CN115186969A

CN115186969A - Multi-guide particle swarm multi-target carpooling problem solving optimization method with variable neighborhood search

Info

Publication number: CN115186969A
Application number: CN202210573923.0A
Authority: CN
Inventors: 苏生; 熊冬文
Original assignee: Yangtze River Delta Research Institute of UESTC Huzhou
Current assignee: Yangtze River Delta Research Institute of UESTC Huzhou
Priority date: 2022-05-24
Filing date: 2022-05-24
Publication date: 2022-10-14

Abstract

The invention relates to the technical field of shared traffic, in particular to a multi-guide solution particle swarm multi-target car-sharing problem optimization method with variable neighborhood search, which comprises the following steps: 1. establishing a non-dominated solution set NS; 2. obtaining a particle swarm S of an initial position by using an initial solution construction algorithm; 3. for particle P _i Obtaining a set of new positions PS of particles by a particle motion operator _i (ii) a 4. For PS _i VNS (virtual network server) variable neighborhood search is carried out to obtain set PS _i '; 5. using PS _i ' update particle P _i Historical best solution set pbest _i (ii) a 6. All particles P _i Of _i Updating the global optimal solution gbest; 7. controlling pbest using non-dominated solution set filtering _i And the number of solutions in gbest; 8. the NS is updated using gbest. The invention can better solve the problem of multi-target car sharingAnd (4) a problem.

Description

Multi-guide solution particle swarm multi-target car-sharing problem optimization method with variable neighborhood search

Technical Field

The invention relates to the technical field of shared traffic, in particular to a multi-guide solution particle swarm multi-target car pooling problem optimization method with variable neighborhood search.

Background

With the improvement of economic income and living standard of people, the number of private cars is increased day by day in the traditional traffic mode, and the problems of traffic jam, insufficient parking spaces, environmental pollution and the like are brought. The existing travel services of taxies, shared cars and the like realize time-sharing leasing 'sharing' by putting in newly increased quantity instead of fully utilizing inventory, and the vacant seat rate is very high in most time periods, so that the serious waste of manpower and vehicle resources is caused. The problems of road congestion, parking position shortage, city management and environmental pollution caused by excessive vehicles in cities can not be solved, and the embarrassment that the existing vehicles compete for resources such as license plates, roads, parking positions and the like is increased.

Many studies have shown that car pooling is an effective way to alleviate the above problems. The travelers share the vehicles with other people in a sharing and co-riding mode, and pay corresponding fees according to the traveling requirements of the travelers. Under the condition that the number of travelers is not changed, if a part of travelers select drivers the same as the destination or similar to the traffic route to take the same place, the empty seats of the vehicle can be effectively utilized. In addition, the car pooling greatly reduces the purchase willingness of some car-free travelers to the private car, thereby reducing the possession of the private car. As the use and ownership of private cars declines, the demand for parking spaces, roads and private car travel-related services will inevitably decrease.

The current car sharing algorithm has a plurality of problems, and the existing research only considers how to allocate resources from one side of drivers, passengers or resources, which results in that the obtained result is difficult to optimize the performance of the three simultaneously, and therefore, the practical problem is difficult to be guided. Most car sharing algorithms mainly solve the problem of one-time static or dynamic car sharing, and do not consider the car sharing problem among specific crowds.

In the multi-target car sharing problem, the existing algorithm cannot well take account of the convergence and diversity of a solution set, but is biased to one aspect, and further improvement space is provided.

Disclosure of Invention

The invention provides a multi-guide particle swarm solution multi-target car-sharing problem optimization method with variable neighborhood search, which can solve the car-sharing problem of staff commuting in the same park and can efficiently acquire a car-sharing scheme.

The multi-guide solution particle swarm multi-target car-sharing problem optimization method with variable neighborhood search comprises the following steps of:

1. establishing a non-dominated solution set NS;

2. obtaining a particle swarm S of an initial position by using an initial solution construction algorithm;

3. for particle P _i Obtaining a set PS of new positions of particles using a particle motion operator _i ；

4. For PS _i VNS (virtual network server) variable neighborhood search is carried out to obtain set PS _i '；

5. Using PS _i ' update particle P _i Historical optimal solution set pbest _i ；

6. All particles P _i Of _i Updating the global optimal solution gbest;

7. controlling pbest using non-dominated solution set filtering _i And the number of solutions in gbest;

8. the NS is updated using gbest.

