CN111784072B - Vehicle path problem optimization method and device - Google Patents
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Abstract
The invention belongs to the technical field of vehicle path problems, and particularly relates to a vehicle path problem optimization method and device. The invention combines the genetic algorithm and the differential evolution idea to solve the problem of vehicle paths, and not directly combines the genetic algorithm and the differential evolution idea, but adjusts the use time of introducing the evolution operation based on the differential evolution idea, namely, when the ratio of the number of evolution iterations to the number of termination of the evolution iterations is larger than a set ratio in the whole calculation process, the first temporary population P' t+1 Performing an evolutionary operation of adjusting individuals in the population based on the inter-individual differences in the population to obtain a new initialized population P t+1 And update the new elite population a t+1 . The invention combines the advantages of genetic algorithm and differential evolution idea, and properly uses local search strategy to further improve the search capability of the whole algorithm, and effectively shortens the increase of solving time caused by complex operation, so that the finally obtained vehicle distribution path is better.
Description
Technical Field
The invention belongs to the technical field of vehicle path problems, and particularly relates to a vehicle path problem optimization method and device.
Background
The vehicle path problem (Vehicle Routing Problem, VRP) was first addressed by Dantzig and Ramser in 1959, one of the most important and widely studied combinatorial optimization problems, related to transportation logistics (e.g., postal, parcel, and distribution services), with the goal of obtaining the lowest cost route set to accomplish providing services to customers. The VRP model adopted by current research mainly for the vehicle path problem is very different from the original model because many factors are not negligible when the VRP is used in combination with real life, such as the number of vehicles, lead time, parking costs, production cycle and workload balance, etc. In view of these real-world factors, VRPs produce several common variations that involve different constraints, such as vehicle travel speed versus already running time, customer setup with a time window, allowing customers to provide received goods while picking up, customer information that can be updated in real-time, etc.
Where the time windowed vehicle path planning problem (Vehicle Routing Problem with Time Windows, VRPTW) is particularly relevant for practical applications, VRPTW is a common variant of VRP problem with limited delivery vehicle capacity, each customer has a specific delivery time window definition, fleet transportation requires customer service to arrive at the customer's location within the customer's time window, otherwise it is subject to a certain penalty. With the rapid development of the internet and e-commerce industries, people's lives are becoming more informatized, and customers of vehicle path problems have fallen from past large supermarkets, production bases, etc. to small customers such as families and individuals. Small customer groups, unlike large production bases or supermarkets, typically only allow a few hours of service to be accepted within a day, so consideration of the time window appears to be necessary, which makes the VRPTW problem even more relevant in the present and future description of vehicle path problems.
Because the vehicle path problem forms a plurality of flexible variants under the development of the current network technology, the targeted clients are various, so that the distribution center responsible for vehicle dispatching also has strong flexibility, and the distribution needs to be carried out by adopting the vehicle types suitable for the different types of clients, thereby effectively reducing the transportation cost and improving the experience of distribution personnel and clients. The Multi-model windowed vehicle path problem (Multi-Type Vehicle Route Problem with Time Windows, MTVRPTW) is the one designed for this situation, MTVRPTW considers not only the customer's time window requirements, but also the requirements of distribution centers with multiple distribution vehicle types.
In recent years, various algorithms have been widely applied to solve MTVRPTW, such as simulated annealing (Simulated Annealing, SA), tabu Search (TS), ant colony optimization (Ant Colony Optimization, ACO), genetic algorithm (Genetic Algorithm, GA), particle swarm optimization (Particle Swarm Optimization, PSO), differential evolution (Differential Evolution, DE), and the like. But using a single algorithm does not work well. For example:
the genetic algorithm is an intelligent optimization algorithm proposed by professor j.hold, university of michigan, usa in 1975. The genetic algorithm is a self-adaptive random search method, is suitable for the combination optimization problem in a non-convex space, and can cope with the problem of complex vehicle paths with time windows. However, the genetic algorithm has slow convergence rate and weak local searching capability, so that the problems of low solution quality, long time consumption and the like frequently occur when the genetic algorithm faces complex problems.
Differential evolution is an evolutionary computing technique that has emerged in recent years. The differential evolution algorithm performs variation operation on individuals according to the differences among the individuals, thereby increasing the purposefulness and the guidance in the evolution process, being applicable to solving the optimization problem in the complex environment and also solving the problem of complex vehicle paths with time windows. However, as the dimensionality of the problem increases, differential evolution algorithms tend to cause the population to prematurely lose diversity and fall into the local optimum of the objective function.
