CN114358675A - Multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning method - Google Patents
Multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning method Download PDFInfo
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Abstract
The invention discloses a multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning method, and belongs to the technical field of unmanned aerial vehicle logistics. The method comprises the following steps: the method comprises the following steps: establishing a mixed integer linear programming model of a multi-unmanned aerial vehicle-multi-truck collaborative logistics distribution path programming problem; step two: carrying out initial planning on a truck delivery path based on a K-Means algorithm and a genetic algorithm; step three: and designing a path planning search operator, introducing a variable neighborhood search framework on the basis of a truck distribution route to jointly optimize a distribution path of the unmanned aerial vehicle and the truck, and solving the constructed mixed integer linear programming model. The method provided by the invention considers different purchase costs of the truck and the unmanned aerial vehicle, reasonably optimizes the purchase quantity and the use quantity of the transport means, effectively reduces the total distribution cost, further optimizes the unmanned aerial vehicle-truck distribution scheme, and makes up for the defects of the existing combined distribution model and method.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle logistics, and particularly relates to a multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning method.
Background
Unmanned Aerial Vehicles (UAVs) are aircraft that are remotely controlled by a control station or that autonomously complete flight. In recent years, with the continuous development of unmanned aerial vehicle technology, unmanned aerial vehicles play more and more important roles in the civil field and the military field. The application of the unmanned aerial vehicle in the civil field relates to multiple aspects of infrastructure construction, agriculture, traffic logistics, safety, disaster management, entertainment and the like, and the unmanned aerial vehicle also becomes a choice of future logistics transportation tools. Compared with the traditional distribution mode, the unmanned aerial vehicle has the characteristics of high speed, no road limitation, low cost and the like, and has wide prospect under the current situation that the current express industry rapidly develops and the last kilometer becomes a difficult problem in the distribution industry. On the other hand, low-altitude express delivery unmanned aerial vehicle is limited by the aircraft volume, has the limitation that the time of endurance is short and the effective load is small compared with truck delivery, and only uses unmanned aerial vehicle to carry out round trip delivery between warehouse and customer to improve the efficiency of express delivery limitedly. And use unmanned aerial vehicle and truck to deliver simultaneously, allow unmanned aerial vehicle to take operations such as take off and land, restock on the truck and then can realize that the advantage of the two is complementary. Therefore, unmanned aerial vehicle-truck combined distribution provides a brand new solution for solving the problem of end logistics distribution.
When the unmanned aerial vehicle-truck is used for carrying out combined delivery, the delivery objects and the delivery sequence of the unmanned aerial vehicle and the truck need to be planned, namely, the unmanned aerial vehicle and the truck are subjected to path planning, and the delivery efficiency is further improved and the service cost is reduced on the basis of ensuring that the unmanned aerial vehicle and the truck can safely complete the delivery tasks of all users through reasonable path planning. The existing method mostly considers the advantage of improving the logistics distribution of the unmanned aerial vehicle from the perspective of transportation time or transportation cost, and neglects the condition that the unmanned aerial vehicle influences the acquisition cost of the distribution tool. However, in practice, the transportation cost is different from the purchase cost of a truck and an unmanned aerial vehicle by orders of magnitude, and the conventional method is still deficient in consideration of reducing the service cost, so that the purchase cost and the transportation cost are comprehensively considered when the unmanned aerial vehicle-truck combined path planning is performed, and the total cost of the path planning scheme is optimized.
Disclosure of Invention
The technical problem of the invention is solved: the defects of the prior art are overcome, the planning method of the multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution route comprehensively considering the acquisition cost and the distribution cost is provided, and an executable and efficient distribution scheme is obtained.
The invention establishes a mixed integer linear programming model capable of describing the problems, provides a two-stage heuristic algorithm framework based on a K-Means algorithm, a genetic algorithm and a variable neighborhood search algorithm, and makes up the defects of the conventional task programming model and method.
The invention provides a multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning, which comprises the following steps:
the method comprises the following steps: establishing a mixed integer linear programming model of a multi-unmanned aerial vehicle-multi-truck cooperative distribution path programming problem;
step two: carrying out initial planning on a truck delivery path based on a K-Means algorithm and a genetic algorithm;
step three: and designing a path planning search operator, introducing a variable neighborhood search framework on the basis of a truck distribution route to jointly optimize a distribution path of the unmanned aerial vehicle and the truck, and solving the constructed mixed integer linear programming model.
The first step is specifically realized as follows:
the method comprises the following steps: establishing a mixed integer linear programming model of a multi-unmanned aerial vehicle-multi-truck collaborative distribution path programming problem:
step 1.1 scene setting:
the distribution network comprises a warehouse and a plurality of customer demand points which are recorded as:
Nc＝{1，，2，…,n}
to distinguish between departure and return, the warehouse uses two numbers N0(Nn+1) Is expressed in which N is0Representing the starting point of the delivery, Nn+1Indicating the end point of the delivery;
the warehouse can store at most W trucks and U unmanned planes.
Taking a single truck and a single unmanned aerial vehicle service customer as an example, as shown in fig. 1, the unmanned aerial vehicle-truck combined delivery scenario involved in the invention is that the unmanned aerial vehicle and the truck leave the warehouse together, and the unmanned aerial vehicle can serve together with the truck while the truck serves the customer, and can also take off from the truck, and land to the truck at another position after carrying goods to serve the single customer, so as to complete the replacement of the battery and the loading of the goods, and prepare for the delivery again. During distribution, a truck may carry multiple drones. And after the distribution of all the customer service points is finished, the truck and the unmanned aerial vehicle return to the warehouse.
