Multi-objective evolution method based on adaptive tabu large neighborhood search method

Abstract

Recently, many studies prove that when the vehicle path problem with uncertain data is solved, the search direction of the solutions is guided through an adaptive large neighborhood search strategy, the solutions are selected in the neighborhood through a multi-objective evolutionary algorithm, and therefore it is feasible to find a group of optimal solutions meeting uncertain environmental constraints. However, a large number of repeated and invalid operations occur in the later period of solution of the adaptive large neighborhood search strategy, so that the efficiency of the method is reduced. The invention provides a robust multi-objective evolution method based on an adaptive taboo large neighborhood search strategy, in the method, a new generation of solution group is generated by using an adaptive taboo large neighborhood search method, and the occurrence frequency of later repeated operation of an algorithm is reduced by using a taboo list, so that the robustness of the algorithm is improved. The method is combined with a Monte Carlo simulation method to simulate a plurality of scenes of a vehicle path problem under determined distribution, and an optimal solution group with robustness is solved, so that the vehicle path problem with uncertain data is solved, as shown in Figure 1. And finally, testing is carried out on a Solomon data set. The result shows that the method has effectiveness in solving the vehicle path problem with uncertainty.

Description

Technical Field

[0001] The present invention relates to the field of multi-objective evolutionary optimization technology and the field of vehicle routing problems, specifically including a multi-objective evolutionary optimization algorithm based on the Pareto frontier and a vehicle routing problem with a time window and uncertain arrival time at a customer. Background Art

[0002] The multi-objective genetic algorithm is a classic algorithm in multi-objective optimization algorithms. The algorithm starts from a set of randomly generated populations and performs evolutionary operations such as selection, crossover, and mutation on the population. After multiple evolutions, the fitness of individuals in the population continues to improve, thus gradually approaching the Pareto optimal solution set of the multi-objective optimization problem. The existing multi-objective evolutionary algorithms can be roughly divided into three different types according to the selection method: Pareto frontier optimization algorithm, decomposition-based optimization algorithm, and utility-based optimization algorithm. The decomposition-based optimization algorithm uses a weight vector to divide its target problem into multiple sub-areas to improve the optimization efficiency of the multi-objective evolutionary algorithm. The utility-based optimization algorithm determines the optimal solution by calculating the utility value of the non-dominated solution in the population. Although the amount of calculation is relatively large, it can accurately identify the optimal solution. The Pareto frontier optimization algorithm divides the population into several frontiers according to the non-dominated sorting strategy, and uses diversity metrics to further identify the optimal solution on the critical frontier, thereby solving a set of optimal solutions. The multi-objective optimization algorithm described above is mainly aimed at multi-objective optimization problems with certain data, but there is also a type of multi-objective optimization problem with uncertain data. To solve this type of multi-objective optimization problem, a robust multi-objective evolutionary algorithm is proposed, which can solve multi-objective optimization problems with uncertain data through Monte Carlo simulation method.

[0003] The vehicle routing problem (VRP) is a classic combinatorial optimization problem that involves planning a set of minimum-cost delivery routes for a logistics company's vehicles. Each vehicle departs from a parking lot, serves a set of geographically dispersed customers with known demands, and finally returns to the parking lot. Each customer can only be visited once by one vehicle. The total customer demand on each delivery route cannot exceed the vehicle capacity. The vehicle routing problem with time windows (VRPTW) is a variant of the VRP, on the basis of which each customer requires service within a given time window. This variant has two cases. In the case of a hard time window, late vehicles are not allowed. In the case of a soft time window, customers accept the service of late vehicles, but incur additional penalties. In the real world, we often face many VRPTWs, and the data information involved is often uncertain. These uncertain data have many types, such as demand uncertainty, travel time uncertainty, customer uncertainty, and time window uncertainty. This series of complex constraints requires that when solving the VRPTW to obtain the minimum cost, its constraints need to be considered simultaneously, which makes the VRPTW abstracted as a multi-objective optimization problem, so that the uncertain VRPTW can be solved using a multi-objective evolutionary algorithm.

