NSGA-II algorithm-based intensive storage network vehicle path crowd target optimization method

Abstract

The invention discloses an intensive storage network vehicle path crowd target optimization method based on an NSGA-II algorithm, and belongs to the technical field of vehicle path optimization, and the method comprises the steps: firstly, building a crowd target optimization model which comprises a plurality of targets such as transportation cost, time cost and path length; thirdly, performing population initialization and selection through an NSGA-II algorithm, and adopting non-dominated sorting and crowding distance calculation to ensure that a Pareto optimal solution is searched in a crowd target space; then, the diversity of solutions is improved through crossover and mutation operation, and therefore the convergence process of the algorithm is accelerated; and finally, continuously iterating and updating the population to ensure that the optimal solution of the global scheme is found. According to the intensive storage network vehicle path crowd target optimization method based on the NSGA-II algorithm provided by the invention, an effective solution is provided for vehicle path optimization of an intensive storage network, and decision makers can be supported to make more reasonable transportation arrangements in a complex logistics environment.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle path optimization, and in particular to a multi-objective optimization method for vehicle paths in an intensive warehousing network based on an NSGA-II algorithm. Background Art

[0002] With the rapid development of the global economy, the demand for logistics industry is growing, especially in e-commerce and manufacturing, where intensive warehousing network has become the key to improving operational efficiency and reducing costs. The design of intensive warehousing network not only involves the site selection and layout of warehouses, but also the scheduling and route optimization of vehicles to achieve the best allocation of resources and efficient logistics services.

[0003] Traditional vehicle routing optimization methods mostly focus on a single objective, such as minimizing transportation costs or maximizing service levels. However, in practical applications, there are conflicts between multiple objectives, such as cost, time, service quality, and environmental impact. In this context, multi-objective optimization has become an important research direction for improving the performance of logistics systems, especially in complex intensive warehousing networks. How to balance these objectives has become an urgent problem to be solved.

[0004] NSGA-II (Non-dominated Sorting Genetic Algorithm II) is an evolutionary algorithm widely used in multi-objective optimization. It has attracted attention for its ability to effectively find Pareto optimal solutions in the objective space. The algorithm maintains the diversity of the population and the non-dominated sorting mechanism, allowing the optimization process to explore the solution space more comprehensively. In the vehicle routing optimization of intensive warehousing networks, NSGA-II can consider multiple objectives at the same time and provide decision makers with more valuable reference solutions, thereby improving overall logistics efficiency and reducing operating costs. With the rapid development of intelligent and digital technologies, combining the NSGA-II algorithm with modern data processing technology can further improve the effect of vehicle routing optimization in intensive warehousing networks and promote the sustainable development of the logistics industry. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-objective optimization method for vehicle paths in an intensive warehousing network based on the NSGA-II algorithm to solve the problems existing in the above-mentioned background technology. The NSGA-Ⅱ multi-objective optimization algorithm is used to optimize the multi-segment paths extracted from OSRM to achieve the optimal path selection that takes into account multiple indicators such as transportation cost, delivery time and service quality.

[0006] To achieve the above object, the present invention provides a multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm, comprising the following steps:

[0007] S1. Clarify the optimization objectives, such as transportation cost, time expenditure and service quality, and establish a multi-objective optimization function model to meet the optimization needs;

[0008] S2, using natural coding to encode feasible routes to form an individual, and extracting the generated map path data from OSRM to support subsequent path evaluation;

[0009] S3, randomly generate n individuals to form an initial population, and perform non-dominated sorting on the individuals, identify the non-inferior level of each individual, and stratify the population for subsequent selection;

[0010] S4, using the two-dimensional tournament selection method, giving priority to individuals with low non-inferior levels, and selecting individuals with high crowding when the levels are the same. On this basis, performing crossover operations to generate new offspring individuals, and performing mutation operations to introduce randomness and enhance population diversity;

[0011] S5, combining the parent and child populations, re-sorting the non-inferior layers and recalculating the crowding degree to form a new population;

[0012] S6, check whether the set termination condition is met, if the condition is met, end the algorithm and output the result;

[0013] S7. Analyze the results of the final population, extract the optimal solution, and verify and evaluate the optimization results.

