Optimization method for multi-mode multi-target charging station site selection problem

Abstract

The invention discloses an optimization method for a multi-modal multi-target charging station site selection problem, and the method comprises the steps: 1, initializing a population, and generating a layout scheme of an initial charging station based on demand point data; step 2, generating a new layout scheme through self-adaptive selection, crossover and mutation operation; and step 3, retaining a multi-modal solution, maintaining population diversity by adopting an improved crowding distance and a special crowding distance, and screening out a high-quality scheme by applying a non-dominated sorting and proportional selection mechanism. According to the novel multi-modal multi-objective optimization method for charging station site selection, optimization is carried out at the same time from the two dimensions of multi-modal features and multi-objective tradeoff, more multi-modal solutions can be found while the Pareto optimal solution is found, and a more efficient solution is selected according to the specific requirements of a user.

Description

Technical Field

[0001] This invention relates to the field of spatial layout optimization and facility site selection technology, and in particular to an optimization method for multimodal and multi-objective charging station site selection problem. Background Technology

[0002] The Electric Vehicle Charging Station Location Problem (EVCSLP) is a classic problem in the field of facility location optimization, dating back to the early days of large-scale electric vehicle deployment in the early 21st century. Its core objective is to determine the optimal location of charging stations within a given region, considering factors such as the transportation network and the distribution of potential charging demand, to meet the charging needs of all electric vehicle users while optimizing objectives such as construction cost, coverage, and grid load. EVCSLP integrates multiple fields including traffic planning, power systems, computational geometry, and multi-objective optimization, and is an important branch of NP-hard problems. In recent years, heuristic and metaheuristic algorithms have demonstrated outstanding performance in this field, such as genetic algorithms, particle swarm optimization, simulated annealing, ant colony systems, and deep reinforcement learning. These algorithms, by simulating natural evolution, swarm intelligence, or physical annealing processes, exhibit their respective advantages under complex constraints and large-scale scenarios.

[0003] With the improvement of computing power and the progress of algorithm research, charging stations, as a key infrastructure supporting the energy supply of electric vehicles, are receiving increasing attention. Appropriate charging station locations can cover high-demand areas, meet the diverse charging needs of taxis, ride-hailing vehicles, and private cars, and also alleviate range anxiety for long-distance travel, ensuring the smooth passage of electric vehicles across cities and provinces. The application scenarios of charging station site selection technology span all levels of urban and transportation systems: in the logistics and ride-hailing industries, it helps fleets optimize battery swapping routes and reduce empty-running rates; on the power grid side, it guides the expansion and upgrading of the distribution network, avoiding the hazards caused by concentrated charging loads; in post-disaster emergency scenarios, site selection algorithms can quickly reconstruct temporary charging networks, ensuring energy replenishment for rescue vehicles, becoming an indispensable infrastructure decision-making tool for resilient cities. By improving resource utilization efficiency and the scientific nature of decision-making, research on charging station site selection has brought significant value and results to various fields in real life.

[0004] The planning and construction of charging stations requires comprehensive consideration of numerous factors, including urban road network layout, station location, and regional needs. To fully meet users' charging demands, these factors must be systematically considered to significantly improve user experience and satisfaction. Therefore, the number and distribution of charging stations are extremely important. On the one hand, it's crucial to ensure that the distribution of charging facilities matches users' actual needs, avoiding inconvenience caused by insufficient infrastructure. On the other hand, it's also essential to avoid resource idleness and waste due to over-construction. Therefore, the site selection and layout of charging stations is essentially a complex and challenging multi-objective optimization problem, requiring a balance between meeting user needs and effectively utilizing resources.