[0004] Recently, many studies have shown that it is feasible to find a set of optimal solutions that meet the constraints of uncertain environments by using an adaptive large neighborhood search strategy to guide the search direction of solutions and a multi-objective evolutionary algorithm to select solutions in the neighborhood when solving the vehicle routing problem with uncertain data. However, the adaptive large neighborhood search strategy will have a large number of repeated and invalid operations in the later stage of the solution, which reduces the efficiency of the method. Therefore, the present invention proposes a multi-objective evolutionary method based on an adaptive taboo large neighborhood search strategy to solve the vehicle routing problem with uncertain data. Summary of the invention

[0005] The present invention proposes a robust multi-objective evolutionary method based on an adaptive taboo large neighborhood search method. First, a group of populations are randomly initialized. Then, the population is subjected to an adaptive taboo large neighborhood search strategy to generate a new generation of populations. Finally, the dominance level of each individual in the population is combined to sort them, and finally a group of Pareto frontiers are obtained as approximate optimal solutions.

[0006] In order to solve the defects of the existing methods, the present invention is implemented by the following technical solutions:

[0007] A robust multi-objective evolutionary method model based on an adaptive taboo large neighborhood search method comprises the following steps:

[0008] 1. The multi-objective evolutionary algorithm method mentioned in the present invention. First, initialize the weight of each operator of the adaptive taboo large neighborhood search, and use the random initialization method to obtain N solution individuals as the initial population o. Then, the adaptive taboo large neighborhood search strategy is used to perform evolutionary calculation on each solution individual in the initial population o to generate a new solution individual, and then the new solution individual is compared with the original solution individual, and the comparison result is used to update the weight of the operation operator. After that, these new solution individuals are merged into the original population to form a new population P, and the same solution individuals in the population (that is, individuals with the same path for the vehicle routing problem) are removed. Secondly, the new population P is sorted according to the fitness dominance level of the solution individuals, and a new generation of initial population O with the same size as the initial population O is selected. ′ , using population O ′ Participate in the next iteration of the algorithm. Finally, when the iteration reaches a certain number of generations, the final population P is obtained as the Pareto optimal solution.

[0009] 2. The taboo adaptive large neighborhood search strategy proposed by the present invention. First, each destruction operator and selection operator has its corresponding weight value. The destruction operator and repair operator to be used in this search are selected according to the weight values ​​of the destruction operator and the selection operator using a roulette wheel selection strategy. Then, new solution individuals are evolved based on the selected destruction operator and repair operator based on the incoming solution individuals, and are added to the taboo list according to the adopted operation operator. In the operation of adding the operation operator to the taboo list, there is a taboo-breaking operation for the operation already in the taboo list. When the new solution individual generated by the same operation is better than the solution individual saved in the taboo list or meets the selection of the simulated annealing algorithm, the operation will be inserted into the taboo list, otherwise it will not be added to the taboo list. Finally, the new individual and the taboo list are returned.

[0010] 3. The method for processing uncertainty data of the vehicle routing problem mentioned in the present invention. Use a robust multi-objective evolutionary method. First, determine the probability distribution model corresponding to the uncertainty information. Then apply Monte Carlo simulation to perform m simulations, initialize the data in the vehicle routing problem solved in the first two steps, and then apply the initialized values ​​to the solution individuals obtained in the first two steps to obtain the fitness value of each solution individual in the uncertainty data. Finally, use step one to sort the obtained solution individuals, and finally obtain a group of robust optimal solutions.

[0011] 4. The proposed method is tested on the Solomon dataset. The proposed method is used to solve the Solomon dataset with 50 and 100 customers respectively to prove the effectiveness of the method. The experiment shows that the algorithm proposed in the present invention can obtain a set of solutions with better performance.

[0012] Compared with the prior art, the present invention has the following characteristics:

[0013] 1. Most existing inventions fail to take into account the uncertainty data in the vehicle routing problem and cannot fit the actual problem well. The present invention uses a probability distribution model to simulate the uncertainty in real life, obtains a set of simulation scenarios based on the probability distribution model, calculates the fitness value of the solution individual in each scenario, and uses the average fitness value under all scenarios as the fitness value of the solution individual under uncertainty, and uses the fitness value as the basis for dominance level evaluation in the multi-objective evolutionary algorithm, thereby obtaining a set of robust optimal solutions.

[0014] 2. Existing studies have shown that the adaptive large neighborhood search strategy has shown good performance in solving the vehicle routing problem, but it is easy to fall into repeated operations in the later stage of the search, which reduces the efficiency of the later search. In view of this problem, the present invention adds a taboo list to it. The taboo list stores the operation information in the recent period. If the subsequent operation is in the taboo list, then the operation will be prohibited unless the operation can obtain a better solution than the same operation in the taboo list.

