However, since the transition from the transition destination node “c ₂ ” to the transition source node “a ₁ ” becomes possible due to the inversion of the arc, the transition source node “b ₁ ” and the transition destination node “c ₂ ” and the transition source node It is possible to reach the transition destination node “f ₂ ” via the node “a ₁ ”.

Now, the irreducible cost from the transition source node “b ₁ ” to the transition source node “a ₁ ” is “5 + 0 = 5”, and the transition source node “b ₁ ” changes to the transition destination node “e ₂ ”. Since it is smaller than the irreducible cost “10” to reach, the distance label of the transition source node “a ₁ ” is fixed to “5” (see FIG. 9).

Next, considering the irreducible cost from the transition source node “b ₁ ” to the transition destination node “f ₂ ”, it is “5 + 0 + 29 = 34”, but from the transition source node “b ₁ ” to the transition destination node “e” _Since the irreducible cost until reaching “ ₂ ” is “10”, it is possible to reach the transition destination node “e ₂ ” with an irreducible cost smaller than that of the transition destination node “f ₂ ”. Therefore, the distance label of the transition destination node “e ₂ ” is fixed to “10”. A node can reach the other from transition destination node "e _2" is due to the absence, determined transition destination node "e _2" to the ultimate node (see Figure 10).

The distance labels of the transition source node “a ₁ ”, the transition source node “b ₁ ”, the transition destination node “c ₂ ”, and the transition destination node “e ₂ ” are determined by the procedure so far. The node potential is updated according to equation (1).

Specifically, the node potential “π (a ₁ )” is updated to “π (a ₁ ) −d (a ₁ ) + d (R) = 6”, and the node potential “π (b ₁ )” is Update to “π (b ₁ ) −d (b ₁ ) + d (R) = 10”. Further, the node potential “π (c ₂ )” is updated to “π (c ₂ ) −d (c ₂ ) + d (R) = 5”, and the node potential “π (e ₂ )” is changed to “π ( e ₂ ) −d (e ₂ ) + d (R) = 0 ”. However, d (R) = d (e ₂ ) = 10.

Further, when the irreducible cost concerned is updated, the irreducible cost “w (b ₁ e ₂ )” is updated to “w (b ₁ e ₂ ) −π (b ₁ ) + π (e ₂ ) = 0”. The irreducible cost “w (b ₁ c ₂ )” is updated to “w (b ₁ c ₂ ) −π (b ₁ ) + π (c ₂ ) = 0”. The irreducible cost “w (a ₁ f ₂ )” is updated to “w (a ₁ f ₂ ) −π (a ₁ ) + π (f ₂ ) = 24”, and the irreducible cost “w (X / Yc ₂ ) ”is updated to“ w (X / Yc ₂ ) −π (X / Y) + π (c ₂ ) = 6 ”.

Up to this point, since the turn when the transition source node “b ₁ ” is the departure node is completed, the arc from the transition source node “b ₁ ” to the transition destination node “e ₂ ” is reversed (see FIG. 11). ).

(C) When the transition source node “c ₁ ” is the departure node The same applies when the transition source node “c ₁ ” is the departure node. First, after initializing the distance labels of all nodes to “∞” The distance label of the transition source node “c ₁ ” is fixed to “0” (see FIG. 12).

Next, since the irreducible cost to reach the transition destination node “d ₂ ” is the smallest at “1”, the distance label of the transition destination node “d ₂ ” is fixed to “1”, and the transition destination node “d” ₂ ”is determined as the final destination node (see FIG. 13). Since the irreducible cost “w (c ₁ d ₂ ) = w (c ₁ f ₂ ) = 1”, the transition destination node “f ₂ ” may be determined as the final destination node. A description will be given assuming that the previous node “d ₂ ” is selected.

Then, the node potential is updated for the transition source node “c ₁ ” and the transition destination node “d ₂ ” for which the distance label is determined, and the irreducible costs related to the node potential are updated. Further, since the turn when the transition source node “c ₁ ” is set as the departure node is completed so far, the arc from the transition source node “c ₁ ” to the transition destination node “d ₂ ” is reversed (FIG. 14). reference).

(D) When transition source node “d ₁ ” is the departure node The same applies when transition source node “d ₁ ” is the departure node. First, after initializing the distance labels of all nodes to “∞” The distance label of the transition source node “d ₁ ” is fixed to “0” (see FIG. 15).

Next, the distance label of the dummy node “X / Y” is fixed to “1” (see FIG. 16). Then, since the irreducible cost until reaching the transition destination node “b ₂ ” is the smallest “1 + 5 = 6”, the distance label of the transition destination node “b ₂ ” is fixed to “6”, and the transition destination node “B ₂ ” is determined as the final destination node (see FIG. 17). Since the irreducible cost “w (X / Yb ₂ ) = w (X / Ya ₂ ) = 5”, the transition destination node “a ₂ ” may be determined as the final destination node. A description will be given assuming that the previous node “b ₂ ” is selected.

Then, the node potential is updated for the transition source node “d ₁ ”, the dummy node “X / Y”, and the transition destination node “b ₂ ” for which the distance label is determined, and the related irreducible costs are updated. Further, since the turn when the transition source node “d ₁ ” is set as the departure node is completed so far, the arc from the transition source node “d ₁ ” to the dummy node “X / Y” and the dummy node “X” / Y ”and the arc from the transition destination node“ b ₂ ”are reversed (see FIG. 18).

(E) When transition source node “e ₁ ” is the departure node The same applies when transition source node “e ₁ ” is the departure node. First, after initializing the distance labels of all nodes to “∞” The distance label of the transition source node “e ₁ ” is fixed to “0” (see FIG. 19).

Next, since the irreducible cost “5” until reaching the transition destination node “d ₂ ” is smaller than the irreducible cost “15” until reaching the dummy node “X / Y”, the transition destination node The distance label of “d ₂ ” is fixed to “5” (see FIG. 20).

Further, the irreducible cost “5 + 0 = 5” until reaching the transition source node “c ₁ ” via the transition destination node “d ₂ ” is more irreducible until reaching the dummy node “X / Y”. Since the cost is smaller than “15”, the distance label of the transition source node “c ₁ ” is fixed to “5” (see FIG. 21).

The irreducible cost “5 + 0 + 0 = 5” until reaching the transition destination node “f ₂ ” via the transition destination node “d ₂ ” and the transition source node “c ₁ ” is the dummy node “X / Y”. since "less than irreducible cost" 15 "to reach the a distance label of the transition destination node" f ₂ "and confirm the" 5 "and confirm transition destination node" f ₂ "to the ultimate node ( (See FIG. 22).

Then, the node potential is updated for the transition source node “e ₁ ”, the transition source node “c ₁ ”, the transition destination node “d ₂ ”, and the transition destination node “f ₂ ” for which the distance label is determined, and the related irreducible costs. Update. Since the turn when the transition source node “e ₁ ” is set as the departure node is completed so far, the arc from the transition source node “e ₁ ” to the transition destination node “d ₂ ” and the transition destination node “ The arc from d ₂ ”to the transition source node“ c ₁ ”and the arc from the transition source node“ c ₁ ”to the transition destination node“ f ₂ ”are reversed (see FIG. 23).