Preferably, the first and second electrodes are formed of a metal,

the initial solution construction algorithm is as follows:

preferably, the first and second liquid crystal display panels are,

the particle motion operator calculation method is as follows:

g is a global optimal solution sequence, p is a historical optimal solution sequence, and each solution in the optimal solution set B is based on the index value D ² After the I is sorted, a plurality of guide solutions are uniformly selected at the same interval; for the extracted global optimal solution subset G _c And historical optimal solution subset P _c Make a combination, 7 th-Row 15 is the result after the particle motion using the new solution set calculated.

Preferably, the first and second electrodes are formed of a metal,

the variable neighborhood searching method comprises the following steps:

performing variable neighborhood search on each solution of the solution set PS obtained by the motion operator, wherein the 6 th to 17 th rows represent one search, sequentially searching in each neighborhood until a new solution which can dominate the current solution is found, and ending the search; in lines 4-16, each solution is searched β times.

Preferably, the first and second liquid crystal display panels are,

the non-dominated solution set filtering method comprises the following steps:

and 4-7, deleting the poor solution from the two solutions with the closest Euclidean distance in turn, and judging the quality of the solution according to the distance between the normalized solution and the reference point.

The invention can improve the problem that the solution set convergence of the PSO algorithm is too fast in the multi-target car sharing problem and falls into local optimization. When the particle motion guide solution is selected, the particle motion guide solution can represent the whole motion trend of the optimal solution set as much as possible. The invention designs a new index to represent the position distribution of the solution in the solution set, and uniformly selects a plurality of guide solutions according to the index, thereby ensuring the convergence of the solution set of the algorithm and simultaneously increasing the diversity of the solution set.

Drawings

FIG. 1 is a flowchart of a multi-objective car-pooling problem optimization method for multi-guided solution particle swarm in the variable neighborhood search in embodiment 1;

FIG. 2 is a diagram of an example of sequence coding possible in embodiment 1;

FIG. 3 is a diagram showing an example of adjustment of a particle movement locus in embodiment 1;

FIG. 4 shows a graph of D in example 1 ² I, a schematic calculation process;

FIG. 5 is a diagram showing an example of a node switching neighborhood in embodiment 1;

FIG. 6 is a diagram showing an example of a node change neighborhood in embodiment 1;

fig. 7 is an exemplary diagram of bus taking order exchange neighborhood in embodiment 1.

Detailed Description

For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not restrictive.

Example 1

The solution of the car sharing problem is converted into a simple sequence code, and the algorithm operation is convenient. And some expansion is made on the PSO algorithm, so that the diversity of the solution set is improved.

The method aims to solve the problems that solution set convergence is too fast and local optimization is involved in the multi-target car sharing problem in the PSO algorithm. When the particle motion guide solution is selected, the particle motion guide solution can represent the overall motion trend of the optimal solution set as much as possible. A new index is designed to represent the position distribution of the solutions in the solution set, a plurality of guide solutions are uniformly selected according to the index, and the diversity of the solutions is increased while the convergence of the algorithm solution set is ensured.

1 sequence coding

As shown in fig. 2, this is a possible solution to the car pool problem, and

travelers

1, 3, and 4 provide the car for the current car pool, and start driving from their locations, respectively, and 1

carries

2, 6, 7,3 carries 8, 11, and 4

carries

5, 9, and 10 in sequence.

In order to express the passenger carrying sequence of the vehicle, a sequence code capable of reflecting the problem solution is designed. The code length is the number of travelers n, each traveler has a serial number, the ith bit of the sequence code represents the serial number of the next traveler of the ith traveler, for example: the next digit of the traveler No. 2 in fig. 2 is No. 6, the digit of the transformed sequence code 2 is No. 6, the next digit of the traveler No. 5 is No. 9, and the digit of the sequence code 5 is 9. If a certain traveler does not have the next traveler after the traveler, but directly arrives at the destination, its corresponding serial code is the code of the destination, here denoted by 0. For example, the 7, 10, 11-numbered travelers in fig. 2 have no next-numbered travelers, and the sequence-coded 7, 10, 11 bit values are all 0.

