CN112733272A - Method for solving vehicle path problem with soft time window - Google Patents

Method for solving vehicle path problem with soft time window Download PDF

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CN112733272A
CN112733272A CN202110041529.8A CN202110041529A CN112733272A CN 112733272 A CN112733272 A CN 112733272A CN 202110041529 A CN202110041529 A CN 202110041529A CN 112733272 A CN112733272 A CN 112733272A
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李军华
李国明
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Abstract

The invention discloses a method for solving the problem of vehicle paths with soft time windows, which aims at minimizing distribution cost and violating time window constraint penalty cost and establishes a random planning model with correction; and a new tabu search algorithm is proposed. According to the characteristics of the problems, an initial solution generation mode and an initial taboo length are determined; three special neighborhood optimization operators are designed; and a new evaluation function is introduced, so that the algorithm is prevented from falling into local optimization. The method can effectively solve the VRPSTW problem, and meanwhile, the method has strong optimizing capacity and high robustness.

Description

Method for solving vehicle path problem with soft time window
Technical Field
The invention belongs to the field of logistics system planning and design, and particularly relates to a method for solving a vehicle path problem with a soft time window based on a tabu search algorithm.
Background
After the 21 st century, with the rapid development of the economy of China, the logistics distribution industry of China is also rapidly developed. Meanwhile, transportation enterprises face difficulties such as too high logistics distribution cost. Vehicle Routing Problem (VRP) the distribution center plans the optimal path according to the distribution and demand of the customers. The VRP can effectively solve the problems of unreasonable route planning, high transportation delay rate and the like in the transportation process, and can greatly reduce the distribution cost. Therefore, VRP has attracted a great deal of attention from many scholars at home and abroad. With the deep research on the VRP, researchers have proposed a Vehicle Routing Problem with a Time window (VRPTW) in consideration of the fact that clients will make demands on the delivery Time of goods, and have proposed a corresponding precise algorithm and a heuristic algorithm for the VRPTW. The problem mainly falls into two different research angles:
(1) vehicle routing problem with hard time windows
During the actual distribution process, the customer may impose a hard requirement on the delivery time interval of the goods, i.e. the vehicle must arrive within the time specified by the customer, otherwise the customer rejects the goods. This type of problem is known as a vehicle path problem with hard time windows. In order to solve the problems, chiffon et al propose a discrete bat algorithm and introduce various search strategies to accelerate the convergence speed of the algorithm. The algorithm has stronger optimizing capability and higher robustness. Perez et al propose a mixed distribution estimation algorithm for the higher complexity of the problem, and use generalized Malllows distribution as a probability model to describe solution spatial distribution. The algorithm has strong optimizing capability but low calculation efficiency. Hamza et al artificially improve the quality of the solution and construct a multiple graph network model; and provides a self-adaptive large neighborhood search heuristic algorithm. The Yassen et al provides a self-adaptive harmony search algorithm by combining five local search algorithms such as a harmony search algorithm and a simulated annealing algorithm aiming at the defect that the convergence speed of solving the problems by the harmony search algorithm is low. The experimental result shows that the algorithm has certain superiority. Nazif et al propose an optimized crossover genetic algorithm by using the advantage of high convergence speed of the genetic algorithm, and add an optimized crossover operator to the algorithm, aiming at the problem of high complexity. The algorithm has certain competitiveness compared with other heuristic algorithms. Aggarwal et al, which addresses this problem with a high complexity, have established a new mathematical model for mixed integer programming and designed a constraint to optimize the number of vehicles delivered. The algorithm can search a better solution in a reasonable time, but is only suitable for the problem of a smaller-scale vehicle path.
