CN111090935B - Public bicycle appointment scheduling and path planning method - Google Patents
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Abstract
The invention discloses a public bicycle appointment scheduling and path planning method, which sequentially comprises the following steps: according to the scheduling information of the public bicycle service station and the existing carrier vehicle resources, problem constraint conditions are determined, and a mathematical model is constructed; converting the model into a pseudo traveler problem model; and solving the pseudo traveler problem model by adopting an improved intelligent water drop algorithm, and solving the sequence of the optimal service stations of each transport vehicle, the number of the used transport vehicle and the number of the public bicycle vehicles originally carried by each transport vehicle. Aiming at the defects that the intelligent water drop algorithm is insufficient in inspiration and easy to fall into local optimum and the like, the invention provides a selection strategy based on an optimum candidate node group, and improves the search efficiency and the algorithm precision; the invention provides a method for converting a public bicycle appointment scheduling and path planning model into a pseudo traveler problem model, provides a corresponding solving method, eliminates the problem of infeasible solution, and improves the efficiency and the precision of the solving method.
Description
Technical Field
The invention relates to the technical field of urban intelligent public transport systems, in particular to a public bicycle reservation scheduling and path planning method.
Background
With the increasing environmental pollution, the concept of 'green travel' is more and more deeply in mind, and the public bicycle system is born in time and is rapidly developed. However, in the actual operation process, the scheduling problem exists, namely how to solve the problem that the users are difficult to borrow and return vehicles and how to minimize the operation cost of urban public transport management institutions always restricts the long-term development of public bicycle systems. According to the operation experience and relevant research results at home and abroad, reasonable scheduling is found to be the key point for solving the problems.
Some people have studied the problems, but the proposed scheduling algorithms are easy to fall into stagnation. For example: the neural network method requires a large amount of training data, the algorithm is slow in convergence, and the searching capability is not high; the ant colony algorithm has the defects of long search time and easy trapping in local optimum; the genetic algorithm has the defects of low calculation speed, easy premature convergence and the like.
The intelligent water drop algorithm is a novel group intelligent algorithm, can obtain a better solution in a short time, and is verified in a plurality of fields, such as: traveler issues, scheduling issues, vehicle path planning issues, etc. The algorithm has the defects of insufficient inspiration and easy falling into local optimization.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in the existing public bicycle appointment scheduling process, a standard intelligent water drop algorithm adopted by a scheduling problem is insufficient in inspiration, slow in convergence speed and low in algorithm searching precision, so that the minimum transportation cost cannot be achieved after solution, and a transport vehicle route is long.
In order to solve the technical problem, the invention provides a public bicycle appointment scheduling and path planning method, which comprises the following steps:
1) establishing a local database, and carrying out data preprocessing, wherein the specific steps are as follows:
1a) reading in the number N of public bicycle service stations c Distance vectors between the service center and the service stations, and distance matrixes between the service stations and the service stations; reading a reserved time period and a scheduling amount of a service site;
1b) reading the number K of public bicycle service center transport vehicles, the loading capacity Q of the transport vehicles and the time for the transport vehicles to serve service stations with different requirements;
1c) setting the transport vehicle to start at the same speed and setting the speed of the transport vehicle, and solving a distance time vector between the service center and the service station and a distance time matrix between the service station and the service station from the distance vector between the service center and the service station obtained in the step 1a) and the distance matrix between the service station and the service station;
2) according to the description of the problem, determining the constraint condition of the problem, and establishing a mathematical model of a public bicycle appointment scheduling and path planning model;
3) converting the mathematical model obtained in the step 2) into a pseudo traveler problem: the method comprises the following steps that (1) stations are regarded as city points, a transport vehicle is regarded as a travel businessman, the transport vehicle searches a loop traversing all the stations, the objective function value of the loop is enabled to be minimum, and each station can only be traversed once;
4) solving the pseudo traveler problem model obtained in the step 3) by adopting an improved intelligent water drop algorithm;
5) and outputting an objective function value of the optimal public bicycle scheduling model, and scheduling path planning results, namely the sequence of service stations of each transport vehicle, the number of the used transport vehicles and the number of the public bicycle vehicles originally carried by each transport vehicle.
