A population-based probabilistic construction method for arbitrary repositioning problem of shared cars

Abstract

The application discloses a population probability construction method for an arbitrary still mode shared car relocation problem, and belongs to the technical field of computer application. Each generation of population is generated by using a probability construction algorithm PCA under the premise of a given virtual employee combination and a virtual cost matrix. The PCA algorithm mainly utilizes an adaptive probability selection function APF, a re-pickup strategy and three neighborhood search operators to construct employee paths one by one, thereby generating a feasible solution (i.e. a population individual) of the problem. The virtual employee combination and the virtual cost matrix are continuously updated in the population iteration process, and the evolution direction of the population is controlled by means of a linear function and relevant parameters. The population probability construction algorithm can effectively solve the arbitrary still mode shared car relocation problem, and can solve a solution with a smaller total cost, with an average saving of 5.84%.

Description

Technical Field

[0001] This invention belongs to the field of computer application technology, and specifically relates to a population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes. Background Technology

[0002] This study focuses on the relocation problem of shared cars operating under the "Free-return" model. To provide users with more flexible car rental services, shared car operators have proposed this model. Under this model, users pick up cars from a parking lot but can return them to any nearby legal parking space. This model leads to a more severe imbalance in the number of vehicles in the parking lot, necessitating vehicle relocation. The relocation problem in the "Free-return" model refers to how operators, considering factors such as parking lot capacity, the minimum number of return spaces per parking lot, and employee capabilities, can assign employees to relocate vehicles to minimize their total relocation cost. The total relocation cost includes the total cost of hiring workers and the total employee travel cost. The total employee travel cost comprises two parts: the cost of driving the shared car to the designated parking lot and the cost of using transportation from the pick-up point to find a shared car to be relocated.

[0003] The Vehicle Relocation Problem in Free-return Car-sharing Systems (VRPFCS) is closely related to the Vehicle Relocation and Staff Rebalancing Problem (VRSR) proposed in existing literature (Nourinejad M, Zhu S, Bahrami S, et al. Vehicle relocation and staff rebalancing in one-way carsharing systems[J]. Transportation Research Part E: Logistics and Transportation Review, 2015, 81: 98-113.) and the Electric Vehicle Routing Problem (E-VRP) proposed in (Jia YH, Mei Y, Zhang M. ABilevel Ant Colony Optimization Algorithm for Capacitated Electric Vehicle Routing Problem[J]. IEEE Transactions on Cybernetics, 2022, 52(10): 10855-10868.). Compared to VRSR and E-VRP problems, VRPFCS has a larger solution space and also adds constraints such as parking lot capacity, minimum number of vehicles in the parking lot, and employee capacity, making VRPFCS more difficult to solve. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes, comprising the following steps:

[0005] S1. Construct the initial population. Given the number of individuals G in the population, generate each individual in the initial population using the following three steps:

[0006] S11. Generate initial virtual employee combinations: Use a random method to generate a virtual employee combination for each individual in the population, such that the sum of the capabilities of each virtual employee combination is equal to the current total number of vehicles to be placed.

[0007] S12. Generate the initial virtual cost matrix: To place a vehicle P to a parking lot D, an employee needs to start from a parking lot, find vehicle P to form the first path, and then drive vehicle P to parking lot D to form the second path. The two paths from placing vehicle P to parking lot D are denoted as a PD-pair. Create a virtual cost matrix with P as the row and D as the column. Each element in the matrix represents the virtual cost of a PD-pair. Calculate the real distance cost of all PD-pairs and store it in the virtual cost matrix.

[0008] S13. Construct feasible solutions to VRPFCS using the probabilistic construction algorithm PCA. Each feasible solution is an individual in the population.

[0009] S2. Implement iterative optimization of the population, establish a population information update strategy and a population evolution direction control strategy, and continue to use PCA to generate individuals in each generation of the population.

[0010] S3. Test the algorithm's stopping condition: reaching the upper limit of population iterations T. max Or at the specified T sta The algorithm stops when the internal solution is not improved.