[0005] Obtaining multiple equivalent solutions is equally important in charging station site selection. Most studies focus only on the number of charging stations to be built, neglecting the selection of which sites to choose. In many practical problems, even if the optimal site selection scheme is found, it may be impractical due to excessive construction costs. For example, if some areas are far from the grid connection point, the high construction cost makes the charging station scheme unreasonable. However, if multiple solutions are provided simultaneously, users can choose a more suitable solution set based on their preferences or the characteristics of the actual problem. Research on multimodal, multi-objective charging station site selection problems is not only theoretically significant but also has a profound impact on optimizing efficiency, reducing costs, and providing more flexible and efficient solutions in practical applications. Summary of the Invention

[0006] This invention conducts an in-depth study on the multimodal and multi-objective nature of the traditional charging station site selection problem. Based on the multimodal and multi-objective site selection problem, it provides a discrete multi-objective optimization method. This optimization method can find the optimal Pareto front while providing multiple multimodal solutions to meet the preferences and needs of different users.

[0007] The technical solution adopted in this invention is as follows:

[0008] An optimization method for the multimodal, multi-objective charging station site selection problem includes the following steps:

[0009] Step 1: Initialize the population and generate an initial layout scheme for charging stations based on demand point data;

[0010] Step 2: Generate offspring layout schemes through adaptive selection, crossover, and mutation operations;

[0011] Step 3: Maintain population diversity by using improved crowding distance and special crowding distance, and select high-quality schemes by combining non-dominated ranking and proportional selection mechanisms.

[0012] Furthermore, in step 1, the specific steps are as follows:

[0013] Step 1.1: Initialize a population of size P, and use 0-1 encoding to represent the charging station site selection scheme for each individual in the population;

[0014] Step 1.2, calculate the two objective function values ​​for each individual in the initial population:

[0015] Objective 1: Number of charging stations, n;

[0016] Objective 2: User satisfaction. Satisfaction is measured by the product of user demand and the distance from the point of demand to the charging station, as shown in the following formula:

[0017]

[0018] Where i represents the demand point, j represents the charging station, and h i d represents the demand at demand point i. ij Let represent the distance from demand point i to charging station j, n represent the number of charging stations to be built, and m represent the number of demand points that need to reach charging station j for charging.

[0019] Furthermore, step 1.2 specifically includes the following steps:

[0020] Step 1.2.1: For each individual, first calculate the number of charging stations and determine the location of the charging stations, and select the nearest charging station for each demand point;

[0021] Step 1.2.2: Collect the area served by each charging station and treat it as a cluster. In the cluster, treat each demand point as a charging station and consider it as a solution.

[0022] Step 1.2.3: Calculate the objective 2 value for each scheme, select the scheme with the smallest objective 2 value, and update the individual.

[0023] Furthermore, step 2 specifically includes the following steps:

[0024] Step 2.1: Enter the main loop and adaptively select five individuals from the entire population using three methods;

[0025] Step 2.2, Mutation operation: Based on the selected individual and the two generated difference vectors, generate the mutated individual according to the following formula;

[0026]

[0027] in, For the selected individuals, r1, r2, r3, r4, and r5 are the indices of the five different individuals selected in step 2.1, and F∈[0,1] is the scaling factor;

[0028] Step 2.3, crossover operation, in the mutated individual v iBinomial crossover is performed between the target individual and the offspring individual u. i ;

[0029] Step 2.4: Iterate continuously before reaching the stopping condition to generate a offspring population O, and calculate the two objective function values ​​for each individual in the offspring population O.

[0030] Furthermore, in step 2.1, the three adaptive selection strategies include the following steps:

[0031] Step 2.1.1, the three selection strategies are as follows:

[0032] Method 1: Randomly select five individuals from the entire population, namely:

[0033] Method 2: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual and the remaining individuals in the entire population in the decision space; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the decision space as the next most popular individual. The other four are respectively

[0034] Method 3: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual in the target space and the remaining individuals in the entire population; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the target space as the target individual. The other four are respectively

[0035] Step 2.1.2: Adaptively select a strategy, choosing method 1 with probability p1, method 2 with probability p2, and method 3 with probability p3, where p1, p2, and p3 are respectively:

[0036]

[0037] p2 = (1 - p1) / 2

[0038] p3 = 1 - p1 - p2

[0039] Among them, G c G represents the current iteration number, and Max_gen represents the maximum iteration number; therefore, as the current generation G increases... c The values ​​gradually increase from 1 to Max_gen, p1 decreases from 1 to 0, while p2 and p3 gradually increase from 0 to 0.5.