In the step 2), according to the description of the problem, determining the constraint condition of the problem, and establishing a mathematical model of a public bicycle appointment scheduling and path planning model, the specific steps are as follows:
2a) establishing a mathematical model, including the following limiting conditions:
(2a1) the number of the public bicycle service centers in the whole area is only 1, and the transport vehicles start from the service centers, service stations one by one along a certain route and finally return to the service centers to form a closed running path;
(2a2) the service receiving time of each station is in a direct proportion relation with the dispatching amount of the station, the larger the dispatching amount is, the longer the loading time is, and the fixed number of bicycles loaded on each transport vehicle is;
(2a3) each station is served by only one transport vehicle, and the service of the station is completed at one time;
(2a4) the dispatching amount of each station can not exceed the maximum number of bicycles which can be loaded by the transport vehicle, and the number of bicycles on the transport vehicle can not exceed the carrying capacity of the transport vehicle in the dispatching process;
(2a5) the time for the transport vehicle to service the station must meet the corresponding time window requirement, the station is not allowed to access the object after the upper limit of the time window, waiting cost is generated when the object is accessed before the lower limit of the time window, and waiting cost is not generated when the object is accessed within the time window;
2b) according to the conditions, a public bicycle reservation scheduling and path planning model is established as follows:
formula (1) shows that the weighted sum of the distance cost, the waiting time, the station service number and the number of the transport vehicles obtains the minimum value, four parts connected by plus signs sequentially represent the distance cost, the waiting time punishment, the punishment of the unserved stations and the punishment of the number of the transport vehicles at the service stations, and the more the number of the transport vehicles is, the higher the cost is. The following constraints are satisfied by equation (1):
x ijk the system comprises a server, a server center and a server, wherein the server is used for storing a transport vehicle, and the server is used for storing transport vehicles, namely a kth transport vehicle, representing whether the kth transport vehicle is served from an ith service station to a jth service station or not, and representing a service center, wherein i and j are 0;
y ik indicating whether the kth transport vehicle serves the ith service station or not;
formula (4) indicates that each station is served by at most one transport vehicle, and the service of the station is completed at one time;
0≤Qk≤Q,k＝1,2,…K (5)
Q k the load capacity of the kth transport vehicle is represented, and Q represents the maximum number of bicycles which can be loaded by the transport vehicle;
|q i |≤Q，i＝1,2,…,N c (6)
|q i | represents the adjustment amount of the ith station; q. q.s i >0 denotes the i-th service station calling in q from the transport vehicle i A bicycle; q. q of i < 0, indicating that the transport vehicle takes away | q from the ith service station i I bicycle;
t i ≤b i ，i＝1,2,…,N c (7)
t i : indicating the time of arrival of the vehicle at the i-th service station, b i An upper limit of the reserved time of the ith site;
wherein:
K 1 : number of transport vehicle not serviced;
N 1 : the number of sites not served;
d ij : a distance matrix between the ith station and the jth station;
wait k : a kth transport vehicle waiting time;
a i a lower limit indicating that the ith station receives a reservation time;
b i an upper limit indicating the reservation time accepted by the ith station;
w δ δ is 1,2, 3: weighting coefficients of each part of the objective function;
the step 4) of solving the pseudo traveler problem model obtained in the step 3) by adopting an intelligent water drop algorithm based on the optimal candidate node subgroup selection strategy specifically comprises the following steps:
4a) reading in data of a transport vehicle and data of a station;
4b) initializing static parameters: setting the number of Water drops N IWD (ii) a Number of nodes N C (ii) a Silt constant InitSoil, velocity variation coefficient-a v Coefficient of variation in velocity of two b v Coefficient of variation of velocity, tri c v The coefficient of variation of silt is s Coefficient of variation of silt s Coefficient of variation of silt c s (ii) a Local silt content update coefficient rho s (ii) a Global silt quantity update coefficient rho n (ii) a Maximum number of iterations N max (ii) a Initializing the sediment quantity soil (i, j) between any two nodes;
4c) randomly generating a global optimal route T according to the number of nodes B And calculating its fitness value S min ；
4d) Initializing dynamic parameters: setting the velocity ve of each Water dropletl IWD Amount of silt carried by each drop IWD Visit list per drop V c (IWD) { }, the number of iterations is one;
4e) set the starting point of each drop and add that point to the access list V c (IWD)；
4f) Calculating the probability of each node which is not accessed for each water drop by adopting a selection strategy based on the optimal candidate node subgroup, and selecting the next node to be accessed; updating the Access List V c (IWD)；
4g) After each water drop goes from the node i to the node j, the speed vel of the water drop is updated IWD ；
4h) Calculating the sediment variation delta soil (i, j) after each water drop goes from the node i to the node j;
wherein, time (i, j; vel) IWD ) Represents the time required for a water droplet to travel from node i to node j:
wherein epsilon v Is a small normal number, and avoids the condition that the denominator is zero. | c (i) -c (j) | | is the distance between node i and node j; c (i) represents the coordinate of the ith node, c (j) represents the coordinate of the jth node, | |, represents the euclidean distance;
4i) updating the sand content soil of each water drop from node i to node j IWD ；
soil IWD (t+1)＝soil IWD (t)+Δsoil(i,j) (12)
4j) After each water drop goes from the node i to the node j, updating the sediment amount soil (i, j) in the path from the node i to the node j;
soil(i,j)＝(1-ρ s )·soil(i,j)-ρ s ·Δsoil(i,j) (13)
4k) repeating the steps 4f) to 4j) for each water drop until all nodes are visited, finishing the iteration, calculating the fitness values corresponding to all the water drops according to the fitness function, and selecting the route with the minimum fitness value as the route T with the minimum total cost in the iteration IB ；
4l) comparing the global optimum fitness value S min And 4k), if the fitness function value in step 4k) is smaller, updating S min And a global optimal route T B ；
4m) updating the sediment amount soil (i, j) in the path by using the sediment amount information among the global optimal paths;
4N) judging whether the maximum iteration number N is reached max If yes, outputting the global optimal path T B And a global optimum objective function value S min (ii) a Otherwise, the iteration number is increased by one, and the step 4e) is returned.