(F) When the transition source node “f ₁ ” is the departure node The same applies when the transition source node “f ₁ ” is the departure node. First, after initializing the distance labels of all nodes to “∞” The distance label of the transition source node “f ₁ ” is fixed to “0” (see FIG. 24).

Next, since the irreducible cost “1” until reaching the transition destination node “d ₂ ” is smaller than the irreducible cost “10” until reaching the dummy node “X / Y”, the transition destination node The distance label “d ₂ ” is fixed to “1” (see FIG. 25).

Further, the irreducible cost “1 + 0 = 1” until reaching the transition source node “e ₁ ” via the transition destination node “d ₂ ” is more irreducible until reaching the dummy node “X / Y”. It is smaller than the cost "10" and confirm the distance label of the transition source node "e _1" to "1" (see FIG. 26).

Then, from the irreducible cost “1 + 0 + 10 = 11” to reach the dummy node “X / Y” via the transition destination node “d ₂ ” and the transition source node “e ₁ ”, and the transition source node “f ₁ ” Comparing the irreducible cost “10” until reaching the dummy node “X / Y” directly, the irreducible cost “10” until reaching the dummy node “X / Y” is smaller. The distance label of the node “X / Y” is fixed to “10” (see FIG. 27).

Next, since the irreducible cost until reaching the transition destination node “a ₂ ” via the dummy node “X / Y” is the smallest at “10 + 0 = 10”, the distance label of the transition destination node “a ₂ ” is set to “ 10 ”and the transition destination node“ a ₂ ”is confirmed as the final destination node (see FIG. 28).

Then, the node potential is set for the transition source node “f ₁ ”, the transition source node “e ₁ ”, the transition destination node “d ₂ ”, the transition destination node “a ₂ ”, and the dummy node “X / Y” for which the distance label is determined. Update and update the irreducible costs involved. Further, since the turn when the transition source node “f ₁ ” is set as the departure node is completed so far, the arc from the transition source node “f ₁ ” to the dummy node “X / Y” and the dummy node “X” / Y ”and the arc from the transition destination node“ a ₂ ”are reversed (see FIG. 29).

  As described above, when all transition source nodes are set as departure nodes, a search is made for a transition destination node that can be reached with a minimum irreducible cost. The correspondence between the starting node and the final destination node obtained by this search is a minimum cost perfect matching.

  Now, a diagram obtained by rewriting the transition normalization diagram in which the minimum cost perfect matching has been calculated into a network format will be referred to as a “post-matching network”. FIG. 30 shows a post-matching network for the transition normalization diagram of FIG.

  In FIG. 30, the minimum cost perfect matching is indicated by a thick arrow. As you can see, for every node except for the dummy node, one arc always goes to any other node, and one arc always comes from any other node. A combination of nodes is obtained.

  A route belonging to the minimum cost perfect matching (that is, a route obtained by following an arrow) includes a route that violates one continuation crew time (hereinafter referred to as “one continuation crew time violation route”). There may be. Here, one continuous crew time refers to a time during which a predetermined crew may continue to carry out crew, and is determined to be “3 hours”, for example. A route refers to a route from one node in the route to another node. A crew member cannot be assigned to a route including this one-continuous crew time violation route.

  Therefore, when the route belonging to the minimum cost perfect matching includes a one-continuous crew time violation route, one arc on the route is deleted. This is because if one arc is deleted, transition between unit crews representing nodes connected by the arc becomes impossible, and the violation of one continuous crew time of the route is eliminated. Then, the minimum cost perfect matching is calculated again.

1-1-4. First route plan extraction process The irreducible cost is obtained for each arc by the minimum cost perfect matching calculation process. Since the irreducible cost represents the value of each arc in the entire crew route network, if routes are screened based on this irreducible cost, it is possible to leave only the routes that are highly necessary in the crew route plan. become able to.

Therefore, in the first route plan extraction process, the route is screened according to the following procedure.
First, a route is selected one by one from the network after matching, and the number of appearances (hereinafter referred to as “appearance count”) of each node excluding the dummy nodes is counted. Then, the path is selected until the smallest number of appearances (hereinafter referred to as “minimum number of appearances”) exceeds a predetermined threshold θ (until the minimum number of appearances> threshold θ). It should be noted that the order in which the routes are selected may be a preset order or may be random.

  Then, when the minimum number of appearances exceeds the threshold θ, the path having the maximum total irreducible cost of arcs included in the path among the already selected paths (hereinafter referred to as “total irreducible cost”). Is deleted, and another route is newly selected from the network after matching. This procedure is repeated until there are no selectable paths.

  When there is no selectable route from the network after matching, it is determined whether or not there is a route including only a node satisfying the condition of occurrence frequency> threshold value θ. Delete the route with the highest cost. Then, this procedure is repeatedly executed until there are no paths including only nodes satisfying the condition that the number of appearances> threshold θ, and when there is no path, the screening of the paths is terminated.

  A case where the screening of the route by the first route plan extraction process is performed on the route included in the post-matching network in FIG. 30 will be described as an example. However, here, the case where the threshold θ is “3” and the route is screened will be described.

FIGS. 31 to 34 are diagrams showing first route plan data 607 which is data used when sieving a route in the first route plan extraction process.
In the first route plan data 607, a route 6071, a total irreducible cost 6073, and a node 6075 are stored in association with each other, and an appearance count 6077 is stored for each node constituting the node 6075.

  The route 6071 is a route selected from the post-matching network, and the total irreducible cost 6073 is the total irreducible cost of the route. The node 6075 is composed of nodes other than the dummy nodes included in the post-matching network, and “maru” is set when the node is included in the selected route. The number of appearances 6077 indicates the number of appearances of each node constituting the node 6075, and the total number of “maru” set in each node is stored.

  FIG. 31 is a diagram showing first route plan data 607 when a route included in the network after matching of FIG. 30 is selected at random and the minimum number of appearances of the node 6075 exceeds the threshold θ. By selecting the route “XbedY”, the number of appearances of the nodes “b”, “d”, and “e” is updated, the minimum number of appearances of the node is “4”, and the threshold “θ = 3” is set. Exceeded state is shown.

  FIG. 32 is a diagram showing the first route plan data 607 when one route having the maximum total irreducible cost is deleted and another route is newly selected after the state of FIG. 31. In FIG. 31, when the minimum number of appearances of the node is “4” and exceeds the threshold “θ = 3”, the route “XcdY” that is the route with the maximum total irreducible cost is deleted, and the network after matching is deleted. The route “XaceY” is newly selected. Along with this, the appearance count 6077 is updated.

  FIG. 33 is a diagram showing first route plan data 607 when the procedure of FIG. 32 is repeatedly executed and there is no route that can be selected from the network after matching. FIG. 34 is a diagram showing the first route plan data 607 when one route including only a node satisfying the condition that the number of appearances> the threshold θ is deleted after the state of FIG.

  Since there is no route that can be selected from the post-matching network, one route that has only the maximum irreducible cost is deleted from the routes that include only nodes that satisfy the condition that the number of appearances> the threshold value θ. In FIG. 33, nodes satisfying the condition that the number of appearances> threshold θ is a node other than “a”, and among the routes not including node “a”, the route “XcedY” having the maximum total irreducible cost is included. The deleted state is shown in FIG. Although the route “XcedY” is deleted here, the route “XbceY”, which is the route having the maximum total irreducible cost, may be deleted as a matter of course.