[0014] Preferably, the multi-objective optimization function model is established in S1, and the specific functions include:

[0015] a. Transportation cost optimization function:

[0016] Where f1 is the total transportation cost, c j is the unit transportation cost of vehicle k performing the jth task, d j is the distance that vehicle k takes to perform the jth task, M is the number of vehicles, and N k is the number of missions for vehicle k;

[0017] b. Delivery time optimization function:

[0018] Where f2 is the total delivery time, t j is the travel time of vehicle k to perform the jth task, and W is the total waiting time at each delivery point;

[0019] c. Service quality optimization function:

[0020] Where f3 is the average service quality, α iis the customer satisfaction score for the time when the k-th vehicle performs the i-th task (the more time it takes, the lower the score), β i is the customer’s service feedback score for the k-th vehicle when performing the i-th task (which can be obtained through customer surveys);

[0021] d. The NSGA-Ⅱ optimization algorithm attempts to find the Pareto Front, on which the improvement of any one objective will lead to the deterioration of at least one other objective.

[0022] Preferably, the natural coding in S2 is specifically as follows: determining a coding scheme, such as representing each feasible path with a natural number, and encoding each customer with a unique natural number; and representing the feasible path as a sequence, which is:

[0023] (0,i 11 ,i 12 ,…,i 1s ,0,i 21 ,…,i 2t ,0,…,0,i m1 ,…,i mw ).

[0024] Preferably, S3 specifically includes:

[0025] S31, randomly generate n individuals, each of which represents a possible path solution to ensure that the entire search space is covered;

[0026] S32. Evaluate each individual to determine its performance on multiple objectives. On this basis, stratify the individuals into multiple non-inferior levels (such as F1, F2, F3, etc.), each of which contains all non-dominated individuals.

[0027] S33. Calculate the crowding degree of individuals in each level to measure the diversity among individuals. The formula is:

[0028]

[0029] Among them, D c represents the congestion degree, M is the number of vehicles, and f i (P j+1 ) is the target f i Next P j+1 The value of f i (P j-1 ) is the target f i Next P j-1 The value of f i max is the target i The maximum value of all individuals under i min is the targeti The minimum value of all individuals.

[0030] Preferably, S4 is specifically as follows: adopting the secondary tournament selection method, first selecting individuals according to the non-inferior level, and if they are in the same level, selecting them according to the crowding degree, and recording the selected individuals for crossover and mutation, which is:

[0031]

[0032] Preferably, the crossover operation in S4 is specifically as follows: two parent individuals are selected for crossover to generate new offspring individuals, and the crossover adopts single-point crossover or multi-point crossover to ensure that the offspring individuals still meet the path feasibility.

[0033] Preferably, the mutation operation in S4 is specifically: mutating each offspring individual with a certain probability, changing part of the path to introduce new genes, and the mutation methods include exchanging positions, inserting or reversing subpaths, etc.

[0034] Preferably, S5 is specifically:

[0035] S51, merging the parent generation and the offspring individuals to form a new population, the size of the new population being the sum of the number of the parent generation and the number of the offspring individuals;

[0036] S52, perform non-dominated sorting on the merged population again, stratify and calculate the crowding degree, identify the best individual and retain it for the next iteration;

[0037] S53, check whether the set termination condition (such as the maximum evolution number MaxGen) is reached. If not, return to S3 to continue execution until the termination condition is met.