[0011] Furthermore, the specific operation process of the PCA algorithm in steps S13 and S2 is as follows:

[0012] Step 1: Based on the given virtual employee combination and virtual cost matrix, plan the placement path starting from the first virtual employee: Starting from the starting node, use the Adaptive Probability Selection Function (APF) to calculate the selection probability of each available PD-pair, and use the roulette wheel method to select a PD-pair to complete the placement of one vehicle. Continue selecting PD-pairs until the current virtual employee's capacity limit is reached, and then arrange for the current virtual employee to return to the starting node. All the above PD-pairs constitute the work path of the first virtual employee. The next virtual employee continues to place the remaining vehicles in the same way until all virtual employees reach their capacity limit or all vehicles are placed. At this point, a feasible solution to the VRPFCS problem is obtained.

[0013] Step 2: Improve the feasible solution found in Step 1 using the Restettlement, relocation, and 2-opt neighborhood search operators. The Restettlement operator is enabled periodically every other generation, while the relocation and 2-opt operators are enabled in every generation of the population.

[0014] Furthermore, in the first step of the PCA algorithm's specific operation, assuming the initial total number of vehicles to be placed is n, and r PD-pairs have already been selected to complete the placement of r vehicles, then among the remaining available N... rThe adaptive probability selection function (APF) for the s-th PD-pair is as follows:

[0015]

[0016] Where C s Let be the virtual cost of the s-th PD-pair; The median virtual cost of all available PD-pairs; μ r An adaptive parameter is calculated using the following three steps:

[0017] ① Set the proportional parameter α, solve the equation N-αln(N)=0, and use its larger root as the threshold N0;

[0018] ②When 0 <N r When ≤N0, set μ r =1;

[0019] ③ When N r When >N0, set in To define a constant parameter between [0,1], the method for determining the function f involves the following four steps:

[0020] ① Set the parameter value range α={2,3,...,8}, N r ={N0,N0+1,...,L×n}, μ r ={0.1,0.2,...,1,2 2 ,...,15 2}, where L is the number of available parking spaces in the parking lot;

[0021] ② Given a set of parameters (α, N) r ,μ r ) Conduct 100 pioneer experiments, with N randomly generated in each experiment. r The virtual cost of each PD-pair consists of a cost set. First calculate The formula is as follows:

[0022]

[0023] Then calculate p based on APF. rs and

[0024] ③ Based on the statistical analysis of all experimental results within the error range All points (α, N) within r ,μ r );

[0025] ④ Perform fitting analysis on the experimental results to determine the function f.

[0026] Furthermore, in the second step of the PCA algorithm's specific operation, the Settlement operator first calculates the true cost of each PD-pair contained in the work path of each employee in the current individual; then it calculates the cost variance of all PD-pairs for each employee, and identifies the employee with the largest cost variance, denoted as k. maxCostStd Filter out k maxCostStd The work path contains all vehicles P and all parking lots D; then find all vehicles related to k. maxCostStd The associated employee work path, i.e., with k maxCostStd If the work path has at least one common parking lot, filter out all vehicles P and all parking lots D contained in all related paths; finally, while retaining other employee paths, replan the employee paths using the MPGA algorithm without the Resettlement operator for all vehicles P and all parking lots D that were filtered out above.

[0027] The Relocation operator uses an enumeration method for neighborhood search. The first enumeration is to extract the first or last PD-pair of the first employee in the current individual and insert it into the work path of each other employee. However, it can only be inserted at the beginning or end of the path and must ensure that it does not exceed the employee's work capacity. The reduction in total cost brought about by this is recorded. Finally, only the extraction and insertion operations with the largest reduction are retained. This process continues until all employees have been enumerated.

[0028] The 2-opt operator also uses enumeration to perform neighborhood search. The first enumeration is for the work path of the first employee in the current individual. It enumerates any two vehicles in the path and swaps their order, records the reduction in total cost resulting from this, and finally only retains the swap operation with the largest reduction. This process continues until all employees have been enumerated.

