CN109919376B - Multi-parking lot and multi-vehicle type vehicle path scheduling control method - Google Patents
Multi-parking lot and multi-vehicle type vehicle path scheduling control method Download PDFInfo
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Abstract
The multi-parking lot and multi-vehicle type vehicle path scheduling control method comprises the following steps: step 1, establishing an objective function by taking the lowest total cost of all distribution vehicles as a target; step 2, encoding step 3, initializing a population; step 4, evaluating all individuals by adopting the target function as a fitness function; step 5, selection and cross operation step 6, mutation operation; step 7, performing neighborhood search on each individual in the population by using an improved extreme value optimization algorithm; step 8, calculating the fitness of all individuals in the population; step 9, selecting; step 10, keeping the elite; step 11, sequentially finishing iteration; step 12, judging whether a termination condition is met, wherein the termination condition is that the iteration time G reaches the maximum iteration time MaxGen or GbKeeping the number Nu of times that the fitness value is kept unchanged to reach the specified number Kbest, if the number Nu of times is met, continuing to execute the step 13, and if the number Nu of times that the fitness value is kept unchanged is not met, returning to execute the step 5; step 13, outputting the individuals GbAnd its fitness value fGb(ii) a Step 14, for the optimal individual GbAnd its fitness value fGbAnd (6) performing interpretation. The invention aims to improve the searching efficiency and the convergence speed of the algorithm.
Description
Technical Field
The invention relates to a multi-parking lot and multi-vehicle type vehicle path scheduling control method.
Background
The Vehicle Routing Problem (VRP) is the core Problem of logistics transportation management optimization, with the rapid development of scientific technology and the stable increase of national economy, the daily life of people is more and more unable to leave the development of logistics industry, the traditional logistics operation mode cannot meet the requirements of people on diversification and punctuality and cannot follow the development of the times, and a high-efficiency and low-cost logistics operation mode is urgently needed by the society, so that the research on the complex Vehicle Routing problems of multiple parking lots, multiple Vehicle types and the like has strong practical significance.
The vehicle path problem refers to a certain number of customers, each customer has a certain number of goods demand, a yard (distribution center) arranges a certain number of vehicles to transport goods to the customers, and a proper driving route is required to be organized, so that the demands of the customers are met, and the goals of shortest distance, shortest time, lowest cost and the like can be achieved under certain constraint conditions. Since the vehicle routing problem was first addressed by Dantzing and Ramser in 1959, it soon attracted attention in academia, and the current research on this problem has been extensive and related extensive research has been conducted on the basis of this problem.
According to the idea of classifying first and then solving, the Surekha and the like solve the problem of vehicle paths of multiple yards, firstly, a C-W (computational-power-consumption) -saving algorithm is adopted to distribute different customers to corresponding yards, and then, a genetic algorithm is utilized to solve and plan vehicle distribution routes; majianhua et al improve the ant colony algorithm to solve the multi-yard multi-vehicle type path problem. Although the method can solve part of problems, the solving quality and the solving efficiency are not high, and especially when the problems of high complexity and large quantity and scale are faced, the current algorithm cannot solve acceptable solutions within a limited time at all.