(2) Vehicle routing problem with soft time windows
In the actual distribution process, the customer can put forward a soft requirement on the delivery time of the goods, namely, the vehicle can arrive outside the time specified by the customer, but the goods need to be punished correspondingly before being distributed to the customer. This type of Problem is known as the Vehicle Routing Problem with Soft Time Windows (VRPSTW). In order to solve such problems, Gong et al propose a set-based particle swarm algorithm, which utilizes a particle swarm algorithm framework to select an optimal subset from a general set. Zhang et al combines a multi-directional local search strategy and a local search chain reinforcement technology, and provides a multi-target cultural genetic algorithm based on a self-adaptive local search chain. Kourank et al effectively combines a column generation algorithm with a meta-heuristic algorithm and proposes a mixed meta-heuristic algorithm based on the column generation algorithm. The Yiyunfei et al provide an improved itai algorithm aiming at the problem of higher complexity, and determine the fluctuation coefficient by adopting a hill-climbing algorithm. Korean Yajuan et al propose a polygonal soft time window for the disadvantage of too linear penalty function of soft time window in the problem; and a heuristic algorithm such as a genetic algorithm, a CW (continuous wave) conservation method and the like is effectively combined, and a hyper-heuristic genetic algorithm is provided. The experimental result shows that the algorithm has certain feasibility and effectiveness. Zhang et al defines a new ant colony algorithm transition probability aiming at the disadvantage that the ant colony algorithm solving the problem is easy to fall into local optimum, introduces a Pareto optimal solution set to guide a global pheromone updating rule, and provides an improved Pareto ant colony algorithm. The algorithm has strong global search capability.
In recent years, with the progress of research on VRPTW, researchers have found that adding hard time window constraints to vehicle routing problems leads to problems such as an increase in the number of delivery vehicles, a low delivery vehicle loading rate, and an excessively long delivery vehicle travel distance. Based on the above analysis, the present invention primarily addresses the vehicle path problem with soft time windows. Aiming at the problems of high complexity and long solving time, a new tabu search algorithm is provided, and the neighborhood operators, evaluation functions and other constituent elements in the tabu search algorithm are improved.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention discloses a method for solving the problem of vehicle paths with soft time windows, which is an effective improvement on a tabu search algorithm. The method can quickly and effectively solve the VRPSTW problem, and meanwhile, the method has strong optimizing capacity and high robustness.
In order to realize the problems, the invention is realized by the following technical scheme:
a method for solving the problem of vehicle routing with soft time windows, comprising the steps of: 1) establishing a random planning model with correction aiming at the minimum distribution cost and the minimum penalty cost violating the time window constraint; 2) and solving the problem by adopting an improved tabu search algorithm so as to solve the problem of the vehicle path with a soft time window.
The step 1) is specifically as follows:
1.1 the vehicle path problem with soft time windows can be described as follows: a logistics transportation enterprise has a logistics distribution center and m vehicles with the load of Q, and n customers distributed at different positions are served. q. q.siRepresenting the demand of customer i; deltaiRepresenting the time required for the vehicle to service customer i; [ e ] ai,li]Indicating the time of arrival of the specified goods by client i, wherein eiIndicating the earliest delivery time of the specified goods, i, of client iiIndicating that the client i specifies the latest delivery time of the goods; dijRepresents the distance between customer i and customer j; t is tijIndicating delivery of vehicle slavesThe time required for the user i to travel to the client j; c. CijRepresenting the cost of the delivery between customer i and customer j.
1.2 establishing an objective function:
Figure BDA0002896059350000041
the objective function (1) requires the minimum delivery cost and the minimum penalty cost against the time window constraint. Wherein, cijRepresents the distance between customer i and customer j; x is the number ofijkIs a decision variable, when the vehicle k serves the customer i, it is driven to the customer j to serve it, and its value is 1; otherwise it is 0. Lambda [ alpha ]djA penalty factor representing a delayed arrival of the vehicle at customer j; e (D)jk) Indicating the expected value of the time that the vehicle k delays to reach customer j. x is the number ofijkThe expression is as follows:
Figure BDA0002896059350000042
in the formula (2), ki→kjIndicating that vehicle k continues to serve customer j after serving customer i.
