Multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search

Abstract

The present invention relates to the field of shared transportation technology, and relates to a multi-target carpooling problem optimization method for a multi-guided particle swarm with variable neighborhood search, comprising: first, establishing a non-dominated solution set NS; second, using an initial solution construction algorithm to obtain a particle swarm S at an initial position; third, performing particle swarm optimization on the particle P. i Use particle motion operator to obtain the new particle position set PS i ; 4. PS i Perform variable neighborhood search VNS to obtain the set PS i '; Five, use PS i 'Update particle P i The historical optimal solution set pbest i ; 6. All particles P i pbest i Update the global optimal solution gbest; 7. Use the non-dominated solution set to filter and control pbest i and the number of solutions in gbest; 8. Use gbest to update NS. The present invention can better solve the multi-objective carpooling problem.

Description

Technical Field

[0001] The present invention relates to the field of shared transportation technology, and in particular to a multi-guided particle swarm optimization method for multi-objective carpooling problems with variable neighborhood search. Background Art

[0002] As incomes and living standards rise, the number of private cars under traditional transportation models is increasing, leading to problems such as traffic congestion, parking shortages, and environmental pollution. Current taxi and car-sharing services rely on adding new vehicles rather than fully utilizing existing ones to achieve "sharing" through time-sharing rentals. This results in high vacancy rates during most periods, leading to a significant waste of human and vehicle resources. This not only fails to address the challenges of road congestion, parking shortages, urban management, and environmental pollution caused by an overabundance of vehicles in cities, but also exacerbates the dilemma of competing with existing vehicles for resources such as license plates, roads, and parking spaces.

[0003] Numerous studies have shown that carpooling is an effective way to alleviate these problems. Travelers share vehicles with others through ridesharing and carpooling, paying a fee tailored to their travel needs. If the number of travelers remains constant, a portion of them can effectively utilize empty seats if they choose to share a vehicle with drivers traveling to the same destination or on similar routes. Furthermore, carpooling significantly reduces the desire of some carless travelers to purchase private vehicles, thereby reducing private car ownership. As private car use and ownership decline, the demand for parking spaces, roads, and services related to private car travel will inevitably decrease.

[0004] Current carpooling algorithms still face numerous challenges. Existing research focuses solely on resource allocation, focusing on drivers, passengers, or resources. This results in results that fail to optimize all three simultaneously, and therefore offer limited guidance for practical applications. Most carpooling algorithms primarily address one-time, static, or dynamic carpooling problems, without considering carpooling between specific groups of people.

[0005] In the multi-objective carpooling problem, existing algorithms cannot balance the convergence and diversity of the solution set well, but tend to favor one aspect, and there is room for further improvement. Summary of the Invention

[0006] The present invention provides a multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search, which can solve the carpooling problem of commuting staff in the same park and can efficiently obtain carpooling solutions.

[0007] The multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search according to the present invention comprises the following steps:

[0008] 1. Establish the non-dominated solution set NS;

[0009] Second, use the initial solution construction algorithm to obtain the particle swarm S at the initial position;

[0010] 3. Particle P i Use particle motion operator to obtain the new particle position set PS i ;

[0011] 4. PS i Perform variable neighborhood search VNS to obtain the set PS i ';

[0012] 5. Use Photoshop i 'Update particle P i The historical optimal solution set pbest i ;

[0013] 6. All particles P i pbest i Update the global optimal solution gbest;

[0014] 7. Use non-dominated solution set filtering to control pbest i and the number of solutions in gbest;

[0015] 8. Use gbest to update NS.

[0016] Preferably,

[0017] The initial solution construction algorithm is as follows:

[0018]

[0019]

[0020] Preferably,

[0021] The particle motion operator calculation method is as follows:

[0022]

[0023] g is the global optimal solution sequence, p is the historical optimal solution sequence, and each solution in the optimal solution set B is calculated based on the index value D. 2 After sorting the size of I, multiple guided solutions are uniformly selected at the same interval; the global optimal solution subset G is taken out c and the historical optimal solution subset P c After the combination is performed, lines 7-15 use the calculated new solution set as the result after the particle movement.

[0024] Preferably,

[0025] The neighborhood search method is changed to:

[0026]

[0027] For the solution set PS obtained by the motion operator, a variable neighborhood search is performed for each solution. Lines 6-17 represent a search, which searches in each neighborhood in turn until a new solution that can dominate the current solution is found, ending the search. In lines 4-16, each solution will be searched β times.