Disclosure of Invention
The invention provides a method and a device for optimizing a vehicle path problem, which are used for solving the problems that the time consumption is long due to the use of a single algorithm or the calculated vehicle distribution path is not optimal due to the fact that the vehicle distribution path is in local optimization.
In order to solve the technical problems, the technical scheme of the invention comprises the following steps:
the invention provides a method for optimizing a vehicle path problem, which comprises the following steps:
1) Establishing a mathematical model of the vehicle path problem according to the vehicle path problem to be solved, wherein the mathematical model comprises a target, decision variables and constraint conditions; the decision variables comprise a client sequence variable and a vehicle type variable, and two variables are respectively encoded by adopting double chromosomes: the client sequence variable is encoded into a client chromosome by using a sequencing encoding mode, and the vehicle type variable is encoded into a vehicle type chromosome by using a real number encoding mode;
2) Randomly generating at least two vehicle delivery paths as an initialization population P t And generates elite population A t Elite population A t Initially empty;
3) According to the initialized population P t And elite population A t Obtaining a mixed population;
4) Carrying out evolutionary operation based on a genetic algorithm on the mixed population to obtain a offspring population OffSringset; obtaining a first temporary population P according to the offSringset of the offspring population t ′ +1 The method comprises the steps of carrying out a first treatment on the surface of the The evolution operation comprises a selection operation, a crossover operation and a mutation operation; the selecting operation adopts a binary tournament selecting mode as a selecting operator; a sequential crossover operator and a crossover mutation operator are adopted for the customer chromosome, and a single-point crossover operator and a single-point mutation operator are adopted for the vehicle type chromosome;
5) Judging whether the ratio of the current evolutionary iteration times to the evolutionary iteration ending times is larger than a set ratio, if so, performing the first temporary population P t ′ +1 Performing evolutionary operation for adjusting individuals in the population based on the differences among the individuals in the population to obtain a second temporary population RSD_LSP t ′ +1 Calculating a second temporary population RSD_LSP t ′ +1 And a first temporary population P t ′ +1 The fitness value of each individual in the population P is selected to be a new initialization population P t+1 ；
6) According to the new initialisation population P t+1 And elite population A t Obtaining a new elite population A t+1 ；
7) New initialization population P t+1 And a new elite population A t+1 And (3) carrying out evolutionary iteration according to the modes from the step (3) to the step (6) until the evolutionary iteration times reach the evolutionary iteration termination times, and selecting an optimal vehicle distribution path from the final generation population.
The beneficial effects of the technical scheme are as follows: the invention combines the genetic algorithm and the differential evolution idea to solve the problem of vehicle paths, and not directly combines the genetic algorithm and the differential evolution idea, but adjusts the use time of introducing the evolution operation based on the differential evolution idea, namely, when the ratio of the number of evolution iterations to the number of termination of the evolution iterations is larger than the set ratio in the whole calculation process, the first temporary population P is subjected to the first temporary population P t ′ +1 Performing an evolutionary operation of adjusting individuals in the population based on the inter-individual differences in the population to obtain a new initialized population P t+1 And update the new elite population a t+1 . The invention combines the advantages of genetic algorithm and differential evolution idea, and properly uses local search strategy to further improve the search capability of the whole algorithm, effectively shorten the increase of solving time caused by complex operation, improve the integration degree, and improve the knowing quality, so that the finally obtained vehicle distribution path is better.
Further, in step 5), if the ratio of the number of evolutionary iterations to the number of evolutionary iteration stops is less than or equal to the set ratio, the first temporary population P t ′ +1 As a new initialization population P t+1 。
Further, in order to obtain an individual located in the upper edge region of the Pareto front, when the targets are at least two targets, step 3) includes: selecting a plurality of sub-populations SP from an initialized population i The number of the sub-populations is consistent with the number of the targets, and one sub-population comprises the first X optimal individuals obtained by selecting one of the targets; combining multiple sub-populations SP i And elite populationA t Mixing to obtain the mixed population; wherein, X > 1, i=1, 2, …, m, m is the total number of sub-populations.
Further, in step 4), the method further includes a step of performing an insert search operation on the offspring population OffSringSet.
Further, to obtain a better elite population for storage, step 6) comprises: mixing a new initializing population P t+1 And elite population A t Obtaining an elite temporary population tempellieseolts; selecting a preferred individual from the elite temporary population tempelite population as the new elite population a t+1 。
Further, in order to quickly select the individual located in the central area on the Pareto front, in step 5) and step 6), the fitness value of the individual is:
where eval (k) is the second temporary population RSD_LSP t ′ +1 Or fitness value of individual k in elite temporary population temp t ′ +1 Or the size of the elite temporary population tempellieseoldivided set.