[0029] Further, in step S2, the population information update strategy includes updating the virtual employee combination and updating the virtual cost matrix. Updating the virtual employee combination: Starting from the second generation of the population, the virtual employee combination of the best individual from the previous generation is retained and used by half of the individuals in the current population. The best individual remains unchanged, and the remaining half of the individuals are used to generate virtual employee combinations using a random method. Updating the virtual cost matrix: In the second generation of the population, the virtual cost matrix is ​​still generated using the real distance cost of all PD-pairs. Starting from the third generation of the population, the virtual cost matrix of the t-th generation is generated using the following two steps:

[0030] ① Optimize the virtual cost per PD-pair for each individual g in the (t-1)th generation population using the following formula:

[0031]

[0032] Where C' t,g (i,j) represents the virtual cost from node i to j in the virtual cost matrix of the g-th individual in generation t; Z t,g c is the target value for the g-th individual in generation t; ij d represents the cost per unit distance from node i to j; ij υ represents the true distance from node i to j; υ is the reward factor, which is usually set to a constant greater than 1. It is the set of all employee paths contained in individual g of the t-th generation population;

[0033] ② Use the following formula to generate the virtual cost per PD-pair for each individual g in the t-th generation population:

[0034]

[0035] Where ρ t λ represents the degree of inheritance of information from the (t-1)th generation population by the t-th generation population; t ω represents the inheritance degree of the best individual in the (t-1)th generation from the t-th generation population; t-1,g The weight of the original information of individual g in generation t-1 is calculated by the following formula:

[0036]

[0037] Where rank(Z) t-1,g ) represents the order of individual g after the population of generation t-1 is sorted in ascending order according to the target value.

[0038] Furthermore, in step S2, the control strategy for the population evolution direction is to control ρ t and λ t Controlling the evolutionary direction of the population. ρ is calculated for the t-th generation population using the following formula. t and λ t :

[0039] ρ t =a ρ (t-1) / (T-1)+b ρ

[0040]

[0041] Where a ρ b ρ and a λ All are user-defined non-negative constant parameters. If consecutive occurrences have already appeared before the t-th generation of the population... If the average target value of all individuals in the population continues to increase, then let λ t =a λ .

[0042] The beneficial effects of this invention are as follows: This invention proposes a population-based probabilistic construction algorithm (MPGA) for the relocation problem of shared cars with arbitrary return modes. In each generation of the population, given a virtual employee combination and a virtual cost matrix, a probabilistic construction algorithm (PCA) is used to generate population individuals. The PCA algorithm utilizes an adaptive probabilistic selection function (APF), a re-picking strategy, and three neighborhood search operators to construct employee paths one by one, thereby generating feasible solutions (i.e., population individuals). During the population iteration process, the virtual employee combination and the virtual cost matrix are continuously updated, and the evolution direction of the population is controlled by relevant parameters through linear functions. Experimental results show that this population-based probabilistic construction algorithm can effectively solve the relocation problem of shared cars with arbitrary return modes. Compared with other algorithms for solving this type of problem, such as the latest two-layer ant colony algorithm BACO, MPGA can find solutions with lower total costs, with an average cost reduction of 5.84%. Attached Figure Description

[0043] Figure 1 This is a flowchart of the Probabilistic Construction Algorithm (PCA) of the present invention;

[0044] Figure 2 This is a flowchart of the population probabilistic construction algorithm (MPGA) of the present invention. Detailed Implementation

[0045] To address the NP-hard problem of relocating shared cars with arbitrary return modes, this invention proposes a population-based probabilistic construction algorithm, providing a new approach and method for the relocation of shared cars with arbitrary return modes and related problems. This algorithm, known as the Multi-iterations Probabilistic Constructive Algorithm (MPCA), is a population-based probabilistic construction method for the relocation of shared cars with arbitrary return modes. Figure 1 As shown, it includes the following steps:

[0046] S1. Construct the initial population. Given the number of individuals G in the population, generate each individual in the initial population using the following three steps:

[0047] S11. Generate initial virtual employee combinations: Use a random method to generate a virtual employee combination for each individual in the population, such that the sum of the capabilities of each virtual employee combination is equal to the current total number of vehicles to be placed.

[0048] S12. Generate the initial virtual cost matrix: Moving a vehicle P to a parking lot D requires an employee to start from a parking lot, find vehicle P (the first path), and then drive vehicle P to parking lot D (the second path). For ease of description, the two paths from vehicle P to parking lot D are denoted as a PD-pair. Create a virtual cost matrix with P as the row and D as the column. Each element in the matrix represents the virtual cost of a PD-pair. Calculate the actual distance cost of all PD-pairs and store it in the virtual cost matrix.