It can be easily understood that 1 to n have no serial numbers appearing in the serial code, indicating that they have no previous traveler, i.e., the traveler to whom the serial numbers correspond is the provider, i.e., driver, of the vehicle. For example, there are no 1, 3, 4 in the sequence code in fig. 2, and the next bit in the sequence is read from these serial numbers until the serial number of the next bit is 0, so that 1, 2, 6, 7,3, 8, 11,4, 5, 9, 10 can be obtained, which corresponds to exactly three passenger-carrying sequences. As long as each passenger carrying sequence is known, travelers on each vehicle can be determined, and the vehicle travel distance and the travel distance of each traveler can be calculated.

2 Algorithm framework

The algorithm 1 gives a framework of the MPSO-VNS algorithm, and has two-point extension on the basic PSO, and the flow is shown in FIG. 1. One is to perform a variable neighborhood search at the location after the particle motion to optimize the solution set. And secondly, when the scale of the non-dominated solution set in the multi-target problem is overlarge, the optimal solution set is filtered, the quantity of the solution sets is controlled, and the similarity between the solutions is reduced.

Algorithm 1MPSO-VNS

3 initial solution construction

Based on the particle swarm optimization algorithm, the initial position of each particle needs to be initialized, namely an initial solution is constructed. Algorithm 2 is the process of constructing the initial solution, because each bit of the solution sequence represents the serial number of the next traveler, the traveler's serial numbers in the sequence are all unique. And sequentially assigning values to each bit of the sequence during initialization. First, a probability value is set, which indicates that the traveler is not the next traveler, but is directly driving to the destination (line 5 of the code). And selecting the serial numbers of travelers which are not obtained in the sequence before the other positions, judging whether the formed partial solution has feasibility, if so, setting the serial numbers at the current position of the sequence, and otherwise, setting the serial numbers as the destinations (lines 7-12 of the codes). The case where the insertion of the traveler number invalidates the solution has two cases, one is that the vehicle is overloaded after joining, and the other is that the order of carrying passengers of the vehicle forms a cycle.

Algorithm 2 initial solution construction

4 particle motion operator

The particle swarm optimization algorithm simulates the movement of birds when a bird swarm forages by designing a particle without mass. The basic idea of the particle swarm optimization algorithm is to find the optimal solution through cooperation and information sharing among individuals in a group. And each particle independently searches an optimal solution in a solution space, the searched optimal solution is recorded as a particle history optimal solution, the particle history optimal solution is shared with other particles in the whole particle swarm, and the optimal individual optimal solution is found and is used as the current global optimal solution of the whole particle swarm. All the particles in the particle swarm adjust the motion trail of the particles according to the historical optimal solution of the particles and the global optimal solution shared by the whole particle swarm, namely the self-knowledge item O _p = rand () (p-s) and global acknowledgement term O _g = rand () (g-s). Where s represents the current position of the particle, p represents the historical optimal solution, and g represents the global optimal solution.

As shown in fig. 3, the sequence s is obtained by the motion of the current solution sequence s through the velocity v _v In the figure, the speed is 3 sequence bits, and the direction is 1 st, 2 nd and 4 th sequence bits. Obtaining a difference value between the global optimal solution sequence g and the current solution sequence s to obtain a partial subsequence g-s, and randomly intercepting partial sequence bits in the subsequence as a global identification item O of particle motion _g Obtaining self-cognition item O of the particle from the historical optimal solution sequence p and the current solution sequence s by the same method _p And finally the sequence s _v Combined with self-authenticationKnowledge items and global knowledge items, resulting in a new solution s' for the particle.

Some researchers have improved the PSO algorithm to solve the multi-objective optimization problem. In multi-objective problems, the optimal solution is no longer a single extremum, but rather a set of non-dominant solutions. In the improved algorithms, only a single solution is taken, and the whole optimal solution set cannot be well represented, so that a method is designed for sampling from the solution set.