[0040] Furthermore, in step 2.3, the crossover operation includes the following steps:

[0041] Step 2.3.1: Using a binomial crossover method, generate a random number rand(0,1) for each dimension j of the individual;

[0042] Step 2.3.2: For each dimension, if rand(0,1) is less than the crossover probability CR, then retain the value from the mutated individual;

[0043] Step 2.3.3, otherwise, retain the original target individual's value.

[0044] Furthermore, in step 3, the environment selection includes the following steps:

[0045] Step 3.1: Combine the parent population P and the offspring population O to form a new population P_combination;

[0046] Step 3.2: Perform non-dominated sorting on P_combination to identify the better solution in the multi-objective optimization problem;

[0047] Step 3.3: Calculate the improved crowding distance for each individual in the combined population P_combination;

[0048] Step 3.4: Calculate the specific crowding distance for each individual;

[0049] Step 3.5: Based on the calculated crowding distance, select a certain proportion of individuals from P_combination to form a new population P, which helps to balance the diversity and quality of the solution.

[0050] Step 3.6: Iterate in a loop until the stopping condition is met. Use the new population obtained in step 3.5 as the parent population in the main loop and execute steps 2 to 3 above. When the termination condition is met, end the loop and output the final optimized population P. These individuals represent the high-quality solutions in the multi-objective optimization problem.

[0051] Furthermore, in step 3.3, the improved calculation of congestion distance includes the following steps:

[0052] Step 3.3.1: In the target space, determine the true neighboring individuals of each individual based on the individuals with lower non-dominant levels that have already been selected;

[0053] Step 3.3.2: Calculate the distance between an individual and its neighboring individuals based on the value of each individual on each objective function;

[0054] Step 3.3.3: Sum the distances across all objective functions to obtain the crowding distance CD of the individual in the objective space. f ;

[0055] Step 3.3.4, in the decision space, calculate the similarity between each individual and its adjacent individuals as its crowding distance CD in the decision space x .

[0056] Furthermore, in Step 3.4, the calculation of the special crowding distance includes the following steps:

[0057] Step 3.4.1, calculate the average crowding distance CD of all individuals in the decision space avg,x and the average crowding distance CD of individuals in the objective space avg,f ;

[0058] Step 3.4.2, compare the CD x 、CD f of each individual with the average crowding distance, and calculate the special crowding distance SCD of the individual through the following formula:

[0059]

[0060] Furthermore, in Step 3.5, the environmental selection includes the following steps:

[0061] Step 3.5.1, according to the calculated crowding distance, select a certain proportion of individuals from P_combination according to the following formula, and only select a certain percentage of the elements in the previous ranking;

[0062]

[0063] where Gc is the current iteration number, and Max_gen is the maximum iteration number; when the iteration number is 1, the proportion of selecting individuals in the Pareto front is R (0 < R < 1); when the iteration number is G, the proportion of selecting individuals in the Pareto front is 1, and in this invention, G is equal to the maximum iteration number Max_gen.

[0064] Step 3.5.2, select corresponding individuals according to the non-dominated sorting and crowding distance sorting to form a new population P, and output the finally optimized high-quality solution.

[0065] The beneficial effects of this invention are as follows:

[0066] 1. This invention proposes an optimization method based on multi-modal multi-objectives for the problem of charging station location. For this multi-objective optimization problem of charging station location, the number of charging stations and the site distribution are crucial: on the one hand, it is necessary to ensure that the distribution of charging facilities matches the actual needs of users to avoid inconvenience in charging due to insufficient facilities; on the other hand, it is also necessary to prevent over-construction resulting in idle and wasted resources. This invention takes the number of built stations and user satisfaction as two optimization objectives, aiming to achieve a balance between meeting user needs and effectively utilizing resources.

[0067] 2. During the selection process, this invention adaptively selects individuals and their neighbors to participate in offspring generation based on the crowding level of solutions in the decision space or target space. This balances the exploration and development capabilities of individuals and enhances their diversity in both the decision and target spaces. Simultaneously, during the environment selection process, individuals with high non-dominant levels are selected in a certain proportion to further enhance the diversity of solutions in the decision space. Therefore, this invention can provide more multimodal solutions while maintaining the objective value unchanged, allowing users to choose a more suitable solution set based on their preferences or the characteristics of the actual problem.