1.3 build constraint function:
(1) vehicle travel path constraint:
Figure BDA0002896059350000043
Figure BDA0002896059350000044
Figure BDA0002896059350000045
Figure BDA0002896059350000046
equation (3) indicates that the delivery vehicle must depart from the delivery center to perform the cargo task. Equation (4) indicates that the delivery vehicle must return to the delivery center after completing the cargo distribution task. Equation (5) indicates that the delivery vehicle must travel away from the customer site after the delivery of the goods to the customer. In formulae (3) to (5), xijkIs a decision variable. When a vehicle k starts from a client i, the vehicle k runs to a client j and serves the client j, and the value of the vehicle k is 1; otherwise it is 0. Equation (6) indicates that each customer can be serviced by at most one vehicle. y iskiIs a decision variable, whose value is 1 when the vehicle k passes and serves the customer i; otherwise it is 0. y iskiThe expression is as follows:
Figure BDA0002896059350000051
in equation (7), k → i indicates that the vehicle k arrives at and serves the customer i.
(2) Capacity constraint:
Figure BDA0002896059350000052
equation (8) shows that when the distribution center plans the vehicle driving path, the total demand of the customers on the path cannot exceed the maximum capacity of the vehicle. When the total demand of the customer reaches the maximum capacity of the vehicle, the path planning is completed. Wherein q isiRepresenting customer i needs; q represents the maximum vehicle load.
(3) Soft time window constraint:
the constraint indicates that the customer will make soft demands on the delivery time of the goods. Vehicles arrive before the customer-specified time, having to wait at the mission point; the vehicle arrives after the customer specified time, and the vehicle can directly serve the customer, but a certain penalty is given.
Aik+wik+δik+tij＝Ajk (9)
wik＝max{ei-Aik,0} (10)
A in formula (9)ikRepresents the arrival time of vehicle k at customer i; w is aikRepresents the waiting time of the vehicle k at the customer i; deltaikRepresenting the service time of the vehicle k to the customer i; t is tijRepresents the time required for the vehicle k to travel from customer i to customer j; a. thejkIndicating the time at which vehicle k arrived at customer j. In the formula (10) eiIndicating that client i specifies the left boundary of the delivery time interval for the good.
(4) Sub-loop cancellation constraint:
the constraint may eliminate sub-loops that do not satisfy the condition that are present in the vehicle travel path.
Figure BDA0002896059350000061
In formula (11) | SkAnd | represents the total number of customers (including the distribution center) on the traveling path of the vehicle k.
The step 2) specifically comprises the following steps:
2.1: initializing a taboo table and determining the length of the taboo;
2.2: randomly generating an initial solution and calculating a target function value of the initial solution;
2.3: generating a candidate solution through a neighborhood optimization operator;
2.4: selecting an optimal candidate solution according to an evaluation function;
2.5: judging whether the optimal solution is superior to the current optimal solution, if so, turning to step 2.6, and if not, selecting the optimal solution which is not taboo in the candidate solutions;
2.6: selecting an optimal candidate solution;
2.7: updating the current solution and updating a tabu table;
2.8: and judging whether the termination condition of the algorithm is met, if so, ending the algorithm and outputting the optimal solution, and if not, turning to the step 2.3 to continue iteration.
Further, the length of the taboo in step 2.1 is determined by experimental comparison. The method comprises the following specific steps: and randomly selecting the algorithms provided by a plurality of arithmetic examples to test, and selecting the taboo length with the smallest total cost as the initial taboo length.
The results of the experiment are shown in FIG. 2. As can be seen from fig. 2, when the tabu length is set to 40, the total cost is the smallest under different examples, i.e. the algorithm performance is optimal. Therefore, the length of the taboo in the modified taboo search algorithm proposed in the present invention is set to 40.