  FIG. 35 is a diagram showing the first route plan data 607 in a state where the procedure of FIG. 34 is repeated and the sieving of the route is completed. Of the paths that include only nodes that satisfy the condition that the number of occurrences> threshold θ, the procedure for deleting the path with the maximum total irreducible cost has been repeatedly executed, and finally there are six paths remaining. .

1-1-5. Set division solution search In the first route plan extraction process, routes are screened based on irreducible costs. After that, a set division solution may be searched from the remaining routes, and the searched set division solution may be used as a crew route plan. Here, the optimal solution for the crew route plan is a combination of routes that minimizes the sum of the basic costs set for the arc. This is because the basic cost is an evaluation value of an arc focusing on the connection between nodes, and it can be said that a route including an arc with a low basic cost is a highly evaluated route.

FIG. 36 is a diagram illustrating crew route plan data 609 that is data of a crew route plan obtained by searching for a set division solution from the routes included in the first route plan data 607 of FIG. 35.
When a set division solution is searched from among the six routes included in the first route plan data 607 of FIG. 35, “XbedY + XacfY” and “XacfdY + XbeY” are searched, and these two become the crew route plan. Further, the sum of the basic costs of the arcs included in the route constituting the crew route plan “XbedY + XacfY” is “21 + 12 = 33”, and the sum of the basic costs of the arcs included in the route constituting the crew route plan “XacfdY + XbeY” is Since “9 + 25 = 34”, the crew route plan “XbedY + XacfY” having a small value is an optimal solution, and the crew route plan “XacfdY + XbeY” is a suboptimal solution.

1-2. Example Next, with reference to FIGS. 37 to 40, 1-1. The crew route planning device 10 that is a device that performs the crew route planning described in the principle will be described.

1-2-1. Configuration First, the configuration will be described.
FIG. 37 is a block diagram illustrating a functional configuration of the crew route planning device 10.
The crew route planning apparatus 10 includes a CPU (Central Processing Unit) 100, an input unit 200, a display unit 300, a communication unit 400, a ROM (Read Only Memory) 500, and a RAM (Random Access Memory) 600. Each unit is a computer system configured to be connected to each other via a bus 700 so that data communication is possible.

  The CPU 100 comprehensively controls each unit in accordance with a system program or the like stored in the ROM 500. Further, the CPU 100 performs the first crew route planning process according to the first crew route planning program 501 stored in the ROM 500 and causes the display unit 300 to display the crew route plan.

  The input unit 200 is realized by a keyboard or the like, for example, and outputs a pressed key signal to the CPU 100. Various data are input by the key operation by the input unit 200.

  The display unit 300 is configured by an LCD (Liquid Crystal Display) or the like, and is a display device that performs various displays based on display signals input from the CPU 100.

  The communication unit 400 is a communication device for exchanging information used inside the device with the outside via a communication network such as the Internet based on the control of the CPU 100.

  The ROM 500 stores programs and the like for realizing various functions of the crew route planning device 10. The ROM 500 is read by the CPU 100 and executed as a first crew route planning process (see FIG. 38), a first crew route planning program 501, train diagram data 505, crew member base data 507, and crew transition conditions. Data 509. The first crew route planning program 501 is executed as the minimum cost perfect matching calculation program 502 executed as the minimum cost perfect matching calculation processing (see FIG. 39) and the first route plan extraction processing (see FIG. 40). The first route plan extraction program 503 is provided as a subroutine.

  In the first crew route planning process, the CPU 100 calculates the minimum cost perfect matching for the crew course network generated based on the train schedule data 505 and the crew member data 507 by the minimum cost perfect matching calculation process. This is a process of sieving the route by the route plan extraction process. Then, the CPU 100 searches for a set division solution from the remaining routes by screening the route, and causes the display unit 300 to display the searched set division solution as a crew route plan. The first crew route planning process will be described later in detail.

  The minimum cost perfect matching calculation process is a process in which the CPU 100 generates a transition normalization diagram based on the crew route network and calculates the minimum cost perfect matching using the generated transition normalization diagram. Then, the CPU 100 generates a post-matching network based on the calculated minimum cost perfect matching. This minimum cost perfect matching calculation process has been described above in detail, but will be described later again in detail using a flowchart.

  The first route plan extraction process is a process in which the CPU 100 screens routes by deleting routes based on the total irreducible cost while selecting a route included in the network after matching. The principle of the first route plan extraction process has been described above, but will be described later again in detail using a flowchart.

  The train diagram data 505 is data on a train diagram during normal operation as shown in FIG. 57, for example, and stores train information of trains constituting the train diagram. Specifically, it is information such as the train number of each train, the arrival and departure times at each station, and the train type.

  The crew member base data 507 is data in which a station serving as a crew member base is determined. The train diagram data 505 and the crew member base data 507 are data used when the CPU 100 generates a crew course network in the first crew course planning process.

  The crew transition condition data 509 is data in which conditions regarding transitions between unit crews and evaluation criteria regarding transitions are defined. The crew transition condition data 509 is data used when the CPU 100 sets the basic cost of each arc of the crew course network in the first crew course planning process.

  The RAM 600 forms a work area for temporarily storing a system program executed by the CPU 100, various processing programs, data being processed in various processing, processing results, and the like. The RAM 600 includes crew route network data 601, transition normalization diagram data 603, post-matching network data 605, first route plan data 607, and crew route plan data 609.

  The crew route network data 601 is data on a crew route network as shown in FIG. 2, for example, and stores a crew route network generated by the CPU 100 in the first crew route planning process. The crew route network data 601 also stores the basic cost set for each arc.

  The transition normalization diagram data 603 is data about a transition normalization diagram as shown in FIGS. 3 to 29, for example, and stores a transition normalization diagram generated by the CPU 100 in the minimum cost perfect matching calculation process. In this transition normalized diagram data 603, distance labels of each node, node potentials, and irreducible costs are also stored.

  The post-matching network data 605 is data about the post-matching network as shown in FIG. 30, for example, and stores the post-matching network generated by the CPU 100 in the minimum cost complete matching calculation process. In this post-matching network data 605, the irreducible cost obtained for each arc is also stored.

  The first route plan data 607 is data in which the route 6071, the total irreducible cost 6073, and the node 6075 are stored in association with each other, and the number of appearances 6077 of each node is stored. This is as shown in FIGS. The first route plan data 607 is generated by the CPU 100 in the first route plan extraction process.

  The crew route plan data 609 is data in which the set division solution searched by the CPU 100 in the first crew route plan process is stored as the crew route plan, and the data configuration example is as shown in FIG. .

1-2-2. Process Flow Next, the process flow will be described.
FIG. 38 is a flowchart showing the flow of the first crew route planning process executed in the crew route planning device 10 by the CPU 100 reading and executing the first crew route planning program 501.

  First, the CPU 100 performs initial setting such as setting of a threshold value θ used when sieving a route in the first route plan extraction process (step A1).

  Next, the CPU 100 generates a crew route network based on the train diagram data 505 and the crew member base data 507 (step A3). Specifically, CPU100 acquires a unit crew by dividing all the train lines of a train diagram by the station where a crew member can change. Then, the CPU 100 uses each unit crew as a node, and generates a crew route network by connecting the nodes of transitionable unit crews with arcs. Thereafter, the CPU 100 stores the generated crew route network as crew route network data 601.