[0049] S13. Construct feasible solutions to VRPFCS using the Probabilistic Constructive Algorithm (PCA). Each feasible solution is an individual in the population.

[0050] S2. Implement iterative optimization of the population. Establish an update strategy for population information (virtual employee portfolio and virtual cost matrix) and a control strategy for the direction of population evolution, and continue to use PCA to generate individuals in each generation of the population.

[0051] S3, Testing the stopping condition of the algorithm: Reaching the upper limit of population iterations T. max Or at the specified T sta The algorithm stops when the internal solution is not improved.

[0052] Furthermore, such as Figure 2 As shown, the specific operation process of the PCA algorithm in steps S13 and S2 is as follows:

[0053] Step 1: Given the virtual employee combination and virtual cost matrix, plan the placement path starting from the first virtual employee: Starting from the initial node, use the Adaptive Probabilistic Selection Function (APF) to calculate the selection probability of each available PD-pair. Use a roulette wheel method to select a PD-pair to complete the placement of one vehicle. Continue selecting PD-pairs until the current virtual employee's capacity limit is reached, then stop and arrange for the current virtual employee to return to the initial node. All the aforementioned PD-pairs constitute the work path of the first virtual employee. The next virtual employee continues to place the remaining vehicles using the same method until all virtual employees reach their capacity limits or all vehicles are placed. At this point, a feasible solution to the VRPFCS problem is obtained.

[0054] Before selecting a PD-pair, access to already occupied vehicles and certain parking lots needs to be blocked. To ensure that the minimum return parking space requirement for each parking lot is met while reducing shortsightedness in the search process, parking lots that have met the minimum parking space requirement are only blocked if the total number of remaining unoccupied vehicles is less than or equal to the number of remaining unmet minimum parking spaces.

[0055] When selecting a PD-pair, a re-selection strategy needs to be incorporated: given the number of re-selections rep, if the cost of selecting a PD-pair is higher than the cost of the previously selected PD-pair by δ times, then a PD-pair is re-selected; if no PD-pair that meets the conditions is found within rep times, then the PD-pair with the lowest cost among the rep times is selected.

[0056] Step 2: Improve the feasible solution found in Step 1 using the Restettlement, relocation, and 2-opt neighborhood search operators. The Restettlement operator is enabled periodically every other generation, while the relocation and 2-opt operators are enabled in every generation of the population.

[0057] Furthermore, in the first step of the PCA algorithm, it is assumed that the initial total number of vehicles to be placed is n, and r PD-pairs have already been selected to complete the placement of r vehicles. Then, among the remaining available N... r The adaptive probabilistic function (APF) for the s-th PD-pair is as follows:

[0058]

[0059] Where C s Let be the virtual cost of the s-th PD-pair; The median virtual cost of all available PD-pairs; μ r An adaptive parameter is calculated using the following three steps:

[0060] ① Set the proportional parameter α, solve the equation N-αln(N)=0, and use its larger root as the threshold N0.

[0061] ②When 0 <N r When ≤N0, set μ r The value is 1.

[0062] ③ When N r When >N0, set in To define a constant parameter between [0,1], the method for determining the function f involves the following four steps:

[0063] ① Set the parameter value range α={2,3,...,8}, N r ={N0,N0+1,...,L×n}, μ r ={0.1,0.2,...,1,2 2 ,...,15 2}, where L is the number of available parking spaces in the parking lot.

[0064] ② Given a set of parameters (α, N) r ,μ r ) Conduct 100 pioneer experiments, with N randomly generated in each experiment. r The virtual cost of each PD-pair consists of a cost set. First calculate The formula is as follows:

[0065]

[0066] Then calculate p based on APF. rs and

[0067] ③ Based on the statistical analysis of all experimental results within the error range All points (α, N) within r ,μ r ).

[0068] ④ Perform fitting analysis on the experimental results to determine the function f.