Further, the specific steps of step 2.3 are as follows: the neighborhood optimization operators are three in number, specifically as follows:
(1) randomly selecting a certain client i on the path l, removing the client i from the path l and inserting the client i into the path k. This operation needs to ensure that the total customer demand on path k does not exceed the maximum vehicle capacity and that customer i meets its own time window constraints.
(2) And randomly selecting the clients i, j on the path l, and turning the path in the middle.
(3) And randomly selecting a client i on the path l and a client j on the path k, and interchanging the path behind the client i and the path behind the client j. This operation is required to ensure that path i and path k both satisfy the capacity constraint after the swap.
The method comprises the steps that a neighborhood optimization operator (1) is preferentially selected to be searched in the searching process, if an optimal solution is not searched in the algorithm after a certain number of iterations, neighborhood optimization operators (2) and (3) are selected to continue searching, and the algorithm is prevented from falling into local optimization.
Further, the evaluation function formula in step 2.4 is as follows:
f(s)＝c(s)+αt(s) (12)
in the formula: c(s) represents vehicle delivery costs; alpha represents a penalty coefficient of the vehicle driving path violating the time window constraint; t(s) represents the total amount of time the vehicle travel path violates the time window constraint.
The invention has the beneficial effects that: establishing a random planning model with correction aiming at the minimum distribution cost and the minimum penalty cost violating the time window constraint; and a new tabu search algorithm is proposed. The method can effectively solve the VRPSTW problem, and has strong optimizing capability and high robustness.
Drawings
FIG. 1 is a flow chart of an improved tabu search algorithm of the present invention;
FIG. 2 is a graph of the comparison results of the improved tabu search algorithm of the present invention at different tabu lengths.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
as shown in fig. 1 and 2, an improved tabu search algorithm for solving a vehicle path problem with a soft time window comprises the following steps:
1) establishing a mathematical model of a vehicle path problem with a soft time window;
the step 1) specifically comprises the following steps:
step 1.1: the vehicle path problem with soft time windows can be described as follows: a logistics transportation enterprise has a logistics distribution center and m vehicles with the load of Q, and n customers distributed at different positions are served. q. q.siRepresenting the demand of customer i; deltaiRepresenting the time required for the vehicle to service customer i; [ e ] ai,li]Indicating the time of arrival of the specified goods by client i, wherein eiIndicating the earliest delivery time of the specified goods, i, of client iiIndicating that the client i specifies the latest delivery time of the goods; dijRepresents the distance between customer i and customer j; t is tijIndicating the time required for the delivery vehicle to travel from customer i to customer j; c. CijRepresenting the cost of the delivery between customer i and customer j.
Step 1.2: establishing an objective function
Figure BDA0002896059350000081
The objective function (1) requires the minimum delivery cost and the minimum penalty cost against the time window constraint. Wherein, cijRepresents the distance between customer i and customer j; x is the number ofijkIs a decision variable, when the vehicle k serves the customer i, it is driven to the customer j to serve it, and its value is 1; otherwise it is 0. Lambda [ alpha ]djA penalty factor representing a delayed arrival of the vehicle at customer j; e (D)jk) Indicating when vehicle k has delayed arrival at customer jThe expected value. x is the number ofijkThe expression is as follows:
Figure BDA0002896059350000082
in the formula (2), ki→kjIndicating that vehicle k continues to serve customer j after serving customer i.
Step 1.3: establishing a constraint function
(1) Vehicle travel path constraint:
Figure BDA0002896059350000083
Figure BDA0002896059350000091
Figure BDA0002896059350000092
Figure BDA0002896059350000093
equation (3) indicates that the delivery vehicle must depart from the delivery center to perform the cargo task. Equation (4) indicates that the delivery vehicle must return to the delivery center after completing the cargo distribution task. Equation (5) indicates that the delivery vehicle must travel away from the customer site after the delivery of the goods to the customer. In formulae (3) to (5), xijkIs a decision variable. When a vehicle k starts from a client i, the vehicle k runs to a client j and serves the client j, and the value of the vehicle k is 1; otherwise it is 0. Equation (6) indicates that each customer can be serviced by at most one vehicle. y iskiIs a decision variable, whose value is 1 when the vehicle k passes and serves the customer i; otherwise it is 0. y iskiThe expression is as follows:
Figure BDA0002896059350000094
in equation (7), k → i indicates that the vehicle k arrives at and serves the customer i.