  Thereafter, the CPU 100 sets the basic cost of each arc included in the crew route network generated in step A3 based on the crew transition condition data 509 (step A5). Specifically, the CPU 100 sets the basic cost so that the value of the arc representing the transition between unit crews with low evaluation becomes larger. Then, the CPU 100 stores the set basic cost in the crew route network data 601.

  Next, the CPU 100 reads and executes the minimum cost perfect matching calculation program 502, thereby performing a minimum cost perfect matching calculation process (step A7).

FIG. 39 is a flowchart showing the flow of the minimum cost perfect matching calculation process.
First, the CPU 100 generates a transition normalization diagram based on the crew route network generated in the first crew route planning process and the basic cost of each set arc (step B1).

  Specifically, the CPU 100 generates a transition normalization diagram by arranging a transition source node, a transition destination node, and a dummy node, and connecting arcs so as to be equivalent to the crew route network. Further, the distance label of each node is initialized to “∞” and the node potential is initialized to “0”, and the basic cost is set as the initial value of the irreducible cost of each arc. Then, the CPU 100 stores the generated transition normalization diagram as transition normalization diagram data 603.

  Next, the CPU 100 calculates a minimum cost perfect matching by searching for a transition destination node that can be reached with a minimum irreducible cost by using each transition source node in the transition normalization diagram as a starting node (step B3). The method of calculating the minimum cost perfect matching is as described with reference to FIGS.

  Thereafter, the CPU 100 generates a post-matching network by rewriting the transition normalization diagram in which the minimum cost perfect matching is calculated in step B3 into a network format (step B5). Then, the CPU 100 stores the generated post-matching network as post-matching network data 605.

  Next, the CPU 100 determines whether or not the route that belongs to the calculated minimum cost perfect matching includes a one-continuous crew time violation route (step B7). Specifically, the CPU 100 refers to the train diagram data 505 and the crew route network data 601 and extracts all arcs whose transition time is “0” from routes belonging to the minimum cost perfect matching, List the paths that do not contain the extracted arcs. Then, the crew time of each enumerated route is calculated, and it is determined whether or not the calculated crew time exceeds a predetermined one-time crew time.

  If it is determined in step B7 that the one-continuous crew time violation route is included (step B7; Yes), the CPU 100 deletes one arc on the one-continuous crew time violation route (step B9), and the step Return to B3.

  On the other hand, if it is determined in step B7 that the one-way crew time violation route is not included (step B7; No), the CPU 100 ends the minimum cost perfect matching calculation process.

  Returning to the first crew route planning process of FIG. 38 and ending the minimum cost perfect matching calculation process, the CPU 100 reads and executes the first route plan extraction program 503 to thereby execute the first route plan extraction process. (Step A9).

FIG. 40 is a flowchart showing the flow of the first route plan extraction process.
First, the CPU 100 selects one path included in the post-matching network generated in the minimum cost perfect matching calculation process (step C1).

  Next, the CPU 100 calculates the total irreducible cost by calculating the total irreducible cost of the arcs included in the selected route, and stores it as the first route plan data 607 together with the route (step C3). And CPU100 updates the appearance frequency of a node by specifying the node contained in the said path (step C5).

  Thereafter, the CPU 100 determines whether or not the minimum number of appearances of the node has exceeded the threshold value θ (step C7). If it is determined that the node has not exceeded the threshold θ (step C7; No), the process proceeds to step C13.

  On the other hand, when it is determined in step C7 that the minimum number of appearances of the node has exceeded the threshold θ (step C7; Yes), the CPU 100 determines that the total irreducible cost among the routes included in the first route plan data 607 is One maximum path is deleted (step C9). And CPU100 updates the appearance frequency of a node by specifying the node contained in the deleted course (step C11).

  Next, the CPU 100 determines whether or not there is no other path that can be selected from the network after matching (step C13), and when it is determined that there is still another path that can be selected (step C13; No), the process proceeds to step C1. And return.

  On the other hand, if it is determined in step C13 that there are no other routes that can be selected (step C13; Yes), the CPU 100 refers to the first route plan data 607 and refers to the node satisfying the condition of the number of appearances> threshold θ. It is determined whether or not there is a route including only (step C15).

  If it is determined in step C15 that there is a route (step C15; Yes), the CPU 100 deletes one of the routes having the maximum total irreducible cost (step C17). And CPU100 updates the appearance frequency of a node by specifying the node contained in the deleted course (step C19), and returns to step C15.

  On the other hand, if it is determined in step C15 that there is no route (step C15; No), the CPU 100 ends the first route plan extraction process.

  Returning to the first crew route planning process of FIG. 38, when the first route plan extracting process is completed, the CPU 100 searches for a set division solution from the remaining routes by sieving (step A11). The set division solution is stored in the crew route plan data 609. Then, the CPU 100 displays the searched set division solution on the display unit 300 as a crew route plan (step A13), and ends the first crew route plan process.

1-3. Effects According to the present embodiment, the minimum cost perfect matching of the node representing the unit crew is calculated, and the routes are screened based on the irreducible cost obtained in the process. Then, a set division solution is searched from the remaining routes by sieving, and a crew route plan is obtained.

  The irreducible cost is not the evaluation value of each arc when viewed from the connection between individual nodes (ie, the local evaluation value), but the evaluation value of each arc when viewed from the entire crew route network (in other words, Since this is a global evaluation value), only the routes with high necessity in the crew route plan remain by screening the routes based on the irreducible costs.

  In addition, since the screening of routes is performed so that the number of appearances of each node always exceeds a predetermined threshold, it is possible to prevent the occurrence of a situation where only the number of route plans including a specific node is extremely small, and A combination of route plans that can be established as a route plan is likely to exist.

2. Second Embodiment 2-1. Principle Next, the principle of crew route planning in the second embodiment will be described.
FIG. 41 is a flowchart showing the flow of the second crew route plan.
The second crew route plan includes crew route network generation (step T1), basic cost setting for each arc (step T3), minimum cost perfect matching calculation processing (step T5), clique extraction processing (step T7), The threshold processing (step T9), the second route plan extraction processing (step T11), and the set division solution search (step T13) are realized by seven steps.

  For the crew route network generation (step T1), the basic cost setting for each arc (step T3), the minimum cost perfect matching calculation process (step T5), and the set division solution search (step T13), refer to 1-1. Since it is the same as the process in the 1st crew route plan demonstrated in the principle, description is abbreviate | omitted.

2-1-1. Clique extraction process First, the clique extraction process will be described.
When the minimum cost perfect matching calculation process is performed in step T5, a set of nodes that cannot be included in the same route is extracted as “clique” from the network after matching.

  Specifically, select one time of the time zone (for example, rush time zone) in which the nodes (unit crew) are considered to be the most dense, and all the nodes related to the selected time (crew at the selected time) The unit crew) is extracted and the set is set as a clique. However, since the clique is insufficient, it is determined whether or not there is a node that cannot be reached from any of the nodes belonging to the clique and cannot reach any of the nodes. Is included in the clique.