[0015] 3. The present invention proposes a multi-objective evolutionary method based on a taboo adaptive large neighborhood search strategy. New individuals are generated through the taboo adaptive large neighborhood search strategy, and these generated new individuals are applied as a population to the multi-objective evolutionary algorithm, so that the multi-objective evolutionary algorithm can solve the vehicle routing problem, and finally obtain a robust optimal solution by combining the data of the simulated uncertainty scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Structure diagram of multi-objective evolutionary method based on taboo adaptive large neighborhood search strategy

[0017] Figure 2 Multi-objective evolutionary algorithm framework diagram

[0018] Figure 3 Taboo adaptive large neighborhood search algorithm framework diagram

[0019] Figure 4 C101 experimental results in the Solomon dataset DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in combination with specific examples and with reference to the accompanying drawings.

[0021] The multi-objective evolutionary method is an effective method to solve multi-objective optimization problems. To this end, the vehicle routing problem is first modeled as a multi-objective optimization problem, which is defined as follows:

[0022]

[0023] where x 0jk Indicates whether vehicle k is traveling from the warehouse node to the customer node j, x ijk Indicates whether vehicle k is from customer node i to customer node j, d ij represents the cost from customer node i to customer node j, t ij It represents the waiting time generated when the vehicle departs from customer node i and arrives at customer node j in advance. Therefore, there are three optimization objectives in the multi-objective optimization problem to be solved by the present invention. The first objective is to minimize the number of vehicles used, the second objective is to minimize the total cost, and the third objective is to minimize the overall waiting time.

[0024] To solve the above multi-objective optimization problem, the overall structure of the multi-objective evolutionary method based on the taboo adaptive large neighborhood search strategy proposed in the present invention is as follows: Figure 1 shown.

[0025] Specifically, the multi-objective evolutionary method adopted by the present invention is the most classic NSGA-II algorithm in the multi-objective evolutionary algorithm, and the algorithm is divided into two stages. The first stage is used to obtain the optimal solution of the vehicle path problem under deterministic conditions. The algorithm is combined with the adaptive taboo large neighborhood search algorithm to solve the vehicle path problem with deterministic data, and a set of optimal solutions under deterministic conditions are obtained. The second stage is used to obtain the optimal solution of the vehicle path problem under uncertain conditions. The Monte Carlo method is used to simulate M scenarios (M is defined according to the situation) with a certain probability distribution model, and then the fitness value of the individual solution obtained in the first stage in the M scenarios is calculated, and then the average value of the fitness value in the M scenarios is calculated as the fitness value of the individual solution under uncertain conditions. Non-dominated sorting is performed according to the obtained fitness value, and finally a set of robust optimal solutions is obtained.

[0026] The specific steps of stage 1 are as follows: First, use the random initialization method to obtain N solution individuals as the initial population O, and initialize the weight value W of each operator in the adaptive taboo large neighborhood search strategy. The definition of the weight value W is as follows:

[0027] W={w i |i∈[1,…,n]}

[0028] Where n is the number of operators used in the adaptive taboo large neighborhood search.

[0029] After the initialization, the multi-objective evolutionary method is used to iterate the initial population O. Each generation of the multi-objective evolutionary method uses an adaptive taboo large neighborhood search strategy to generate a new solution individual S' based on each solution individual S in the initial population O. After the new solution individual is generated, the new individual S ′ Perform a dominance comparison with the original solution individual S, and update the weight value W of the operator used in the adaptive taboo large neighborhood search algorithm according to the comparison result. The update method of the weight W is as follows:

[0030]

[0031] in, is the updated weight value, is the weight value before updating, σ is the fixed reward value set after comparing the new solution individual with the original solution individual, and η is the custom coefficient.

[0032] After the weight value is updated, these solution individuals are combined with the original population to form a new population P. Secondly, the new population P is sorted according to the fitness dominance level of the solution individuals, and a new generation of initial population O with the same size as the initial population O is selected. ′ At the same time, the same solution individuals in the population (i.e. individuals with the same path for the vehicle routing problem) are removed to ensure that the solution individuals in the new population P are different. Finally, when the termination condition of the multi-objective evolutionary method is met, the algorithm ends and the final population P is output as the Pareto optimal solution. The specific algorithm framework is as follows: Figure 2 shown.

[0033] The adaptive taboo large neighborhood search strategy used in the first stage has the following specific execution steps: First, each destruction operator and selection operator has its corresponding weight value. The destruction operator and repair operator to be used in this search are selected according to the weight values ​​of the destruction operator and the selection operator using the roulette wheel selection strategy. Then, new solution individuals are evolved based on the selected destruction operator and repair operator based on the incoming solution individuals. Finally, the fitness value of the new solution individual is compared with the fitness value of the incoming solution individual, and the weight value of the selected destruction operator and selection operator is updated according to the comparison result. The specific algorithm framework is as follows: Figure 3 As shown. The present invention designs three destruction operators and three insertion operators for this strategy. Among them, the three destruction operators are as follows:

[0034] 1. Random destruction operator: Randomly select U client nodes from the solution individuals for deletion.