(2) Capacity constraint:
Figure BDA0002896059350000095
equation (8) shows that when the distribution center plans the vehicle driving path, the total demand of the customers on the path cannot exceed the maximum capacity of the vehicle. When the total demand of the customer reaches the maximum capacity of the vehicle, the path planning is completed. Wherein q isiRepresenting customer i needs; q represents the maximum vehicle load.
(3) Soft time window constraint:
the constraint indicates that the customer will make soft demands on the delivery time of the goods. Vehicles arrive before the customer-specified time, having to wait at the mission point; the vehicle arrives after the customer specified time, and the vehicle can directly serve the customer, but a certain penalty is given.
Aik+wik+δik+tij＝Ajk (9)
wik＝max{ei-Aik,0} (10)
A in formula (9)ikRepresents the arrival time of vehicle k at customer i; w is aikRepresents the waiting time of the vehicle k at the customer i; deltaikRepresenting the service time of the vehicle k to the customer i; t is tijRepresents the time required for the vehicle k to travel from customer i to customer j; a. thejkIndicating the time at which vehicle k arrived at customer j. In the formula (10) eiIndicating that client i specifies the left boundary of the delivery time interval for the good.
(4) Sub-loop cancellation constraint:
the constraint may eliminate sub-loops that do not satisfy the condition that are present in the vehicle travel path.
Figure BDA0002896059350000101
In formula (11) | SkAnd | represents the total number of customers (including the distribution center) on the traveling path of the vehicle k.
Step 2) an improved tabu search algorithm is designed to solve the problem, and the method specifically comprises the following steps:
step 2.1: initializing a taboo table and determining the length of the taboo;
step 2.2: randomly generating an initial solution and calculating a target function value of the initial solution;
step 2.3: generating a candidate solution through a neighborhood optimization operator;
step 2.4: selecting an optimal candidate solution according to an evaluation function;
step 2.5: judging whether the optimal solution is superior to the current optimal solution, if so, turning to step 2.6, and if not, selecting the optimal solution which is not taboo in the candidate solutions;
step 2.6: selecting an optimal candidate solution;
step 2.7: updating the current solution and updating a tabu table;
step 2.8: and judging whether the termination condition of the algorithm is met, if so, ending the algorithm and outputting the optimal solution, and if not, turning to the step 2.3 to continue iteration.
The effects of the present invention can be further illustrated by the following simulations:
1 simulation Condition
(1) Simulation data:
the test examples are all from 6 types of VRPTW examples of Solomon (56 examples are total of C1 type, C2 type, R1 type, R2 type, RC1 type and RC2 type), wherein in the VRPTW examples of C1 type, R1 type and RC1 type, the vehicle load is small, and the time window is narrow; in the VRPTW calculation examples of the C2 type, the R2 type and the RC2 type, the vehicle load is heavy, and the time window is loose.
(2) Simulation parameters:
the related experiments in this chapter are all performed in the same experimental environment, wherein the CPU host frequency is 2.80GHz, the memory is 8GB, the operating system is 64-bit Windows10, and the programming language is C + +. The maximum iteration times of the improved tabu search algorithm is 2000 times, and the initial tabu length is 40.
2 simulation content
(1) Experiment 1:
based on 6 types of VRPTW examples of Solomon, selecting the first 50 customers to construct a new algorithm for example test; then, the provided algorithm is compared with an ant colony algorithm, a self-adaptive large neighborhood search algorithm and a simulated annealing algorithm, and the experimental results are shown in table 1. In table 1, OS is the optimal solution obtained after the algorithm has run independently 10 times; AS is the average solution obtained after the algorithm runs independently for 10 times; bold numbers indicate that the improved tabu search algorithm of the present invention solves better than the other three algorithms.