  FIG. 42 is a diagram illustrating a result of extracting a clique node from the network after matching in FIG. Here, nodes “e” and “f” are extracted as cliques as nodes that cannot be included in the same route. Since nodes “a” and “b” cannot be included in the same route, nodes “a” and “b” may be extracted as cliques.

2-1-2. Threshold processing Next, threshold processing will be described.
In the threshold process, an evaluation value called a relative cost is calculated for each of a path not including a node belonging to the clique extracted by the clique extraction process and a path including a node belonging to the clique.

Specifically, first, a route that minimizes the total irreducible cost is identified from among routes that do not include nodes belonging to the clique, and the total irreducible cost of the identified route is set as the minimum total irreducible cost RC ₀ . Then, for each route that does not include a node belonging to the clique, a difference between the total irreducible cost of the route and the minimum total irreducible cost RC ₀ is calculated, and the calculated value is set as a relative cost. If the calculated relative cost exceeds a predetermined threshold α, the threshold excess flag for the route is set to ON, and if not exceeded, OFF.

Further, the following processing is performed for each node belonging to the clique. That is, the route that minimizes the total irreducible cost is identified from the routes including the node “n”, and the total irreducible cost of the identified route is set as the minimum total irreducible cost RC _n . Then, for each path including the node "n" to calculate the total irreducible cost of the path, the difference between the minimum total irreducible cost RC _n, the calculated values and relative cost. If the calculated relative cost exceeds a predetermined threshold α, the threshold excess flag for the route is set to ON, and if not exceeded, OFF.

  The case where this threshold processing is performed on the post-matching network in which the nodes “e” and “f” illustrated in FIG. 42 are extracted as cliques will be described below. However, here, a case where threshold processing is performed with the threshold α set to “4” will be described.

First, FIG. 43 shows a post-matching network that does not include nodes “e” and “f” belonging to a clique.
In after matching network of FIG. 43, the path to minimize the total irreducible cost is path "XacdY" or "XbcdY", the sum irreducible cost because it is "9", the minimum total irreducible cost RC ₀ Becomes “9”.

  At this time, when the relative cost is calculated for each route included in the network after matching in FIG. 43, “9-9 = 0” for the routes “XacdY” and “XbcdY” and “10−” for the route “XcdY”. 9 = 1 ”. Further, since the relative cost of each route is smaller than the threshold value “α = 4”, the threshold value excess flag for each route is turned OFF. FIG. 44 shows threshold processing data 623 which is data indicating the relationship between the route 6231, the total irreducible cost 6233, the relative cost 6235, and the threshold excess flag 6237 in this case.

Next, FIG. 45 shows a post-matching network including the node “e” belonging to the clique.
In after matching network of FIG. 45, the path to minimize the total irreducible cost is path "XbedY", the sum irreducible cost because it is "0", the minimum total irreducible cost RC _e is "0" It becomes.

  At this time, when the relative cost is calculated for each route included in the network after matching in FIG. 45, the routes “XacedY” and “XbcedY” are “4-0 = 4”, and the routes “XaceY”, “XcedY” and “XbceY” is “5-0 = 5”. The route “XceY” is “6-0 = 6”, the route “XbedY” is “0-0 = 0”, and the route “XbeY” is “1-0 = 1”. For the routes “XaceY”, “XceY”, “XceY”, and “XbceY”, the relative cost exceeds the threshold value “α = 4”, and therefore the threshold value excess flag is set to ON. FIG. 46 shows threshold processing data 623 in this case.

Similarly, FIG. 47 shows a post-matching network including the node “f” belonging to the clique.
In the network after matching in FIG. 47, the route that minimizes the total irreducible cost is the route “XacfY”, “XacfdY”, “XbcfY”, or “XbcfdY”, and the total irreducible cost is “0”. The minimum total irreducible cost RC _f is “0”.

  At this time, when the relative cost is calculated for each route included in the network after matching in FIG. 47, the routes “XafY” and “XafdY” are “24-0 = 24”, and the routes “XacfY”, “XacfdY”, “XbcfY” and “XbcfdY” are “0-0 = 0”. Further, the routes “XcfY” and “XcfdY” are “1-0 = 1”. For the routes “XafY” and “XafdY”, since the relative cost exceeds the threshold “α = 4”, the threshold excess flag is set to ON. The threshold processing data 623 in this case is shown in FIG.

2-1-3. Second route plan extraction processing The second route plan extraction processing is 1-1-4. Although it is almost the same as the process described in the first route plan extraction process, the route for which the threshold setting flag is set to ON by the threshold process is not subject to sieving, and is not the total irreducible cost, The route is deleted based on the relative cost calculated in the processing, which is different from the first route plan extraction processing.

  FIG. 49 shows the result of screening the routes included in the post-matching network shown in FIG. 30 by the second route plan extraction process. However, here, the case where the threshold θ is “3” and the route is screened will be described.

  FIG. 49 is a diagram showing second route plan data 625 that is data for screening routes in the second route plan extraction process. In the second route plan data 625, a route 6251, a relative cost 6253, and a node 6255 are stored in association with each other, and the appearance count 6257 is stored for each node constituting the node 6255. Here, a state in which seven routes having a relatively small relative cost remain as a result of screening the routes is shown.

  When the second route plan extraction process ends, 1-1-5. Similar to the optimal solution search, a set division solution is searched from the routes remaining by sieving, and the searched set division solution is set as a crew route plan. The optimum solution for the crew route plan is a combination of routes that minimizes the sum of the basic costs set for the arc.

FIG. 50 is a diagram illustrating crew route plan data 609 obtained by searching for a set division solution from routes included in the second route plan data 625 of FIG. 49.
When the set division solution is searched from among the seven routes included in the second route plan data 625 of FIG. 49, “XbedY + XacfY” and “XacfdY + XbeY” are searched, and these two become the crew route plan. Further, the sum of the basic costs of the arcs included in the route constituting the crew route plan “XbedY + XacfY” is “21 + 12 = 33”, and the sum of the basic costs of the arcs included in the route constituting the crew route plan “XacfdY + XbeY” is Since “9 + 25 = 34”, the crew route plan “XbedY + XacfY” having a small value is an optimal solution, and the crew route plan “XacfdY + XbeY” is a suboptimal solution.

  In the second route plan extraction process, the routes are screened based on the relative cost in order to prevent the routes including the nodes belonging to the clique from being deleted intensively. For example, it is assumed that a route including one node belonging to a clique is only a route having a large total irreducible cost. This is a phenomenon that may occur when the irreducible cost of an arc connecting the node and a node adjacent to the node is extremely large.

  In this case, when the routes are screened based on the total irreducible cost, the routes including the node are deleted intensively because the routes are deleted in order from the route with the largest total irreducible cost. Since nodes belonging to the clique cannot be included in the same route, if the routes including the node are deleted intensively, the nodes are inevitably biased. This is an obstacle to search for a set partitioning solution.

  However, the relative cost is not an absolute evaluation value of each route seen from all routes, but a relative evaluation value of each route seen by each node belonging to the clique. When the division is performed, the route including the node is not intensively deleted.

  In addition, since the sieving is performed only for the route whose relative cost does not exceed the predetermined threshold value, the processing time is shorter as compared with the case where the sieving is performed for all the routes.

2-2. Example Next, referring to FIGS. 51 to 56, 2-1. The crew route planning device 20 that is a device that performs the crew route planning described in the principle will be described.

