CN114358661A

CN114358661A - Shared bus scheduling method based on pyramid variant group evolution

Info

Publication number: CN114358661A
Application number: CN202210232373.6A
Authority: CN
Inventors: 苏生; 何甜甜
Original assignee: Yangtze River Delta Research Institute of UESTC Huzhou
Current assignee: Yangtze River Delta Research Institute of UESTC Huzhou
Priority date: 2022-03-10
Filing date: 2022-03-10
Publication date: 2022-04-15

Abstract

The invention relates to the technical field of shared vehicle scheduling, in particular to a shared bus scheduling method based on pyramid variant group evolution, which comprises the following steps: selecting feasible vehicles by the fitness of the vehicles through a roulette method according to the requirements of passengers at specific time and places, and generating an initial feasible solution and an initial population; secondly, performing improved cross operation on the generated population iteration; thirdly, performing variable neighborhood search on the feasible solution formed after crossing; fourthly, when the population is iterated to a designated algebra, pyramid variety group operation is executed; and fifthly, summarizing the optimal number of vehicles of each vehicle type in the obtained approximate optimal solution. The invention can better perform shared bus scheduling.

Description

Shared bus scheduling method based on pyramid variant group evolution

Technical Field

The invention relates to the technical field of shared vehicle scheduling, in particular to a shared bus scheduling method based on pyramid variant group evolution.

Background

With the arrival of the economic sharing era, the sharing travel mode gradually enters the visual field of the public and is concerned and favored by the public. Compared with the traditional traveling modes of buses, private cars, subways, taxis and the like, the sharing bus has the advantages of being comfortable compared with the buses, saving worry compared with self-driving, saving labor compared with the subways and saving money compared with renting.

The shared bus scheduling problem is a combinatorial optimization problem with NP difficulty, and its core technology is the vehicle Path Planning Algorithm (PPA). Algorithms commonly used for vehicle path planning at present include Genetic Algorithm (GA), particle swarm algorithm (PSO), simulated annealing algorithm (SA), ant colony Algorithm (ACO), neighborhood search algorithm (NS), and the like. These methods all have their own advantages, but also have certain limitations, such as high computational complexity, poor convergence, easy trapping in local parts, slow iteration speed, etc., so that path planning is a bottleneck.

For a traditional vehicle Path Planning Algorithm (PPA), there are several categories of single-vehicle type in a single vehicle yard, multiple-vehicle type in a single vehicle yard, and multiple-vehicle type in a multiple vehicle yard. The classification modes have corresponding application scenes, but all of them only distribute vehicles according to known fixed routes for the vehicles in the parking lot or distribute fixed routes for the known vehicles.

Research shows that the genetic algorithm can effectively solve the vehicle scheduling problem. However, the conventional genetic algorithm can only solve the continuous problem, and the shared bus problem has discreteness. In addition, the traditional genetic algorithm also has the problems of fixed population scale, low convergence speed, unsatisfactory accuracy and the like. Aiming at the problems, the predecessors combine other algorithms on the basis of the genetic algorithm, such as jagged variant group evolution, halving variant group evolution and the like to optimize the population and solve the practical problem, but the research on shared vehicle scheduling is little.

Disclosure of Invention

The invention provides a shared bus scheduling method based on pyramid variant group evolution, which can be well applied to shared vehicle scheduling problems.

The invention discloses a shared bus scheduling method based on pyramid variant group evolution, which comprises the following steps:

selecting feasible vehicles by the fitness of the vehicles through a roulette method according to the requirements of passengers at specific time and places, and generating an initial feasible solution and an initial population;

secondly, performing improved cross operation on the generated population iteration;

thirdly, performing variable neighborhood search on the feasible solution formed after crossing;

fourthly, when the population is iterated to a designated algebra, pyramid variety group operation is executed;

and fifthly, summarizing the optimal number of vehicles of each vehicle type in the obtained approximate optimal solution.

Preferably, in the first step, the problem is converted into a code to form a chromosome, the fitness of the genes on the chromosome is marked according to the principle of minimum cost, and then the genes are selected by adopting a roulette method, so that an initial feasible solution is formed; the fitness of each gene is calculated by the following formula:

（1）

（2）

（3）

（4）

wherein the formula (1) represents the cost of each vehicle

Fixed cost by current car P1_cAnd running cost P2_cThe product of the driving distance R and the running distance R is obtained; (2) in the formula V_maxThe maximum value of all available vehicle costs; (3) in the formula

Actual values representing each vehicle participating in the roulette wheel calculation; (4)in the formula P_cThe proportion of the current available vehicle in the wheel disc is represented;

eventually the routes of all vehicles are linked together to form the entire initial feasible solution.