Further, in step 5), in order to further improve the quality of the individuals, the step of adjusting the evolution operation of the individuals in the population based on the differences between the individuals in the population is an rsd_ls operation, where the rsd_ls operation refers to: and selecting two individuals with different fitness values from the population, determining the difference between the two individuals, and evolving the worse individuals towards the better individuals according to the difference.
Further, in step 5), the set ratio is 50%.
The invention also provides a device for optimizing the vehicle path problem, which comprises a memory and a processor, wherein the processor is used for executing instructions stored in the memory to realize the method for optimizing the vehicle path problem and achieve the same effects as the method.
Drawings
FIG. 1 is a flow chart of a method of optimizing a vehicle path problem of the present invention;
FIG. 2 is a schematic representation of MS-HMOEA-GL double chromosome coding according to the present invention;
FIG. 3 is a schematic representation of MS-HMOEA-GL double chromosome decoding according to the present invention;
FIG. 4-1 is a schematic representation of crossover operations performed on a custom chromosome in MS-HMOEA-GL according to the present invention;
FIG. 4-2 is a schematic diagram of the crossover operation of the model chromosome in MS-HMOEA-GL of the present invention;
FIG. 5-1 is a schematic representation of the mutation of a custom chromosome in MS-HMOEA-GL according to the present invention;
FIG. 5-2 is a schematic diagram showing the mutation of the chromosome of the vehicle model in MS-HMOEA-GL according to the present invention;
FIG. 6 is a schematic diagram of the primary mechanism of the FSS-GS of the present invention;
FIG. 7 is a schematic diagram of the main mechanism of the RSD-LS of the present invention;
fig. 8 is a block diagram of an optimizing apparatus for a vehicle path problem according to the present invention.
Detailed Description
The invention combines the genetic algorithm and the differential evolution idea, combines the global searching capability of the genetic algorithm and the local searching capability of the differential evolution algorithm, takes the traditional genetic algorithm as global searching, introduces the differential idea into the genetic algorithm as local searching strategy, and solves the vehicle path problem of multiple vehicle types with time windows by using the hybrid evolution algorithm. According to different stages of the evolution process, the local search strategy is fused with the global search strategy, and the degree of fusion is controlled, so that the speed of processing the vehicle path problem of multiple vehicle types with time windows by the hybrid evolution algorithm is increased, and the solution quality is improved.
Aiming at the problem of the vehicle path with a time window of multiple vehicle types, the invention provides a multi-objective evolutionary algorithm (Multi Stage Hybrid Multiobjective Evolutionary Algorithm with Fast Sampling Strategy-based Global Search and Route Sequence Difference-based Local Search, MS-HMOEA-GL) which is formed by mixing global search based on a rapid sampling strategy and local search based on route sequence difference in a staged manner.
MS-HMOEA-GL combines a fast sampling strategy based global search (Fast Sampling Strategy-based Global Search, FSS-GS) and a route sequence difference based local search (Route Sequence Difference-based Local Search, RSD-LS).
FSS-GS is designed as a global search strategy, including a center region elite sampling strategy and an edge region sampling strategy, as shown in FIG. 6, wherein individuals in the center region on the Pareto front can be quickly picked out according to the center region elite sampling strategy of the fitness function (Pareto Dominating and Dominated Relationship-based Fitness Function, PDDR-FF) of the Pareto dominance; the edge region sampling strategy based on the vector evaluation genetic algorithm (Vector Evaluated Genetic Algorithm, VEGA) is more preferable to individuals positioned in the edge region on the Pareto front surface, so that the problem of insufficient distribution performance of the center region elite sampling strategy can be effectively solved, and the problem depends on the center region elite sampling strategy. By using a mixture of these two strategies and executing the appropriate genetic operators, FSS-GS can rapidly improve convergence and distribution performance for the center and edge regions of the pareto boundary. As a subsequent step, as shown in fig. 7, RSD-LS, which borrowed from the evolution strategy of DE, is used to further improve the quality of individuals, which RSD-LS is able to direct the approach of individuals with poor performance towards individuals with better performance. By mixing FSS-GS and RSD-LS, MS-HMOEA-GL can achieve fast convergence and adequate distribution. The MS-HMOEA-GL is divided into a plurality of stages, and local search based on route sequence difference is applied at proper time, so that the search capability of an algorithm can be effectively improved, and the required calculation time is reduced. Meanwhile, a reasonable mathematical model is constructed aiming at the specificity of the MTVRPTW, and a feasible coding and decoding mode and a proper genetic operator are designed.
In the following, with reference to the drawings and the embodiments, how to apply the MS-HMOEA-GL to the multi-model time-windowed vehicle path problem will be described in detail.