Table 1 experiment 1 comparative results
Figure BDA0002896059350000121
(2) Experiment 2:
the algorithm is tested by adopting 6 types of VRPTW (variable weighted round robin) examples of Solomon, and then the comparison experiment is carried out on the algorithm, the ant colony algorithm, the self-adaptive large neighborhood search algorithm and the simulated annealing algorithm, and the experiment result is shown in Table 2. In table 2, OS is the optimal solution obtained after the algorithm has run independently 10 times; AS is the average solution obtained after the algorithm runs independently for 10 times; bold numbers indicate that the improved tabu search algorithm of the present invention solves better than the other three algorithms.
Table 2 experiment 2 comparative results
Figure BDA0002896059350000131
3 simulation analysis
The experimental results show that: the improved tabu search algorithm can effectively solve the VRPSTW problem, and meanwhile, the algorithm has strong optimizing capability and high robustness.

Claims (4)

1. A method for solving the problem of vehicle routing with soft time windows, comprising the steps of: 1) establishing a random planning model with correction aiming at the minimum distribution cost and the minimum penalty cost violating the time window constraint; 2) solving the problem by adopting an improved tabu search algorithm to solve the problem of the vehicle path with a soft time window;
the step 1) is specifically as follows: 1.1 describes the vehicle path problem with the soft time window: a logistics transportation enterprise is provided with a logistics distribution center and m vehicles with the load of Q, and is used for serving n customers distributed at different positions; q. q.siRepresenting the demand of customer i; deltaiRepresenting the time required for the vehicle to service customer i; [ e ] ai,li]Indicating the time of arrival of the specified goods by client i, wherein eiIndicating the earliest delivery time of the specified goods, i, of client iiIndicating that the client i specifies the latest delivery time of the goods; dijRepresents the distance between customer i and customer j; t is tijIndicating the time required for the delivery vehicle to travel from customer i to customer j; c. CijRepresents the delivery cost between customer i and customer j;
1.2 establishing an objective function:
Figure FDA0002896059340000011
the objective function formula (1) requires the minimum distribution cost and the minimum penalty cost violating the time window constraint; wherein, cijRepresents the distance between customer i and customer j; x is the number ofijkIs a decision variable, when the vehicle k serves the customer i, it is driven to the customer j to serve it, and its value is 1; otherwise, the value is 0; lambda [ alpha ]djA penalty factor representing a delayed arrival of the vehicle at customer j; e (D)jk) A desired value representing the time at which vehicle k is delayed to reach customer j; x is the number ofijkThe expression is as follows:
Figure FDA0002896059340000012
in the formula (2), ki→kjIndicating that the vehicle k continues to serve the customer j after serving the customer i;
1.3 build constraint function:
(1) vehicle travel path constraint:
Figure FDA0002896059340000013
Figure FDA0002896059340000021
Figure FDA0002896059340000022
Figure FDA0002896059340000023
equation (3) indicates that the delivery vehicle must depart from the delivery center to perform the cargo task; the formula (4) indicates that the delivery vehicle must return to the delivery center after completing the cargo distribution task; equation (5) represents that the delivery vehicle must travel away from the customer site after the delivery vehicle has delivered the goods to the customer; in formulae (3) to (5), xijkIs a decision variable; when a vehicle k starts from a client i, the vehicle k runs to a client j and serves the client j, and the value of the vehicle k is 1; otherwise, the value is 0; equation (6) indicates that each customer can be serviced by at most one vehicle; y iskiIs a decision variable, whose value is 1 when the vehicle k passes and serves the customer i; otherwise, the value is 0; y iskiThe expression is as follows:
Figure FDA0002896059340000024
in the formula (7), k → i indicates that the vehicle k arrives at and serves the customer i;
(2) capacity constraint:
Figure FDA0002896059340000025