And sorting all the optimal solutions during sampling, and uniformly selecting a specified number of solutions as guide solutions. In order to select a 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). Firstly, the normalization processing is carried out on each solution of the current solution s and the optimal solution set B by using a formula (1), and f _i,max Representing the maximum of all ith objective functions in the solution set s ≦ B, f _i,min Expressing the minimum value of all ith objective functions in the solution set s & ltU & gt B;

as shown in fig. 4, the current solution s and the optimal solution set(s) are evaluated ₁ ,s ₂ ,s ₃ ,…,s _n ) After normalization, (f) is taken _1,min , f _2,min ,…,f _m,min ) Is the reference point r. With the optimal solution s ₂ For the purpose of example only,

is the current solution s to the optimal solution s ₂ The vector of (a) is determined,

is the vector from the current solution s to the reference point r, and theta is the vector

Sum vector

The included angle of (a). The optimal solution phase can be calculated by equations 2 and 3An index value D for the current solution ² I, wherein ω ₁ And ω ₂ Respectively representing the direction weight and distance weight of the optimal solution with respect to the current solution.

Each solution in the optimal solution set B is according to D ² After sorting the sizes of I, a plurality of guide solutions are uniformly selected at the same interval. For the extracted global optimal solution subset G _c And historical optimal solution subset P _c The combination is performed and the new solution set calculated is used as the result after the particles have moved (lines 7 to 15 of the code).

Algorithm 3 particle motion operator

5-variant neighborhood search

Neighborhood searching has proven to be an effective strategy to improve the quality of the non-dominated solution set. And performing variable neighborhood search on the solution set after the particles move, and providing three neighborhoods.

The first neighborhood: two random nodes are selected, and the positions of the two nodes in the sequence are exchanged. Referring to fig. 5, the next place of the 2 # traveler is the 6 # and the next place of the 3 # traveler is the 8 # and after exchanging two node positions, the next place of the 2 # traveler is the 8 # and the next place of the 3 # traveler is the 6 # traveler

The second neighborhood: a random node is selected and the value at the node location is modified. As shown in FIG. 6, if the value of the 4 th bit in the sequence is modified from 5 to 3, the next bit of the No. 4 traveler is changed from No. 5 to No. 3

Third neighborhood: randomly selecting a vehicle with the number of travelers larger than one, randomly selecting two travelers with continuous boarding sequence, and exchanging the sequence of the two travelers. As shown in fig. 7, the traveler sequence of the original vehicle is 4, 5, 9, 10, and becomes 4, 9, 5, 10 after the neighborhood change.

And (3) performing variable neighborhood search on each solution of the solution set PS obtained by the motion operator, wherein lines 6-17 of the code represent one search, searching in each neighborhood in sequence until a new solution which can dominate the current solution is found, and ending the search. In algorithm 4, each solution is searched β times (lines 4-16 of the code).

Algorithm 4-variable neighborhood search

6 non-dominant solution set Filtering

The number of solutions in the optimal solution set obtained by the algorithm has a trend of increasing with the number of iterations, and when the number is too large, the time for selecting the leaders for particle motion is also obviously increased, so that the solution set needs to be filtered to limit the scale of the optimal solution set. The algorithm deletes the poor solution (code lines 4-7) in the two solutions with the closest Euclidean distance in turn, and the quality of the solution is judged by the distance between the normalized solution and the reference point (origin).

Algorithm 5 non-dominated solution set filtering

Experiment of

Algorithm index

To evaluate the effectiveness of the algorithm, three indicators were selected experimentally: inverted Generation Distance (IGD), hyper volume index (HV), C-metric solution coverage.

1、IGD

IGD is the average of the distance of each reference point to the nearest solution. The IGD values are obtained from equation (4) for a set of uniformly distributed reference points P taken at the algorithmically solved solution set P and at the pareto front. d (x, y) represents the euclidean distance between a point x in the reference set P to a 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. Smaller IGD values indicate that the solution set is closer to the pareto front and the distribution is more uniform.