Disclosure of Invention
In order to overcome the defects of poor universality, low search efficiency, narrow search space, low convergence speed, low stability and poor solution quality of the conventional multi-parking lot multi-vehicle type vehicle path scheduling control method, the invention provides the improved genetic extreme value optimization algorithm which has the advantages of strong universality, high search efficiency, wide search space, high convergence speed, high solved quality and high stability.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the multi-parking lot and multi-vehicle type vehicle path scheduling control method comprises the following steps:
step 1, establishing the following objective function by taking the lowest total cost of all distribution vehicles as a target:
wherein z represents the total cost of all delivery vehicles; h represents the total number of vehicles of different models in a plurality of yards; h represents a vehicle;
indicating that delivery is made by vehicle h from node i to node j; qhRepresents the load amount of the vehicle h; c1hRepresents a fixed cost for vehicle h; c2hA variable cost representing a unit distance traveled by vehicle h; giRepresenting the demand of customer i; n represents the total number of customers; dijRepresenting the distance between the node i and the node j;
step 2, encoding: the method adopts a multi-chromosome coding mode, the number of individual chromosomes is equal to the total number of vehicles in a parking lot, the numbers 1-N represent customers, the numbers N + 1-N + H represent vehicles, for example, the problem of multi-vehicle type vehicle path scheduling in a multi-parking lot which comprises two vehicle types (type I and type II), 5 vehicles in total and 10 service customers is solved, the numbers 1-10 represent customers, and the numbers 11-15 represent vehicles, so that the possible coding modes are [11, 8, 1, 3; 12, 6, 2; 13, 10, 5; 14; 15, 7, 4, 9], respectively, indicating that the vehicle 11 departs from the yard, first serves the customer 8, then 1 and 3, and finally returns to the original yard; and so on, the vehicle 14 is not invoked;
step 3And population initialization: determining the population size NP, the iteration times MaxGen, the optimal solution keeping invariant times Kbest and the cross probability PcProbability of variation PmThe initial temperature T and the cooling rate q generate NP initial populations, and the specific process is as follows:
step 3.1, randomly sequencing the numbers 1-N to form a new sequence;
step 3.2, randomly selecting a vehicle from N +1 to N + H, and distributing the first client of the new sequence to the vehicle;
step 3.3, judging whether the vehicle is overloaded, if not, the customer is served by the vehicle, if so, randomly selecting one vehicle from the rest vehicles, judging whether the vehicle is overloaded again, and so on until the customer is allocated to a certain vehicle;
step 3.4, sequentially distributing the remaining clients of the new sequence to the remaining vehicles according to the method, wherein the sequence of the clients distributed to the vehicles is the sequence of the vehicle service clients;
and step 5, selecting and cross-operating: the specific process is as follows:
step 5.1, determining the cross probability Pc, wherein the Pc is a random floating point number between 0 and 1, randomly selecting two individuals A and B in the population to generate a random floating point number ri between 0 and 1, and if r is the random floating point number riiIf the number of individuals in the population is less than Pc, performing cross operation, and sequentially performing the steps 5.2-5.6, otherwise, not performing cross operation, randomly selecting two individuals again, and judging whether to perform cross operation or not until all the individuals in the population are selected;
step 5.2, generating a random natural number between 1 and H, representing the numbers of two individual chromosomes to be subjected to crossover operation, and recording the numbers as a and b, wherein a is equal to b;
step 5.3, respectively storing the client genes shared by the chromosomes a and b into a gene bank FabIn (1), unique client genes are respectively stored in the gene bank FaAnd FbPerforming the following steps;
step 5.4, exchanging client genes of the chromosome a and the chromosome b in sequence;
step 5.5, traverse the client genes of chromosomes other than chromosome a in individual A and combine them with FbComparing the genes in (1), and deleting all common genes; then, the same operation is carried out on the individual B in the same way;
step 5.6, randomly select FaInserting one client gene into other random positions behind the vehicle gene of any chromosome in the individual A, judging whether the overload exists, if so, randomly inserting the client gene into the next chromosome, and judging the overload again until FaIf the gene is empty, all genes are distributed; by analogy, the same operation is carried out on the individual B;
step 6.1, insertion mutation: the specific process is as follows:
step 6.1.1 setting the mutation probability Pe，PeIs a random floating point number between 0 and 1, the first gene of each individual chromosome representing the vehicle does not generate variation, and for each other customer gene of the chromosome, a random floating point number r between 0 and 1 is generatediIf r isiLess than PeStoring the gene into a variant gene library G, and correspondingly deleting the corresponding client gene in the original chromosome; if r isiGreater than or equal to PeThen the gene is not mutated, i.e. does not make any changes; by analogy, the client genes of all chromosomes in the individual execute the above operations;
step 6.1.2, randomly selecting one client gene in G, inserting the client gene into other random positions behind the vehicle genes of any chromosome of an individual, judging whether the client gene is overloaded or not, if so, randomly inserting the client gene into the next chromosome, and judging overload again until the G is empty, namely all the client genes in the G are distributed;
step 6.2, rearrangement mutation: the specific process is as follows:
step 6.2.1, aiming at each chromosome in an individual, generating two random natural numbers between 2 and the length of the chromosome, wherein the larger value is named as max, and the smaller value is named as min;
step 6.2.2, inverting the client gene in the chromosome from number min to max, for example from 456 to 654;
step 6.2.3, calculating the fitness of the chromosome before and after inversion, if the fitness after rearrangement is smaller, storing the rearrangement operation, otherwise, not inverting the chromosome;
6.3, performing mutation operation on each individual in the population;
step 7.1, define fitness λ of each node (customer) i in the chromosome except the vehicle genesiThe following were used:
λi＝(d(yimin，yi)+d(yi，yimin2))-(d(yi-1，yi)+d(yi，yi+1)) (3)
wherein, yiminAnd yimin2Respectively represent distance clients yiNearest customer and second nearest customer, d (y)i-1，yi) Representing node yi-1And yiThe distance between them;
step 7.2, according to the formula
Selecting a client gene i to be subjected to neighborhood search, wherein r is more than or equal to 1 and less than or equal to t, representing the sequence of the client gene fitness, r is 1 representing the client gene with the minimum fitness, r is t representing the client gene with the maximum fitness, t is the number of the client genes in the chromosome, tau is a coefficient which can be adjusted and is more than or equal to 0, and p (r) represents the gene of the r th fitnessProbability of being selected;
step 7.3, according to the formula
Selecting a neighboring node (client) j for performing a neighborhood search client gene, where s represents that the client gene is s near the client gene i to be subjected to the neighborhood search, e.g., s-1 represents that the client gene is closest to the neighborhood search client gene i, s-2 represents that the client gene is 2 nd near the client gene i, and so on, h represents the total number of all genes on the chromosome, including the client gene and the vehicle gene, μ is an adjustable coefficient of 0 or more, and p(s) represents the probability that the client gene s near the client gene i is selected;
7.4, redistributing the selected customer gene i for neighborhood search and the adjacent gene j thereof, exploring a larger space, wherein the redistribution mainly comprises the following six conditions:
(1) the same yard customer is moved. When the customer genes i and j belong to different routes but are served by the same distribution center, one customer is redistributed from one route to another route;
(2) the same yard route sections are exchanged. When the client genes i and j belong to different routes but are served by the same distribution center, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(3) the same yard customers are interchanged. When the client genes i and j are on the same route, the client genes i and j are interchanged;
(4) and the customers in different yards are moved. When the customer genes i and j belong to different routes and are served by different distribution centers, one customer is redistributed from one route to another route;
(5) the different yard route sections are interchanged. When the client genes i and j belong to different routes and are served by different distribution centers, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(6) and exchanging the car yards. And when the client genes i and j belong to different parking lots, the parking lots of the two routes are exchanged. 7.5, executing a neighborhood search strategy for each individual in the population, wherein in the executing process, the solution after each neighborhood search must be a feasible solution and meets the requirements of vehicle capacity constraint and the like, otherwise, performing neighborhood search again until the maximum search times G;
step 7.6, receiving a solution of neighborhood search according to a simulated annealing strategy, which comprises the following specific steps: calculating a solution f (x ') after the neighborhood search according to the formula (1), wherein x ' represents a vehicle route after the neighborhood search, if f (x ')<f (x), accepting the solution of the neighborhood search, otherwise, using probability exp (- (f (x') -f (x))/Tg) Accepting a solution, T, of a neighborhood searchgRepresents the temperature at the g-th iteration;