The specific method for initializing the sand amount soil (i, j) between any two nodes in the step 4b) comprises the following steps: generating a random number r between (0-1) by adopting an initial silt amount randomization method n And a random number r n The product of the silt constant InitSoil is given to soil (i, j) as its initial value.
The device for calculating the water drop adaptability value in the step 4c) and the step 4k) is a heuristic decoding device based on a pseudo traveler problem model, and the decoding method sequentially comprises the following steps:
a) the initial time of placing each transport vehicle is t init Selecting a transport vehicle, and setting the current service transport vehicle number asSetting the currently selected node number i to 1;
b) setting the initial time point of the current transport vehicle as t m And t is m ＝t init Sequentially selecting corresponding unprocessed nodes; set initial vehicle load range [ lower, higher ]]Is [0, Q]I.e. lower equals 0 and higher equals Q, the waiting time wait of the kth transport vehicle is set k Temporary waiting time t of 0 temp ＝0；
c) If K > K, go to step K);
d) if the scheduling quantity of the service site corresponding to the current node is more than 0, setting lower to lower + q i (ii) a Otherwise, put high ═ high + q i ；
e) If lower is larger than high, k is set to k +1, and then the step b) is carried out;
f) from the transport vehicle at an initial point in time t m Calculating the time t of the transport vehicle reaching the service site corresponding to the current node n If the time point is above the upper limit of the reserved time of the station, setting k to k +1, and turning to the step b);
g) if the time point is below the lower limit of the station reservation time, calculating the temporary waiting time t temp ＝a i -t n ；
h) Updating the waiting time of the transport vehicle and executing wait k ＝wait k +t temp ；
i) The time point t of the transport vehicle reaching the service site corresponding to the current node n Waiting time and service time, and obtaining the time point t of the transport vehicle leaving the service station corresponding to the current node m Adding the service station serial number to a service list of the transport vehicle;
j) let i be i +1, judge whether the node number i is less than the public bicycle service station number N c (ii) a If yes, go to step d);
k) calculating an objective function comprising a distance cost, a waiting cost, a punishment cost of an unserviceable station and a punishment cost of the number of vehicles of the transport vehicle providing service;
l) outputting an objective function value, and scheduling a path planning result, namely the sequence of service stations of each transport vehicle, the number of used transport vehicle vehicles and the number of public bicycle vehicles originally carried by each transport vehicle.
The step 4f) adopts a selection strategy based on the optimal candidate node subgroup, and the specific process of selecting the next node to be accessed is as follows:
4f1) reading all nodes which are not visited, calculating the amount of silt between the current node i and all candidate nodes V (IWD), and selecting an optimal subgroup elite (IWD) with a certain proportion as a candidate node according to a selection proportion coefficient gamma from low to high according to the amount of silt, wherein the formula is as follows:
elite(IWD)＝γ·V(IWD) (15)
4f2) calculating the probability P of each candidate node according to a probability formula (16) i IWD (j)，
Wherein k is a candidate node and is a node which is not visited by the water drop; f (soil (i, j)) is a correlation function of the sediment quantity of the path from the node i to the node j, and is specifically expressed as the following formula:
wherein epsilon s Is a small normal number, and avoids the condition that the denominator is zero. g (soil (i, j)) is a function for converting the sand content of the path from the node i to the node j into a positive number, and is specifically expressed by the following formula:
wherein,
the minimum value of the silt quantity of the paths from the current node i to all the candidate nodes is obtained;
4f3) according to each candidate sectionProbability of a point
Selecting the next node j using the roulette strategy and updating the access list V with that node c (IWD)。
The invention has the following advantages:
the invention provides a selection strategy based on the optimal candidate node subgroup, thereby improving the search efficiency and the algorithm precision; the method of the invention can achieve the aim of minimizing the transportation cost and simplify the service route of the transport vehicle.