2-2-1. Configuration First, the configuration will be described.
The configuration of the crew route planning device 20 is 1-2. Although it is almost the same as the configuration of the crew route planning apparatus 10 described in the embodiment, the configuration of the ROM and the RAM is different from that of the crew route planning apparatus 10. Therefore, the description of the configuration other than the ROM and RAM will be omitted, and the functional units will be represented by the CPU 120, the input unit 220, the display unit 320, the communication unit 420, the ROM 520, the RAM 620, and the bus 720, respectively. Moreover, the same code | symbol is attached | subjected about the component same as the crew route planning apparatus 10, and the description is abbreviate | omitted.

FIG. 51 is a diagram illustrating a configuration of the ROM 520 included in the crew route planning device 20.
The ROM 520 is read by the CPU 120 and executed as the second crew route planning process (see FIG. 53), the second crew route plan program 521, the train diagram data 505, the crew member base data 507, and the crew transition conditions. Data 509. The second crew route planning program 521 includes a minimum cost perfect matching calculation program 502 executed as a minimum cost perfect matching calculation process (see FIG. 39) and a clique extraction executed as a clique extraction process (see FIG. 54). The program 522, a threshold processing program 523 executed as threshold processing (see FIG. 55), and a second route proposal extraction program 524 executed as second route proposal extraction processing (see FIG. 56) are provided as subroutines. ing.

  The second crew route planning process is a clique extraction process in which the CPU 120 calculates the minimum cost perfect matching for the crew route network generated based on the train diagram data 505 and the crew member data 507 by the minimum cost perfect matching calculation process. This is a process for performing threshold processing based on the clique extracted by. Then, the CPU 120 screens the route by the second route plan extraction process, searches for a set division solution from the remaining routes, and causes the display unit 320 to display the searched set division solution as a crew route plan. The second crew route planning process will be described later in detail.

  The clique extraction process is a process in which the CPU 120 extracts a clique by extracting all nodes at the time when the nodes are considered to be the most dense from the post-matching network. This clique extraction process has been described above in detail, but will be described later again in detail using a flowchart.

  The threshold processing is a process in which the CPU 120 performs threshold determination based on the relative cost for each of a path not including a node belonging to the clique and a path including each node belonging to the clique, and the relative cost exceeds the threshold α. Is a process in which the threshold excess flag is set to ON, and a path that has not exceeded is set to OFF. This threshold processing has been described above in detail with reference to a flowchart.

  The second route plan extraction process is a process in which the CPU 120 sifts the route by deleting the route based on the relative cost while selecting the route included in the post-matching network. The principle of the second route plan extraction process has been described above, but will be described later again in detail using a flowchart.

FIG. 52 is a diagram illustrating a configuration of the RAM 620 included in the crew route planning device 20.
The RAM 620 includes crew route network data 601, transition normalization diagram data 603, post-matching network data 605, clique data 621, threshold processing data 623, second route plan data 625, and crew route plan data. 609.

  The clique data 621 is data regarding cliques, and stores nodes extracted as cliques from the network after matching by the CPU 120 in the clique extraction process.

  The threshold processing data 623 is data in which a route 6231, a total irreducible cost 6233, a relative cost 6235, and a threshold excess flag 6237 are stored in association with each other. The threshold processing data 623, as shown in FIG. 48, is generated by the CPU 120 in the threshold processing.

  The second route plan data 625 is data in which the route 6251, the relative cost 6253, and the node 6255 are stored in association with each other, and the number of appearances 6257 of each node is stored. It is as shown in. The second route plan data 625 is generated by the CPU 120 in the second route plan extraction process.

2-2-2. Process Flow Next, the process flow will be described.
FIG. 53 is a flowchart showing the flow of the second crew route planning process executed in the crew route planning device 20 by the CPU 120 reading out and executing the second crew route planning program 521.

  First, the CPU 120 performs initial setting (step D1). Specifically, the CPU 120 sets a threshold value α used when determining a threshold value of a path in threshold processing, a threshold value θ used when screening a path in the second path plan extraction process, and the like.

  Next, the CPU 120 generates a crew route network based on the train schedule data 505 and the crew member base data 507 (step D3). Specifically, CPU120 acquires a unit crew by dividing all the train lines of a train diagram by the station where a crew member can change. And CPU120 makes each unit crew a node, and produces | generates a crew course network by connecting between the nodes of the unit crews which can be changed by arc. Thereafter, the CPU 120 stores the generated crew route network as the crew route network data 601.

  Thereafter, the CPU 120 sets the basic cost of each arc included in the crew route network generated in step D3 based on the crew transition condition data 509 (step D5). Specifically, the CPU 120 sets the basic cost so that the value of the arc indicating the transition between unit crews with low evaluation increases. Then, the CPU 120 stores the set basic cost in the crew route network data 601.

  Next, the CPU 120 reads and executes the minimum cost perfect matching calculation program 502 to perform a minimum cost perfect matching calculation process (step D7). Thereafter, the CPU 120 reads out and executes the clique extraction program 522 to perform clique extraction processing (step D9).

FIG. 54 is a flowchart showing the flow of clique extraction processing.
First, the CPU 120 refers to the train diagram data 505 and the post-matching network data 605, and selects one time at which nodes are considered to be most dense (step E1).

  Then, the CPU 120 extracts all the nodes at the selected time, sets the set as a clique (step E3), and stores the nodes extracted as the clique as clique data 621.

  Next, the CPU 120 determines whether or not there is a node that cannot be reached from any node belonging to the clique and cannot reach any node (step E5). If it is determined that there is a node (step E5; Yes), the node is included in the clique (step E7), and the process returns to step E5. On the other hand, when it is determined in step E5 that there is no node (step E5; No), the CPU 120 ends the clique extraction process.

  Returning to the second crew route planning process in FIG. 53, when the clique extraction process is completed, the CPU 120 reads out and executes the threshold process program 523 to perform the threshold process (step D11).

FIG. 55 is a flowchart showing the flow of threshold processing.
First, the CPU 120 refers to the post-matching network data 605 and the clique data 621, and calculates the minimum total irreducible cost RC ₀ of the path not including the node belonging to the clique (step F1).

Then, the CPU 120 repeatedly executes the process of the loop A for each path not including the node belonging to the clique.
In loop A, the CPU 120 calculates the relative cost of the route (step F3). Specifically, the CPU 120 calculates the total irreducible cost of the route, calculates the difference between the total irreducible cost and the minimum total irreducible cost RC ₀ calculated in step F1, and sets it as the relative cost.

  Next, the CPU 120 determines whether or not the relative cost calculated in step F3 exceeds the threshold value α (step F5). If it is determined that the relative cost exceeds (step F5; Yes), the threshold value excess flag of the route is determined. Is set to ON (step F7), and the process proceeds to the next route.

  On the other hand, when it is determined in step F5 that the relative cost does not exceed the threshold value α (step F5; No), the CPU 120 sets the threshold value excess flag of the relevant route to OFF (step F8), and the next route. The process is transferred to. Then, the CPU 120 completes the process of the loop A after performing the process for all the paths not including the nodes belonging to the clique.

Next, the CPU 120 repeatedly executes the process of loop B for each node belonging to the clique.
In the loop B, the CPU 120 refers to the post-matching network data 605 and the clique data 621, and calculates the minimum total irreducible cost RC _n of the route including the node (step F9).