[0068] 3. Addressing the discrete nature of the charging station site selection problem, this invention improves the initialization process and congestion distance calculation of the continuous optimization algorithm, effectively transforming it from a continuous optimization process to a discrete optimization problem. This not only enhances the algorithm's global search capability and convergence efficiency but also effectively balances multiple optimization objectives such as site coverage and user convenience, providing a new solution for high-dimensional combinatorial optimization problems like charging station site selection. Attached Figure Description

[0069] Figure 1 Here is the overall flowchart of the algorithm;

[0070] Figure 2 A location map of the demand points;

[0071] Figure 3 Comparison of the number of multimodal solutions for different algorithms;

[0072] Figure 4 A comparison of the Pareto fronts of different algorithms;

[0073] Figure 5 The graph shows the convergence curves for different algorithms. Detailed Implementation

[0074] The present invention will be further described below with reference to the accompanying drawings and examples.

[0075] The following is an embodiment of the present invention. In this embodiment, charging demand data from 30 regions are used, as shown in Table 1. Each region is considered a demand point, and each demand point may be identified as a potential charging station. The locations of the 30 demand points are as follows: Figure 2 As shown.

[0076] Table 1 Demand for each region

[0077]

[0078]

[0079] This invention is an optimization method for the multimodal, multi-objective charging station site selection problem, comprising the following steps:

[0080] Step 1: Randomly initialize the solution and generate an initial charging station layout scheme based on the demand point data; the specific steps are as follows:

[0081] Step 1.1: Initialize the population according to the problem size. The population size is P. Each individual in the population represents a potential solution, using 0-1 encoding. The lower bound of the decision variable is 0, and the upper bound is 1.

[0082] Step 1.2, calculate the two objective function values ​​for each individual in the initial population:

[0083] Objective 1: Number of charging stations, n;

[0084] Objective 2: User satisfaction. Satisfaction is measured by the product of user demand and the distance from the point of demand to the charging station. The longer the total distance, the lower the satisfaction; the shorter the total distance, the higher the satisfaction, as shown in the following formula:

[0085]

[0086] Where i represents the demand point, j represents the charging station, and h i d represents the demand at demand point i. ij Let represent the distance from demand point i to charging station j, n represent the number of charging stations to be built, and m represent the number of demand points that need to reach charging station j for charging.

[0087] Step 1.2 specifically includes the following steps:

[0088] Step 1.2.1: For each individual, first calculate the number of charging stations and determine the location of the charging stations, and select the nearest charging station for each demand point;

[0089] Step 1.2.2: Collect the area served by each charging station and treat it as a cluster. In the cluster, treat each demand point as a charging station and consider it as a solution.

[0090] Step 1.2.3: Calculate the objective 2 value for each scheme, select the scheme with the smallest objective 2 value, and update the individual.

[0091] like Figure 1 As shown, an initial population of P size is randomly generated in the search space, and the fitness values ​​of the population are evaluated. Based on the above example, the population size in this invention is 200. After calculating the fitness values ​​of individuals in the population, the process proceeds to step 2.

[0092] Step 2: Based on the initial population obtained in Step 1, new layout schemes are generated through adaptive selection, crossover, and mutation operations. Specific steps include:

[0093] Step 2.1: Enter the main loop and adaptively select five individuals from the entire population using three methods, thereby increasing the diversity of the decision space and the target space;

[0094] In step 2.1, the three adaptive selection strategies include the following steps:

[0095] Step 2.1.1, the three selection strategies are as follows:

[0096] Method 1: Randomly select five individuals from the entire population, namely:

[0097] Method 2: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual and the remaining individuals in the entire population in the decision space; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the decision space as the next most popular individual. The other four are respectively

[0098] Method 3: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual in the target space and the remaining individuals in the entire population; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the target space as the target individual. The other four are respectively

[0099] Step 2.1.2: Adaptively select a strategy, choosing method 1 with probability p1, method 2 with probability p2, and method 3 with probability p3, where p1, p2, and p3 are respectively:

[0100]

[0101] p2 = (1 - p1) / 2

[0102] p3 = 1 - p1 - p2

[0103] Among them, G c G represents the current iteration number, and Max_gen represents the maximum iteration number; therefore, as the current generation G increases... c The values ​​gradually increase from 1 to Max_gen, p1 decreases from 1 to 0, while p2 and p3 gradually increase from 0 to 0.5.