[0028] Preferably,

[0029] The non-dominated solution set filtering method is:

[0030]

[0031]

[0032] Lines 4-7 delete the worse solution of the two solutions with the closest Euclidean distance in turn. The quality of the solution is judged by the normalized distance between the solution and the reference point.

[0033] This invention improves the problem of the PSO algorithm in multi-objective carpooling problems where the solution set converges too quickly, leading to local optimization. When selecting particle motion guiding solutions, the present invention strives to ensure that they represent the overall motion trend of the optimal solution set. A new metric is designed to represent the positional distribution of solutions within the solution set. Based on this metric, multiple guiding solutions are evenly selected, increasing the diversity of the algorithm's solution set while ensuring convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a flowchart of a multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search in Example 1;

[0035] Figure 2 This is an example diagram of the sequence encoding of a feasible solution in Example 1;

[0036] Figure 3 This is an example diagram of particle motion trajectory adjustment in Example 1;

[0037] Figure 4 D in Example 1 2 I. Schematic diagram of the calculation process;

[0038] Figure 5 This is an example diagram of the node exchange neighborhood in Example 1;

[0039] Figure 6 This is an example diagram of the node change neighborhood in Example 1;

[0040] Figure 7 This is an example diagram of the neighborhood for exchanging the boarding order in Example 1. DETAILED DESCRIPTION

[0041] In order to further understand the content of the present invention, the present invention is described in detail with reference to the accompanying drawings and embodiments. It should be understood that the embodiments are merely for explaining the present invention and are not intended to limit the present invention.

[0042] Example 1

[0043] The solution to the carpooling problem is converted into a concise sequence code to facilitate algorithm calculation. In addition, some extensions are made to the PSO algorithm to improve the diversity of the solution set.

[0044] To address the problem of the PSO algorithm converging too quickly and becoming trapped in local optimization in the multi-objective carpooling problem, we designed a new metric to represent the distribution of solutions within the solution set. This metric is then used to evenly select multiple guiding solutions, ensuring convergence while increasing diversity.

[0045] 1 Sequence Encoding

[0046] like Figure 2 As shown in the figure, this is a feasible solution to the carpooling problem. Travelers 1, 3, and 4 provide vehicles for this carpooling. They drive from their own locations respectively. 1 picks up passengers 2, 6, and 7 in turn, 3 picks up passengers 8 and 11 in turn, and 4 picks up passengers 5, 9, and 10 in turn.

[0047] To represent the order in which vehicles pick up passengers, a sequence code that reflects the solution to the problem is designed. The code length is the number of travelers n. Each traveler has a sequence number, and the i-th bit of the sequence code represents the sequence number of the next traveler after the i-th traveler. For example: Figure 2 The next person to traveler No. 2 is No. 6, so the second position of the converted sequence code is 6. The next person to traveler No. 5 is No. 9, so the fifth position of the sequence code is 9. If a traveler does not have a next traveler and arrives at the destination directly, the corresponding sequence code is the code of the destination, which is represented by 0. Figure 2 There is no next traveler for travelers No. 7, 10, and 11, and the values ​​of the 7th, 10th, and 11th bits of the sequence code are all 0.

[0048] It is easy to know that the numbers 1 to n do not appear in the sequence code, which means that there is no previous traveler, that is, the travelers corresponding to these numbers are the providers of the vehicles, that is, the drivers. Figure 2 The sequence code in the figure does not contain 1, 3, or 4. Starting from these numbers, we read the next digit in the sequence until the next digit is 0, and we get 1, 2, 6, 7, 3, 8, 11, 4, 5, 9, and 10, which correspond exactly to the three passenger loading sequences. Once the loading sequence is known, the passengers on each vehicle can be determined, and the mileage of the vehicle and the mileage of each passenger can be calculated.

[0049] 2 Algorithm Framework

[0050] Algorithm 1 gives the framework of the MPSO-VNS algorithm, which has two extensions on the basic PSO. The process is as follows: Figure 1 As shown in Figure 2. First, a variable neighborhood search is performed on the position of the particle after movement to optimize the solution set. Second, when the non-dominated solution set in a multi-objective problem is too large, the optimal solution set is filtered to control the number of solution sets while also reducing the similarity between solutions.