Then, the CPU 120 repeatedly executes the process of the loop C for each path including the node.
In loop C, the CPU 120 calculates the relative cost of the route (step F11). Specifically, CPU 120 calculates the total irreducible cost of the path, the sum already about costs, by calculating the difference between the minimum total irreducible cost RC _n calculated in step F9, the relative cost.

  Next, the CPU 120 determines whether or not the relative cost calculated in step F11 exceeds the threshold value α (step F13). If it is determined that the relative cost exceeds (step F13; Yes), the threshold value excess flag for the route is determined. Is set to ON (step F15), and the process proceeds to the next route.

  On the other hand, if it is determined in step F13 that the relative cost does not exceed the threshold value α (step F13; No), the CPU 120 sets the threshold value excess flag for the relevant route to OFF (step F16), and the next route. The process is transferred to. Then, the CPU 120 completes the process of the loop C after performing the process for all the routes including the node. Further, the CPU 120 performs the process for all the nodes belonging to the clique, ends the process of the loop B, and ends the threshold process.

  Returning to the second crew route planning process of FIG. 53, when the threshold value processing is finished, the CPU 120 reads out and executes the second route plan extraction program 524, thereby performing the second route plan extraction process (step). D13).

FIG. 56 is a flowchart showing the flow of the second route plan extraction process.
First, the CPU 120 selects one path included in the post-matching network generated in the minimum cost perfect matching calculation process (step G1).

  Next, the CPU 120 determines whether or not the threshold value excess flag for the route selected in step G1 is set to ON (step G3). If it is determined to be set to ON (step G3; Yes), The process proceeds to step G15.

  On the other hand, when it is determined in step G3 that the threshold excess flag is not set to ON, that is, set to OFF (step G3; No), the CPU 120 sets the relative cost of the selected route along with the route. 2 is stored as route plan data 625 (step G5). And CPU120 updates the appearance frequency of a node by specifying the node contained in the selected route (step G7).

  Next, the CPU 120 determines whether or not the minimum number of appearances of the node has exceeded the threshold value θ (step G9). If it is determined that the node has not exceeded the threshold θ (step G9; No), the process proceeds to step G15.

  On the other hand, if it is determined in step G9 that the minimum number of appearances of the node has exceeded the threshold θ (step G9; Yes), the CPU 120 has the largest relative cost among the routes included in the second route plan data 625. One route is deleted (step G11). And CPU120 updates the appearance frequency of a node by specifying the node contained in the deleted path (step G13).

  Thereafter, the CPU 120 determines whether or not there are no other routes that can be selected from the network after matching (step G15). If it is determined that there are still other routes that can be selected (step G15; No), the process proceeds to step G1. And return.

  On the other hand, when it is determined in step G15 that there are no other routes that can be selected (step G15; Yes), the CPU 120 refers to the second route plan data 625 and refers to a node that satisfies the condition of the number of appearances> the threshold θ. It is determined whether or not there is a route including only (step G17).

  In step G17, when it is determined that there is a path including only a node satisfying the condition that the number of appearances> the threshold θ (step G17; Yes), the CPU 120 selects one path with the maximum relative cost among the paths. Delete (step G19). And CPU120 updates the appearance count of a node by specifying the node contained in the deleted path (step G21), and returns to step G17.

  On the other hand, if it is determined in step G17 that there is no path including only a node satisfying the condition that the number of appearances> the threshold θ (step G17; No), the CPU 120 ends the second path plan extraction process.

  Returning to the second crew route planning process of FIG. 53, when the second route plan extracting process is completed, the CPU 120 searches for a set division solution from the remaining routes by sieving (step D15). The set division solution is stored in the crew route plan data 609. Then, the CPU 120 displays the searched set division solution on the display unit 320 as a crew route plan (step D17), and ends the second crew route plan process.

2-3. Effects According to the present embodiment, a clique is extracted from the post-matching network, and a path threshold determination is performed based on the extracted clique. Then, only for the route determined not to exceed the threshold, the route is screened based on the relative cost calculated from the total irreducible cost, and the set partition solution is searched from the routes remaining by the screening. It is considered as a crew route plan.

  Relative cost is not an absolute evaluation value of each route seen from all routes, but a relative evaluation value of each route seen by each node belonging to the clique. As a result, routes including nodes belonging to the clique are not deleted intensively.

  Further, since sieving is performed only for paths whose relative cost does not exceed a predetermined threshold, processing time is shorter than when sieving is performed for all paths.

3. Modification 3-1. Set Cover Solution Search In the above-described embodiment, a set division solution is searched from the routes remaining after sieving to obtain a crew route plan. However, a set cover solution is searched for a crew route plan. May be. A set covering solution refers to a combination of paths that allow the same node to appear multiple times and that all nodes appear at least once. In this case, with respect to the part where the nodes overlap, one crew member may be a crew member and another crew member may be a piggybacker.

3-2. Sieving of the route The sieving of the route described in the first embodiment may be performed as follows, for example.
That is, after all routes are selected from the post-matching network, the presence / absence of a route including only a node satisfying the condition that the number of appearances> the threshold θ is determined. Then, the process of deleting one path with the maximum total irreducible cost is repeatedly executed until there are no more paths that satisfy the condition.

  Alternatively, routes are selected one by one from the network after matching, and when the minimum number of appearances exceeds the threshold value θ, the presence / absence of a route including only nodes satisfying the condition that the number of appearances> threshold value θ is determined. Then, the process of deleting one path with the maximum total irreducible cost is repeatedly executed until there is no path satisfying the condition, and when there is no path, another path is selected from the network after matching. Note that the sieving of the route described in the second embodiment can be performed in the same manner.

3-3. Threshold determination In the second embodiment, after performing the threshold determination of the route by the threshold processing, it has been described as performing the screening of the route by the second route plan extraction process. However, the screening of the route is performed while performing the threshold determination. You may make it do.

  Specifically, one route is selected from the network after matching, and the relative cost of the route is calculated. If the calculated relative cost exceeds the threshold value α, the route is not selected as a screening target, and the next route is selected from the network after matching. On the other hand, if the calculated relative cost does not exceed the threshold value α, the route is subjected to sieving, the number of appearances of the node is updated, and the route including only the node that satisfies the condition of appearance number> threshold θ is included. After deleting one, the next route is selected from the network after matching.

  Furthermore, a threshold value process may be included in the second route plan extraction process. Specifically, in the second route plan extraction process, first, threshold determination is performed for all routes. Then, only the path determined that the relative cost does not exceed the threshold value α is extracted.