[0038] Preferably, S6 is specifically:

[0039] S61, setting termination conditions, including the maximum number of iterations, fitness threshold and population diversity. At the end of each iteration, collecting the best individual fitness, average fitness and diversity index of the current population;

[0040] S62. Evaluate whether the termination condition is met. If the maximum number of iterations or the fitness threshold exceeds the set threshold or the diversity is lower than the set threshold, record the result and terminate the algorithm; otherwise, continue to perform selection, crossover and mutation to generate a new population and enter the next round of iteration.

[0041] Preferably, S7 is specifically:

[0042] S71, extracting individuals with high fitness in the final population as the optimal solution, and evaluating their performance;

[0043] S72. Use visualization tools to display the fitness changes and diversity during the optimization process, help analyze the performance of the algorithm, collect feedback to identify excellent individuals and operations, and adjust algorithm parameters when necessary to improve the results of subsequent iterations; if the results do not meet the preset requirements, re-evaluate the optimization model and proceed to the next round of iterations.

[0044] Therefore, the present invention adopts the above-mentioned multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm, which has the following beneficial effects:

[0045] (1) Improve the efficiency and reliability of vehicle dispatch by solving multi-objective optimization problems;

[0046] (2) It effectively balances multiple optimization objectives and generates a high-quality Pareto solution set, which can provide decision support for actual vehicle scheduling problems;

[0047] (3) The NSGA-II algorithm shows good adaptability in dealing with complex constraints and trade-offs between multiple objectives. Compared with traditional path optimization methods, it significantly improves the intelligence level of path planning and the operating efficiency of the system.

[0048] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic diagram of a multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm of the present invention;

[0050] Figure 2 It is a schematic diagram of iterative operation in the present invention;

[0051] Figure 3 Schematic diagram of the multi-vehicle path population model in the present invention. DETAILED DESCRIPTION

[0052] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] See also Figure 1 , a multi-objective optimization method for vehicle routing in intensive warehousing networks based on the NSGA-II algorithm, which achieves optimal configuration of vehicle routing by simultaneously considering multiple objectives such as transportation cost, delivery time and service quality, so as to improve the overall operation efficiency of the warehousing network. Specifically, it includes the following steps:

[0054] S1. Use natural number coding to encode feasible routes.

[0055] (0,i 11 ,i 12 ,…,i 1s ,0,i 21 ,…,i 2t ,0,…,0,i m1 ,…,i mw );

[0056] This is denoted as an individual I, where i kj Indicates the i kj task, k represents the vehicle number. It can be understood as starting from the starting transfer station 0 and passing the task location i 11 ,i 12 ,…,i 1s After that, it finally returns to the starting point transfer station 0, forming sub-path 1; then it starts from starting point 0 and passes through task location i 21 ,…,i 2t Then return to the starting point 0 to form subpath 2; and repeat this process until all task locations have been visited.

[0057] S2. Extract all map path data created in S1 returned from OSRM.

[0058] Specifically, you can use the Python program to run code instructions:

[0059] returnf'http: / / router.project-osrm.org / route / v1 / driving /

[0060] {start_coords[1]},{start_coords[0]};{end_coords[1]},{end_coords[0]}'

[0061] This returns the path data required in OSRM.

[0062] S3. Define target optimization functions. Define target optimization functions such as the shortest time or distance function, the minimum fuel consumption function, and the minimum highway toll function.

[0063] The specific optimization function is as follows:

[0064] (1) Transportation cost optimization function:

[0065]

[0066] Where f1 is the total transportation cost, c jis the unit transportation cost of vehicle k to perform the jth task (depending on the specific situation), d j is the distance that vehicle k takes to perform the jth task, M is the number of vehicles, and N k is the number of missions for vehicle k.

[0067] (2) The delivery time optimization function is as follows:

[0068]

[0069] Where f2 is the total delivery time, t j is the travel time of vehicle k to perform the jth task, and W is the total waiting time at each delivery point.