Method embodiment:
the flow of the method for optimizing the vehicle path problem is shown in fig. 1, and the specific process is as follows:
first, according to the description of the vehicle path problem, a mathematical model is established, wherein the mathematical model comprises targets and constraint conditions, and a coding and decoding method of MS-HMOEA-GL is defined. Constraints include vehicle load limits, vehicle volume limits, delivery time window limits, and the like.
The targets in this embodiment include two targets, namely, target 1 and target 2, and target 1 is: the number of vehicles is reduced as much as possible, and the object 2 is to reduce the situation that the dispenser reaches the destination in advance during the distribution process, so as to reduce the wasted time.
The coding of MS-HMOEA-GL comprises two parts, one part representing the client sequence and the other part representing the selection of the vehicle type of chromosome, as shown in FIG. 2. For the client chromosome, which is constructed using a sequencing code, a gene on the client chromosome represents a client, and the same client appears no more than once in one client chromosome, there is no distribution center in the client chromosome, but in the decoding process, it is necessary to add distribution centers at the beginning and end of each sub-path. For the vehicle type chromosome part, a real number coding mode is used for constructing a vehicle type chromosome. Setting the length of this part of the chromosome to the number of all customer vertices that need to be serviced first ensures that the length of the chromosome is sufficient to avoid illegal solutions. However, during evolution, only a part of genes on the model chromosome, where one gene represents the type of delivery vehicle used for a certain sub-path included in the solution, will actually affect the fitness function performance of the individual, and the length of the part of genes is determined by the number of delivery vehicles needed for decoding the individual. At initialization, both parts of the chromosome are randomly generated.
Upon MS-HMOEA-GL decoding, the genes of both parts of the chromosome are traversed from left to right. As shown in fig. 3, the type of vehicle used for the current sub-route is first determined by distributing the vehicle model chromosomes, and then clients in the chromosome client section are sequentially added to the current sub-route. Each time a customer is added to a sub-path, constraint judgment is made, if the customer meets the condition of adding to the current sub-path, the customer is added, if not, the customer is stopped being added and the distribution center is added at the end of the current sub-path, and meanwhile, the operation on the current sub-path is ended. Thereafter, the type of vehicle to be used for the next sub-path is determined again, and the customer who cannot join the previous sub-path is taken as the first service object of the new sub-path. It should be noted that each sub-path needs to add a distribution center at the start point and the end point, and the judgment of the constraint includes the time window constraint of the customer and the upper load limit of the vehicle.
Step two, randomly generating a plurality of vehicle distribution paths and taking the vehicle distribution paths as an initialization population P t Generating elite population A t Elite population A t Initially empty.
Step three, according to the initialized population P t And elite population A t A mixed population is obtained. The method comprises the following specific steps:
1. from an initial population P t Selecting the individuals with better performance on the target 1 as the sub-population SP 1 For example, the front X will perform better on target 1 1 Individual as a sub-population SP 1 ；
2. From an initial population P t Selecting the individuals with better performance on the target 2 as the sub-population SP 2 For example, the front X will perform better on target 2 2 Individual as a sub-population SP 2 ，X 1 ＝X 2 Or X 1 ≠X 2 All can be used;
3. sub-population SP 1 、SP 2 And elite population A t Mixing to form a mating pool.
Step four, carrying out selection, crossing and mutation operations based on a genetic algorithm on the mixed population to obtain a offspring population OffSringset; simple insert search operation is carried out on the offspring population OffSringset to obtain a temporary population P t ′ +1 (i.e., the first temporary population).
1. Selection operation
In this embodiment, a binary tournament selection mode is used as the selection operator. Also when directed to using edge area sampling strategies, the manner in which binary tournament selection is employed forms the sub-population required by the algorithm. Two individuals are randomly selected, their fitness function values are compared, an individual that is excellent in a particular target is selected, and then placed into the corresponding sub-population. The central region elite sampling strategy sorts the evaluated individuals in the population according to their fitness function values, and selects the best part of them as elite population. The binary tournament is used as a selection operator of the algorithm, so that the aim of protecting individuals with high fitness can be achieved without losing diversity.