Preferably, the second step specifically comprises the following steps:

(1) selecting 10% feasible solutions with the best fitness from the current population to form a TOPN optimal solution set;

(2) performing cross operation on each feasible solution and the high-quality solution in the population;

(2.1) randomly selecting a high-quality solution from TOPN high-quality solutions;

(2.2) selecting cross segments from the quality solution;

(2.3) replacing fragments corresponding to the common solutions with high-quality fragments;

(3) adjusting other parts except the crossed fragments of the crossed common solution to change the new solution into a feasible solution;

(4) and obtaining a new population.

Preferably, in step three, the variable neighborhood search includes two ways:

a. completely exchanging all routes of two vehicles with different models;

b. any two routes in all sites at the same time are arbitrarily swapped.

Preferably, in step four, the method for operating the pyramid variety group comprises:

A. and (3) population evolution: population elimination only occurs in a designated generation number; if the current iteration times are smaller than the next level of the pyramid, maintaining the population scale of the current level for evolution;

B. and (3) dividing the population: when the population evolves to the algebra where the pyramid level is located, dividing the current population into N groups;

C. and (3) population screening: selecting chromosomes with a certain proportion and good fitness from the N groups respectively;

D. and (3) population merging: merging the high-quality chromosomes selected from the N groups into a new population;

and circulating the process until the evolution is finished.

6. The pyramid variant group evolution-based shared bus scheduling method of claim 1, wherein: in the fifth step, the formula for generating the optimal number of the vehicles is as follows:

（5）

（6）

wherein the content of the first and second substances,

is a vehicle set, N represents the optimal total number of vehicles,

representing a particular vehicle. (5) The formula indicates that the optimal vehicle total number is calculated by the vehicles in the vehicle set; (6) the constraint of equation (5) indicates that each vehicle is only calculated if it is 1, i.e. scheduled.

The invention can be better applied to shared vehicle scheduling and can obtain better and more stable effect; the method comprises the following specific steps:

(1) the dispatch of all vehicles is completely shared, i.e. the concept of a dead-yard. All shared vehicles in the designated range do not need to return to the 'yard' after the passengers are picked up, and the shared vehicles can wait for the next picking-up task at the terminal of the picked-up passengers.

(2) The starting point of the vehicle transfer is not fixed. In the traditional vehicle scheduling problem, all the driving nodes are known, and the vehicle only needs to consider which node the vehicle goes to at the next moment; in the shared bus dispatch problem, the pick-up route of a vehicle at each dispatch moment is dynamically determined by the passenger demand at the pick-up point.

(3) A novel variant group evolution idea is provided, so that an evolution algorithm is better applied to the discrete shared vehicle scheduling problem.

(4) The optimal number of vehicles of each vehicle type is predicted more accurately.

Drawings

FIG. 1 is a flowchart of a shared bus scheduling method based on pyramid variant group evolution in embodiment 1;

FIG. 2 is a diagram showing the generation of an initial population in example 1;

FIG. 3 is a schematic diagram of the crossover algorithm in example 1;

FIG. 4 is a schematic diagram of the ACVR algorithm in example 1;

FIG. 5 is a schematic diagram of the CTRS search in example 1;

FIG. 6 is a schematic view of a pyramid variation population process in example 1;

FIG. 7(a) is a comparison graph of the two modes in the aspect of scheduling cost in example 1;

FIG. 7(b) is a comparison of the two modes in the total number of scheduled vehicles in example 1;

FIG. 8(a) is a comparison of scheduling costs for 1000 iterations in example 1;

FIG. 8(b) is a schematic diagram showing a comparison of scheduling costs for 3000 iterations in example 1;

FIG. 8(c) is a schematic diagram showing a comparison of scheduling costs for 5000 iterations in example 1;

FIG. 9(a) is a comparison of the scheduling cases of 1000 iterations for each vehicle type in example 1;

FIG. 9(b) is a comparative diagram showing the scheduling of each vehicle type in example 1 after 3000 iterations;