Step 1.2 model assumptions:
based on the definition of the problem scenario in step 1.1, this step makes assumptions before building the model, which are listed as follows:
1. due to the fact that the purchase cost is high, the distribution tasks are completed for many times after purchase, and the purchase cost is shared by the distribution tasks every time in the using process. Therefore, when the transportation cost of transportation tool distribution is considered, the transportation cost and the purchase cost are more reasonable to calculate by taking the times that the transportation can be carried out before the complete aging of a truck or an unmanned aerial vehicle;
2. one truck can carry a plurality of unmanned aerial vehicles, and the unmanned aerial vehicles can take off and land on different trucks;
3. the load capacity of the truck is strong, the truck is set to carry all goods to be delivered when starting from a warehouse, midway replenishment is not needed, and the load capacity of the unmanned aerial vehicle is weak, so that a single unmanned aerial vehicle is supposed to serve only one customer point in a single delivery process, and then the truck needs to be returned to for replenishment;
4. the unmanned aerial vehicle returns to the truck and can change the battery that the electric quantity is sufficient, and is equipped with the battery that is full of enough electric quantity on the truck.
Step 1.3, setting parameters and variables:
in the logistics distribution model, the network mainly comprises a warehouse N0(Nn+1) Customer demand node Nc1, 2, …, n and the arc between nodes, the distance between each node being dijIt is shown, where arc (i, j) is ∈ a if the truck can travel from node i to node j, and similarly, arc (i, j) is ∈ B if the drone can travel from node i to node j. The delivery task is jointly completed by the truck and the unmanned plane, wherein the set of customer nodes which can be served by the unmanned plane is set as NUThe set of feasible paths (i, j, k) for the drones is set as E. To calculate the total cost of distribution, the purchase costs of the truck and the unmanned aerial vehicle are set to be FW、FUThe transport cost per unit travel distance is CW、CUThe single truck and the single unmanned aerial vehicle can be used for T times after purchase, and the maximum driving distance after single takeoff of the unmanned aerial vehicle is DU。
When a truck with the number w travels from node i to node j during the design of a delivery plan, xijwWhen the unmanned plane with the number u travels from the node i to the node j as 1, yijku1. Variable miThe order in which the ith client node was visited, zw、zuThen the use of the w truck and the u drone in the distribution scheme are recorded separately.
Step 1.4 model construction:
the objective function in the present invention is to minimize the acquisition and transportation costs required for truck and drone delivery. Wherein the purchase cost of the truck may be multiplied by the unit price of the truck by the number of trucks used in the delivery; the cost of truck delivery may be multiplied by the sum of the paths taken by all trucks during delivery, multiplied by the cost of truck delivery per unit distance, multiplied by the number of deliveries it can make before it completely ages. The same calculations can be performed for drones. Therefore, the objective function of the model is as shown in equation (1):
in the whole distribution process, each truck needs to start from the warehouse, finally completes the distribution task and returns to the warehouse, and only temporarily stops at the customer demand point, so that the flow balance constraint shown in the formula (2) is met:
because the problem of delivery rationality, the truck can not wait at same customer point that unmanned aerial vehicle accomplishes the delivery and return and just go to the next customer point that needs the delivery, consequently restricts same unmanned aerial vehicle and can only take off or land once at every take off and land point, promptly:
in the actual distribution process, a customer point is often only distributed by a truck or a drone, and the cargo is not required to be distributed separately to the truck and the drone, so that each demand point is only visited by the truck or the drone once, and the following constraints are generated:
according to the contents of the model assumption part, the taking-off and landing of the unmanned aerial vehicle can only be completed on a truck, so if the unmanned aerial vehicle takes off at customer i, serves customer j, and lands at point k, the truck must pass through i and k to join with the unmanned aerial vehicle:
since the number of trucks and drones dispatched need to be used in calculating the total cost of dispatching trucks and drones in the path plan, the z-pair is requiredwAnd zuTwo variables are constrained, where z iswThe constraints of (2) are as follows:
from the above equation, it can be seen that constraints (7) - (8) determine the dispatch condition for each truck, Σ if the w-th truck is not servicing any customers during the delivery process(i,j)∈Axijw-1-0, constraint (7) such that z isw0; if it serves the customer, Σ(i,j)∈Axijw-1 ≧ 1, constraint (8) such that zw1. To zuTwo constraints can also be established in the same way:
path planning based on the current model may create situations where the truck loops between customer points, and therefore constraints need to be added to avoid this, as follows:
for constraint (11), if the drone takes off at customer i, serves customer j, and lands at customer k, then
mk-miThe number of the customers is more than or equal to 1, and the truck visits the i customer and then visits the k customer; if the unmanned aerial vehicle has no take-off and landing process at the i customer and the k customer, mk-miAnd more than or equal to 1- (n +2) ═ n-1, wherein n is the total number of the customer points, namely the access sequence of the customer i and the customer k is not particularly limited.
Constraints (12) limit the truck from traveling in a loop between customer sites. If the path from i to j exists, the right side value of the inequality is 0, mi-mj+1 ≦ 0, the visit order for customer i must precede customer j, avoiding the truck from traveling in a loop between customer sites.
The navigation of unmanned aerial vehicle is supplied with power by the battery, has the restriction of electric quantity, consequently all has the upper limit of its single flight distance to every unmanned aerial vehicle, takes off from unmanned aerial vehicle on the truck to the in-process of delivering and returning to the truck, and the mileage that unmanned aerial vehicle traveles can not exceed this upper limit, promptly:
for integer variable miIt represents the order in which the ith node is visited by the truck, i.e.:
in addition, the 0-1 variable constraints in the model are as follows:
therefore, a mixed integer linear programming model of the multi-unmanned aerial vehicle-multi-truck collaborative distribution path programming problem is established.
The second step is as follows: carrying out initial planning on a truck delivery path based on a K-Means algorithm and a genetic algorithm:
in the present invention, the taking off and landing of the drone are all done on the truck, i.e. the flight path of the drone is generated on the path of the truck, so this step will generate a route for delivery only with the truck.