the formula (8) shows that when the distribution center plans the vehicle driving path, the total demand of the customers on the path can not exceed the maximum capacity of the vehicle; when the total demand of the customer reaches the maximum capacity of the vehicle, the path planning is finished; wherein q isiRepresenting customer i needs; q represents the maximum vehicle load;
(3) soft time window constraint:
the constraint indicates that the customer will make a soft request for the delivery time of the goods; vehicles arrive before the customer-specified time, having to wait at the mission point; the vehicle arrives after the time specified by the customer, and the vehicle can directly serve the customer, but certain punishment needs to be given;
Aik+wik+δik+tij＝Ajk (9)
wik＝max{ei-Aik,0} (10)
a in formula (9)ikRepresents the arrival time of vehicle k at customer i; w is aikRepresents the waiting time of the vehicle k at the customer i; deltaikRepresenting the service time of the vehicle k to the customer i; t is tijRepresents the time required for the vehicle k to travel from customer i to customer j; a. thejkRepresents the time at which vehicle k arrives at customer j; in the formula (10) eiA left boundary representing a time interval during which customer i designates delivery of goods;
(4) sub-loop cancellation constraint:
the constraint may eliminate sub-loops that do not satisfy the condition that are present in the vehicle travel path;
Figure FDA0002896059340000031
in formula (11) | SkL represents the total number of customers on the driving path of the vehicle k;
the step 2) specifically comprises the following steps:
2.1: initializing a taboo table and determining the length of the taboo;
2.2: randomly generating an initial solution and calculating a target function value of the initial solution;
2.3: generating a candidate solution through a neighborhood optimization operator;
2.4: selecting an optimal candidate solution according to an evaluation function;
2.5: judging whether the optimal solution is superior to the current optimal solution, if so, turning to step 2.6, and if not, selecting the optimal solution which is not taboo in the candidate solutions;
2.6: selecting an optimal candidate solution;
2.7: updating the current solution and updating a tabu table;
2.8: and judging whether the termination condition of the algorithm is met, if so, ending the algorithm and outputting the optimal solution, and if not, turning to the step 2.3 to continue iteration.
2. A method for solving the problem of vehicle path with soft time window according to claim 1, wherein the tabu length in step 2.1 is determined by experimental comparison; and selecting the taboo length with the smallest total cost as the initial taboo length by randomly selecting a plurality of arithmetic examples to test the algorithm.
3. A method for solving the problem of vehicle path with soft time windows according to claim 1, characterized in that the specific steps of step 2.3 are as follows: the neighborhood optimization operators are three in number, specifically as follows:
(1) randomly selecting a certain client i on the path l, removing the certain client i from the path l and inserting the certain client i into the path k, wherein the operation needs to ensure that the total demand of the client on the path k does not exceed the maximum capacity of the vehicle, and the client i meets the time window constraint of the client i;
(2) randomly selecting a client i, j on the path l, and turning the path in the middle;
(3) randomly selecting a client i on a path l and a client j on a path k, and interchanging the path behind the client i and the path behind the client j, wherein the operation needs to ensure that the path l and the path k both meet the capacity constraint after the interchange;
the method comprises the steps that a neighborhood optimization operator (1) is preferentially selected to be searched in the searching process, if an optimal solution is not searched in the algorithm after a certain number of iterations, neighborhood optimization operators (2) and (3) are selected to continue searching, and the algorithm is prevented from falling into local optimization.
4. A method for solving the problem of vehicle path with soft time window according to claim 1, wherein the evaluation function formula in step 2.4 is:
f(s)＝c(s)+αt(s) (12)
in the formula: c(s) represents vehicle delivery costs; alpha represents a penalty coefficient of the vehicle driving path violating the time window constraint; t(s) represents the total amount of time the vehicle travel path violates the time window constraint.
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