step 8, calculating the fitness of all individuals in the population according to the formula (1), namely calculating the objective function value of the route corresponding to the individual;
and 9, selecting: according to individual fitness, selecting individuals with better fitness with probability, reserving excellent genes thereof, and realizing population evolution, wherein the specific process is as follows:
step 9.1, according to the formula
Transforming the fitness of the individual, wherein fkDenotes the fitness of the individual before transformation, fkIndication of fitness after transformation, fmaxDenotes the maximum fitness of the individual in the population, fminRepresenting the minimum fitness of individuals in the population, and gamma represents the average fixed cost of vehicle use;
step 9.2, selecting the individuals according to the probability, wherein the larger the fitness of the individuals is, the larger the probability reserved by the selection is, and the specific process is as follows:
step 9.2.1, calculate the sum of fitness F ═ Σ F for all individualskiRelative probability P of individual iri＝fki' F, cumulative probability of individual i Pci＝∑Prj；
Step 9.2.2, generating a random floating point number r between 0 and 1iIf r isiLess than PciThen the first individual in the population is selected, otherwise the selection can be made Pc(i-1)＜ri≤PciThe ith individual in the establishment;
step 9.3, repeatedly executing the step 9.2 for NP times, wherein NP individuals form a new population;
let the optimal individual in the initial population be GbEvery time an evolution is carried out, G isbComparing with fitness of all individuals in the population if individual GbIf the fitness value is more optimal, G is usedbReplacing the individuals with the worst fitness value in the population, otherwise, GbReplaced by the best individual in the population;
step 11, one iteration is completed, the iteration time g is g +1, and the current temperature T isg＝T*q；
Step 14, for the optimal individual GbInterpretation, GbIs [ N +1, a, f, …, b; n +2, d, c, …, e; …, respectively; n + H-1, g, k, …, H; n + H, j, i, …, m](ii) a Wherein [ a, b, …, k, …, m, …]Representing N customers, (N +1) to (N + H) representing H vehicles, according to the result GbArranging the vehicle N +1 to sequentially serve the customers a, f, …, b, finally returning to the original yard, arranging the vehicle N +2 to sequentially serve the customers d, c, …, e, finally returning to the original yard, …, arranging the vehicle N + H-1 to sequentially serve the customers g, k, …, H,finally returning to the original parking lot, arranging the vehicles N + H to sequentially serve the customers j, i, … and m, and finally returning to the original parking lot, wherein the total cost of the vehicles scheduled and distributed is fGb。
The invention has the following beneficial effects: an integer planning model containing multi-parking lot and multi-vehicle type vehicle path problems is established, and unified planning is carried out on the multi-parking lot and multi-vehicle type problems and the single-parking lot and single-vehicle type problems in the traditional sense; the genetic algorithm is combined with the extremum optimization algorithm, so that the global optimizing capability of the genetic algorithm and the local searching capability of the extremum optimization algorithm are fully exerted; the method provides an expression mode of population individuals coded by multiple chromosomes, each chromosome represents a driving route of a vehicle, and the coding mode is more favorable for the crossing of the chromosomes and avoids the problems of infeasible solutions and even illegal solutions generated by the crossing of the traditional coding mode; in the process of chromosome variation, two variation modes of insertion variation and rearrangement variation are adopted, the insertion variation helps better information exchange among different chromosomes, the search depth of the algorithm is increased, the diversity of the population is improved, and the rearrangement variation is beneficial to the chromosome to generate a better customer service sequence; local optimization is carried out by utilizing an improved extremum optimization algorithm, the diversity of chromosomes is enriched, the local searching capability of the algorithm is enhanced, and the algorithm is prevented from falling into a local optimal solution too early; the acceptance principle of the simulated annealing algorithm is introduced, so that a relatively poor solution is accepted to a certain extent, and the diversity of the population is increased; the traditional proportional selection method is improved, and premature convergence of the algorithm is avoided, so that the algorithm falls into a local optimal solution; the method adopts the mode of selecting and reserving the optimal individual gene by elite, thereby ensuring that the algorithm evolves towards the correct direction without the phenomenon of degeneration; the search efficiency and the convergence speed of the algorithm are improved, and meanwhile the understanding quality is guaranteed.
Drawings
FIG. 1 is a schematic flow diagram of the present invention.
FIG. 2 is a schematic view of vehicle delivery.
FIG. 3 is a schematic of chromosome inversion.
FIG. 4 is a schematic diagram of a neighborhood search.