[0069] Furthermore, in the second step of the PCA algorithm, the Settlement operator first calculates the true cost of each PD-pair contained in the work path of each employee in the current individual; then it calculates the cost variance of all PD-pairs for each employee, and finds the employee with the largest cost variance, denoted as k. maxCostStd Filter out k maxCostStd The work path contains all vehicles P and all parking lots D; then find all vehicles related to k. maxCostStd The associated employee work path, i.e., with k maxCostStd If the work path has at least one common parking lot, filter out all vehicles P and all parking lots D contained in all related paths; finally, while retaining other employee paths, replan the employee paths using the MPGA algorithm without the Settlement operator for all vehicles P and all parking lots D that were filtered out above.

[0070] The Relocation operator uses an enumeration method for neighborhood search. The first enumeration is to extract the first or last PD-pair of the first employee in the current individual and insert it into the work path of each other employee. However, it can only be inserted at the beginning or end of the path and must ensure that it does not exceed the employee's work capacity. The reduction in total cost brought about by this is recorded. Finally, only the extraction and insertion operations with the largest reduction are retained. This process continues until all employees have been enumerated.

[0071] The 2-opt operator also uses enumeration to perform neighborhood search. The first enumeration is for the work path of the first employee in the current individual. It enumerates any two vehicles in the path and swaps their order, records the reduction in total cost resulting from this, and finally only retains the swap operation with the largest reduction. This process continues until all employees have been enumerated.

[0072] Furthermore, the update strategy for population information (virtual employee combination and virtual cost matrix) and the control strategy for population evolution direction in step S2 are as follows;

[0073] Strategy 1: Update the virtual employee combination. Starting from the second generation of the population, retain the virtual employee combination of the best individual from the previous generation and use it for half of the individuals in the current population (the best individual remains unchanged). The remaining half of the individuals will generate virtual employee combinations using a random method.

[0074] Strategy 2: Update the virtual cost matrix. In the second generation population, the virtual cost matrix is ​​still generated using the real distance costs of all PD-pairs. Starting from the third generation population, the virtual cost matrix for the t-th generation population is generated using the following two steps:

[0075] ① Optimize the virtual cost per PD-pair for each individual g in the (t-1)th generation population using the following formula:

[0076]

[0077] Where C' t,g (i,j) represents the virtual cost from node i to j in the virtual cost matrix of the g-th individual in generation t; Z t,g c is the target value for the g-th individual in generation t; ij d represents the cost per unit distance from node i to j; ij υ represents the true distance from node i to j; υ is the reward factor, which is usually set to a constant greater than 1. It is the set of paths consisting of all employee paths contained in individual g of the t-th generation population.

[0078] ② Use the following formula to generate the virtual cost per PD-pair for each individual g in the t-th generation population:

[0079]

[0080] Where ρ t λ represents the degree of inheritance of information from the (t-1)th generation population by the t-th generation population; t ω represents the inheritance degree of the best individual in the (t-1)th generation from the t-th generation population; t-1,g The weight of the original information of individual g in generation t-1 is calculated by the following formula:

[0081]

[0082] Where rank(Z) t-1,g ) represents the order of individual g after the population of generation t-1 is sorted in ascending order according to the target value.

[0083] Strategy 3: By controlling ρ t and λ t Controlling the evolutionary direction of the population. ρ is calculated for the t-th generation population using the following formula. t and λ t :

[0084] ρ t =a ρ (t-1) / (T-1)+b ρ

[0085]

[0086] Where a ρ b ρ and a λ All are user-defined non-negative constant parameters. If consecutive occurrences have already appeared before the t-th generation of the population... If the average target value of all individuals in the population continues to increase, then let λ t =a λ .

[0087] This section uses simulation experiments to verify the effectiveness of the population-based probabilistic construction algorithm as a new approach and method in solving the problem of relocation of shared cars with arbitrary return modes.

[0088] The experimental data are as follows:

[0089] Based on two months of vehicle dispatch data provided by car-sharing operators, 24 test cases were generated. Each case had different scales of waiting vehicle numbers, parking lot numbers, available staff, parking lot capacity, minimum number of return parking spaces, and node distribution. For each case, the unit distance cost of car-sharing was set to be three times the unit distance cost of employees using other modes of transportation, and the cost of hiring one employee per day was 65 times the unit distance cost of employees using other modes of transportation. We set the stopping parameter of the MPGA algorithm to T. max =50,T sta =20, and the BACO and MPGA algorithms were tested on 24 cases using the same algorithm parameters and the same stopping conditions.