IGD can simultaneously evaluate convergence and diversity of the solution set. Since the reference point of the problem cannot be obtained in advance, a non-dominated solution set obtained by combining solution sets obtained by all algorithms is used as the reference point of the index. In order to balance the weights of the three objective function values in index calculation, each solution in the solution set P is normalized by formula (10).

2、HV

HV is the volume of the union of the non-dominated solution set obtained by the algorithm and the reference point in the target space enclosing the region. For the solution set P obtained by the algorithm, the HV index can be obtained by equation (5). Wherein r = (r) ₁ ,r ₂ ,..., r _m ) For the reference point, m is the target number, and L () represents Lebesgue measure. HV can also evaluate the convergence and diversity of the solution set, and the larger the value of HV, the better the comprehensive performance of the algorithm.

HV(P,r ^* )＝L(∪ _x∈P [f ₁ (x),r ₁ ]×,…,[f _m (x),r _m ]) (5)

In the experiment, each solution in the solution set P is normalized by the formula (1), then r = (1.0 ) is selected as a reference point, lebesgue measure is calculated for the normalized solution, and finally the HV value is obtained. HV is more complex to calculate, referring to the calculation method of Fonseca et al.

3. C-metric solution set coverage

The coverage rate C (a, B) of the solution set a to the solution set B is given by equation (6), a numerator represents the number of solutions in the solution set B that are dominated by at least one solution in the solution set a, and a denominator represents the number of solutions in the solution set B.

The larger the value of C (A, B), the higher the degree to which solution set A dominates solution set B. Evaluation of solution set a and solution set B requires comparison of C (a, B) and C (B, a).

Results and analysis of the experiments

All experiments were performed on a computer with an Intel core i5 processor and 16.00GB memory, and the algorithm was written in Java 8. Because no test data is available, the effect of the algorithm is evaluated here with 20 simulation cases generated randomly. The number of travelers is from 10 to 100, the number of travelers is increased by 10 equal-difference, each number of travelers has two cases, and the place of the travelers is randomly selected from one area. For any traveler, the working hours are random numbers from 8 to 9, with a unit time of 10 minutes. The destination is a random point that does not overlap with the location of any traveler.

1 Algorithm comparison

The experiment compares the MPSO-VNS algorithm with six optimization algorithms of NSGA-II, MOEA/D, PSO, maPSO, VNS and Two-Level VNS. The 7 algorithms all use the same initial solution set and the number of solutions is 100. Tables 1 and 2 show three index values of the non-dominated solution set obtained after 7 algorithm iterations of the initial solution set are respectively carried out for 1000 times.

Table 1 shows the C-metric values of MPSO-VNS relative to MPSO-VNS for other algorithms as well as other algorithms. As can be seen from the data in the table, in most cases, the solution set coverage of the MPSO-VNS to other algorithms is higher than that of other algorithms, and the performance is more obvious as the number of travelers in the case increases. In cases 70-2, 90-1, 100-1, even the other algorithms are 0 with respect to the C-metric value of the MPSO-VNS, which means that the solutions in the non-dominant solution set of the MPSO-VNS are not dominated by the solutions of the other algorithms. This data demonstrates that in the same case, for each algorithm's non-dominant solution set, the overall solution for MPSO-VNS is closer to the pareto frontier than the other algorithms.

TABLE 1C-metric values for MPSO-VNS and other algorithms

Table 2 shows IGD and HV values for all algorithms and cases. Both of these indices can evaluate the convergence and diversity of the solution set. For small scale cases such as 10-1, 10-2, etc., the two index values for the 7 algorithms do not differ much because each non-dominated solution set is already close to the pareto frontier. The difference between the algorithms is more obvious as the number of case travelers increases. As can be seen from the data in the table, the HV and IGD indexes of the MPSO-VNS are superior to those of other algorithms, which shows that the overall performance of the non-dominated solution set of the MPSO-VNS on convergence and diversity is superior to that of other algorithms. In addition, the metrics of both VNS algorithms are superior to the others, and the NSGA-II algorithm performs the worst of these algorithms.