Step 2.1, the K-Means algorithm realizes the clustering of the demand points of the customers according to the spatial distribution:
in order to minimize the driving cost of the truck, the customer points are clustered according to the spatial position distribution of the customer demand points through a K-Means algorithm. Such preprocessing also helps to reduce the time complexity of subsequent calculations.
Step 2.2 generating a single delivery path of the truck based on a genetic algorithm:
based on the cluster label assigned to each customer node in step 2.1, customers of the same label are delivered by the same truck. The delivery route for each truck is planned in this step using a genetic algorithm to minimize the delivery route for the truck and also to minimize the transportation cost of the truck during delivery.
Thus, a route planning scheme for only delivery by truck required by the invention is established.
The third step is that: designing a path planning search operator, introducing a variable neighborhood search framework on the basis of a truck delivery route to jointly optimize a delivery path of an unmanned aerial vehicle and a truck, and solving a constructed mixed integer linear programming model:
after the initial feasible truck route is obtained, a multi-drone-multi-truck joint delivery path may be generated using a variable neighborhood search algorithm (VNS) based on the truck delivery path. The invention designs four neighborhood search operators to obtain the optimal solution of the joint delivery path, when the algorithm starts, the first operator is repeatedly executed on the initial solution until the local optimal solution under the first operator is obtained, then the second operator is executed, when a new optimal solution is found, the first operator is executed again, and so on, and the specific contents of the four operators are respectively introduced below.
Step 3.1 unmanned aerial vehicle service customer point selection operator:
the objective of implementing this operator is to convert as many customers as possible, originally delivered by trucks, to delivery by drones, with a resulting overall cost reduction. When the operator is executed, customer demand points served by each truck are sequentially detected, whether the customer demand points can be served by the unmanned aerial vehicle is judged firstly, namely whether the customer points are within the range of the endurance mileage of the unmanned aerial vehicle, whether the weight of the required goods is lower than the upper limit of the load of the unmanned aerial vehicle, if the customer is judged to meet the requirement, feasible take-off and landing points are appointed for the unmanned aerial vehicle serving the customer points, whether the customer points are better than the original solution after the customer points are distributed by the unmanned aerial vehicle is calculated, if new optimal solutions are obtained, the customer points are determined to be the customer points served by the unmanned aerial vehicle, and the take-off and landing points set in the front are adopted. It should be noted that a customer that has been assigned to a particular drone service cannot be selected again. The operator is called for multiple times at the beginning of the algorithm, so that a scheme for joint delivery of the unmanned aerial vehicle and the truck is greedily generated.
Step 3.2, selecting an operator for the unmanned aerial vehicle take-off and landing point:
the new scheme obtained through the operator only needs delivery cost superior to initial cost to determine the take-off and landing points of the unmanned aerial vehicle, so that the current delivery scheme cannot be guaranteed to be a global optimal solution, the operator searches the take-off and landing points of the unmanned aerial vehicle for the unmanned aerial vehicle service client points again on the basis of the current truck delivery path, if the total delivery cost can be reduced again under the condition that the truck route is not changed, the first operator is returned to be used again to optimize the current solution, finally, the local optimal solution which is also achieved in a second neighborhood is achieved, and then a third operator is executed.
Step 3.3, the unmanned aerial vehicle client point puts back operators:
because the greedy algorithm is adopted in the first operator to search the unmanned aerial vehicle client points, the unmanned aerial vehicle client points are easy to trap into local optimization, and after the lifting points are optimized, it is impossible to determine which transport means the client points finish distribution relatively better. Therefore, in the operator, each customer point distributed by the unmanned aerial vehicle needs to be reset to be distributed by the truck, whether the optimal solution at the moment is updated or not is evaluated, if a better result is obtained, the point is converted into a node distributed by the truck, the first operator is returned, and neighborhood searching is restarted.
Step 3.4 truck visit order exchange operator:
because the genetic algorithm also belongs to a heuristic algorithm and can only approach the optimal solution, but cannot ensure that the optimal solution is obtained certainly, the feasible solution obtained after the initial solution of the variable neighborhood search is solved by the three operators is the upper bound of the current local optimal solution, in the fourth operator, the visited sequences of any two customers served by the truck in the current truck distribution path are exchanged randomly, the total cost before and after the exchange is compared, and whether a new optimal solution can be found or not is searched, so that the current local optimal solution is further approached.
Step 3.5 perturbation function (Shake) operator:
the current local optimal solution for planning the unmanned aerial vehicle-truck combined delivery path can be obtained through the four neighborhood search operators, and at the moment, a Shake function is needed to jump out the local optimal solution. The specific operation mode is to randomly disturb the visited sequence of all customers under the condition of keeping the number of the customers served by the trucks and the unmanned planes constant. And then re-planning the delivery routes of trucks and drones among all customers. And obtaining a new local optimal solution by applying the four operators after obtaining the new solution.
Therefore, the needed planning scheme for the multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path is obtained, and the conditions are met.
The invention has the advantages and beneficial effects that:
(1) aiming at the problem of planning the multi-unmanned aerial vehicle-multi-truck collaborative logistics distribution path, the invention establishes a combined optimization model capable of accurately depicting the problem, and considers various practical factors, so that the established model is further close to the practical situation and has practical application value;
(2) the invention provides a two-stage heuristic algorithm framework based on a K-Means algorithm, a genetic algorithm and a variable neighborhood search algorithm, effectively solves the problem of planning the multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution route, obtains a feasible distribution scheme, coordinates and orders the unmanned aerial vehicle and the truck in the scheme to carry out distribution tasks, and efficiently finishes the whole distribution task.
(3) The multi-unmanned aerial vehicle-multi-truck collaborative logistics distribution route planning method comprehensively considers the acquisition cost and the transportation cost, reduces the distribution cost and improves the distribution speed compared with the traditional distribution mode, and simultaneously considers the acquisition cost to ensure that a logistics company can more reasonably acquire and keep the required number of unmanned aerial vehicles and trucks. Meanwhile, with the further development of the unmanned aerial vehicle technology and the further reduction of the transportation cost per unit distance in the future, the transportation cost of unmanned aerial vehicle distribution is possibly lower, and the advantages of unmanned aerial vehicle logistics are further highlighted.