The flowchart which shows the flow of a 1st crew route plan. The figure which shows an example of a crew route network. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of a transition normalization figure. The figure which shows an example of the network after a matching. The figure which shows an example of 1st route plan data. The figure which shows an example of 1st route plan data. The figure which shows an example of 1st route plan data. The figure which shows an example of 1st route plan data. The figure which shows an example of 1st route plan data. The figure which shows an example of crew course plan data. The block diagram which shows the function structure of the crew route planning apparatus in 1st Embodiment. The flowchart which shows the flow of a 1st crew route plan process. The flowchart which shows the flow of the minimum cost perfect matching calculation process. The flowchart which shows the flow of a 1st route plan extraction process. The flowchart which shows the flow of a 2nd crew route plan. The figure which shows an example of the node which belongs to a clique. The figure which shows the path | route which does not include the node which belongs to a clique. The figure which shows an example of the data for threshold value processing. The figure which shows the path containing the node which belongs to a clique. The figure which shows an example of the data for threshold value processing. The figure which shows the path containing the node which belongs to a clique. The figure which shows an example of the data for threshold value processing. The figure which shows an example of 2nd route plan data. The figure which shows an example of crew course plan data. The figure which shows the structure of ROM of the crew route planning apparatus in 2nd Embodiment. The figure which shows the structure of RAM of the crew route planning apparatus in 2nd Embodiment. The flowchart which shows the flow of a 2nd crew route plan process. The flowchart which shows the flow of a clique extraction process. The flowchart which shows the flow of a threshold value process. The flowchart which shows the flow of a 2nd route plan extraction process. The figure which shows an example of a train schedule. The figure which shows an example of a crew course plan.

Explanation of symbols

10 Crew Route Planning Device 100 CPU
200 Input unit 300 Display unit 400 Communication unit 500 ROM
501 First crew route planning program 502 Minimum cost perfect matching calculation program 503 First route plan extraction program 505 Train diagram data 507 Crew member data 509 Crew transition condition data 600 RAM
601 Flight route network data 603 Transition normalization map data 605 Network data after matching 607 First route plan data 609 Flight route plan data 700 Bus

Claims (7)

Dividing all train streaks included in a given train schedule into unit crews, which are units of crew sections where crew members can ride, and configuring the crew's route by combining transitions between the unit crews, A program for requesting a crew route plan by combining the flight routes of the configured crew,
Network generating means for generating a crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
A cost setting means for setting a cost based on a predetermined evaluation standard regarding a transition between the unit crews for each arc of the generated crew route network;
Crew route network data storage means for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. Matching calculation means,
A route for extracting, as a route plan, a predetermined number of routes having a relatively small sum of the irreducible costs for the arc included in the route among the routes of the crew members represented by the combination of the node-to-node connections according to the arc. Draft extraction means,
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means that makes the combination an optimal crew route plan,
A program for causing the computer to function as Dividing all train streaks included in a given train schedule into unit crews, which are units of crew sections where crew members can ride, and configuring the crew's route by combining transitions between the unit crews, A program for requesting a crew route plan by combining the flight routes of the configured crew,
Network generating means for generating a crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
A cost setting means for setting a cost based on a predetermined evaluation standard regarding a transition between the unit crews for each arc of the generated crew route network;
Crew route network data storage means for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. Matching calculation means,
Clique extraction means for extracting a set of nodes that cannot be included in the same route in the crew's route represented by the combination of connections between nodes according to the arc,
Of the paths that do not include the nodes belonging to the extracted clique, the paths that do not include the nodes that belong to the extracted clique with respect to the total of the irreducible costs of the path that has the smallest total irreducible cost for the arc included in the path. A first relative cost calculating means for calculating a relative cost of a sum of irreducible costs with respect to arcs included in each of the paths;
For each node belonging to the extracted clique, among the paths including the node, each path including the node with respect to the total irreducible cost of the path with the smallest total irreducible cost for the arc included in the path. A second relative cost calculating means for calculating a relative cost of the sum of irreducible costs with respect to the included arc;
A route plan extraction means for extracting a predetermined number of routes having a relatively low relative cost as a route plan among the crew members' routes represented by a combination of the internode connections according to the arc,
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means that makes the combination an optimal crew route plan,
A program for causing the computer to function as   The program according to claim 2, wherein the clique extraction unit causes the computer to function as a clique to extract a set of nodes representing unit crews at one time when unit crews are densely packed.   The route plan extracting means according to any one of claims 1 to 3 for causing the computer to function so as to screen and extract a route plan on condition that each of the nodes appears a predetermined number of times or more. The listed program.   The perfect matching calculating means has a judging means for judging whether or not a combination of inter-node connections satisfying a predetermined violation condition is included in a part of a path represented by the obtained perfect matching, the judgment Claims for causing the computer to function to delete a single arc constituting the combination of connection between nodes and recalculate complete matching and irreducible cost when it is determined that it is included by the means. The program as described in any one of 1-4. All train streaks included in a given train schedule are divided into unit crews, which are units of crew sections that can be used by the crew, and the crew's course is constructed by combining the transitions between the unit crews. A crew route planning device that obtains a crew route plan by combining the crew's routes,
Network generating means for generating the crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
A cost setting means for setting a cost based on a predetermined evaluation criterion regarding a transition between the unit crews, for each arc of the generated crew route network;
Crew route network data storage means for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. And the matching calculation means,
A route for extracting, as a route plan, a predetermined number of routes having a relatively small sum of the irreducible costs for the arc included in the route among the routes of the crew members represented by the combination of the node-to-node connections according to the arc. Plan extraction means;
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means that makes the combination an optimal crew route plan,
A crew route planning device with All train streaks included in a given train schedule are divided into unit crews, which are units of crew sections that can be used by the crew, and the crew's course is constructed by combining the transitions between the unit crews. A crew route planning device that obtains a crew route plan by combining the crew's routes,
Network generating means for generating the crew route network in which the unit crews are represented by nodes and the transitionable nodes are connected by arcs;
A cost setting means for setting a cost based on a predetermined evaluation criterion regarding a transition between the unit crews, for each arc of the generated crew route network;
Crew route network data storage means for storing the generated crew route network and the set cost;
Each node of the stored crew route network is set as a transition source and a transition destination, and a graph is generated by connecting the arc from the transition source node to the transition destination node so as to be equivalent to the stored crew route network. , based on the cost for the arc stored in the flight path network data storing means, to calculate a minimum cost perfect matching which minimizes the sum of the cost to the transition destination node from the transition source node of the graph And, based on the potential of the node representing the distance from the final arrival point to each node on the path of the minimum cost calculated by the minimum cost perfect matching, and the potential difference of the two nodes connected by the arc The irreducible cost, which is the updated value of the arc cost, is calculated. And the matching calculation means,
Clique extraction means for extracting, as a clique, a set of nodes that cannot be included in the same route in the crew's route represented by a combination of the internode connections according to the arc;
Of the paths that do not include the nodes belonging to the extracted clique, the paths that do not include the nodes that belong to the extracted clique with respect to the total of the irreducible costs of the path that has the smallest total irreducible cost for the arc included in the path. First relative cost calculation means for calculating a relative cost of a total of irreducible costs for arcs included in each of the paths;
For each node belonging to the extracted clique, among the paths including the node, each path including the node with respect to the total irreducible cost of the path with the smallest total irreducible cost for the arc included in the path. A second relative cost calculating means for calculating a relative cost of a sum of irreducible costs with respect to an arc included;
A route plan extraction means for extracting a predetermined number of routes having a relatively small relative cost as a route plan, among crew members' routes represented by a combination of the internode connections according to the arc;
A search is made for a combination of route plans that can be established as a crew route plan from the extracted route plans, and among the searched route plan combinations, a route plan that minimizes the sum of the costs for the arc to be used. A crew route plan calculation means that makes the combination an optimal crew route plan,
A crew route planning device with

Images