[0051] Algorithm 1MPSO-VNS

[0052]

[0053] 3 Initial solution construction

[0054] Based on the particle swarm optimization algorithm, it is necessary to initialize the initial position of each particle, that is, to construct the initial solution. Algorithm 2 is the process of constructing the initial solution. Because each bit in the solution sequence represents the sequence number of the next traveler, the sequence numbers of travelers in the sequence are unique. During initialization, each bit of the sequence is assigned a value sequentially. First, a probability value is set. This part of the travelers does not have a next traveler and instead drives directly to the destination (line 5 of the code). The remaining positions select the sequence numbers of travelers that were not previously taken in the sequence to determine whether the constructed partial solution is feasible. If feasible, the sequence number is set to the current position in the sequence; otherwise, it is set to the destination (lines 7 to 12 of the code). There are two situations in which the insertion of the traveler sequence number invalidates the solution: one is that the vehicle is overloaded after the addition, and the other is that the passenger order of the vehicle forms a cycle.

[0055] Algorithm 2 Initial solution construction

[0056]

[0057] 4 Particle motion operator

[0058] The particle swarm optimization algorithm simulates the movement of birds when foraging by designing a massless particle. The basic idea of ​​the particle swarm optimization algorithm is to find the optimal solution through collaboration and information sharing among individuals in the swarm. Each particle searches for the optimal solution in the solution space independently. The optimal solution found is recorded as the historical optimal solution of the particle and is shared with other particles in the entire particle swarm. The best individual optimal solution is found as the current global optimal solution of the entire particle swarm. All particles in the particle swarm adjust their own movement trajectory based on their own historical optimal solution and the global optimal solution shared by the entire particle swarm, which is the self-cognition term O. p = rand() × (ps) and the global cognitive term O g= rand() × (gs). Where s represents the current position of the particle, p represents the historical optimal solution, and g represents the global optimal solution.

[0059] like Figure 3 As shown, the particle's current solution sequence s is converted into sequence s after moving at speed v. v , the speed in the figure is 3 sequence bits, and the direction is the 1st, 2nd, and 4th sequence bits. The global optimal solution sequence g is subtracted from the current solution sequence s to obtain a partial subsequence gs, and a partial sequence bit in the subsequence is randomly intercepted as the global cognitive item O of the particle motion. g , and use the same method to obtain the particle's self-cognition item O from the historical optimal solution sequence p and the current solution sequence s p , and finally the sequence s v Combining the self-cognitive term and the global cognitive term, a new solution s' of the particle is obtained.

[0060] Some researchers have improved the PSO algorithm to solve multi-objective optimization problems. In multi-objective problems, the optimal solution is no longer a single extreme value, but rather a set of non-dominated solutions. These improved algorithms only take a single solution, which does not adequately represent the entire set of optimal solutions. Therefore, a method has been designed to sample from the set of solutions.

[0061] When sampling, all the optimal solutions are sorted, and then a specified number of solutions are uniformly selected as guide solutions. In order to select the guide solution from the optimal solution set, an index value D of the optimal solution relative to the current solution is introduced. 2 I (direction & distance index). First, use formula (1) to normalize the current solution s and each solution in the optimal solution set B, f i,max represents the maximum value of all i-th objective functions in the solution set s∪B, f i,min represents the minimum value of all i-th objective functions in the solution set s∪B;

[0062]

[0063] like Figure 4 As shown, in the current solution s and the optimal solution set (s1, s2, s3, ..., s n ) after normalization, take (f 1,min ,f 2,min ,…,f m,min ) is the reference point r. Taking the optimal solution s2 as an example, is the vector from the current solution s to the optimal solution s2, is the vector from the current solution s to the reference point r, θ is the vector and vector The angle between the optimal solution and the current solution can be calculated by using formulas 2 and 3. 2I, where ω1 and ω2 represent the direction weight and distance weight of the optimal solution relative to the current solution, respectively.

[0064]

[0065]

[0066] Each solution in the optimal solution set B is based on D 2 After sorting the size of I, multiple guided solutions are uniformly selected at the same interval. The global optimal solution subset G is taken out c and the historical optimal solution subset P c Perform the combination and use the calculated new solution set as the result after the particle movement (code lines 7 to 15).