Drawings
Fig. 1 is a schematic diagram of a multi-drone-multi-truck collaborative logistics distribution path planning method of the present invention;
FIG. 2 is a flow chart of an implementation of the method for planning the logistics distribution route in cooperation of multiple UAVs and multiple trucks according to the present invention;
FIG. 3 is a schematic flow chart of a K-Means algorithm illustrating an exemplary step of an embodiment of the present invention;
FIG. 4 is a flow chart of a genetic algorithm illustrating an exemplary step two of the present invention;
FIG. 5 is a flow chart illustrating exemplary steps of a method of implementing the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
The method provided by the invention comprehensively considers the acquisition cost and the transportation cost of the unmanned aerial vehicle and the truck, reasonably configures the number of the unmanned aerial vehicle and the truck, optimizes the distribution scheme and overcomes the defects of the existing model and method for the unmanned aerial vehicle-truck combined distribution problem.
As shown in fig. 2, the embodiment of the present invention is as follows:
the method comprises the following steps: establishing a mixed integer linear programming model of a multi-unmanned aerial vehicle-multi-truck collaborative distribution path programming problem:
step 1.1 scene setting:
the distribution network comprises a warehouse and a plurality of customer demand points which are recorded as:
Nc＝{1,,2,…,n}
to distinguish between departure and return, the warehouse uses two numbers N0(Nn+1) Is expressed in which N is0Representing the starting point of the delivery, Nn+1Indicating the end point of the delivery;
the warehouse can store at most W trucks and U unmanned planes.
Taking a single truck and a single unmanned aerial vehicle service customer as an example, as shown in fig. 1, the unmanned aerial vehicle-truck combined delivery scenario involved in the invention is that the unmanned aerial vehicle and the truck leave the warehouse together, and the unmanned aerial vehicle can serve together with the truck while the truck serves the customer, and can also take off from the truck, and land to the truck at another position after carrying goods to serve the single customer, so as to complete the replacement of the battery and the loading of the goods, and prepare for the delivery again. During distribution, a truck may carry multiple drones. And after the distribution of all the customer service points is finished, the truck and the unmanned aerial vehicle return to the warehouse.
Step 1.2 model assumptions:
based on the definition of the problem scenario in step 1.1, this step makes assumptions before building the model, which are listed as follows:
5. due to the fact that the purchase cost is high, the distribution tasks are completed for many times after purchase, and the purchase cost is shared by the distribution tasks every time in the using process. Therefore, when the transportation cost of transportation tool distribution is considered, the transportation cost and the purchase cost are more reasonable to calculate by taking the times that the transportation can be carried out before the complete aging of a truck or an unmanned aerial vehicle;
6. one truck can carry a plurality of unmanned aerial vehicles, and the unmanned aerial vehicles can take off and land on different trucks;
7. the load capacity of the truck is strong, the truck is set to carry all goods to be delivered when starting from a warehouse, midway replenishment is not needed, and the load capacity of the unmanned aerial vehicle is weak, so that a single unmanned aerial vehicle is supposed to serve only one customer point in a single delivery process, and then the truck needs to be returned to for replenishment;
8. the unmanned aerial vehicle returns to the truck and can change the battery that the electric quantity is sufficient, and is equipped with the battery that is full of enough electric quantity on the truck.
Step 1.3, setting parameters and variables:
in the logistics distribution model, the network mainly comprises a warehouse N0(Nn+1) Customer demand node Nc1, 2, …, n and the arc between nodes, the distance between each node being dijIt is shown, where arc (i, j) is ∈ a if the truck can travel from node i to node j, and similarly, arc (i, j) is ∈ B if the drone can travel from node i to node j. The delivery task is jointly completed by the truck and the unmanned plane, wherein the set of customer nodes which can be served by the unmanned plane is set as NUThe set of feasible paths (i, j, k) for the drones is set as E. To calculate the total cost of distribution, the purchase costs of the truck and the unmanned aerial vehicle are set to be FW、FUThe transport cost per unit travel distance is CW、CUThe single truck and the single unmanned aerial vehicle can be used for T times after purchase, and the maximum driving distance after single takeoff of the unmanned aerial vehicle is DU。
The key element set required to be set for constructing the model and the parameters in the model are shown in table 1:
set, parameters in the model of Table 1
When a truck with the number w travels from node i to node j during the design of a delivery plan, xijwWhen the unmanned plane with the number u travels from the node i to the node j as 1, yijku1. Variable miThe order in which the ith client node was visited, zw、zuThen the use of the w truck and the u drone in the distribution scheme are recorded separately. All variables involved in the model are shown in table 2.