[0070] (3) Service quality optimization function:

[0071]

[0072] Where f3 is the average service quality, α i is the customer satisfaction score for the time when the k-th vehicle performs the i-th task (the more time it takes, the lower the score), β i is the customer feedback score for the k-th vehicle when performing the i-th task (which can be obtained through customer surveys). The optimization algorithm tries to find a Pareto Front where an improvement in any one objective will lead to a deterioration in at least one other objective.

[0073] S4, generate the initial population. Randomly generate n individuals I1, I2, ..., I according to the coding structure in S1. n Among them, each individual represents a path selection, including the number of vehicles and the sub-path data of each vehicle.

[0074] Next, the fitness of each individual in the initial population generated in S4 is evaluated, that is, the transportation cost optimization function f1, the delivery time optimization function f2 and the service quality optimization function f3 of each path plan are calculated.

[0075] S5. Non-inferior stratification, also known as non-dominated sorting. There is a non-dominated definition in the NSGA-II algorithm, that is, if path A performs well under multiple objectives, there is no path B that satisfies all objectives and is not inferior to A, and at least one objective is better than A, then A is called the optimal solution under the multi-objective problem, that is, A is non-dominated. Such A is listed as the first non-inferior layer, and the individuals in this non-inferior layer are also regarded as the individuals with the highest fitness. In order to find the next non-inferior layer, the best non-inferior solution A can be removed from the population first, and the best non-inferior solution can be found in the remaining population to form the second non-inferior layer. And so on, until all individuals in the entire population are included in all levels of non-inferior layers.

[0076] S6. Crowding calculation. Calculate the crowding of each individual as the basis for selection. Crowding is used to measure the degree of "crowding" of an individual in its non-inferior layer. In other words, crowding can indicate the sparseness of an individual in the target space. The greater the crowding, the fewer solutions there are around the individual, and vice versa. Crowding can help the algorithm select more representative individuals to maintain the diversity of the population and prevent premature convergence. The specific calculation formula is as follows:

[0077]

[0078] Among them, D c represents the degree of crowding, M is the number of targets, and f i (P j+1 ) is the target f i Next P j+1 The value of f i (P j-1 ) is the target f i Next P j-1 The value of f i max is the target i The maximum value of all individuals under i min is the target i The minimum value of all individuals.

[0079] S7, selection operation. In this embodiment, the two-dimensional tournament selection is used, that is, two individuals are randomly selected from the entire population for comparison. First, the non-inferior levels of the two are compared, and the individual with a lower level, that is, the better individual, is selected; if the levels of the two are the same, the crowding of the two is compared, and the individual with a higher crowding level, that is, a higher diversity, is selected. The selected individuals are recorded for subsequent crossover and mutation operations.

[0080] Specifically:

[0081] Randomly select T individuals I1,I2,…,I T ;

[0082] Calculate the fitness for each individual;

[0083] Select the individual with the highest fitness as the selected individual, that is

[0084]

[0085] S8, crossover operation. The crossover operation aims to fuse two parent individuals to generate new offspring individuals. Specifically:

[0086] Randomly select two individuals P1 = (1, 2, 3, 4) and P2 = (5, 6, 7, 8) as parents, select crossover points for crossover combination to produce new offspring C1 = (1, 2, 7, 8) and C2 = (5, 6, 3, 4).

[0087] In the vehicle routing optimization problem, A, B, C, D, and E represent locations. The first two locations in parent generation 1 (A, B, C, D, E) can be combined with the last three locations in parent generation 2 (B, A, D, E, C) to form a child generation (A, B, D, E, C). This is a crossover operation and a new child generation is generated.

[0088] S9, mutation operation. Used to introduce randomness to prevent the algorithm from falling into a local optimal solution. In the multi-objective vehicle routing optimization problem, mutation usually involves random changes to the path. In the NSGA-II algorithm, crossover and mutation operations are usually used in combination. The mutation operation is used on the new individuals generated after the crossover operation in the previous step to further explore the space and enhance the diversity of the population.