Fig. 5 is a best effort path diagram.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 5, a vehicle path scheduling control method based on an improved genetic extremum optimization algorithm includes the following steps:
step 1, determining a target function of vehicle path scheduling;
the following objective function is established with the goal of minimizing the total cost of all delivery vehicles:
wherein z represents the total cost of all delivery vehicles; h represents the total number of vehicles of different models in a plurality of yards; h represents a vehicle;
indicating that delivery is made by vehicle h from node i to node j; qhRepresents the load amount of the vehicle h; c1hRepresents a fixed cost for vehicle h; c2hA variable cost representing a unit distance traveled by vehicle h; giRepresenting the demand of customer i; n represents the total number of customers; dijRepresenting the distance between the node i and the node j;
step 2, encoding: the method adopts a multi-chromosome coding mode, the number of individual chromosomes is equal to the total number of vehicles in a parking lot, the numbers 1-N represent customers, the numbers N + 1-N + H represent vehicles, for example, the problem of multi-vehicle type vehicle path scheduling in a multi-parking lot which comprises two vehicle types (type I and type II), 5 vehicles in total and 10 service customers is solved, the numbers 1-10 represent customers, and the numbers 11-15 represent vehicles, so that the possible coding modes are [11, 8, 1, 3; 12, 6, 2; 13, 10, 5; 14; 15, 7, 4, 9], respectively, indicating that the vehicle 11 departs from the yard, first serves the customer 8, then 1 and 3, and finally returns to the original yard; and so on, the vehicle 14 is not invoked;
step 3.1, randomly sequencing the numbers 1-N to form a new sequence;
step 3.2, randomly selecting a vehicle from N +1 to N + H, and distributing the first client of the new sequence to the vehicle;
step 3.3, judging whether the vehicle is overloaded, if not, the customer is served by the vehicle, if so, randomly selecting one vehicle from the rest vehicles, judging whether the vehicle is overloaded again, and so on until the customer is allocated to a certain vehicle;
step 3.4, sequentially distributing the remaining clients of the new sequence to the remaining vehicles according to the method, wherein the sequence of the clients distributed to the vehicles is the sequence of the vehicle service clients;
and step 5, selecting and cross-operating: the specific process is as follows:
step 5.1, determining the cross probability Pc, wherein the Pc is a random floating point number between 0 and 1, randomly selecting two individuals A and B in the population, generating a random floating point number Ri between 0 and 1, if Ri is smaller than Pc, performing cross operation, and sequentially performing the steps 5.2 to 5.6, otherwise, not performing cross operation, randomly selecting two individuals again, and judging whether to perform cross operation or not until all the individuals in the population are selected;
step 5.2, generating a random natural number between 1 and H, representing the numbers of two individual chromosomes to be subjected to crossover operation, and recording the numbers as a and b, wherein a is equal to b;
step 5.3, respectively storing the client genes shared by the chromosomes a and b into a gene bank FabIn (1), unique client genes are respectively stored in the gene bank FaAnd FbPerforming the following steps;
step 5.4, exchanging client genes of the chromosome a and the chromosome b in sequence;
step 5.5, traverse the client genes of chromosomes other than chromosome a in individual A and combine them with FbComparing the genes in (1), and deleting all common genes; then, the same operation is carried out on the individual B in the same way;
step 5.6, randomly select FaInserting one client gene into other random positions behind the vehicle gene of any chromosome in the individual A, judging whether the overload exists, if so, randomly inserting the client gene into the next chromosome, and judging the overload again until FaIf the gene is empty, all genes are distributed; by analogy, the same operation is carried out on the individual B;
step 6.1, insertion mutation: the specific process is as follows:
step 6.1.1 setting the mutation probability Pe，PeIs a random floating point number between 0 and 1, the first gene of each individual chromosome representing the vehicle does not generate variation, and for each other customer gene of the chromosome, a random floating point number r between 0 and 1 is generatediIf r isiLess than PeStoring the gene into a variant gene library G, and correspondingly deleting the corresponding client gene in the original chromosome; if r isiGreater than or equal to PeThen the gene is not mutated, i.e. does not make any changes; by analogy, all chromosomes in an individualThe gene carries out the above operations;
step 6.1.2, randomly selecting one client gene in G, inserting the client gene into other random positions behind the vehicle genes of any chromosome of an individual, judging whether the client gene is overloaded or not, if so, randomly inserting the client gene into the next chromosome, and judging overload again until the G is empty, namely all the client genes in the G are distributed;
step 6.2, rearrangement mutation: the specific process is as follows:
step 6.2.1, aiming at each chromosome in an individual, generating two random natural numbers between 2 and the length of the chromosome, wherein the larger value is named as max, and the smaller value is named as min;
step 6.2.2, inverting the client gene in the chromosome from number min to max, for example from 456 to 654;
step 6.2.3, calculating the fitness of the chromosome before and after inversion, if the fitness after rearrangement is smaller, storing the rearrangement operation, otherwise, not inverting the chromosome;
6.3, performing mutation operation on each individual in the population;
step 7.1, define fitness λ of each node (customer) i in the chromosome except the vehicle genesiThe following were used:
λi＝(d(yimin，yi)+d(yi，yimin2))-(d(yi-1，yi)+d(yi，yi+1)) (3)
wherein, yiminAnd yimin2Respectively represent distance clients yiNearest customer and second nearest customer, d (y)i-1，yi) Representing node yi-1And yiThe distance between them;
step 7.2, according to the formula