Variables in the model of Table 2
Step 1.4 model construction:
the model objective function is to minimize acquisition costs and transportation costs required for truck and drone delivery. Wherein the purchase cost of the truck may be multiplied by the unit price of the truck by the number of trucks used in the delivery; the cost of truck delivery may be multiplied by the sum of the paths taken by all trucks during delivery, multiplied by the cost of truck delivery per unit distance, multiplied by the number of deliveries it can make before it completely ages. The same calculations can be performed for drones. Therefore, the objective function of the model is as shown in equation (1):
in the whole distribution process, each truck needs to start from the warehouse, finally completes the distribution task and returns to the warehouse, and only temporarily stops at the customer demand point, so that the flow balance constraint shown in the formula (2) is met:
because the problem of delivery rationality, the truck can not wait at same customer point that unmanned aerial vehicle accomplishes the delivery and return and just go to the next customer point that needs the delivery, consequently restricts same unmanned aerial vehicle and can only take off or land once at every take off and land point, promptly:
in the actual distribution process, a customer point is often only distributed by a truck or a drone, and the cargo is not required to be distributed separately to the truck and the drone, so that each demand point is only visited by the truck or the drone once, and the following constraints are generated:
according to the contents of the model assumption part, the taking-off and landing of the unmanned aerial vehicle can only be completed on a truck, so if the unmanned aerial vehicle takes off at customer i, serves customer j, and lands at point k, the truck must pass through i and k to join with the unmanned aerial vehicle:
due to the number of trucks and drones that need to be dispatched in calculating the total cost of dispatching the trucks and drones in the path planTherefore, it is necessary to be aligned with zwAnd zuTwo variables are constrained, where z iswThe constraints of (2) are as follows:
from the above equation, it can be seen that constraints (7) - (8) determine the dispatch condition for each truck, Σ if the w-th truck is not servicing any customers during the delivery process(i，j)∈Axijw-1-0, constraint (7) such that z isw0; if it serves the customer, Σ(i，j)∈Axijw-1 ≧ 1, constraint (8) such that zw1. To zuTwo constraints can also be established in the same way:
path planning based on the current model may create situations where the truck loops between customer points, and therefore constraints need to be added to avoid this, as follows:
for constraint (11), if the drone takes off at customer i, serves customer j, and lands at customer k, then
mk-miThe number of the customers is more than or equal to 1, and the truck visits the i customer and then visits the k customer; if the unmanned aerial vehicle has no take-off and landing process at the i customer and the k customer, mk-miAnd more than or equal to 1- (n +2) ═ n-1, wherein n is the total number of the customer points, namely the access sequence of the customer i and the customer k is not particularly limited.
Constraints (12) limit the truck from traveling in a loop between customer sites. If the path from i to j exists, the right side value of the inequality is 0, mi-mj+1 ≦ 0, the visit order for customer i must precede customer j, avoiding the truck from traveling in a loop between customer sites.
The navigation of unmanned aerial vehicle is supplied with power by the battery, has the restriction of electric quantity, consequently all has the upper limit of its single flight distance to every unmanned aerial vehicle, takes off from unmanned aerial vehicle on the truck to the in-process of delivering and returning to the truck, and the mileage that unmanned aerial vehicle traveles can not exceed this upper limit, promptly:
for integer variable miIt represents the order in which the ith node is visited by the truck, i.e.:
in addition, the 0-1 variable constraints in the model are as follows:
therefore, a mixed integer linear programming model of the multi-unmanned aerial vehicle-multi-truck collaborative distribution path programming problem is established.
Step two: carrying out initial planning on a truck delivery path based on a K-Means algorithm and a genetic algorithm:
in the present invention, the taking off and landing of the drone are all done on the truck, i.e. the flight path of the drone is generated on the path of the truck, so this step will generate a route for delivery only with the truck.
Step 2.1, the K-Means algorithm realizes the clustering of the demand points of the customers according to the spatial distribution:
in order to minimize the driving cost of the truck, the customer points are clustered according to the spatial position distribution of the customer demand points through a K-Means algorithm. The preprocessing is simultaneously beneficial to reducing the time complexity of subsequent calculation, a K-Means algorithm flow chart is shown in FIG. 3, and assuming that the number of dispatched vehicles is w, an algorithm flow for clustering the customer demand points is as follows:
step 1 randomly appointing w points as the center of the cluster;
step 2, allocating the customer demand point to the nearest center;
step 3, calculating the average positions of the customer demand points of w clusters as new cluster center points;
and Step 4, judging whether the termination condition is reached, if so, returning to Step 2, and otherwise, ending the algorithm.
Step 2.2 generating a single delivery path of the truck based on a genetic algorithm:
based on the cluster label assigned to each customer node in step 2.1, customers of the same label are delivered by the same truck. The delivery route for each truck is planned in this step using a genetic algorithm to minimize the delivery route for the truck and also to minimize the transportation cost of the truck during delivery. The genetic algorithm flow chart is shown in fig. 4, and the flow is illustrated as follows:
step 1 randomly generating a scheme of q path plans as an initial solution set p*Namely an initial population of the genetic algorithm, and setting a genetic algebra a, a cross probability b and a variation probability c in the algorithm;
step 2, calculating the truck distribution cost of all solutions in the current solution set, wherein the lower the cost is, the higher the fitness is, and finding out the optimal solution s in the solution set*At a cost of f*Keeping it to the next generation population;
step 3, determining q individuals in a new population p by using a roulette method;
step 4, determining whether each individual in the new population is crossed or not according to the crossing probability b, if so, randomly generating a crossing point, and exchanging a route behind the crossing point to generate a new population;
step 5, determining whether each individual in the new population is mutated or not according to the mutation probability c, if so, randomly selecting two customer demand points, and exchanging the accessed sequence to generate a new population p;
step 6, calculating the truck distribution cost of all solutions for the new population p, finding the optimal solution s in the solution set, wherein the cost is f, and if f is f<f*Then the optimal solution s is retained to the next generation population and let s*＝s，f*F, otherwise, s*And f*The change is not changed;
step 7, judging whether the genetic algebra reaches a, if not, returning to Step 3; if so, ending the algorithm;
the final obtained single delivery path scheme of the truck at Step 8 is s*。
Thus, a route planning scheme for only delivery by truck required by the invention is established.
Step three: designing a path planning search operator, introducing a variable neighborhood search framework on the basis of a truck delivery route to jointly optimize a delivery path of an unmanned aerial vehicle and a truck, and solving a constructed mixed integer linear programming model:
after the initial feasible truck route is obtained, a multi-drone-multi-truck joint delivery path may be generated using a variable neighborhood search algorithm (VNS) based on the truck delivery path. The invention designs four neighborhood search operators to obtain the optimal solution of the joint distribution path, when the algorithm starts, the first operator is repeatedly executed on the initial solution until the local optimal solution under the first operator is obtained, then the second operator is executed, when a new optimal solution is found, the first operator is executed again, and so on, the whole flow of the three steps is shown in figure 5, and the specific contents of the four operators are respectively introduced.