[0089] There are two specific mutation operations:

[0090] (1) Exchange mutation:

[0091] Randomly select two genes i and j in individual I.

[0092] Swap the genes at these two positions:

[0093] I[i],I[j]→I[j],I[i];

[0094] (2) Reversal mutation:

[0095] Randomly select two positions C1 and C2 in individual I (C1 <C2);

[0096] Reverse the gene order of I[C1:C2]:

[0097] I[C1:C2]=reverse(I[C1:C2]).

[0098] S10, population update. Combine the parent and child populations, recalculate the non-inferiority stratification and crowding, and select the individuals with the best fitness from the combined population to be retained in the next generation. Usually, the first N individuals with the highest fitness are retained.

[0099] P″={I|I∈P∪P′, sorted by fitness}

[0100] Finally, the population is updated to P″, that is, P=P″.

[0101] S11, repeat steps 5 to 10 until the termination condition is reached. Regarding the setting of the termination condition, the maximum evolution number is used as a benchmark, that is, a maximum evolution number MaxGen is defined, and the termination condition is when the number of iterations reaches the maximum evolution number.

[0102] Furthermore, a fitness threshold can be defined, and when the fitness function reaches the threshold, the iteration operation is terminated.

[0103] Pareto frontier analysis:

[0104] After the optimization is completed, the Pareto front is extracted and analyzed to select a suitable solution.

[0105] like Figure 2 As shown in the figure, first, the population of initial solutions is randomly generated, and non-dominated sorting is performed according to the objective function (such as cost and time) to identify the superior solution; then, the congestion degree of each solution is calculated to maintain diversity. In the selection stage, the tournament selection method is used to select excellent individuals from the current population for crossover and mutation to generate the next generation population, which is then combined with the old population to select the top N items with the best fitness to form a new algorithm population to complete an iterative operation.

[0106] like Figure 3 As shown in the figure, each individual represents a path plan. In the individual shown in the figure, three vehicles travel three sub-paths to complete the entire task (the number of vehicles and sub-paths performing the task should be increased or decreased according to actual needs during the specific implementation). Finally, multiple such individuals form the population in the NSGA-II algorithm.

[0107] Therefore, the present invention adopts the above-mentioned multi-objective optimization method for vehicle paths in intensive warehousing networks based on the NSGA-II algorithm, and uses the NSGA-II multi-objective optimization algorithm to optimize the multi-segment paths extracted from OSRM, so as to achieve the optimal path selection that takes into account multiple indicators such as transportation cost, delivery time and service quality. First, the multi-segment path data is extracted from OSRM and preprocessed to conform to the format of algorithm calculation, and the path objective optimization function is defined. Secondly, the NSGA-II algorithm is introduced to generate the initial population, the individual fitness is evaluated and the non-dominated sorting and non-inferior layer crowding distance calculation are performed, and on this basis, a new generation of parent groups is selected. Finally, crossover and mutation operations are performed to generate offspring, the parent generation and the offspring are merged, and individuals with high fitness and diversity are selected, and it is continuously iterated until the final conditions are met.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm, characterized in that: The following steps are involved: S1. Clarify the optimization objectives and establish a multi-objective optimization function model; S2, encoding feasible routes using natural coding to form an individual, and extracting the generated map path data from OSRM; S3, randomly generate n individuals to form an initial population, and perform non-dominated sorting on the individuals, identify the non-inferior level of each individual, and stratify the population for subsequent selection; S4, using the two-dimensional tournament selection method, giving priority to individuals with low non-inferior levels, and selecting individuals with high crowding when the levels are the same. On this basis, a crossover operation is performed to generate new offspring individuals, and a mutation operation is performed to introduce randomness; S5, combining the parent and child populations, re-sorting the non-inferior layers and recalculating the crowding degree to form a new population; S6, check whether the set termination condition is met, if the condition is met, end the algorithm and output the result; S7. Analyze the results of the final population, extract the optimal solution, and verify and evaluate the optimization results.