[0067] Algorithm 3 Particle motion operator

[0068]

[0069] 5-variable neighborhood search

[0070] Neighborhood search is proved to be an effective strategy to improve the quality of non-dominated solution set. Three neighborhoods are proposed by performing variable neighborhood search on the solution set after particle movement.

[0071] First neighborhood: Select two random nodes and exchange their positions in the sequence. Figure 5 , the next person to traveler No. 2 is No. 6, and the next person to traveler No. 3 is No. 8. After exchanging the two nodes, the next person to traveler No. 2 is No. 8, and the next person to traveler No. 3 is No. 6.

[0072] Second neighborhood: Select a random node and modify the value at the node position. Figure 6 , change the value of the 4th position in the sequence from 5 to 3, then the next person who travels No. 4 will be No. 3 instead of No. 5.

[0073] The third neighborhood: randomly select a car with more than one traveler, randomly select two travelers whose boarding order is consecutive, and swap the order of the two. Figure 7 The original order of travelers in a car is 4, 5, 9, 10, and after the neighborhood change, it becomes 4, 9, 5, 10.

[0074] For each solution set PS obtained by the motion operator, a variable neighborhood search is performed. Lines 6-17 represent a search, which searches each neighborhood in turn until a new solution that dominates the current solution is found, ending the search. In Algorithm 4, each solution undergoes β searches (lines 4-16).

[0075] Algorithm 4: Variable Neighborhood Search

[0076]

[0077]

[0078] 6 Non-dominated solution set filtering

[0079] The number of optimal solutions obtained by the algorithm increases with the number of iterations. When the number of solutions is too large, the time required to select leaders for the particle movement increases significantly. Therefore, filtering the solution set is necessary to limit its size. The algorithm sequentially removes the worst solution from the two solutions with the closest Euclidean distance (lines 4-7 of the code). The quality of the solution is determined by its normalized distance from the reference point (origin).

[0080] Algorithm 5 Non-dominated solution set filtering

[0081]

[0082] experiment

[0083] Algorithm indicators

[0084] In order to evaluate the effectiveness of the algorithm, the experiment selected three indicators: Inverted Generational Distance (IGD), Hypervolume (HV), and C-metric solution set coverage.

[0085] 1. IGD

[0086] IGD is the average distance from each reference point to the nearest solution. For the solution set P obtained by the algorithm and a set of uniformly distributed reference points P* obtained from the Pareto front, the value of IGD is obtained by formula (4). d(x,y) represents the Euclidean distance between point x in the reference set P* and point y in the solution set P. IGD represents the average of the minimum Euclidean distances from all points in the reference set P* to the solution set P. The smaller the IGD value, the closer the solution set is to the Pareto front and the more uniformly distributed it is.

[0087]

[0088] IGD can simultaneously evaluate the convergence and diversity of the solution set. Since the reference point of the problem cannot be obtained in advance, the non-dominated solution set obtained by merging the solution sets obtained by all algorithms is used as the reference point of this indicator. The value ranges of the three objectives in the problem vary greatly. In order to balance the weights of the three objective function values ​​in the indicator calculation, each solution in the solution set P is normalized using formula (10).

[0089] 2. HV

[0090] HV is the volume of the union of the non-dominated solution set obtained by the algorithm and the area enclosed by the reference point in the target space. For the solution set P obtained by the algorithm, its HV index can be obtained by formula (5). m ) is the reference point, m is the number of targets, and L() represents the Lebesgue measure. HV can also evaluate the convergence and diversity of the solution set. A larger HV value indicates better overall algorithm performance.

[0091] HV(P,r * )=L(∪ x∈P [f1(x),r1]×,…,[f m (x),r m ]) (5)

[0092] In the experiment, each solution in the solution set P is first normalized using formula (1). Then, r* = (1.0, 1.0) is selected as the reference point. The Lebesgue measure is calculated for the normalized solution, and finally the HV value is obtained. The calculation complexity of HV is relatively high, and the calculation method of Fonseca et al. is referenced.

[0093] 3. C-metric solution set coverage

[0094] The coverage rate C(A,B) of solution set A for solution set B is obtained by formula (6), where the numerator represents the number of solutions in solution set B that are dominated by at least one solution in solution set A, and the denominator represents the number of solutions in solution set B.

[0095]

[0096] The larger the value of C(A,B), the more solution set A dominates solution set B. The evaluation of solution sets A and B requires comparing C(A,B) and C(B,A).