Step 3.1 unmanned aerial vehicle service customer point selection operator:
the objective of implementing this operator is to convert as many customers as possible, originally delivered by trucks, to delivery by drones, with a resulting overall cost reduction. When the operator is executed, customer demand points served by each truck are sequentially detected, whether the customer demand points can be served by the unmanned aerial vehicle is judged firstly, namely whether the customer points are within the range of the endurance mileage of the unmanned aerial vehicle, whether the weight of the required goods is lower than the upper limit of the load of the unmanned aerial vehicle, if the customer is judged to meet the requirement, feasible take-off and landing points are appointed for the unmanned aerial vehicle serving the customer points, whether the customer points are better than the original solution after the customer points are distributed by the unmanned aerial vehicle is calculated, if new optimal solutions are obtained, the customer points are determined to be the customer points served by the unmanned aerial vehicle, and the take-off and landing points set in the front are adopted. It should be noted that a customer that has been assigned to a particular drone service cannot be selected again. The operator is called for multiple times at the beginning of the algorithm, so that a scheme for joint delivery of the unmanned aerial vehicle and the truck is greedily generated.
Step 3.2, selecting an operator for the unmanned aerial vehicle take-off and landing point:
the new scheme obtained through the operator only needs delivery cost superior to initial cost to determine the take-off and landing points of the unmanned aerial vehicle, so that the current delivery scheme cannot be guaranteed to be a global optimal solution, the operator searches the take-off and landing points of the unmanned aerial vehicle for the unmanned aerial vehicle service client points again on the basis of the current truck delivery path, if the total delivery cost can be reduced again under the condition that the truck route is not changed, the first operator is returned to be used again to optimize the current solution, finally, the local optimal solution which is also achieved in a second neighborhood is achieved, and then a third operator is executed.
Step 3.3, the unmanned aerial vehicle client point puts back operators:
because the greedy algorithm is adopted in the first operator to search the unmanned aerial vehicle client points, the unmanned aerial vehicle client points are easy to trap into local optimization, and after the lifting points are optimized, it is impossible to determine which transport means the client points finish distribution relatively better. Therefore, in the operator, each customer point distributed by the unmanned aerial vehicle needs to be reset to be distributed by the truck, whether the optimal solution at the moment is updated or not is evaluated, if a better result is obtained, the point is converted into a node distributed by the truck, the first operator is returned, and neighborhood searching is restarted.
Step 3.4 truck visit order exchange operator:
because the genetic algorithm also belongs to a heuristic algorithm and can only approach the optimal solution, but cannot ensure that the optimal solution is obtained certainly, the feasible solution obtained after the initial solution of the variable neighborhood search is solved by the three operators is the upper bound of the current local optimal solution, in the fourth operator, the visited sequences of any two customers served by the truck in the current truck distribution path are exchanged randomly, the total cost before and after the exchange is compared, and whether a new optimal solution can be found or not is searched, so that the current local optimal solution is further approached.
Step 3.5 perturbation function (Shake) operator:
the current local optimal solution for planning the unmanned aerial vehicle-truck combined delivery path can be obtained through the four neighborhood search operators, and at the moment, a Shake function is needed to jump out the local optimal solution. The specific operation mode is to randomly disturb the visited sequence of all customers under the condition of keeping the number of the customers served by the trucks and the unmanned planes constant. And then re-planning the delivery routes of trucks and drones among all customers. And obtaining a new local optimal solution by applying the four operators after obtaining the new solution.
Specifically, after the operation of each operator is determined, the corresponding algorithm steps are explained as follows:
step 1 setting the most in the algorithmThe number N of the large neighborhoods is 4, the maximum iteration number K is obtained, and the current optimal solution s is recorded*The cost value is f*；
Step 2, obtaining a current local optimal solution s and the cost f of the optimal solution by using a variable neighborhood descent search algorithm and four neighborhood search operators;
step 3 comparison f*And the value of f if<f*Then let s*＝s，f*＝f；
Step 4, judging whether the iteration frequency reaches K or not, if so, terminating the algorithm to obtain the optimal solution s*The lowest cost is f*Otherwise, continuing Step 5;
step 5 gets a new solution through the Shake function and returns to Step 2.
Therefore, the needed planning scheme for the multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path is obtained, and the conditions are met.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (7)
1. A multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path planning method is characterized by comprising the following steps:
the method comprises the following steps: establishing a mixed integer linear programming model of a multi-unmanned aerial vehicle-multi-truck collaborative logistics distribution path programming problem;
step two: carrying out initial planning on a truck delivery path based on a K-Means algorithm and a genetic algorithm;
step three: and designing a path planning search operator, introducing a variable neighborhood search framework on the basis of a truck distribution route to jointly optimize a distribution path of the unmanned aerial vehicle and the truck, and solving the constructed mixed integer linear programming model.