2. According to claim 1, a multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm is characterized in that: The multi-objective optimization function model in S1 includes the following functions: a. Transportation cost optimization function: Where f1 is the total transportation cost, c j is the unit transportation cost of vehicle k performing the jth task, d j is the distance that vehicle k takes to perform the jth task, M is the number of vehicles, and N k is the number of missions for vehicle k; b. Delivery time optimization function: Where f2 is the total delivery time, t j is the travel time of vehicle k to perform the jth task, and W is the total waiting time at each delivery point; c. Service quality optimization function: Where f3 is the average service quality, α i is the customer's satisfaction score for the time when the k-th vehicle performs the i-th task, β i is the customer's service feedback score for the k-th vehicle when performing the i-th task; d. The NSGA-Ⅱ optimization algorithm tries to find the Pareto frontier, on which the improvement of any one objective will lead to the deterioration of at least one other objective.

3. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: The natural coding in S2 is specifically as follows: determining a coding scheme, such as each feasible path is represented by a natural number, and each customer is encoded with a unique natural number; And the feasible path is represented as a sequence: (0,i 11 ,i 12 ,…,i 1s ,0,i 21 ,…,i 2t ,0,…,0,i m1 ,…,i mw )。 4. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: S3 specifically includes: S31. Randomly generate n individuals, each of which represents a path solution; S32. Evaluate each individual to determine its performance on multiple goals, and on this basis, stratify the individuals into multiple non-inferior levels, each of which contains all non-dominated individuals; S33. Calculate the crowding degree of individuals in each level. The formula is: Among them, D c represents the congestion degree, M is the number of vehicles, and f i (P j+1 ) is the target f i Next P j+1 The value of f i (P j-1 ) is the target f i Next P j-1 The value of f i max is the target i The maximum value of all individuals under i min is the target i The minimum value of all individuals.

5. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: S4 is specifically as follows: using the two-dimensional tournament selection method, first select individuals according to the non-inferior level, if they are in the same level, select them according to the crowding degree, and record the selected individuals for crossover and mutation use, which is:

6. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: The crossover operation in S4 is specifically as follows: two parent individuals are selected for crossover to generate new offspring individuals, and the crossover adopts single-point crossover or multi-point crossover.

7. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: The mutation operation in S4 is as follows: mutate each offspring individual with a certain probability, change the path to introduce new genes, and the mutation methods include exchanging positions, inserting or reversing subpaths.

8. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1 is characterized in that: S5 is as follows: S51, merging the parent generation and the offspring individuals to form a new population, the size of the new population being the sum of the number of the parent generation and the number of the offspring individuals; S52, perform non-dominated sorting on the merged population again, stratify and calculate the crowding degree, identify the best individual and retain it for the next iteration; S53, check whether the set termination condition is met, if not, return to S3 to continue execution until the termination condition is met.

9. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1, characterized in that: S6 is specifically: S61, setting termination conditions, including the maximum number of iterations, fitness threshold and population diversity. At the end of each iteration, collecting the best individual fitness, average fitness and diversity index of the current population; S62. Evaluate whether the termination condition is met. If the maximum number of iterations or the fitness threshold exceeds the set threshold or the diversity is lower than the set threshold, record the result and terminate the algorithm; otherwise, continue to perform selection, crossover and mutation to generate a new population and enter the next round of iteration.

10. The multi-objective optimization method for vehicle routing in an intensive warehousing network based on the NSGA-II algorithm according to claim 1, characterized in that: S7 is specifically: S71, extracting individuals with high fitness in the final population as the optimal solution, and evaluating their performance; S72. Use visualization tools to display the fitness changes and diversity during the optimization process, collect feedback to identify excellent individuals and operations, and if the results do not meet the preset requirements, re-evaluate the optimization model and proceed to the next round of iteration.

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