2. Crossover operation
Since the present invention is faced with the problem of the vehicle path with time window of multiple vehicle types, the problem expression is carried out by adopting a coding mode of double chromosomes, as shown in fig. 4-1 and 4-2, wherein the chromosomes consist of two parts, and therefore, in the MS-HMOEA-GL, the crossover operator is also designed into two parts. For a portion of a client chromosome, the sequence crossover is used to perform a genetic recombination process for the client chromosome portion. The sequential crossing not only reserves the marked partial gene sequence, namely the partial sub-path, but also tries to keep the customer connection after marking the points, the crossing mode focuses more on the continuity of the customer in the solution generated after chromosome decoding, and is more suitable for solving the problem of the vehicle path with the time window of multiple vehicle types. For a model chromosome segment, a single point crossover is used as the crossover operator for that segment. Wherein the mark positions of the single point crossings are random integers between 1 and the effective length. The effective length exists because genes on the model chromosome are not necessarily all used for decoding, and a model gene exceeding the effective length defined as the minimum value of the number of use of delivery vehicles by two parent individuals would be meaningless.
3. Mutation operation
In MS-HMOEA-GL, as shown in FIGS. 5-1 and 5-2, the mutation operator is also composed of two parts. First, mutation operators of the client part of the chromosome of the individual adopt a mode of exchanging mutation. Secondly, the chromosome variation is completed by adopting a single-point variation mode for the chromosome part of the vehicle type, a gene is randomly selected in the effective length range of the vehicle type part of the individual chromosome, and the type of the delivery vehicle indicated in the gene is randomly adjusted to other delivery vehicle types.
4. Simple insert search operation
The simple insert search operation is a partial search for the purpose of reducing the number of vehicles used. The method specifically comprises the steps of inserting a customer to be serviced next into a link in a front route of a current vehicle, and adjusting the service sequence of certain customers to reduce the number of vehicles. For example, as shown in fig. 3, the order in which the clients are serviced by the clients that are originally set is: after constraint judgment is made, the client 1, the client 2, the client 3, the client 4, the client 5 and the client 6 form the scheme as follows: customer 1 and customer 2 use vehicle model 2, customer 3 and customer 4 use vehicle model 1, and customer 5 and customer 6 use vehicle model 2, requiring a total of three vehicles. After the simple insert search operation is used, for example, the client 4 is inserted between the client 1 and the client 2, so that the service sequence of the clients is changed, constraint judgment is continuously performed, and the formed scheme may be that the client 1, the client 4 and the client 2 use the vehicle type 2, and the client 3, the client 5 and the client 6 use the vehicle type 1, and then a total of two vehicles are needed to finish. Of course, if the order of service of the customers changes, resulting in an increase in the number of vehicles (e.g., four vehicles) used, this approach is abandoned.
Step five, judging whether the ratio of the current evolutionary iteration times to the evolutionary iteration termination times is greater than 50%: if the ratio is greater than 50%, then the temporary population P t ′ +1 Performing rsd_ls on individuals in (a) to generate rsd_ls temporary population rsd_lsp t ′ +1 (i.e., a second temporary population), rsd_lsp, from rsd_ls temporary population according to pddr_ff strategy t ′ +1 And a temporary population P t ′ +1 Selecting better individuals as a new initialization population P t+1 And executing the step six; if the ratio is less than or equal to 50%, the temporary population P is obtained t ′ +1 As a new initialization population P t+1 And executing the step six.
1、RSD_LS
Differential evolution is an efficient evolutionary algorithm that can guide the evolution of individuals based on their differences. MS-HMOEA-GL references the idea of DE to further improve the performance of the algorithm. By appropriate evolutionary operations, FSS-GS can quickly find an effective solution, and MS-HMOEA-GL uses a local search method called route sequence difference-based in order to further improve the quality of the solution. RSD-LS is an additional search operation performed on a population generated by FSS-GS during an MS-HMOEA-GL iteration, the main idea being to pick out two individuals from the population with different fitness values, determine the difference between the two individuals, and evolve the individual with higher fitness value (worse individual) towards the individual with lower fitness value (better individual) according to the difference, which can be roughly divided into four steps:
1) An individual is randomly extracted from the population generated by the FSS-GS.
2) Randomly extracting another individual from the FSS-GS, and executing the next step if the fitness function value is better or worse than that of the individual extracted in the step 1), otherwise repeating the step 2).
3) The route sequence differences between the individuals selected in step 1) and step 2) are determined using the exchange sequence.
4) Intercepting the difference sequence obtained in the step 3) according to a certain proportion, and then acting on the individuals with poorer performance in the individuals randomly extracted in the step 1 and the step 2.
In addition, because the custom chromosome coding in MS-HMOEA-GL uses sequencing coding, the MS-HMOEA-GL uses the exchange order to determine route sequence differences between individuals.
2. PDDR_FF strategy
The fitness function corresponding to the pddr_ff strategy is:
where eval (k) is RSD_LS temporary population RSD_LSP t ′ +1 The fitness value of individual k in (a), q (k) is the number of individuals that are dominated by k, p (k) is the number of individuals that are dominated by k, pSize is the rsd_ls temporary population rsd_lsp t ′ +1 Is of a size of (a) and (b).