2. The multi-drone-multi-truck collaborative logistics distribution path planning method of claim 1, characterized in that: the first step is specifically realized as follows:
step 1.1 scene setting:
the distribution network comprises a warehouse and a plurality of customer demand points which are recorded as:
Nc＝{1，，2，...，n}
to distinguish between departure and return, the warehouse uses two numbers N0(Nn+1) Is expressed in which N is0Representing the starting point of the delivery, Nn+1Indicating the end point of the delivery;
at most, W trucks and U-frame unmanned aerial vehicles can be stored in the warehouse;
step 1.2 model definition:
based on the definition of the problem scenario in step 1.1, the definition is made before the model is built:
1) when the transportation cost of transportation tool distribution is considered, the transportation cost and the acquisition cost are calculated reasonably by taking the times of distribution by a truck or an unmanned aerial vehicle before complete aging;
2) one truck can carry a plurality of unmanned aerial vehicles, and the unmanned aerial vehicles take off and land on different trucks;
3) when the truck starts from the warehouse, all goods to be delivered are carried, midway replenishment is not needed, the single unmanned aerial vehicle can only serve one customer point in the single delivery process, and then the truck needs to be returned to for replenishment;
4) the unmanned aerial vehicle returns to the truck, so that the battery with sufficient electric quantity can be replaced, and the truck is provided with the battery;
step 1.3, setting parameters and variables:
in the logistics distribution model, the network is composed of a warehouse N0(Nn+1) Customer demand node Nc1, 2, n, and an arc between nodes, the distance between each node being dijIndicating that if the truck travels from node i to node j, the arc (i, j) belongs to A, and if the unmanned plane travels from node i to node j, the arc (i, j) belongs to B;the distribution task is jointly completed by the truck and the unmanned aerial vehicle, wherein the set of customer nodes served by the unmanned aerial vehicle is set as NUSetting the set of feasible paths (i, j, k) of the unmanned plane as E; the purchase costs of the truck and the unmanned aerial vehicle are respectively FW、FUThe transport cost per unit travel distance is CW、CUThe single truck and the single unmanned aerial vehicle can be used for T times after purchase, and the maximum driving distance after single takeoff of the unmanned aerial vehicle is DU；
When a truck with the number w travels from node i to node j during the design of a delivery plan, xijwWhen the unmanned plane with the number u travels from the node i to the node j as 1, yijku1 is ═ 1; variable miThe order in which the ith client node was visited, zw、zuRespectively recording the use conditions of the w truck and the u unmanned aerial vehicle in the distribution scheme;
step 1.4 model construction:
the objective function of the model is to minimize acquisition and transportation costs required for delivery of trucks and drones; wherein the purchase cost of the truck may be multiplied by the unit price of the truck by the number of trucks used in the delivery; the transportation cost of the truck is obtained by multiplying the total sum of paths traveled by all trucks in the distribution process by the transportation cost of the truck in unit distance and then by the number of times of distribution before complete aging, and further establishing an objective function;
in the whole distribution process, each truck needs to start from the warehouse, finally completes the distribution task and returns to the warehouse, and only temporarily stops at the customer demand point, so that the flow balance constraint shown in the formula (2) is met:
the same unmanned aerial vehicle is limited to take off or land only once at each take-off and landing point, namely:
in the actual distribution process, a customer point is often only distributed by a truck or a drone, and the cargo is not required to be distributed separately to the truck and the drone, so that each demand point is only visited by the truck or the drone once, and the following constraints are generated:
according to the contents of the model assumption part, the taking-off and landing of the unmanned aerial vehicle can only be completed on a truck, so if the unmanned aerial vehicle takes off at customer i, serves customer j, and lands at point k, the truck must pass through i and k to join with the unmanned aerial vehicle:
since the number of trucks and drones dispatched need to be used in calculating the total cost of dispatching trucks and drones in the path plan, for zwAnd zuTwo variables are constrained, where z iswThe constraints of (2) are as follows:
constraints (7) - (8) determine the dispatch status of each truck, sigma if the w-th truck is not servicing any customers during the dispatch(i，j)∈Axijw-1-0, constraint (7) such that z isw0; if the customer is serviced, Σ(i，j)∈Axijw-1 ≧ 1, constraint (8) such that zw1 is ═ 1; to zuTwo constraints are also established in the same way:
path planning based on the current model may create situations where the truck loops between customer points, and therefore constraints need to be added to avoid this, as follows:
for constraint (11), if the drone takes off at customer i, serves customer j, and lands at customer k, then
The truck visits the i customer and then visits the k customer; if the unmanned aerial vehicle has no take-off and landing process at the i customer and the k customer, mk-mi1- (n +2) ═ n-1, n is the total number of customer points, i.e. the access order of customer i and customer k is not specially limited;
constraints (12) limit the truck from traveling in a loop between customer points;if the path from i to j exists, the right side value of the inequality is 0, mi-mj+1 ≦ 0, the visit order for customer f must precede customer j to avoid the truck from traveling in a loop between customer sites;
the navigation of unmanned aerial vehicle is supplied with power by the battery, has the restriction of electric quantity, consequently all has the upper limit of its single flight distance to every unmanned aerial vehicle, takes off from unmanned aerial vehicle on the truck to the in-process of delivering and returning to the truck, and the mileage that unmanned aerial vehicle traveles can not exceed this upper limit, promptly:
for integer variable miIt represents the order in which the ith node is visited by the truck, i.e.:
in addition, the 0-1 variable constraints in the model are as follows:
3. the multi-drone-multi-truck collaborative logistics distribution path planning method of claim 1, characterized in that: the second step is realized as follows:
step 2.1, the K-Means algorithm realizes the clustering of the demand points of the customers according to the spatial distribution:
clustering the customer points according to the spatial position distribution of the customer demand points by a K-Means algorithm;
step 2.2 generating a single delivery path of the truck based on a genetic algorithm:
based on the clustering labels given to each customer node in step 2.1, customers with the same label are delivered by the same truck; the delivery route is planned for each truck using a genetic algorithm to minimize the delivery route for the truck and also to minimize the transportation cost of the truck during delivery.