[0035] 2. Maximum correlation destruction operator: Calculate the correlation between each customer node, and select the customer node to delete based on the largest U value. The calculation formula is as follows:

[0036]

[0037] Among them, d ij is the distance between client node i and node j, q i is the demand of client node i, t i is the waiting time of client node i.

[0038] 3. Maximum cost destruction operator: Calculate the cost value of each customer node, and select the customer node to delete based on the largest U value. The cost value calculation formula for each node is as follows:

[0039] cost i =d i-1,i +d i,i+1

[0040] The three insertion operators are as follows:

[0041] 1. Randomly insert operators: randomly insert the destroyed operators into the destroyed solution individual paths.

[0042] 2. Minimum cost insertion operator: Insert according to the cost value of the insertion position, and insert each deleted node to the position that can minimize the total cost.

[0043] 3. Minimum waiting time insertion operator: Insert according to the waiting time of the insertion position, and insert each deleted node to the position that can minimize the total waiting time.

[0044] After the first stage is completed, the second stage begins, which is the solution of the vehicle routing problem under uncertainty. In the second stage, the Monte Carlo simulation method is first used to simulate each piece of information in the vehicle routing problem using the following formula:

[0045]

[0046] in, For deterministic data, is the data after the uncertainty environment disturbance, δ is the range [-δ max , δ max ], which follows the prescribed probability distribution model.

[0047] After the simulation, M scenarios are obtained. Then, the solution individuals obtained in the first stage are calculated in each scenario and the average fitness value of all scenarios is used as the fitness value under the uncertainty environment. After all the solution individuals have calculated the fitness values, these solution individuals are sorted using non-dominated sorting, and the last N solution individuals are taken as the final robust optimal solution for data, and the whole method ends.

[0048] Finally, the present invention is tested on the Solomon dataset, and the results are as follows: Figure 4 As shown in Figure 2, due to the large number of data types in the Solomon dataset, Figure 4 Only results for one type of path are shown.

[0049] It should be noted that although the embodiments of the present invention described above are illustrative, they are not intended to limit the present invention, and therefore the present invention is not limited to the above specific embodiments. Without departing from the principles of the present invention, any other embodiments obtained by those skilled in the art under the guidance of the present invention are deemed to be within the protection of the present invention.

Claims

1. A robust multi-objective evolutionary method model based on an adaptive taboo large neighborhood search method, comprising the following steps: Step 1, the multi-objective evolutionary algorithm method mentioned in the present invention. First, initialize the weight of each operator of the adaptive taboo large neighborhood search, and use the random initialization method to obtain N solution individuals as the initial population O. Then, the adaptive taboo large neighborhood search strategy is used to perform evolutionary calculations on each solution individual in the initial population O to generate new solution individuals, and these new solution individuals are merged into the original population to form a new population P, while the same solution individuals in the population (that is, individuals with the same path for the vehicle path problem) are removed. Secondly, sort the new population P according to the fitness dominance level of the solution individuals, and select a new generation of initial population O' with the same size as the initial population O, use population O' to participate in the next iteration of the algorithm, and update related data at the same time. Finally, when the iteration reaches a certain generation, the final population P is obtained as the Pareto optimal solution. Step 2: Adaptive taboo large neighborhood search strategy proposed by the present invention. First, each destruction operator and selection operator has its corresponding weight value. The destruction operator and repair operator to be used in this search are selected by roulette selection strategy according to the weight values ​​of the destruction operator and the selection operator. Then, new solution individuals are evolved based on the selected destruction operator and repair operator based on the incoming solution individuals. Finally, the fitness value of the new solution individual is compared with the fitness value of the incoming solution individual, and the weight values ​​of the selected destruction operator and selection operator are updated according to the comparison result. Step 3, the method for processing uncertainty data of the vehicle routing problem mentioned in the present invention, that is, the robust multi-objective evolutionary method. First, determine the probability distribution model corresponding to the uncertainty information. Then apply Monte Carlo simulation to perform m simulations, initialize the data in the vehicle routing problem solved in the first two steps, and then apply the initialized values ​​to the solution individuals obtained in the first two steps to obtain the fitness value of each solution individual in the uncertainty data. Finally, use step one to sort the obtained solution individuals, and finally obtain a group of robust optimal solutions. Step 4: Test the proposed method on the Solomon dataset. The proposed method is used to solve the Solomon dataset with 50 and 100 customers respectively to prove the effectiveness of the method. The experiment shows that the algorithm proposed in the present invention can obtain a set of solutions with better performance.