The invention effectively eliminates the problem of infeasible solution caused by the common intelligent water drop algorithm by converting the public bicycle appointment scheduling and path planning model into the problem of pseudo travelers.
The invention reasonably distributes the transport vehicle resources by heuristic decoding rules, can meet the requirement of reasonable dispatching of the transport vehicle resources by urban public transport management organizations, and achieves the optimization of the transport vehicle service routes.
Drawings
FIG. 1 is a flow chart of an improved intelligent water droplet algorithm;
FIG. 2 is a flow chart of a heuristic decoding algorithm of the public bicycle reservation scheduling and path planning model;
FIG. 3 is a schematic diagram of a public bicycle reservation scheduling and path planning model transformed into a pseudo traveler problem model.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
1) The public bicycle dispatching center receives the station dispatching application, inquires station information including station position, dispatching time and dispatching amount; after preprocessing the information, importing the information into a local database;
2) according to the service information, determining constraint conditions of problems, and establishing a mathematical model of a public bicycle appointment scheduling and path planning model, which comprises the following specific steps:
2a) establishing a mathematical model, including the following limiting conditions:
(2a1) the number of the public bicycle service centers in the whole area is only 1, and the transport vehicles start from the service centers, service stations one by one along a certain route and finally return to the service centers to form a closed running path;
(2a2) the service receiving time of each station is in a direct proportion relation with the dispatching amount of the station, the larger the dispatching amount is, the longer the loading time is, and the fixed number of bicycles loaded on each transport vehicle is;
(2a3) each station is served by only one transport vehicle, and the service of the station is completed at one time;
(2a4) the dispatching amount of each station can not exceed the maximum number of bicycles which can be loaded by the transport vehicle, and the number of bicycles on the transport vehicle can not exceed the carrying capacity of the transport vehicle in the dispatching process;
(2a5) the time for the transport vehicle to service the station must meet the corresponding time window requirement, the station is not allowed to access the object after the upper limit of the time window, waiting cost is generated when the object is accessed before the lower limit of the time window, and waiting cost is not generated when the object is accessed within the time window;
2b) according to the conditions, a public bicycle appointment scheduling and path planning model is established as follows:
formula (1) shows that the weighted sum of the distance cost, the waiting time, the station service number and the number of the transport vehicles obtains the minimum value, four parts connected by plus signs sequentially represent the distance cost, the waiting time punishment, the punishment of the unserved stations and the punishment of the number of the transport vehicles at the service stations, and the more the number of the transport vehicles is, the higher the cost is. The formula (1) satisfies the following constraints:
x ijk is shown asWhether k transport vehicles serve from the ith service station to the jth service station or not is judged, wherein i and j are 0 and represent a service center;
y ik indicating whether the kth transport vehicle serves the ith service station or not;
formula (4) indicates that each station is served by at most one transport vehicle, and the service for the station is completed at one time;
0≤Qk≤Q,k＝1,2,…K (5)
Q k the load capacity of the kth transport vehicle is represented, and Q represents the maximum number of bicycles which can be loaded by the transport vehicle;
|q i |≤Q，i＝1,2,…,N c (6)
|q i | represents the adjustment amount of the ith station; q. q.s i >0 denotes the i-th service station calling in q from the transport vehicle i A bicycle; q. q.s i < 0, indicating that the transport vehicle takes away | q from the ith service station i I bicycle;
t i ≤b i ，i＝1,2,…,N c (7)
t i : indicating the time of arrival of the vehicle at the i-th service station, b i An upper limit of the reserved time of the ith site;
wherein:
K 1 : number of non-serviced transport vehicle vehicles;
N 1 : the number of sites not served;
d ij : a distance matrix between the ith station and the jth station;
wait k : a kth transport vehicle waiting time;
a i a lower limit indicating that the ith station receives a reservation time;
b i an upper limit of the reserved time of the ith site;
w δ δ is 1,2, 3: weighting coefficients of each part of the objective function;
3) converting the mathematical model obtained in 2) into a pseudo traveler problem: namely, the sites are regarded as city points, the transport vehicle is regarded as a travel businessman, and the essence of the problem is that the transport vehicle searches a loop traversing all the sites, so that the objective function value of the loop is minimum, and each site can only be traversed once;
4) solving the pseudo traveler problem model obtained in the step 3) by adopting an intelligent water drop algorithm based on the optimal candidate node group selection strategy;
5) and outputting an objective function value of the optimal public bicycle scheduling model, and scheduling path planning results, namely the sequence of service stations of each transport vehicle, the number of the used transport vehicles and the number of the public bicycle vehicles originally carried by each transport vehicle.