[0090] Table 1 summarizes the test results, where BACO.T and BACO.Obj represent the time and total cost of solving the problem using the BACO algorithm, respectively; MPGA.T and MPGA.Obj represent the time and total cost of solving the problem using the MPGA algorithm, respectively; and gap represents the improvement of the MPGA algorithm over BACO in terms of total cost. The last row of Table 1 shows the average test results for 24 examples, clearly indicating that MPGA saves an average of 5.84% in total cost compared to BACO. The experimental results demonstrate that the proposed population-based probabilistic construction algorithm for the arbitrary return mode shared car relocation problem can effectively solve the shared car relocation problem and save related costs.

[0091] Table 1. Experimental results of BACO and MPGA algorithms

[0092]

[0093] To solve the relocation problem of shared cars with arbitrary return modes, this invention proposes a population-based probabilistic construction algorithm (MPGA). In each generation of the population, given a virtual employee combination and a virtual cost matrix, the probabilistic construction algorithm (PCA) is used to generate population individuals. The PCA algorithm utilizes an adaptive probabilistic selection function (APF), a re-picking strategy, and three neighborhood search operators to construct employee paths one by one, thereby generating feasible solutions (i.e., population individuals). During the population iteration process, the virtual employee combination and virtual cost matrix are continuously updated, and the evolution direction of the population is controlled by relevant parameters through linear functions. Experimental results show that the population-based probabilistic construction algorithm can effectively solve the relocation problem of shared cars with arbitrary return modes. Compared with other algorithms for solving this type of problem, such as the latest two-layer ant colony algorithm BACO, MPGA can find solutions with lower total costs, achieving an average cost reduction of 5.84%.

[0094] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes, characterized in that, Includes the following steps: S1. Construct the initial population, given the number of individuals in the population. Each individual in the initial population is generated using the following three steps: S11. Generate initial virtual employee combinations: Use a random method to generate a virtual employee combination for each individual in the population, such that the sum of the capabilities of each virtual employee combination equals the current total number of vehicles to be placed; S12. Generate the initial virtual cost matrix: To place a vehicle P to a parking lot D, an employee needs to start from a parking lot, find vehicle P to form the first path, and then drive vehicle P to parking lot D to form the second path. The two paths from placing vehicle P to parking lot D are denoted as a PD-pair. Create a virtual cost matrix with P as the row and D as the column. Each element in the matrix represents the virtual cost of a PD-pair. Calculate the real distance cost of all PD-pairs and store it in the virtual cost matrix. S13. Use the probabilistic construction algorithm PCA to construct feasible solutions to the VRPFCS problem of arbitrary return mode shared car relocation. Each feasible solution is an individual in the population. S2. Implement iterative optimization of the population, establish a population information update strategy and a population evolution direction control strategy, and continue to use PCA to generate individuals in each generation of the population. S3. Test the algorithm's stopping condition: reaching the maximum number of population iterations. Or in the specified The algorithm stops when the intramolecular solution does not improve. The specific operation process of the PCA algorithm in steps S13 and S2 is as follows: Step 1: Based on the given virtual employee combination and virtual cost matrix, plan the placement path starting from the first virtual employee: Starting from the starting node, use the Adaptive Probability Selection Function (APF) to calculate the selection probability of each available PD-pair, and use the roulette wheel method to select a PD-pair to complete the placement of one vehicle. Continue selecting PD-pairs until the current virtual employee's capacity limit is reached, and then arrange for the current virtual employee to return to the starting node. All the above PD-pairs constitute the work path of the first virtual employee. The next virtual employee continues to place the remaining vehicles in the same way until all virtual employees reach their capacity limit or all vehicles are placed. At this point, a feasible solution to the arbitrary return mode shared car relocation problem VRPFCS is obtained. Step 2: Improve the feasible solution found in Step 1 using the Resettlement, relocation, and 2-opt neighborhood search operators. The Resettlement operator is enabled periodically every other generation, while the relocation and 2-opt operators are enabled in every generation of the population. In the first step of the PCA algorithm's specific operation, it is assumed that the initial total number of vehicles to be placed is... , already chosen One PD-pair completed The placement of the remaining vehicles will be handled during the remaining available time. The first PD-pair The adaptive probability selection function (APF) for each PD-pair is as follows: in For the first The virtual cost of a PD-pair; The median virtual cost of all available PD-pairs; An adaptive parameter is calculated using the following three steps: ① Set the scaling parameters Solve the equation Use its larger root as the threshold. ; ②When When, set =1; ③When When, set ,in For customization constant parameters between functions The method for determining it includes the following four steps: ① Set the parameter value range , , ,in This refers to the number of available parking spaces in the parking lot. ② Given a set of parameters 100 pioneer experiments were conducted, with each experiment randomly generated. The virtual cost of each PD-pair consists of a cost set. First calculate The formula is as follows: Then calculate based on APF. and ; ③ Based on the statistical analysis of all experimental results within the error range All points within ; ④ Perform fitting analysis on the experimental results to determine the function. .