FIG. 9(c) is a comparison of the scheduling cases of each vehicle type for 5000 iterations in example 1;

FIG. 9(d) is a comparison diagram of the number of dispatched vehicles in example 1;

FIG. 10(a) is a schematic diagram showing five cost comparisons after 1000 iterations of three algorithms BGAD, PME and EOUV in example 1;

FIG. 10(b) is a schematic diagram showing five cost comparisons after 1000 iterations of the three algorithms BGAD, PME and HMPE in example 1;

FIG. 10(c) is a schematic diagram showing five cost comparisons after 1000 iterations of the three algorithms BGAD, PME and SMPE in example 1;

FIG. 10(d) is a schematic diagram of transverse comprehensive comparison after 1000 iterations of five algorithms of BGAD, PME, EOUV, HMPE and SMPE in example 1;

FIG. 11 is a diagram showing the analysis of the sensitivity parameter in example 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 limiting.

Example 1

The overall flow of the PME algorithm proposed in this embodiment is as follows:

1. and selecting feasible vehicles by the wheel roulette method according to the requirements of passengers at specific time and places according to the fitness of the vehicles, thereby generating an initial feasible solution and an initial population.

2. And performing improved cross operation on the generated population iteration.

3. And performing variable neighborhood search on the feasible solution formed after the intersection.

4. And performing pyramid variety group operation when the population is iterated to a designated algebra.

5. And summarizing the optimal number of vehicles of each vehicle type in the obtained approximate optimal solution.

First phase Generation of initial population

The generation of the initial feasible solution in the traditional genetic algorithm adopts a random mode, the method has the advantages that the solution generated by cross variation in the evolution process has more possibility, and the defect is that the iteration speed is slow. For the continuous problem, the random selection can exert the advantages thereof, because the solution generated by the random selection is always in a feasible domain, and the shared bus vehicle scheduling problem to be solved belongs to the discrete problem, so the advantages of the traditional genetic algorithm cannot be highlighted, and the opposite defects are amplified.

In the improved PME algorithm, fitness is marked on genes on a chromosome according to the principle of minimum cost, and then the genes are selected in a roulette method mode, so that an initial feasible solution is formed. The fitness of each gene is calculated by the following formula:

（1）

（2）

（3）

（4）

wherein, the formula (1) expresses that the cost of each vehicle is obtained by multiplying the fixed cost P1 of the current vehicle and the driving cost P2 with the driving mileage R. (2) Where Vmax is the maximum of all available vehicle costs. (3) The equation represents the actual value of each vehicle that is participating in the roulette wheel calculation. (4) Wherein Pc represents the proportion of the current available vehicle in the wheel disc.

Because the fitness of each gene is different, the probability that each gene is selected in the process of selecting genes using roulette is also different. Genes with higher fitness are more likely to be selected, and meanwhile, the roulette mode also ensures the randomness of gene selection, so that the finally obtained initial feasible solution is more like the result obtained after the traditional initial feasible solution is evolved by N generations compared with the initial feasible solution obtained by the traditional genetic algorithm. The method greatly improves the iteration speed of the population.

Eventually the routes of all vehicles are linked together to form our chromosome (initial feasible solution), as shown in fig. 2.

Improvements in evolutionary operations

The most important part of the evolutionary operation of traditional genetic algorithms is crossover and mutation. Firstly, selecting two chromosomes in the current population by adopting a roulette method according to fitness, then carrying out cross operation on the two chromosomes according to a certain probability, exchanging partial genes of the two chromosomes to generate a new chromosome, and carrying out mutation operation on the new chromosome according to a certain probability so as to obtain a new population. In the continuous type problem, the population quality is better because the newly generated chromosomes are always in the feasible region of the problem, but in the discrete type problem, the roulette mode is adopted according to the fitness, so that some chromosomes with weaker fitness are always not selected, and the result after cross mutation has certain limitation.

Aiming at the problem, the improved PME algorithm provided by the invention modifies the evolution operation of the population:

1. selecting 10% feasible solutions with the best fitness from the current population to form a TOPN optimal solution set;

2. performing cross operation on each feasible solution and the high-quality solution in the population;

2.1 randomly selecting a high-quality solution from TOPN high-quality solutions;

2.2 selecting cross segments from the high-quality solution;

2.3 replacing the corresponding fragment of the common solution with the high-quality fragment;

3. adjusting other parts except the crossed fragments of the crossed common solution to change the new solution into a feasible solution;

4. a new population is obtained.