The step 4) of solving the pseudo traveler problem model obtained in the step 3) by adopting an intelligent water drop algorithm based on the optimal candidate node subgroup selection strategy specifically comprises the following steps:
4a) reading in data of a transport vehicle and data of a station;
4b) initializing static parameters: setting the number of Water drops N IWD (ii) a Number of nodes N C (ii) a Silt constant InitSoil, velocity variation coefficient-a v Coefficient of variation in velocity of two b v Coefficient of variation of velocity, tri c v The coefficient of variation of silt is s Coefficient of variation of silt s Silt variation coefficient of three c s (ii) a Local silt amount update coefficient rho s (ii) a Global silt quantity update coefficient rho n (ii) a Maximum number of iterations N max (ii) a Initializing the sediment quantity soil (i, j) between any two nodes;
4c) randomly generating a global optimal route T according to the number of nodes B And calculating the fitness value S by the formula (1) min ；
4d) Initialization deviceState parameters: setting the speed vel of each water drop IWD Amount of silt carried by each drop IWD Visit list per drop V c (IWD) { }, the number of iterations is one;
4e) set the starting point of each drop and add that point to the access list V c (IWD)；
4f) Calculating the probability of each node which is not accessed for each water drop by adopting a selection strategy based on the optimal candidate node subgroup, and selecting the next node to be accessed; updating the Access List V c (IWD)；
4g) After each water drop goes from the node i to the node j, the speed vel of the water drop is updated IWD ；
4h) Calculating the sediment variation delta soil (i, j) after each water drop goes from the node i to the node j;
wherein, time (i, j; vel) IWD ) Represents the time required for a water droplet to travel from node i to node j:
wherein epsilon v Is a small normal number, and avoids the condition that the denominator is zero. | c (i) -c (j) | | is the distance between node i and node j; c (i) represents the coordinate of the ith node, c (j) represents the coordinate of the jth node, | |, represents the euclidean distance;
4i) updating the sand content soil of each water drop from node i to node j IWD ；
soil IWD (t+1)＝soil IWD (t)+Δsoil(i,j) (12)
4j) After each water drop goes from the node i to the node j, updating the sediment quantity soil (i, j) in the path from the node i to the node j;
soil(i,j)＝(1-ρ s )·soil(i,j)-ρ s ·Δsoil(i,j) (13)
4k) repeating the steps 4f) to 4j) for each water drop until all nodes are visited, finishing the iteration, calculating the fitness values corresponding to all the water drops according to the formula (1), and selecting the route with the minimum fitness value as the route T with the minimum total cost in the iteration IB ；
4l) comparison of the global optimum fitness value S min And the magnitude of the fitness function value in 4k), if the fitness function value in 4k) is smaller, updating S min And a global optimal route T B ；
4m) updating the sediment amount soil (i, j) in the path by using the sediment amount information among the global optimal paths;
4N) judging whether the maximum iteration number N is reached max If yes, then outputting the global optimal path T B And a global optimum objective function value S min (ii) a Otherwise, the iteration number is increased by one, and the step 4e) is returned.
In the step 4b), in order to improve the convergence rate of the algorithm and increase the diversity of node selection at the initial time, a specific method for initializing the sand amount soil (i, j) between any two nodes is as follows: generating a random number r between 0 and 1 by adopting an initial silt amount randomization strategy n And a random number r n The product of the silt constant InitSoil is given to soil (i, j) as its initial value.
The device for calculating the water drop adaptability value in the step 4c) and the step 4k) is a heuristic decoding device based on a quasi-traveler problem model, and the decoding method sequentially comprises the following steps:
a) the initial time of placing each transport vehicle is t init Selecting a transport vehicle, setting the number of the current service transport vehicle as k equal to 1, and setting the currently selected node number i equal to 11；
b) Setting the initial time point of the current transport vehicle as t m And t is m ＝t init Sequentially selecting corresponding unprocessed nodes; set initial vehicle load range [ lower, higher ]]Is [0, Q]I.e. lower equals 0 and higher equals Q, the waiting time wait of the kth transport vehicle is set k Temporary waiting time t of 0 temp ＝0；
c) If K > K, go to step K);
d) if the scheduling quantity of the service site corresponding to the current node is more than 0, setting lower to lower + q i (ii) a Otherwise, put high ═ high + q i ；
e) If lower is larger than high, k is set to k +1, and then the step b) is carried out;
f) from the initial point in time t of the vehicle m Calculating the time t of the transport vehicle reaching the service site corresponding to the current node n If the time point is above the upper limit of the reserved time of the station, setting k to k +1, and turning to the step b);
g) if the time point is below the station reservation time lower limit, calculating the temporary waiting time t temp ＝a i -t n ；
h) Updating the waiting time of the transport vehicle and executing wait k ＝wait k +t temp ；
i) The time point t of the transport vehicle reaching the service site corresponding to the current node n Waiting time and service time, and obtaining the time point t of the transport vehicle leaving the service station corresponding to the current node m Adding the service station serial number to a service list of the transport vehicle;
j) let i be i +1, judge whether the node number i is less than the public bicycle service station number N c (ii) a If yes, turning to the step d);
k) calculating an objective function, including a distance cost, a waiting cost, a punishment cost of an unserved station and a punishment cost of the number of vehicles of the transport vehicle providing service;
l) outputting an objective function value, and scheduling a path planning result, namely the sequence of service stations of each transport vehicle, the number of used transport vehicle vehicles and the number of public bicycle vehicles originally carried by each transport vehicle.