Step six, according to the new initialized population P t+1 And elite population A t Obtaining a new elite population A t+1 . The method comprises the following specific steps:
1. fusing a new initialization population P t+1 And elite population A t As elite temporary population tempellieseoldivided set;
2. selecting better individuals from the elite temporary population tempellieseoldivided set according to PDDR_FF strategy as a new elite population A t+1 The formula of the fitness value refers to formula (1).
Seventh, the new initialization population P t+1 And a new elite population A t+1 And (3) carrying out evolutionary iteration according to the mode from the third step to the sixth step, judging whether the evolutionary iteration number reaches the evolutionary iteration termination number, and selecting an optimal vehicle distribution path from the final generation population when the evolutionary iteration termination number is reached.
Thus, the optimization method of the vehicle path problem can be completed. The invention combines the global search based on the rapid sampling strategy and the local search based on the route sequence difference, can rapidly improve the convergence and distribution performance of the pareto boundary center and the edge area, further improves the quality of individuals, guides the individuals with poor performance to approach to the individuals with better performance, and realizes rapid convergence and sufficient distribution. And according to different stages of the evolution process (the current evolution iteration times are half of the evolution iteration termination times), the local search strategy is fused with the global search strategy, and the degree of fusion is controlled, so that the speed of processing the multi-vehicle-type vehicle path problem with the time window by the hybrid evolution algorithm is increased, and the solution quality is improved.
In the fifth step of this embodiment, after determining that the ratio of the current number of evolutionary iterations to the number of evolutionary iteration stops is greater than 50%, the temporary population P is subjected to t ′ +1 Performing rsd_ls on individuals in (a) to generate rsd_ls temporary population rsd_lsp t ′ +1 . As other embodiments, after a determination of a ratio greater than 50%, the temporary population P may be subjected to existing differential evolution operations t ′ +1 The individuals in the population undergo evolutionary operations to obtain temporary populations and subsequent processing. The method also combines the advantages of the differential evolution algorithm to obtain the optimal solution.
The timing of introducing RSD-LS was obtained experimentally. In the later searching stage of the algorithm, the RSD-LS is introduced to effectively guide the individuals with poor performance to the vicinity of the near-optimal solution to participate in searching, so that the real Pareto front is continuously approached. According to the invention, through the test of the Solomon reference problem R101 problem of the MS-HMOEA-GL under the condition of multiple vehicle types, the proper use time of the RSD-LS in the algorithm is verified. 100% in Table 1 is expressed as RSD-LS added to the algorithm from the beginning, participating in the whole evolution process of the algorithm; 33% h indicates that RSD-LS is used during the evolution from the beginning to the first third of the algorithm and is not used during the rest of the algorithm; similarly, 50% h and 66% h represent that RSD-LS is used during the evolution from the beginning of the algorithm to the first half and two thirds of the algorithm. While 33% e indicates that RSD-LS is added to the second third of the process of the algorithm, and the first two third of the process of the algorithm does not use RSD-LS; the same 50% e and 66% e indicate that RSD-LS is not added until half and one third of the algorithm iterations, and that the earlier evolution process is not used.
From experimental results, the application of adding RSD-LS at the early stage of the algorithm can lead the MS-HMOEA-GL to have better performance in the distribution indexes Spacing and Spacing than the performance of using RSD-LS in the whole course, but have poorer performance in the convergence indexes GD, IGD and HV; the MS-HMOEA-GL added in the later stage of the algorithm has obvious improvement on convergence indexes GD, IGD and HV, but has slightly inferior performance on the distribution indexes than the MS-HMOEA-GL added in the early stage.
In a practical vehicle path problem, the number of delivery vehicles is reduced as much as possible because excessive use of delivery vehicles results in high costs. While with fewer vehicles, different possible solutions span larger in the target space, there are fewer solutions, so the performance of the algorithm in terms of convergence performance needs to be more emphasized, so it is considered that the operation of RSD-LS is feasible to add when the algorithm goes to the later stage. Comparing three algorithms for adding RSD-LS at different moments later in MS-HMOEA-GL, the results obtained by using RSD-LS when the algorithm is performed to one half are more excellent. Compared with the algorithm of the whole course of the RSD-LS participation, by adjusting the use time of the RSD-LS, the proper use of the local search strategy can not only further improve the search capability of the algorithm, but also effectively shorten the increase of the solving time caused by complex operation.
TABLE 1 use of RSD-LS in MS-HMOEA-GL%
The effectiveness of the inventive optimization method of the vehicle path problem is verified by comparative experiments.