Because the TOPN-optimized gene is a more excellent gene in the contemporary population, the common solution, after the crossover operation with the TOPN-optimized solution, enables the quality of the feasible solution to be improved probably, thereby enabling the whole population to evolve towards a better direction. Meanwhile, each feasible solution is subjected to cross operation, so that the coverage rate of population evolution operation is one hundred percent, and the phenomenon that evolution falls into local optimization is avoided. A schematic of the cross section is shown in figure 3.

Variable neighborhood search

After the crossover operation is completed, neighborhood searching is adopted to further optimize the feasible solution after crossover. Specifically, to the problem of bus sharing to be solved, the neighborhood search refers to performing neighborhood search on a driving route of a specific vehicle, and the embodiment is implemented by two ways:

1. complete exchange of all routes of two vehicles of different type (ACVR)

Suppose that the two vehicles to be exchanged are a type a vehicle No. 1 (with a passenger load of 30) and a type B vehicle No. 5 (with a passenger load of 10). Their original routes are respectively:

vehicle No. 1: 2- >1- >3- >5

Vehicle No. 5: 1- >5- >4- >2- >1

Then after the swap, the routes of the two vehicles become:

vehicle No. 1: 1- >5- >4- >2- >1

Vehicle No. 5: 2- >1- >3- >5

The specific schematic diagram is shown in fig. 4.

2. Arbitrarily exchanging any two routes (CTRS) in all locations at the same time

Assuming that passengers need to arrange vehicles at 10 o' clock places 1,2,3,4,5,6,7,8 and 9, 30 passengers need to dispatch for the place 2, and the place 2 originally arranges the vehicle 2 with the passenger capacity of 10 and the vehicle 3 with the passenger capacity of 20 to complete the pick-up; for the 6 th place, 10 passengers need to dispatch, and the 1 st car with the passenger capacity of 30 is originally arranged to complete the pick-up. The scheme is a car dispatching scheme for exchanging the place No. 2 and the place No. 6.

Considering that the whole chromosome is composed of the routes of all vehicles, and two vehicles at the same time are to be exchanged, we need to find all vehicles corresponding to the exchange time, select two vehicles from the vehicles, and then exchange the routes of the two vehicles.

The specific schematic diagram is shown in fig. 5.

Because the models of the cars are different, there are several possibilities after exchanging the two routes:

(1) the switching results in increased scheduling costs.

(2) The switching results in reduced scheduling cost.

(3) The scheduling cost is kept unchanged after the exchange.

In conclusion, the result of the neighborhood search is good or bad, and for the scheme of reducing the scheduling cost after the neighborhood search, the cross operation is optimized, and the neighborhood search result can be reserved at the moment; for the scheme that the scheduling cost is increased or kept unchanged after the neighborhood search, no optimization is carried out on the cross operation, and the scheme is directly abandoned.

Pyramid variant group scale optimization population evolution

The pyramid variant population scale is a second level algorithm on top of the PME-based evolutionary algorithm. The size of the population is crucial to population evolution, too large a population size can cause the iteration speed to be very slow, and too small a population size can cause the population to be trapped in local convergence. Compared with the fixed population and multi-population parallel evolution of the traditional evolutionary algorithm, the method has the advantage that a pyramid hierarchical population changing mode with better performance is provided. In the pyramid algorithm, the population scales of all layers are different, and the population scale of the bottom layer is larger, and the population scale of the top layer is smaller. In the whole population evolution process, population elimination is carried out once when iteration is carried out to a designated generation number until the population reaching the top of the pyramid is the population with excellent genes. The process of the variant group scale pyramid algorithm can be described as:

and (3) population evolution: population elimination of the gold tower algorithm only occurs in a designated generation number. And if the current iteration times are less than the next level of the pyramid, maintaining the population scale of the current level for evolution.

And (3) dividing the population: when the population evolves to the generation number of the pyramid level, the current population is divided into N groups.

And (3) population screening: and respectively selecting chromosomes with better fitness in a certain proportion from the N groups. This example was 75%.

And (3) population merging: the selected good chromosomes from the N groups are combined into a new population.