Referring to fig. 3, there are 10 public bicycle service stations, and 1 to 10 are numbers of the service stations, wherein an arrow represents that the next station can be serviced next before the previous station is serviced, and a dotted line represents that the next station can not be serviced next before the previous station is serviced, and the transport vehicle needs to be replaced. According to the decoding manner, it can be determined that the 10 public bicycle service stations in the sequence need 3 transport vehicles for service, and a service list of each transport vehicle is obtained. Wherein the service site list of the first transport vehicle is [1,6,3 ]; a list of service stations [2,7] for the second vehicle; the list of service stations for the third vehicle is [4,5,8,9,10 ].
In the step 4f), in order to improve the heuristic deficiency of the algorithm and improve the search precision of the algorithm, a strategy of an optimal candidate node subgroup is adopted to select a next node to be accessed, and the method sequentially comprises the following steps:
4f1) reading all nodes which are not visited, calculating the amount of silt between the current node i and all candidate nodes V (IWD), and selecting an optimal subgroup elite (IWD) with a certain proportion as a candidate node according to a selection proportion coefficient gamma from low to high according to the amount of silt, wherein the formula is as follows:
elite(IWD)＝γ·V(IWD) (15)
4f2) according to a formula of probability
The probability of each of the candidate nodes is calculated,
wherein k is a candidate node and is a node which is not visited by the water drop. f (soil (i, j)) is a correlation function of the sediment quantity of the path from the node i to the node j, and is specifically expressed as the following formula:
wherein epsilon s Is a small normal number, and avoids the condition that the denominator is zero. g (soil (i, j)) is a function for converting the sand content of the path from the node i to the node j into a positive number, and is specifically expressed by the following formula:
wherein,
the minimum value of the silt quantity of the path from the current node i to all the candidate nodes is obtained;
4f3) according to the probability of each candidate node
Selecting the next node j using the roulette strategy and updating the access list V with that node c (IWD)。
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A public bicycle appointment scheduling and path planning method is characterized by comprising the following steps:
1) establishing a local database, and carrying out data preprocessing, wherein the specific steps are as follows:
1a) reading in the number N of public bicycle service stations c Distance vectors between the service center and the service stations, and distance matrixes between the service stations and the service stations; reading a reserved time period and a scheduling amount of a service site;
1b) reading the number K of public bicycle service center transport vehicles, the loading capacity Q of the transport vehicles and the time for the transport vehicles to serve service stations with different requirements;
1c) setting the transport vehicle to start at the same speed and setting the speed of the transport vehicle, and solving a distance time vector between the service center and the service station and a distance time matrix between the service station and the service station from the distance vector between the service center and the service station obtained in the step 1a) and the distance matrix between the service station and the service station;
2) according to the description of the problem, determining the constraint condition of the problem, and establishing a mathematical model of a public bicycle appointment scheduling and path planning model;
3) converting the mathematical model obtained in the step 2) into a pseudo traveler problem: the method comprises the following steps that (1) sites are regarded as city points, a transport vehicle is regarded as a travel businessman, the transport vehicle searches a loop traversing all the sites, the objective function value of the loop is minimum, and each site can only be traversed once;
4) solving the pseudo traveler problem model obtained in the step 3) by adopting an intelligent water drop algorithm;
5) outputting the objective function value of the optimal public bicycle scheduling model, and scheduling path planning results, namely the sequence of service stations of each transport vehicle, the number of the used transport vehicles and the number of public bicycle vehicles originally carried by each transport vehicle;
the step 4) adopts an intelligent water drop algorithm based on an optimal candidate node subgroup selection strategy to solve the pseudo traveler problem model obtained in the step 3), and specifically comprises the following steps:
4a) reading in data of a transport vehicle and data of a station;
4b) initializing static parameters: set the number of water drops N IWD (ii) a Number of nodes N C (ii) a Silt constant InitSoil, velocity variation coefficient-a v Coefficient of variation in velocity of two b v Coefficient of variation of velocity, tri c v The coefficient of variation of silt is s Coefficient of variation of silt di b s Coefficient of variation of silt c s (ii) a Local silt amount update coefficient rho s (ii) a Global silt quantity update coefficient rho n (ii) a Maximum number of iterations N max (ii) a Initializing the amount soil (i, j) of sand between any two nodes;
4c) randomly generating a global optimal route T according to the number of nodes B And calculating its fitnessValue S min ；
4d) Initializing dynamic parameters: setting the speed vel of each water drop IWD Amount of silt carried by each drop IWD Visit list per drop V c (IWD) { }, the number of iterations is one;
4e) sets a starting point of each water drop and adds the point to the access list V c (IWD)；