[0097] Experimental results and analysis

[0098] All experiments were conducted on a computer with an Intel Core i5 processor and 16.00GB of RAM. The algorithm was written in Java 8. Because no test data was available, this paper evaluated the algorithm using 20 randomly generated simulated use cases. The number of travelers ranged from 10 to 100, increasing in increments of 10. Each traveler size had two use cases, and the travelers' locations were randomly selected from a region. For each traveler, the commute time was a random number between 8:00 and 9:30, with a time unit of 10 minutes. The destination was a random point that did not overlap with any other traveler's location.

[0099] 1 Algorithm Comparison

[0100] The experiment compared the MPSO-VNS algorithm with six optimization algorithms: NSGA-II, MOEA / D, PSO, MaPSO, VNS, and Two-Level VNS. All seven algorithms used the same initial solution set of 100 solutions. Tables 1 and 2 show the three metrics of the non-dominated solution sets obtained after 1000 iterations of the initial solution set by each of the seven algorithms.

[0101] Table 1 shows the C-metric values ​​of MPSO-VNS compared to other algorithms and other algorithms relative to MPSO-VNS. The data in the table shows that, in most cases, MPSO-VNS's solution set coverage of other algorithms is higher than that of other algorithms. This phenomenon becomes more pronounced as the number of travelers in the case increases. In cases 70-2, 90-1, and 100-1, the C-metric values ​​of other algorithms relative to MPSO-VNS are even 0, indicating that the solutions in the non-dominated solution set of MPSO-VNS are not dominated by the solutions of other algorithms. This data shows that, for the non-dominated solution set of each algorithm, the MPSO-VNS solution is generally closer to the Pareto front than the other algorithms.

[0102] Table 1 C-metric values ​​of MPSO-VNS and other algorithms

[0103]

[0104]

[0105] Table 2 shows the IGD and HV values ​​for all algorithms and cases. Both metrics evaluate the convergence and diversity of the solution set. For small cases, such as 10-1 and 10-2, the values ​​of the two metrics for the seven algorithms are not significantly different, as each non-dominated solution set is close to the Pareto front. However, as the number of travelers in the case increases, the differences between the algorithms become more pronounced. The data in the table shows that MPSO-VNS outperforms the other algorithms in both HV and IGD metrics, indicating that MPSO-VNS's non-dominated solution set performs better than the other algorithms in terms of convergence and diversity. Furthermore, the metrics of the two VNS algorithms also outperform the other algorithms, while the NSGA-II algorithm performs the worst among these algorithms.

[0106] Table 2 IGD and HV values ​​of all algorithms

[0107]

[0108] To further analyze the differences among the seven algorithms during the iterative process, we extracted non-dominated solution sets after a certain number of iterations and analyzed their performance metrics. NSGA-II, MOEA / D, PSO, and MaPSO algorithms converged quickly in the early stages, but experienced minimal changes later on. VNS and Two-Level VNS algorithms, on the other hand, exhibited smoother performance curves and gradually surpassed the first four algorithms. MPSO-VNS, combining the strengths of both algorithms, converged quickly in the early stages and showed gradual improvement later on.

[0109] 2 Parameter sensitivity analysis

[0110] To understand the impact of the number of leaders, the number of historically optimal solutions, the number of globally optimal solutions, and the speed and weight of the particle motion operator on the quality of the solution set in the MPSO-VNS algorithm, several parameters were tested. While keeping other parameters constant, the values ​​of the tested parameters were varied, and the IGD and HV indicators were calculated for the resulting solution sets.

[0111] As the number of leaders increases, HV increases, while IGD decreases, indicating that the quality of the solution set improves. The improvement in solution quality is most pronounced when the number of leaders is 2. Given that the algorithm's time consumption increases significantly with the number of leaders, choosing 2 or 3 leaders yields the best overall results.

[0112] As the number of solutions in the historical and global optimal solution sets increases, HV increases and IGD decreases, indicating an improvement in the overall quality of the solution set. Similar to the number of leaders, a larger optimal solution set increases the algorithm's time consumption. When the particle speed is 1, the solution set quality is optimal. Beyond 1, the solution set quality deteriorates.

[0113] As the distance weights increase, HV shows a downward trend and IGD shows an upward trend. However, the jitter is too intense to determine whether the quality of the solution set is decreasing. 2 There is no obvious pattern in the effect of I weight on the quality of the final solution set.