And circulating the process until the evolution is finished. A schematic of the pyramid variant population scale process is shown in fig. 6.

Generating an optimal number of vehicles for a vehicle type

The generation of the optimal number of vehicles for each vehicle type is the third layer of algorithm on the PME basic evolution algorithm, in the PME algorithm, the number of available vehicles given initially is certainly larger than the number of vehicles actually needed finally, otherwise, the condition that the vehicles are not dispatched enough occurs. Therefore, for vehicles without dispatching, the optimal vehicle number of each vehicle type can be generated and discarded, and only the vehicles to be dispatched are reserved. The specific formula is as follows:

（5）

（6）

wherein the content of the first and second substances,

is a vehicle set, N represents the optimal total number of vehicles,

Comparison of experiments

The experiment was performed on a computer with a processor of Intel (R) core (TM) i7-9750H CPU @ 2.60GHz 2.59 GHz and a memory of 16 GB.

The experiment is compared from two aspects of modes and algorithms:

1. on the mode

The traditional vehicle scheduling problem takes the following form: firstly, generating a route, generating a plurality of routes which can be connected in series according to the scheduling requirement of each place at each time, and then respectively scheduling vehicles for the routes. And the improved PME algorithm can realize vehicle scheduling sharing under the condition of unknown routes. Fig. 7 shows a comparison of the two modes in terms of both the cost of dispatch and the total number of vehicles dispatched.

As seen from fig. 7(a) and 7(b), the shared scheduling method is superior to the conventional scheduling, regardless of the scheduling cost or the total number of scheduled vehicles. In accordance with this expectation, the conventional scheduling mode is to generate a plurality of routes which can be connected in series according to the scheduling requirement of each place at each time, and then to schedule vehicles for the routes respectively. The disadvantage of this approach is that the scheduling requirements for each location at each time may be different, and once they are connected in series into a route, the vehicle can only be scheduled according to the maximum requirement of each node on the route, which may cause the full load rate of the vehicle to be too low.

The sharing dispatching mode is that approximately optimal dispatching vehicles are directly arranged according to the requirements of each place at each time, and then a dispatching route in one day is generated for each vehicle, so that the full load rate is guaranteed to the maximum extent, and the cost is reduced.

2. Algorithmically

Comparing the PME algorithm with the conventional genetic algorithm and the neighborhood search algorithm in terms of both the dispatching cost and the number of dispatched vehicles, the experimental results are shown in fig. 8(a), fig. 8(b), fig. 8(c), fig. 9(a), fig. 9(b), fig. 9(c) and fig. 9 (d).

The model is respectively iterated 1000 times, 3000 times and 5000 times by adopting PME, GA and NS algorithms, and the accuracy of the PME algorithm provided by the embodiment is far better than that of the traditional genetic algorithm and the neighborhood search algorithm. At the same time, we found that from 500 generations, the iteration efficiency of the conventional genetic algorithm was extremely slow, which is consistent with expectations. In the discrete problem, the roulette method in the conventional genetic algorithm makes part of the common solutions always unselected, so that the whole population is liable to fall into local convergence during the evolution process. The PME algorithm provided by the embodiment well avoids the defect.

Fig. 9(a), 9(b), and 9(c) show the scheduling conditions of each vehicle type when the three algorithms are iterated 1000 times, 3000 times, and 5000 times, and it can be seen from the figures that the scheduling of each vehicle type by the PME algorithm proposed by the present invention is relatively balanced, and the number of schedules is relatively small. As can be seen from fig. 9(d), the number of scheduled vehicles required by the pyramid variant group evolution algorithm combined with neighborhood search proposed by the present invention is much smaller than the total number of scheduled vehicles of the conventional genetic algorithm and neighborhood search.

Regarding variable population iteration, two modes of a halving method variable population and a sawtooth variant population are proposed by the predecessor, and through understanding and reproduction, the invention provides a better pyramid variant population evolution mode of grouping, optimizing and combining, and successfully applies the pyramid variant population evolution mode to a PME basic evolution algorithm. Fig. 10 shows the results of comparing the PME algorithm with the PME basic evolution algorithm by introducing pyramid iteration, i.e., grouping variant population, and the halving variant population and jagging variant population proposed in the previous.