4f) Calculating the probability of each node which is not accessed for each water drop by adopting a selection strategy based on the optimal candidate node subgroup, and selecting the next node to be accessed; updating the Access List V c (IWD)；
4g) After each water drop goes from the node i to the node j, the speed vel of the water drop is updated IWD ；
4h) Calculating the sediment variation Delta soil (i, j) after each water drop goes from the node i to the node j;
wherein, time (i, j; vel) IWD ) Represents the time required for a water droplet to travel from node i to node j:
wherein epsilon v Is a very small normal number, and avoids the condition that the denominator is zero; | c (i) -c (j) | | is the distance between node i and node j; c (i) represents the coordinate of the ith node, c (j) represents the coordinate of the jth node, | |, represents the euclidean distance;
4i) updating the sand content soil of each water drop from node i to node j IWD ；
soil IWD (t+1)＝soil IWD (t)+Δsoil(i,j) (12)
4j) After each water drop goes from the node i to the node j, updating the sediment quantity soil (i, j) in the path from the node i to the node j;
soil(i,j)＝(1-ρ s )·soil(i,j)-ρ s ·Δsoil(i,j) (13)
4k) repeating the steps 4f) to 4j) on each water drop until all nodes are visited, finishing the iteration, calculating the fitness values corresponding to all the water drops according to the fitness function, and selecting the route with the minimum fitness value as the route T with the minimum total cost in the iteration IB ；
4l) comparison of the global optimum fitness value S min And 4k), if the fitness function value in step 4k) is smaller, updating S min And a global optimal route T B ；
4m) updating the sediment amount soil (i, j) in the path by using the sediment amount information among the global optimal paths;
4N) judging whether the maximum iteration number N is reached max If yes, outputting the global optimal path T B And a global optimum objective function value S min (ii) a Otherwise, the iteration number is increased by one, and the step 4e) is returned.
2. The method for scheduling and path planning for public bike reservation according to claim 1, wherein in the step 2), constraint conditions of the problem are determined according to the description of the problem, and a mathematical model of a model for scheduling and path planning for public bike reservation is established, which comprises the following specific steps:
2a) establishing a mathematical model, including the following limiting conditions:
(2a1) the number of the public bicycle service centers in the whole area is only 1, and the transport vehicles start from the service centers, service stations one by one along a certain route and finally return to the service centers to form a closed running path;
(2a2) the service receiving time of each station is in a direct proportion relation with the dispatching amount of the station, the larger the dispatching amount is, the longer the loading time is, and the fixed number of bicycles loaded on each transport vehicle is;
(2a3) each station is served by only one transport vehicle, and the service of the station is completed at one time;
(2a4) the dispatching amount of each station can not exceed the maximum number of bicycles which can be loaded by the transport vehicle, and the number of bicycles on the transport vehicle can not exceed the carrying capacity of the transport vehicle in the dispatching process;
(2a5) the time for the transport vehicle to service the station must meet the corresponding time window requirement, the station is not allowed to access the object after the upper limit of the time window, waiting cost is generated when the object is accessed before the lower limit of the time window, and waiting cost is not generated when the object is accessed within the time window;
2b) according to the conditions, a public bicycle appointment scheduling and path planning model is established as follows:
formula (1) shows that the weighted sum of the distance cost, waiting time, station service number and the number of the transport vehicles obtains the minimum value, four parts connected by plus signs sequentially represent the distance cost, the waiting time punishment, the punishment of unserviced stations and the punishment of the number of the transport vehicles at the service stations, and the more the number of the transport vehicles is, the higher the cost is;
the following constraints are satisfied by equation (1):
x ijk indicating whether the k-th transport vehicle is from the i-th service stationPerforming service to the jth service station, wherein i and j are 0 and represent a service center;
y ik indicating whether the kth transport vehicle serves the ith service station or not;
formula (4) indicates that each station is served by at most one transport vehicle, and the service of the station is completed at one time;
0≤Qk≤Q,k＝1,2,…K (5)
Q k the load capacity of the kth transport vehicle is represented, and Q represents the maximum number of bicycles which can be loaded by the transport vehicle;
|q i |≤Q，i＝1,2,…,N c (6)
|q i l represents the adjustment amount of the ith site; q. q.s i >0 denotes the i-th service station calling in q from the transport vehicle i A bicycle; q. q.s i < 0, indicating that the transport vehicle takes away | q from the ith service station i I bicycle;
t i ≤b i ，i＝1,2,…,N c (7)
t i : indicating the time of arrival of the vehicle at the i-th service station, b i An upper limit of the reserved time of the ith site;
wherein:
K 1 : number of transport vehicle not serviced;
N 1 : the number of sites not served;
d ij : a distance matrix between the ith station and the jth station;
wait k : a kth transport vehicle waiting time;
a i a lower limit indicating that the ith station receives a reservation time;
b i an upper limit indicating the reservation time accepted by the ith station;
w δ δ is 1,2, 3: weighting coefficients of the parts of the objective function.