2. The population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes as described in claim 1, characterized in that, In the second step of the PCA algorithm's specific operation, the Settlement operator first calculates the true cost of each PD-pair in each employee's work path within the current individual; then it calculates the cost variance of all PD-pairs for each employee, and identifies the employee with the largest cost variance, denoted as... Filter out The work path contains all vehicles P and all parking lots D; then find all vehicles P and all parking lots D that are connected to the work path. Related employee work paths, i.e. If the work path has at least one common parking lot, filter out all vehicles P and all parking lots D contained in all related paths; finally, while retaining other employee paths, replan the employee paths using the MPGA algorithm without the Resettlement operator for all vehicles P and all parking lots D that were filtered out above. The relocation operator uses an enumeration method for neighborhood search. The first enumeration is performed on the th element in the current individual. For each employee's work path, extract its first or last PD-pair and insert it into the work path of every other employee. However, it can only be inserted at the beginning or end of the path and must not exceed the employee's work capacity. Record the reduction in total cost resulting from this. Finally, only the extraction and insertion operations with the largest reduction are retained. This process continues until all employees have been enumerated. The 2-opt operator also uses enumeration for neighborhood search. The first enumeration is performed on the th element in the current individual. For each employee's work path, enumerate any two vehicles on that path and swap their order, recording the reduction in total cost resulting from this. Finally, only retain the swap operation with the largest reduction, and so on, until all employees have been enumerated.

3. The population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes as described in claim 1, characterized in that, In step S2, the population information update strategy one is to update the virtual employee combination. Starting from the second generation of the population, the virtual employee combination of the best individual in the previous generation is retained and used by half of the individuals in the current population. The best individual remains unchanged, and the virtual employee combination of the remaining half of the individuals is generated using a random method.

4. The population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes as described in claim 1, characterized in that, In step S2, the second population information update strategy is to update the virtual cost matrix. In the second generation population, the virtual cost matrix is ​​still generated using the real distance costs of all PD-pairs. Starting from the third generation population, the following two steps are used to generate the virtual cost matrix. Virtual cost matrix of the generation population: ① Optimize the following formula Each individual in the population Virtual cost per PD-pair: in For the first The generation From the virtual cost matrix of each individual node arrive Virtual costs; For the first The generation The target value for each individual; For the node arrive Unit distance cost; For nodes arrive The actual distance; The reward factor is usually set to be greater than The constant; It is the first Individuals in a generation The path set consisting of all employee paths included; ② Use the following formula to generate the first Each individual in the population Virtual cost per PD-pair: in Indicates the first generational populations on the first The degree of inheritance of overall information in a generational population; Indicates the first generational populations on the first The inheritance degree of the best individual in the population; Represents the (t-1)th generation individual The weight of the original information is calculated using the following formula: in This represents the population of generation t-1 arranged in ascending order according to the target value. The corresponding order.

5. The population-based probabilistic construction method for the relocation problem of shared cars with arbitrary return modes as described in claim 1, characterized in that, In step S2, the control strategy for the direction of population evolution is: by controlling... and Controlling the direction of population evolution; for the first The population size is calculated using the following formula. and : in , and All are user-defined non-negative constant parameters. If in the... Continuous occurrences have occurred in previous generations of populations. If the average target value of all individuals in the population continues to increase, then let .

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