2. According to the robust multi-objective evolutionary method model based on the adaptive taboo large neighborhood search method of claim 1, in step 1: The multi-objective evolutionary method adopted in the present invention is divided into two stages. The first stage is used to obtain the optimal solution to the vehicle routing problem under deterministic conditions. The NSGA-II in the multi-objective evolutionary algorithm is combined with the adaptive taboo large neighborhood search algorithm to solve the vehicle routing problem with deterministic data, and a set of optimal solutions under deterministic conditions are obtained. The second stage is used to obtain the optimal solution to the vehicle routing problem under uncertain conditions. The Monte Carlo method is used to simulate M scenarios (M is defined according to the situation) with a certain probability distribution model, and then the fitness values ​​of the individual solutions obtained in the first stage in the M scenarios are calculated, and then the average of the fitness values ​​in the M scenarios is calculated as the fitness value of the individual solution under uncertain conditions. Non-dominated sorting is performed according to the obtained fitness values, and finally a set of robust optimal solutions is obtained. The specific steps of stage 1 are as follows: First, use the random initialization method to obtain N solution individuals as the initial population O, and initialize the weight value W of each operator in the adaptive taboo large neighborhood search strategy. The definition of the weight value W is as follows: W={w i |i∈[1,...,n]} in, n is the number of operators used in the adaptive tabu large neighborhood search. After initialization, the multi-objective evolutionary method is used to iterate the initial population O. Each generation of the multi-objective evolutionary method uses the adaptive taboo large neighborhood search strategy to generate a new solution individual S' based on each solution individual S in the initial population O. After the new solution individual is generated, the new individual S' is compared with the original solution individual S, and the weight value W of the operator used in the adaptive taboo large neighborhood search algorithm is updated according to the comparison result. The update method of the weight W is as follows: in, is the updated weight value, is the weight value before updating, σ is the fixed reward value set after comparing the new solution individual with the original solution individual, and η is the custom coefficient. After the weight value is updated, these solution individuals are combined with the original population to form a new population P. Secondly, the new population P is sorted according to the fitness dominance level of the solution individuals, and a new generation of initial population O' with the same size as the initial population O is selected. At the same time, the same solution individuals in the population (that is, individuals with the same path for the vehicle routing problem) are removed to ensure that the solution individuals in the new population P are different. Finally, when the termination condition of the multi-objective evolutionary method is met, the final population P is output as the Pareto optimal solution. In step 2: The present invention designs three destruction operators and three insertion operators for this strategy. Among them, the three destruction operators are as follows: (1) Random destruction operator: Randomly select U client nodes from the solution individuals and delete them. (2) Maximum correlation destruction operator: Calculate the correlation between each client node and select the client node to be deleted based on the largest U value. The calculation formula is as follows: Among them, d ij is the distance between client node i and node j, q i is the demand of client node i, t i is the waiting time of client node i. (3) Maximum cost destruction operator: Calculate the cost value of each customer node and select the customer node to be deleted based on the largest U values. The cost value calculation formula for each node is as follows: cost i =d i-1,i +d i，i+1 The three insertion operators are as follows: (1) Randomly insert operators: randomly insert the destroyed operators into the destroyed solution individual paths. (2) Minimum cost insertion operator: Insertion is performed based on the cost value of the insertion position, and each deleted node is inserted into the position that minimizes the total cost. (3) Minimum waiting time insertion operator: Insertion is performed based on the waiting time of the insertion position, and each deleted node is inserted into the position that can minimize the total waiting time. In step 3: First, the Monte Carlo simulation method is used to simulate each piece of information in the vehicle routing problem using the following formula: in, For deterministic data, is the data after the uncertainty environment disturbance, δ is the range [-δ max , δ max ], which follows the prescribed probability distribution model. After the simulation, M scenarios are obtained. Then, the solution individuals obtained in the first stage are calculated in each scenario and the average fitness value of all scenarios is used as the fitness value under the uncertainty environment. After all the solution individuals have calculated the fitness values, these solution individuals are sorted using non-dominated sorting, and the last N solution individuals are taken as the final robust optimal solution for data, and the whole method ends.

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