3. The method for scheduling and planning the reservation of the public bike according to claim 1, wherein the step 4b) initializes the amount of silt (i, j) between any two nodes by the following specific method: generating a random number r between 0 and 1 by adopting an initial silt amount randomization method n And a random number r n The product of the silt constant InitSoil is given to soil (i, j) as its initial value.
4. The method as claimed in claim 1, wherein the means for calculating the water droplet adaptability value in steps 4c) and 4k) is a heuristic decoding device based on a pseudo traveler problem model, and the decoding method sequentially comprises the following steps:
a) the initial time of placing each transport vehicle is t init Selecting a transport vehicle, setting the number k of the current service transport vehicle as 1, and setting the number i of the currently selected node as 1;
b) setting the initial time point of the current transport vehicle as t m And t is m ＝t init Sequentially selecting corresponding unprocessed nodes; set initial vehicle load range [ lower, higher ]]Is [0, Q ]]I.e. lower equals 0 and higher equals Q, the waiting time wait of the kth transport vehicle is set k Temporary waiting time t of 0 temp ＝0；
c) If i is more than K, go to step K);
d) if the scheduling quantity of the service site corresponding to the current node is more than 0, setting lower to lower + q i (ii) a Otherwise, put high ═ high + q i ；
e) If lower is larger than high, k is set to k +1, and then the step b) is carried out;
f) from the initial point in time t of the vehicle m Calculating the time t of the transport vehicle reaching the service site corresponding to the current node n If the time point is above the station reservation time upper limit, setting k as k +1, and turning to the step b);
g) if the time point is below the lower limit of the station reservation time, calculating the temporary waiting time t temp ＝a i -t n ；
h) Updating the waiting time of the transport vehicle and executing wait k ＝wait k +t temp ；
i) The time point t of the transport vehicle reaching the service site corresponding to the current node n Waiting time and service time, and obtaining the time point t of the transport vehicle leaving the service station corresponding to the current node m Adding the serial number of the service station to a service list of the transport vehicle;
j) let i be i +1, judge whether the node number i is less than the public bicycle service station number N c (ii) a If yes, turning to the step d);
k) calculating an objective function, including a distance cost, a waiting cost, a punishment cost of an unserved station and a punishment cost of the number of vehicles of the transport vehicle providing service;
l) outputting an objective function value, and scheduling a path planning result, namely the sequence of service stations of each transport vehicle, the number of used transport vehicle vehicles and the number of public bicycle vehicles originally carried by each transport vehicle.
5. The method for reserving, scheduling and path planning for public bicycles according to claim 1, wherein the step 4f) adopts a selection strategy based on an optimal candidate node subgroup, and the specific process of selecting the next node to be visited is as follows:
4f1) reading all nodes which are not visited, calculating the amount of silt between the current node i and all candidate nodes V (IWD), selecting an optimal subgroup of elite (IWD) in a certain proportion as candidate nodes according to a selection proportion coefficient gamma from low to high according to the amount of silt, wherein the formula is as follows:
elite(IWD)＝γ·V(IWD) (15)
4f2) calculating the probability P of each candidate node according to a probability formula (16) i IWD (j)，
Wherein k is a candidate node and is a node which is not visited by the water drop; f (soil (i, j)) is a correlation function of the sediment quantity of the path from the node i to the node j, and is specifically expressed as the following formula:
wherein epsilon s Is a very small normal number, and avoids the condition that the denominator is zero; g (soil (i, j)) is a function for converting the sand content of the path from the node i to the node j into a positive number, and is specifically expressed by the following formula:
wherein,
the minimum value of the silt quantity of the path from the current node i to all the candidate nodes is obtained;
4f3) according to the probability P of each candidate node i IWD (j) Using roulette strategy to select the next node j and update the access list V with this node c (IWD)。
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