Wherein BGAD represents a basic evolution algorithm of an unadditized variant population, PME represents the evolution of an introduced grouped variant population, EOUV represents the evolution of an unadditized variant population, HMPE represents the evolution of a halved variant population, and SMPE represents the evolution of a jagged variant population. Fig. 10(a) shows five cost comparisons after 1000 iterations of three algorithms of BGAD, PME, and EOUV, fig. 10(b) shows five cost comparisons after 1000 iterations of three algorithms of BGAD, PME, and HMPE, fig. 10(c) shows five cost comparisons after 1000 iterations of three algorithms of BGAD, PME, and SMPE, and fig. 10(d) shows a horizontal comprehensive comparison after 1000 iterations of five algorithms of BGAD, PME, EOUV, HMPE, and SMPE.

Through four sets of experiments in fig. 10(a), fig. 10(b), fig. 10(c) and fig. 10(d), it can be seen that the overall effect of the pyramid variant group evolution, i.e. the grouped variant group iteration-PME algorithm proposed by the present invention is the best. The method is consistent with expectation, in the population screening process of the grouping variation population, the population is firstly divided into n groups, and then a certain proportion of high-quality chromosomes are selected from the n groups to form a new population, so that under the condition that the high-quality chromosomes are reserved, some chromosomes which are not high-quality at present still have the opportunity of being selected, more possibility is provided for population evolution, and the finally obtained effect is better.

Fig. 11 is a comparison of five algorithms, namely BGAD, PME, EOUV, HMPE, and SMPE, from three dimensions of maximum, minimum, and average values, and it can be found that the cost of the PME algorithm is less than that of the other algorithms, regardless of the maximum, minimum, and average values, and the solution quality of the PME algorithm is relatively stable.

Table 1 shows the comparison in the init, best, avg, and worst dimensions for six algorithms of GA, NS, PME, EOUV, HMPE, and SMPE at the time and place scales of 3x3, 5x5, 8x8, and 10x10, respectively. Experimental data show that the comprehensive performance of the PME algorithm provided by the invention is the best no matter best, or avg or worst. In different scales, the best value of the rest algorithms is better than that of the PME algorithm, but the stability of the rest algorithms is found to be poor through multiple experimental comparisons, so that the avg value and the worst value are always larger than that of the PME algorithm.

TABLE 1 comparison of Algorithm Performance

The present invention and its embodiments have been described above schematically, without limitation, 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, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.

Claims

1. The shared bus scheduling method based on pyramid variant group evolution is characterized by comprising the following steps: the method comprises the following steps:

2. The pyramid variant group evolution-based shared bus scheduling method of claim 1, wherein: in the first step, the problem is converted into a code to form a chromosome, the fitness of the gene on the chromosome is marked according to the principle of minimum cost, and then the gene is selected by adopting a roulette method, so that an initial feasible solution is formed; the fitness of each gene is calculated by the following formula:

(1)

(2)

(3)

(4)

wherein the formula (1) represents the cost of each vehicle

Fixed cost by current car P1_cAnd running cost P2_cThe product of the driving distance R and the running distance R is obtained; (2) in the formula V_maxThe maximum value of all available vehicle costs; (3) the actual value of each vehicle participating in the wheel disc calculation is represented in the formula; (4) in the formula P_cThe proportion of the current available vehicle in the wheel disc is represented;

3. The pyramid variant group evolution-based shared bus scheduling method of claim 1, wherein: in the second step, the method specifically comprises the following steps:

(2.2) selecting cross segments from the quality solution;

(4) and obtaining a new population.

4. The pyramid variant group evolution-based shared bus scheduling method of claim 1, wherein: in step three, the variable neighborhood search includes two ways:

a. completely exchanging all routes of two vehicles with different models;

b. any two routes in all sites at the same time are arbitrarily swapped.

5. The pyramid variant group evolution-based shared bus scheduling method of claim 1, wherein: in the fourth step, the method for operating the pyramid variety group comprises the following steps:

and circulating the process until the evolution is finished.

（5）

（6）

wherein the content of the first and second substances,

is a vehicle set, N represents the optimal total number of vehicles,

on behalf of a specific vehicle or vehicles,

(5) the formula indicates that the optimal vehicle total number is calculated by the vehicles in the vehicle set; (6) the constraint of equation (5) indicates that each vehicle is only calculated if it is 1, i.e. scheduled.