Selecting a client gene i to be subjected to neighborhood search, wherein r is more than or equal to 1 and less than or equal to t, the client gene is represented in the sequence of fitness, r is 1 and represents the client gene with the minimum fitness, r is t and represents the client gene with the maximum fitness, t is the number of the client genes in the chromosome, tau is a coefficient which can be adjusted and is more than or equal to 0, and p (r) represents the probability that the gene with the r-th fitness is selected;
step 7.3, according to the formula
Selecting a neighboring node (client) j for performing a neighborhood search client gene, where s represents that the client gene is s near the client gene i to be subjected to the neighborhood search, e.g., s-1 represents that the client gene is closest to the neighborhood search client gene i, s-2 represents that the client gene is 2 nd near the client gene i, and so on, h represents the total number of all genes on the chromosome, including the client gene and the vehicle gene, μ is an adjustable coefficient of 0 or more, and p(s) represents the probability that the client gene s near the client gene i is selected;
7.4, redistributing the selected customer gene i for neighborhood search and the adjacent gene j thereof, exploring a larger space, wherein the redistribution mainly comprises the following six conditions:
(1) the same yard customer is moved. When the customer genes i and j belong to different routes but are served by the same distribution center, one customer is redistributed from one route to another route;
(2) the same yard route sections are exchanged. When the client genes i and j belong to different routes but are served by the same distribution center, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(3) the same yard customers are interchanged. When the client genes i and j are on the same route, the client genes i and j are interchanged;
(4) and the customers in different yards are moved. When the customer genes i and j belong to different routes and are served by different distribution centers, one customer is redistributed from one route to another route;
(5) the different yard route sections are interchanged. When the client genes i and j belong to different routes and are served by different distribution centers, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(6) and exchanging the car yards. And when the client genes i and j belong to different parking lots, the parking lots of the two routes are exchanged. 7.5, executing a neighborhood search strategy for each individual in the population, wherein in the executing process, the solution after each neighborhood search must be a feasible solution and meets the requirements of vehicle capacity constraint and the like, otherwise, performing neighborhood search again until the maximum search times G;
step 7.6, receiving a solution of neighborhood search according to a simulated annealing strategy, which comprises the following specific steps:
calculating a solution f (x ') after the neighborhood search according to the formula (1), wherein x ' represents a vehicle route after the neighborhood search, if f (x ')<f (x), accepting the solution of the neighborhood search, otherwise, using probability exp (- (f (x') -f (x))/Tg) Accepting a solution, T, of a neighborhood searchgRepresents the temperature at the g-th iteration;
step 8, calculating the fitness of all individuals in the population according to the formula (1), namely calculating the objective function value of the route corresponding to the individual;
and 9, selecting: according to individual fitness, selecting individuals with better fitness with probability, reserving excellent genes thereof, and realizing population evolution, wherein the specific process is as follows:
step 9.1, according to the formula
Transforming the fitness of the individual, wherein fkDenotes the fitness of the individual before transformation, fkIndication of fitness after transformation, fmaxDenotes the maximum fitness of the individual in the population, fminRepresenting the minimum fitness of individuals in the population, and gamma represents the average fixed cost of vehicle use;
step 9.2, selecting the individuals according to the probability, wherein the larger the fitness of the individuals is, the larger the probability reserved by the selection is, and the specific process is as follows:
step 9.2.1, calculate the sum of fitness F ═ Σ F for all individualskiRelative probability P of individual iri＝fki' F, cumulative probability of individual i Pci＝∑Prj；
Step 9.2.2, generating a random floating point number r between 0 and 1iIf r isiLess than PciThen the first individual in the population is selected, otherwise the selection can be made Pc(i-1)＜ri≤PciThe ith individual in the establishment;
step 9.3, repeatedly executing the step 9.2 for NP times, wherein NP individuals form a new population;
let the optimal individual in the initial population be GbEvery time an evolution is carried out, G isbComparing with fitness of all individuals in the population if individual GbIf the fitness value is more optimal, G is usedbReplacing the individuals with the worst fitness value in the population, otherwise, GbReplaced by the best individual in the population;
step 11, one iteration is completed, the iteration time g is g +1, and the current temperature T isg＝T*q；
step 14, for the optimal individual GbInterpretation is carried out, e.g. GbIs [11, 5, 2; 12, 8, 1, 7, 9; 13, 3, 10; 14, 6, 4; 15]Then arrangeThe vehicle 11 serves the customers 5 and 2 in turn and then returns to the original yard; arranging for the vehicle 12 to service customers 8, 1, 7 and 9 in sequence and then returning to the original yard; arranging the vehicles 13 to serve the customers 3 and 10 in turn and then returning to the original yard; arranging for customer 14 to service customers 6 and 4 in sequence and then return to the original yard; the vehicle 15 has no assignment of tasks; the total cost of the vehicles scheduled for delivery is fGb。
Example (c): a certain tobacco company has three distribution centers, 8 vehicles are divided into three types, and currently, material distribution is carried out for 36 customers, the specific information of the materials is shown in tables 1 and 2 respectively, and the vehicles and the distributed driving routes are required to be reasonably arranged, so that the total cost of all the vehicles is minimized.