Experiments the performance of the proposed MS-HMOEA-GL was verified by using a set of published benchmark problem data generated by Solomon. The problem numbers used in the data are R101-R104, C101-C104 and RC101-RC104, which are randomly generated with a short scheduling time between clients. Each benchmarking problem provides information about the warehouse and 100 customers, including coordinate location, required cargo volume, time window, and service time. The metrics were used GD, IGD, HV, spacing and Spread to evaluate the performance of the algorithm as shown in tables 2, 3, 4, 5, 6, respectively. Algorithms for comparison experiments included MS-HMOEA-GL, NSGA-II, SPEA2, MOEA/D, and the Multi-target evolutionary Algorithm with FSS-GS but without RSD-LS (MOEA-G). The test problems used in the experiment are 12 Solomon-based benchmark problems, and the multi-model conditions of additional vehicle models are added on the basis of the benchmark problems. Each algorithm was performed 30 times and the solution was recorded in pareto approximations each time.
Experimental results show that MS-HMOEA-GL has very excellent performance on GD indexes, the first performance is obtained in Solomon standard problems under the condition of 12 tested multi-vehicle types, MOEA-G has the same excellent performance on GD indexes, and the second performance is obtained on 12 tested problems, which is inferior to MS-HMOEA-GL. The IGD index is used for evaluating the results of five algorithms participating in the test on twelve test problems, and the results show that the MS-HMOEA-GL is still excellent in performance on the IGD index, 11 test problems among 12 test problems are ranked first, MOEA-G is better in performance, the second rank is obtained among 6 test problems, and the third rank is obtained among 5 test problems. The HV index evaluates the advantages and disadvantages of the algorithm according to the size of a space formed between a solution set obtained by the algorithm and a reference point, from the data reflected by experiments, 11 test problems of the MS-HMOEA-GL are obtained from 12 test problems, and the remaining test problem is obtained from the second score; MOEA-G achieved a second over 11 test questions and a first over another test question. The MS-HMOEA-GL has more general performance on the Spacing index and the Spacing index, 2 test questions on the Spacing index are ranked first, 2 test questions are ranked second, and a third ranking is obtained on the 2 test questions; 2 test questions were ranked first on the Spread index, 2 test questions were ranked second, and 1 test question was ranked third. There are also situations where the number of viable solutions in the solution space decreases as the number of delivered vehicles decreases. This means that when the solution space area with a smaller number of delivery vehicles is more approached, the difference in total waiting time between solutions with different numbers of delivery vehicles will be larger, the solution distribution in the solution space is more uneven, and MS-HMOEA-GL and MOEA-G can and tend to find solutions with a smaller number of vehicles, thus possibly resulting in their overall poor performance in the Spacing index and the Spread index. But in general, the distribution performance achieved by MS-HMOEA-GL is acceptable.
Overall, the MS-HMOEA-GL achieved better convergence performance and distribution performance over the Solomon benchmark problem with 12 multi-model cases, compared to algorithms NSGA-II, SPEA2, MOEA/D and MOEA-G, which were evaluated using five metrics GD, IGD, HV, spacing and bead. It can be said that the crossover operator and mutation operator designed for the coding mode of the double chromosomes can complete the genetic recombination task of the algorithm, and the proposed FSS-GS, RSD-LS, and use timing and HMOEA-GL frameworks are proper and effective.
TABLE 2 comparative algorithm GD indicator Performance for participation in experiments
TABLE 3 comparative algorithm IGD index Performance for participation in experiments
TABLE 4 comparative algorithm HV indicator Performance in experiments
TABLE 5 comparative Algorithm Spacing index Performance for participation in experiments
TABLE 6 comparative Algorithm Spread index Performance for participation in experiments
Device example:
this embodiment provides an optimizing apparatus for a vehicle path problem, as shown in fig. 8, which includes a memory, a processor, and an internal bus, where the processor and the memory complete communication and data interaction with each other through the internal bus. The memory includes at least one software functional module stored in the memory, and the processor executes various functional applications and data processing by running the software program and the module stored in the memory, so as to implement a method for optimizing a vehicle path problem in the method embodiment of the present invention, that is, the steps of the method embodiment are implemented by the program to instruct the relevant hardware, and the program executes the steps including the method embodiment. The optimization method of the vehicle path problem is realized through programming, and the optimization device based on the vehicle path problem is implemented.
The processor may be a microprocessor MCU, a programmable logic device FPGA, or other processing device. The memory is used for storing a program, and the processor executes the program after receiving the execution instruction.