[0104] The adaptive selection strategy balances an individual's exploration and development capabilities, and enhances the diversity of individuals in the decision space and goal space.

[0105] Step 2.2, Mutation operation: Based on the selected individual and the two generated difference vectors, generate the mutated individual according to the following formula;

[0106]

[0107] in, To select individuals, r1, r2, r3, r4, and r5 are the indices of the five different individuals selected in step 2.1, and F∈[0,1] is the scaling factor; in this embodiment, F is 0.5; the specific mutation process is as follows:

[0108]

[0109] v i =0 1 0 1 0.5 1 0 0 -1 1.5

[0110] For mutated individuals, a truncation process is applied: when a value in a certain dimension exceeds a preset upper limit, the upper limit value is used; when it falls below a preset lower limit, the lower limit value is used; only when the value is between the upper and lower limits is the original value retained.

[0111] v i =0 1 0 1 1 1 0 0 0 1.

[0112] Step 2.3, crossover operation, in the mutated individual v i Crossing with the target individual to generate offspring individuals u i The specific steps are as follows:

[0113] Step 2.3.1: Using a binomial crossover method, generate a random number rand(0,1) for each dimension j of the individual;

[0114] m=0.05 0.2 0.7 0.3 0.03 0.5 0.4 0.7 0.06 0.9

[0115] Step 2.3.2: For each dimension, if rand(0,1) is less than the crossover probability CR, then the value from the mutated individual is retained. In this invention, the crossover probability CR is taken as 0.1, so m can be taken as:

[0116] m = 1 0 0 0 1 0 0 0 1 0

[0117] Therefore, the values ​​of the variant individuals are preserved at positions 1, 5, and 9.

[0118] Step 2.3.3: If rand(0,1) is greater than or equal to the crossover probability CR, retain the original values ​​of the target individual. That is, retain the original values ​​of the target individual at positions 2, 3, 4, 6, 7, 8, and 10, where n is the target individual. iThe value is [1 1 0 0 1 0 0 1 0 0], therefore the offspring individuals u produced by crossover are... i as follows:

[0119] u i =0 1 0 0 1 0 0 1 0 0

[0120] Step 2.4: Iterate continuously before reaching the stopping condition to generate offspring population O, and evaluate offspring population O (in the same way as in step 1.2) to calculate the value of each individual on the multi-objective function.

[0121] Based on the parent population obtained in step 1 and the offspring population obtained in step 2, proceed to step 3.

[0122] Step 3: Retain multimodal solutions, maintain population diversity using improved crowding distance ICD and special crowding distance SCD, and select high-quality solutions using non-dominated ordination and proportional selection mechanisms.

[0123] Step 3.1: Combine the parent population P and the offspring population O to form a new population P_combination;

[0124] Step 3.2: Perform non-dominated sorting on P_combination to identify the solution that performs better in the multi-objective optimization problem;

[0125] Step 3.3: Calculate the improved crowding distance for each individual in the merged population P_combination;

[0126] In step 3.3, the improved calculation of congestion distance includes the following steps:

[0127] Step 3.3.1: In the target space, determine the true neighbors of each individual based on the individuals with low non-dominant levels who have already been selected;

[0128] Step 3.3.2: Calculate the distance between an individual and its neighboring individuals based on the value of each individual on each objective function;

[0129] Step 3.3.3: Sum the distances across all objective functions to obtain the crowding distance CD of the individual in the objective space. f ;

[0130] Step 3.3.4: In the decision space, calculate the similarity between each individual and its neighboring individuals as its crowding distance CD in the decision space. x .