4. The multi-drone-multi-truck collaborative logistics distribution path planning method of claim 1, characterized in that: the third step is realized as follows:
step 3.1 unmanned aerial vehicle service customer point selection operator:
the objective of executing the operator is to convert customers originally delivered by trucks to be delivered by unmanned planes on the premise of reducing the total cost; when an operator is executed, customer demand points served by each truck are sequentially detected, whether the customer demand points can be served by the unmanned aerial vehicle is judged firstly, namely whether the customer points are within the range of the driving mileage of the unmanned aerial vehicle, whether the weight of the required goods is lower than the upper limit of the load of the unmanned aerial vehicle, if the customer is judged to meet the requirement, feasible take-off and landing points are appointed for the unmanned aerial vehicle serving the customer points, whether the customer points are better than the original solution after the customer points use the unmanned aerial vehicle for distribution is calculated, if new optimal solutions are obtained, the customer points are determined as the customer points served by the unmanned aerial vehicle, and the take-off and landing points are set in the front; (ii) a
Step 3.2, selecting an operator for the unmanned aerial vehicle take-off and landing point:
the unmanned aerial vehicle take-off and landing point selection operator searches the unmanned aerial vehicle take-off and landing points for the unmanned aerial vehicle service customer points again on the basis of the current truck delivery path, if the total delivery cost is reduced again under the condition that the route of the truck is not changed, the first operator is returned to be used again to optimize the current solution, finally the local optimal solution which is also reached in the second neighborhood is obtained, and then the unmanned aerial vehicle customer point release operator is executed;
step 3.3, the unmanned aerial vehicle client point puts back operators:
resetting each customer point distributed by the unmanned aerial vehicle as the customer point distributed by the truck, evaluating whether the optimal solution is updated at the moment, if a better result is obtained, converting the optimal solution into a node distributed by the truck, returning to the unmanned aerial vehicle service customer point selection operator, and restarting neighborhood search;
step 3.4 truck visit order exchange operator:
in the truck access sequence exchange operator, randomly exchanging the access sequences of any two customers served by the truck in the current truck delivery path, comparing the total cost before and after the exchange, and searching whether a new optimal solution can be found or not so as to approach the current local optimal solution;
step 3.5 perturbation function operator:
obtaining a current local optimal solution for planning the unmanned aerial vehicle-truck combined delivery path by the four neighborhood search operators, wherein a Shake function is needed to jump out the local optimal solution; the specific operation mode is that the visited sequence of all customers is randomly disturbed under the condition that the number of the customers served by the trucks and the unmanned planes is kept unchanged; then, re-planning the delivery routes of the trucks and the unmanned aerial vehicles among all the clients; and obtaining a new local optimal solution by applying the four operators after obtaining the new solution.
5. The multi-drone-multi-truck collaborative logistics distribution path planning method of claim 1, characterized in that: when the distribution scheme is designed, if the truck with the number w runs from the node i to the nodePoint j, then xijwWhen the unmanned plane with the number u travels from the node i to the node j as 1, yijku1 is ═ 1; variable miThe order in which the ith client node was visited, zw、zuRespectively recording the use conditions of the w truck and the u unmanned aerial vehicle in the distribution scheme;
clustering the customer points according to the spatial position distribution of the customer demand points by a K-Means algorithm; the preprocessing is simultaneously beneficial to reducing the time complexity of subsequent calculation, and assuming that the number of dispatched vehicles is w, the algorithm flow for clustering the customer demand points is as follows:
step 1 randomly appointing w points as the center of the cluster;
step 2, allocating the customer demand point to the nearest center;
step 3, calculating the average positions of the customer demand points of w clusters as new cluster center points;
and Step 4, judging whether the termination condition is reached, if so, returning to Step 2, and otherwise, ending the algorithm.
6. The multi-UAV-multi-truck collaborative logistics distribution path planning method of claim 3, wherein:
step 2.2 generating a single delivery path of the truck based on a genetic algorithm:
based on the clustering labels given to each customer node in step 2.1, customers with the same label are delivered by the same truck; planning a delivery route for each truck by using a genetic algorithm, so that the delivery route of the truck is shortest, and the transportation cost of the truck in the delivery process is lowest; the genetic algorithm flow is as follows:
step 1 randomly generating a scheme of q path plans as an initial solution set p*Namely an initial population of the genetic algorithm, and setting a genetic algebra a, a cross probability b and a variation probability c in the algorithm;
step 2, calculating the truck distribution cost of all solutions in the current solution set, wherein the lower the cost is, the higher the fitness is, and finding out the optimal solution s in the solution set*At a cost of f*Keep it to the next generation population；
Step 3, determining q individuals in a new population p by using a roulette method;
step 4, determining whether each individual in the new population is crossed or not according to the crossing probability b, if so, randomly generating a crossing point, and exchanging a route behind the crossing point to generate a new population;
step 5, determining whether each individual in the new population is mutated or not according to the mutation probability c, if so, randomly selecting two customer demand points, and exchanging the accessed sequence to generate a new population p;
step 6, calculating the truck distribution cost of all solutions for the new population p, finding the optimal solution s in the solution set, wherein the cost is f, and if f is less than f*Then the optimal solution s is retained to the next generation population and let s*＝s，f*F, otherwise, s*And f*The change is not changed;
step 7, judging whether the genetic algebra reaches a, if not, returning to Step 3; if so, ending the algorithm;
the final obtained single delivery path scheme of the truck at Step 8 is s*；
To this end, the required truck only delivery path planning scheme is established.
7. The multi-UAV-multi-truck collaborative logistics distribution path planning method of claim 4, wherein:
after the operation of each operator is determined, the corresponding algorithm steps are explained as follows:
step 1 sets the maximum neighborhood number N in the algorithm to be 4 and the maximum iteration number K, and records the current optimal solution s*The cost value is f*；
Step 2, obtaining a current local optimal solution s and the cost f of the optimal solution by using a variable neighborhood descent search algorithm and four neighborhood search operators;
step 3 comparison f*And f, if f < f*Then let s*＝s，f*＝f；
Step 4, judging whether the iteration frequency reaches K or not, if so, terminating the algorithm to obtain the optimal solution s*The lowest cost is f*Otherwise, continuing Step 5;
step 5 obtains a new solution through a Shake function and returns to Step 2;
therefore, the needed planning scheme of the multi-unmanned aerial vehicle-multi-truck cooperative logistics distribution path is obtained, and the conditions are met.
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