TABLE 2 IGD and HV values for all algorithms

In order to further observe the difference of the 7 algorithms in the iteration process, after the algorithms are separated by a certain iteration number, a non-dominated solution set of the algorithms is extracted for index analysis. The NSGA-II, MOEA/D, PSO and MaPSO algorithms have high convergence speed in the early stage, but have small subsequent change range, and index change curves of the VNS and Two-Level VNS algorithms are smoother and are gradually surpassed in the first 4 algorithms in the subsequent stage. MPSO-VNS combines the characteristics of the two parties, and has rapid convergence in the early stage and gradual improvement in the later stage.

2 parameter sensitivity analysis

In order to know the influence of the numbers of leaders, the number of historical optimal solution sets, the number of global optimal solution sets, the speed and the weight in a particle motion operator on the quality of the solution sets in the MPSO-VNS algorithm. In the experiment, several parameters are tested respectively, under the condition that other parameters are not changed, the value of the parameter to be tested is changed, and then IGD and HV indexes are calculated for the obtained solution set.

As the number of leaders increases, HV tends to increase and IGD tends to decrease, indicating that the quality of the solution set is better. When the numbers of leaders are 2, the improvement of solution set quality is most obvious. Considering that the time consumption of the algorithm is obvious along with the increase of the number of the leaders, the comprehensive effect is best when 2 or 3 leaders are selected.

As the number of solutions in the historical optimal solution set and the global optimal solution set is increased, HV is in an ascending trend, IGD is in a descending trend, and the comprehensive quality of the solution sets is better. Similar to the number of leaders, the larger the optimal solution set scale is, the higher the algorithm time consumption is. When the particle movement speed is 1, the solution quality is best, and when the speed exceeds 1, the solution quality is worse and worse.

As distances weight increases, HV generally decreases and IGD generally increases, but jitter is too severe to determine that the quality of the solution set is decreasing. Thus D ² The impact of the I-weight on the final solution quality is not a significant rule.

The present invention and its embodiments have been described above schematically, and the description is not intended to be limiting, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, without departing from the spirit of the present invention, a person of ordinary skill in the art should understand that the present invention shall not be limited to the embodiments and the similar structural modes without creative design.

Claims

1. The optimization method of the multi-guide solution particle swarm multi-target car sharing problem with variable neighborhood search is characterized by comprising the following steps of: the method comprises the following steps:

1. establishing a non-dominated solution set NS;

6. All particles P _i Pbest of _i Updating the global optimal solution gbest;

8. the NS is updated using gbest.

2. The method for optimizing the multi-objective car-pooling problem of the multi-guided solution particle swarm according to the variable neighborhood search, which is characterized in that:

the initial solution construction algorithm is as follows:

3. the method for optimizing the multi-objective car-pooling problem of the multi-guided solution particle swarm according to the variable neighborhood search, which is characterized in that:

the particle motion operator calculation method is as follows:

g is a global optimal solution sequence, p is a historical optimal solution sequence, and each solution in the optimal solution set B is according to an index value D ² After I is sorted, a plurality of guide solutions are uniformly selected at the same interval; for the extracted global optimal solution subset G _c And historical optimal solution subset P _c The combination is performed, lines 7-15 using the new calculated solution set as the result after the particles have moved.

4. The method for optimizing the multi-objective car-pooling problem of the multi-guided solution particle swarm according to the variable neighborhood search, which is characterized in that:

the variable neighborhood searching method comprises the following steps:

performing variable neighborhood search on each solution of the solution set PS obtained by the motion operator, wherein lines 6-17 represent one search, searching in each neighborhood in sequence until a new solution which can dominate the current solution is found, and ending the search; in lines 4-16, each solution is searched β times.

5. The multi-objective car-pooling problem optimization method for the multi-guided solution particle swarm with the variable neighborhood search function according to claim 1, wherein the method comprises the following steps of:

the non-dominated solution set filtering method comprises the following steps:

and 4, sequentially deleting the poorer solution of the two solutions with the Euclidean distance from the line 4 to the line 7, and judging the quality of the solution according to the distance between the normalized solution and the reference point.