[0131] Step 3.4: Calculate the specific crowding distance for each individual;

[0132] In step 3.4, the specific steps for calculating the special congestion distance are as follows:

[0133] Step 3.4.1, calculate the average crowding distance CD of all individuals in the decision space avg,x and the average crowding distance CD of individuals in the objective space avg,f ;

[0134] Step 3.4.2, compare the CD x , CD f of each individual with the average crowding distance, and calculate the special crowding distance SCD of the individual through the following formula:

[0135]

[0136] Introduce the non-dominated rank into the special crowding distance to increase the possibility of individuals with a higher non-dominated rank being selected during the evolution process and enhance the population diversity.

[0137] Step 3.5, select a certain proportion of individuals from P_combination according to the calculated crowding distance to form a new population P, which helps to balance the diversity and quality of the solutions;

[0138] Furthermore, in Step 3.5, the proportional selection includes the following steps:

[0139] Step 3.5.1, select a certain proportion of individuals from P_combination according to the calculated crowding distance according to the following formula, and only select a certain percentage of the elements in the previous sorting;

[0140]

[0141] where Gc is the current iteration number, and Max_gen is the maximum iteration number; when the iteration number is 1, the proportion of individuals selected in the Pareto front is R (0 < R < 1), and in this invention, R takes 0.5; when the iteration number is G, the proportion of individuals selected in the Pareto front is 1, and in this invention, G is equal to the maximum iteration number Max_gen. ​​​​​​​There are two key points in solving the multimodal, multi-objective charging station site selection problem: first, how to balance the two optimization objectives of the number of charging stations to be built and user demand; and second, how to quickly converge to the optimal solution within limited computing resources while obtaining as many multimodal solutions as possible. To solve this problem, this invention proposes a novel multimodal, multi-objective optimization method, the core of which lies in simultaneously optimizing from two dimensions: multimodal characteristics and multi-objective trade-offs.

[0145] Regarding the first key point, this invention uses the number of websites and user satisfaction as two optimization objectives. Fewer websites result in lower construction costs, but also lower user satisfaction; a larger number of websites significantly improves user satisfaction, but over-construction can lead to low utilization rates for some sites, resulting in resource waste. Therefore, this invention optimizes both objectives simultaneously, providing users with a solution where both objective values ​​are better.

[0146] Regarding the second key point, to retain more multimodal solutions, this invention first employs an improved crowding distance, treating individuals with low non-dominated levels as neighborhood individuals. Second, it introduces non-dominated levels when calculating special crowding distances. Since individuals with higher non-dominated levels are far from the Pareto front in the target space and are unlikely to be selected for the next generation, the diversity of their decision space is more important than the diversity of the target space. By increasing the diversity of the decision space, the search range can be expanded, increasing the probability of finding more Pareto optimal solutions. At the same time, individuals with high non-dominated levels are selected in a certain proportion during environment selection to maintain the diversity of the decision space, thereby obtaining more multimodal solutions.

[0147] Combining the above strategies, this invention can ensure rapid convergence to the optimal Pareto front within limited computational resources in the multimodal and multi-objective charging station site selection problem, avoid getting trapped in local optima, and obtain as many multimodal solutions as possible.

[0148] In the above example, three optimization algorithms were used to solve the problem: MMODE_ICD (a multimodal multi-objective differential evolution algorithm based on improved crowding distance), MO_Ring_PSO_SCD_Bi (a multi-objective particle swarm optimization algorithm based on ring topology and special crowding distance), and MOPSO (a multi-objective particle swarm optimization algorithm). The population size for each algorithm was set to 200, and the maximum number of iterations was 500. The results obtained by different algorithms were evaluated using the number of equivalent subsets and the inverse generation distance (IGD).