The memory can be various memories for storing information by utilizing an electric energy mode, such as RAM, ROM and the like; various memories for storing information by using magnetic energy, such as hard disk, floppy disk, magnetic tape, magnetic core memory, bubble memory, USB flash disk, etc.; various memories for optically storing information, such as CDs, DVDs, etc. Of course, there are other ways of memory, such as quantum memory, graphene memory, etc.
Claims (9)
1. A method for optimizing a vehicle path problem, comprising the steps of:
1) Establishing a mathematical model of the vehicle path problem according to the vehicle path problem to be solved, wherein the mathematical model comprises a target, decision variables and constraint conditions; the decision variables comprise a client sequence variable and a vehicle type variable, and two variables are respectively encoded by adopting double chromosomes: the client sequence variable is encoded into a client chromosome by using a sequencing encoding mode, and the vehicle type variable is encoded into a vehicle type chromosome by using a real number encoding mode; the constraint conditions comprise time window constraint of clients and load constraint of vehicles of various vehicle types;
2) Randomly generating at least two vehicle delivery paths as an initialization population P t And generates elite population A t Elite population A t Initially empty;
3) According to the initialized population P t And elite population A t Obtaining a mixed population;
4) Carrying out evolutionary operation based on a genetic algorithm on the mixed population to obtain a offspring population OffSringset; obtaining a first temporary population P according to the offSringset of the offspring population t ′ +1 The method comprises the steps of carrying out a first treatment on the surface of the The evolution operation comprises a selection operation, a crossover operation and a mutation operation; the selecting operation adopts a binary tournament selecting mode as a selecting operator; a sequential crossover operator and a crossover mutation operator are adopted for the customer chromosome, and a single-point crossover operator and a single-point mutation operator are adopted for the vehicle type chromosome;
5) Judging whether the ratio of the current evolutionary iteration times to the evolutionary iteration ending times is larger than a set ratio, if so, performing the first temporary population P t ′ +1 Performing evolutionary operation for adjusting individuals in the population based on the differences among the individuals in the population to obtain a second temporary population RSD_LSP t ′ +1 Calculating a second temporary population RSD_LSP t ′ +1 And a first temporary population P t ′ +1 The fitness value of each individual in the population P is selected to be a new initialization population P t+1 ；
6) According to the new initialisation population P t+1 And elite population A t Obtaining a new elite population A t+1 ；
7) New initialization population P t+1 And a new elite population A t+1 And (3) carrying out evolutionary iteration according to the modes from the step (3) to the step (6) until the evolutionary iteration times reach the evolutionary iteration termination times, and selecting an optimal vehicle distribution path from the final generation population.
2. The method according to claim 1, wherein in step 5), if the ratio of the number of evolutionary iterations to the number of evolutionary iteration stops is equal to or smaller than a set ratio, the first temporary population P is selected t ′ +1 As a new initialization population P t+1 。
3. The method of optimizing a vehicle path problem according to claim 1, wherein when the targets are at least two targets, step 3) includes: selecting a plurality of sub-populations SP from an initialized population i The number of the sub-populations is consistent with the number of the targets, and one sub-population comprises the first X optimal individuals obtained by selecting one of the targets; combining multiple sub-populations SP i And elite population A t Mixing to obtain the mixed population; wherein, X > 1, i=1, 2, …, m, m is the total number of sub-populations.
4. The method of claim 1, further comprising the step of performing an insert search operation on the offspring population OffSringSet in step 4).
5. The method of optimizing a vehicle path problem according to claim 1, wherein step 6) includes: mixing a new initializing population P t+1 And elite population A t Obtaining an elite temporary population tempellieseolts; selecting a preferred individual from the elite temporary population tempelite population as the new elite population a t+1 。
6. The method for optimizing a vehicle path problem according to claim 1 or 5, wherein in step 5) and step 6), the fitness value of the individual is:
where eval (k) is the second temporary population RSD_LSP t ′ +1 Or fitness value of individual k in elite temporary population temp t ′ +1 Or the size of the elite temporary population tempellieseoldivided set.
7. The method for optimizing a vehicle path problem according to claim 1, wherein in step 5), the operation of adjusting the evolution of the individuals in the population based on the inter-individual differences in the population is an rsd_ls operation, which refers to: and selecting two individuals with different fitness values from the population, determining the difference between the two individuals, and evolving the worse individuals towards the better individuals according to the difference.
8. The method for optimizing a vehicle path problem according to claim 1, wherein in step 5), the set ratio is 50%.
9. An apparatus for optimizing a vehicle path problem, comprising a memory and a processor for executing instructions stored in the memory to implement the method for optimizing a vehicle path problem according to any one of claims 1 to 8.
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