[0114] The above is a schematic description of the present invention and its embodiments, which is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by this and, without departing from the purpose of the present invention, designs a structure and embodiment similar to this technical solution without inventiveness, they shall fall within the scope of protection of the present invention.

Claims

1. A multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search, characterized by: The following steps are involved:

1. Establish a non-dominated solution set NS ; 2. Use the initial solution construction algorithm to obtain the particle swarm at the initial position S ; 3. Particles P i Use particle motion operators to obtain the new particle position set PS i ; The particle motion operator calculation method is as follows: 2.1) Input particle current solution s , the global optimal solution set gbest , the historical optimal solution set pbest ; 2.2) New particle position set PS= ; 2.3) Yes gbest ∪ s Normalization; 2.4) Calculation D 2 I g , g gbest ; 2.5) Yes gbest Sorting, evenly selecting subsets G c ; 2.6) Use the same method to pbest Select a subset P c ; 2.7) Assume g ∈ G c , p ∈ P c ; 2.8) Random intercept g and s difference sequence gs , and obtain the global cognitive term O g , randomly intercepted p and s difference sequence ps , get self-awareness items O p , s Passing speed v After the movement of s v , s'=s v +O g +O p , PS=PS ∪ s' ; 2.9) Output PS ; g is the global optimal solution sequence, p is the historical optimal solution sequence, each solution in the optimal solution set B is based on the index value D 2 After sorting the size of I, multiple guided solutions are uniformly selected at the same interval; For the extracted global optimal solution subset G c and the historical optimal solution subset P c To perform the combination, step 2.8) is to use the calculated new solution set as the result after the particle movement; 4. PS i Perform variable neighborhood search VNS to obtain the set PS i ' ; The neighborhood search method is changed to: 3.1) Input PS ; 3.2) Set up new Q = PS ; 3.3) Assume q ∈ PS ,i∈range(0, ); 3.4) Execute the neighborhood operation operator 1 to obtain q 1 ;if q 1 Not q Domination, then Q = Q ∪ q 1 ; 3.5) Execute the neighborhood operation operator 2 to obtain q 2 ;if q 2 Not q Domination, then Q = Q ∪ q 2 ; 3.6) Execute the neighborhood operation operator 3 to obtain q 3 ;if q 2 Not q Domination, then Q = Q ∪ q 3 ; 3.7) Obtain Q The optimal non-dominated solution set of P.S. ; 3.8) Output P.S. ; For the solution set PS obtained by the motion operator, each solution is searched in a variable neighborhood. Steps 3.4) to 3.6) represent a search, and each neighborhood is searched in turn until a new solution that can dominate the current solution is found, and the search ends. In steps 3.4) to 3.6), each solution is searched in a variable neighborhood. Searches; 5. Use PS i ' Update Particles P i The historical optimal solution set pbest i ; 6. All particles P i of pbest i Update the global optimal solution gbest ; 7. Using non-dominated solution sets for filtering control pbest i and gbest the number of intermediate solutions; The non-dominated solution set filtering method is: 4.1) Input B ; 4.2) Yes B Normalized processing N ; 4.3）i = | N |； 4.4) Assume i > α; 4.5) Obtain N The two solutions with the closest distance between them, choose the worse solution w , B = B - w ; 4.6) i = i - 1, perform loop calculation; 4.7) Output B ; Steps 4.4) to 4.6) sequentially delete the worse solution of the two solutions with the closest Euclidean distance. The quality of the solution is judged by the normalized distance between the solution and the reference point.

8. Use gbest renew NS .

2. The multi-guided particle swarm optimization method for multi-objective carpooling problem with variable neighborhood search according to claim 1 is characterized by: The initial solution construction algorithm is as follows: 1.1) Let the new particle be P , solution sequence seq = ; 1.2) Assume i=0; 1.3) When i < the number of travelers n, if the random number falls within the probability value, then the i-th position in the sequence seq i The value is set to the destination, otherwise, a sequence is selected seq Traveler number not found in a ; 1.4) If seq i = a Make the solution invalid, then seq i The value is set to the destination, otherwise, seq i =a ; 1.5) Set i=i+1 and perform loop calculation; 1.6) Get the historical optimal solution set pbest= { seq }.

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