[0149] Figure 3 This reflects the number of multimodal solutions found by three different algorithms across 30 demand points. Figure 3As can be seen, regardless of the number of charging stations built, the MOPSO algorithm can only find one optimal station construction scheme because it removes equivalent subsets during the environment selection process. When planning to build two charging stations, the MMODE_ICD algorithm performs slightly worse, finding only two equivalent multimodal solutions, while the MO_Ring_PSO_SCD_Bi algorithm finds 11 multimodal solutions. When building three charging stations, the MO_Ring_PSO_SCD_Bi algorithm finds six multimodal solutions, while the MMODE_ICD algorithm finds seven. When the number of charging stations is greater than three, the MO_Ring_PSO_SCD_Bi algorithm, like the MOPSO algorithm, can only provide one solution set, i.e., one scheme. However, the MMODE_ICD algorithm can provide multimodal solutions in most cases. Figure 3 As can be seen, both MMODE_ICD and MO_Ring_PSO_SCD_Bi can provide decision-makers with better solutions for charging station construction. However, the MMODE_ICD algorithm used in this invention finds more multimodal solutions and has better performance.

[0150] Figure 4 The Pareto fronts (PF) obtained by the three algorithms are shown. Figure 4 As shown, the MMODE_ICD algorithm outperforms MO_Ring_PSO_SCD_Bi and MOPSO. This is because, when the planned number of charging stations is the same, MMODE_ICD can find a better solution than MO_Ring_PSO_SCD_Bi and MOPSO. Although the power factor (PF) of the MMODE_ICD and MOPSO algorithms are very similar, MMODE_ICD can find a larger solution set and its obtained PF range is wider.

[0151] Figure 5 The convergence curves of the three algorithms are shown. The IGD value of the MMODE_ICD algorithm decreases rapidly in the early iterations and gradually drops to near 0 after about 100 iterations. Therefore, it can be seen from the figure that the convergence speed of the MMODE_ICD algorithm is significantly better than the other two algorithms. Furthermore, the MMODE_ICD algorithm maintains the lowest IGD value throughout the entire iteration process, indicating that its solution set is closest to the true PF and has the best performance.

[0152] In summary, the MMODE_ICD algorithm outperforms other algorithms in terms of multimodal performance, providing users with a more flexible and efficient solution. Although its performance is relatively poor in some charging station scenarios, it can still find multimodal solutions. Therefore, the MMODE_ICD algorithm is superior to other algorithms overall.

Claims

1. An optimization method for a multimodal, multi-objective charging station site selection problem, characterized in that, Includes the following steps: Step 1: Initialize the population and generate an initial layout scheme for charging stations based on demand point data; Step 2: Generate offspring layout schemes through adaptive selection, crossover, and mutation operations; Step 3: Maintain population diversity by using improved crowding distance and special crowding distance, and select high-quality schemes by combining non-dominated ranking and proportional selection mechanisms.

2. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1.1: Initialize a population of size P, and use 0-1 encoding to represent the charging station site selection scheme for each individual in the population; Step 1.2, calculate the two objective function values ​​for each individual in the initial population: Objective 1: Number of charging stations, n; Objective 2: User satisfaction. Satisfaction is measured by the product of user demand and the distance from the point of demand to the charging station, as shown in the following formula: Where i represents the demand point, j represents the charging station, and h i d represents the demand at demand point i. ij Let represent the distance from demand point i to charging station j, n represent the number of charging stations to be built, and m represent the number of demand points that need to reach charging station j for charging.

3. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 2, characterized in that, Step 1.2 specifically includes the following steps: Step 1.2.1: For each individual, first calculate the number of charging stations and determine the location of the charging stations, and select the nearest charging station for each demand point; Step 1.2.2: Collect the area served by each charging station and treat it as a cluster. In the cluster, treat each demand point as a charging station and consider it as a solution. Step 1.2.3: Calculate the objective 2 value for each scheme, select the scheme with the smallest objective 2 value, and update the individual.

4. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 2.1: Enter the main loop and adaptively select five individuals from the entire population using three methods; Step 2.2, Mutation operation: Based on the selected individual and the two generated difference vectors, generate the mutated individual according to the following formula; in, For the selected individuals, r1, r2, r3, r4, and r5 are the indices of the five different individuals selected in step 2.1, and F∈[0,1] is the scaling factor; Step 2.3, crossover operation, in the mutated individual v i Binomial crossover is performed between the target individual and the offspring individual u. i ; Step 2.4: Iterate continuously before reaching the stopping condition to generate a offspring population O, and calculate the two objective function values ​​for each individual in the offspring population O.

5. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 4, characterized in that, In step 2.1, the three adaptive selection strategies include the following steps: Step 2.1.1, the three selection strategies are as follows: Method 1: Randomly select five individuals from the entire population, namely: Method 2: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual and the remaining individuals in the entire population in the decision space; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the decision space as the next most popular individual. The other four are respectively Method 3: Select a certain number of neighboring individuals based on the Euclidean distance between the current individual in the target space and the remaining individuals in the entire population; then, randomly select five neighbors from the selected number of neighboring individuals, and choose the individual with the largest crowding distance in the target space as the target individual. The other four are respectively Step 2.1.2: Adaptively select a strategy, choosing method 1 with probability p1, method 2 with probability p2, and method 3 with probability p3, where p1, p2, and p3 are respectively: p2 = (1 - p1) / 2 p3 = 1 - p1 - p2 Among them, G c G represents the current iteration number, and Max_gen represents the maximum iteration number; therefore, as the current generation G increases... c The values ​​gradually increase from 1 to Max_gen, p1 decreases from 1 to 0, while p2 and p3 gradually increase from 0 to 0.

5.

6. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 4, characterized in that, In step 2.3, the crossover operation includes the following steps: Step 2.3.1: Using a binomial crossover method, generate a random number rand(0,1) for each dimension j of the individual; Step 2.3.2: For each dimension, if rand(0,1) is less than the crossover probability CR, then retain the value from the mutated individual; Step 2.3.3, otherwise, retain the original target individual's value.

7. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 1, characterized in that, In step 3, the environment selection includes the following steps: Step 3.1: Combine the parent population P and the offspring population O to form a new population P_combination; Step 3.2: Perform non-dominated sorting on P_combination to identify the better solution in the multi-objective optimization problem; Step 3.3: Calculate the improved crowding distance for each individual in the combined population P_combination; Step 3.4: Calculate the specific crowding distance for each individual; Step 3.

5. Select a certain proportion of individuals from P_combination according to the calculated crowding distance to form a new population P, which helps to balance the diversity and quality of solutions; Step 3.

6. Iterate in a loop until the stopping condition is reached. Use the new population obtained in Step 3.5 as the parent population to participate in the main loop, and execute Steps 2 to 3 above; when the termination condition is satisfied, end the loop and output the finally optimized population P. These individuals represent high-quality solutions in the multi-objective optimization problem.

8. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 7, characterized in that, In Step 3.3, the improvement of the calculation of the crowding distance includes the following steps: Step 3.3.

1. In the objective space, determine the true neighboring individuals of each individual according to the individuals with a lower non-dominated rank that have been selected. Step 3.3.

2. Calculate the distance between an individual and its neighboring individuals according to the values of the individual on each objective function. Step 3.3.3: Sum the distances across all objective functions to obtain the crowding distance CD of the individual in the objective space. f ; Step 3.3.4: In the decision space, calculate the similarity between each individual and its neighboring individuals as its crowding distance CD in the decision space. x .

9. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 7, characterized in that, In Step 3.4, the calculation of the special crowding distance includes the following steps: Step 3.4.1: Calculate the average crowding distance CD for all individuals in the decision space. avg,x The average crowding distance CD between individuals in the target space avg,f ; Step 3.4.2, transfer the CD of each individual. x CD f The individual's specific crowding distance (SCD) is calculated by comparing it with the average crowding distance and using the following formula:

10. The optimization method for the multimodal, multi-objective charging station site selection problem according to claim 7, characterized in that, In Step 3.5, the environmental selection includes the following steps: Step 3.5.

1. Select a certain proportion of individuals from P_combination according to the calculated crowding distance according to the following formula, and only select a certain percentage of the elements in the previous sorting; where Gc is the current iteration number and Max_gen is the maximum iteration number; when the iteration number is 1, the proportion of individuals selected in the Pareto front is R (0 < R < 1); when the iteration number is G, the proportion of individuals selected in the Pareto front is 1. Step 3.5.

2. Select the corresponding individuals according to the non-dominated sorting and the crowding distance sorting to form a new population P, and output the finally optimized high-quality solution.

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