TABLE 1 customer information Table
Table 2 distribution center information table
| Distribution center | A | A | A | B | B | C | C | C |
| Abscissa of the |
20 | 20 | 20 | 50 | 50 | 60 | 60 | 60 |
| Ordinate of the |
20 | 20 | 20 | 30 | 30 | 50 | 50 | 50 |
| Vehicle number | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
| Type of vehicle | III | III | III | III | I | I | II | II |
| Fixed cost | 100 | 100 | 100 | 100 | 80 | 80 | 90 | 90 |
| |
10 | 10 | 10 | 10 | 8 | 8 | 9 | 9 |
| Bearing capacity | 80 | 80 | 80 | 80 | 60 | 60 | 70 | 70 |
Determining the parameter population size NP as 400, the maximum iteration number MaxGen as 1000, the optimal solution keeping invariant number Kbest as 200 and the cross probability Pc0.7, probability of mutation Pm0.05, 1000 initial temperature T and 0.9 cooling rate q. The embodiment aims at minimizing the total transportation cost, and after a multi-yard and multi-vehicle type vehicle path scheduling control method based on an improved genetic extremum optimization algorithm is executed, the path of the optimal distribution scheme shown in fig. 5 is obtained, and the specific scheduling scheme is shown in table 3.
TABLE 3 vehicle scheduling scheme
The method provided by the invention is adopted to solve the problem of vehicle path scheduling of multiple parking lots and multiple vehicle types, the model universality is strong, the method search efficiency is high, the search space is wide, the convergence speed is high, and the solved quality and stability are obviously improved.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.
Claims (1)
1. The multi-parking lot and multi-vehicle type vehicle path scheduling control method comprises the following steps:
step 1, establishing the following objective function by taking the lowest total cost of all distribution vehicles as a target:
wherein z represents the total cost of all delivery vehicles; h represents the total number of vehicles of different models in a plurality of yards; h represents a vehicle;
indicating that delivery is made by vehicle h from node i to node j; qhRepresents the load amount of the vehicle h; c1hRepresents a fixed cost for vehicle h; c2hA variable cost representing a unit distance traveled by vehicle h; giRepresenting the demand of customer i; n represents the total number of customers; dijRepresenting the distance between the node i and the node j;
step 2, encoding: the method comprises the following steps of (1) adopting a multi-chromosome coding mode, wherein the number of individual chromosomes is equal to the total number of vehicles in a parking lot, the numbers 1-N are used for representing customers, the numbers N + 1-N + H are used for representing vehicles, the multi-parking lot multi-vehicle type vehicle path scheduling problem comprises two types of vehicles I and II, 5 vehicles in total and 10 service customers, the numbers 1-10 are used for representing the customers, and the numbers 11-15 are used for representing the vehicles, so that the possible coding mode is [11, 8, 1, 3; 12, 6, 2; 13, 10, 5; 14; 15, 7, 4, 9], respectively, indicating that the vehicle 11 departs from the yard, first serves the customer 8, then 1 and 3, and finally returns to the original yard; and so on, the vehicle 14 is not invoked;
step 3, population initialization: determining the population size NP, the iteration times MaxGen, the optimal solution keeping invariant times Kbest and the cross probability PcProbability of variation PmThe initial temperature T and the cooling rate q generate NP initial populations, and the specific process is as follows:
step 3.1, randomly sequencing the numbers 1-N to form a new sequence;
step 3.2, randomly selecting a vehicle from N +1 to N + H, and distributing the first client of the new sequence to the vehicle;
step 3.3, judging whether the vehicle is overloaded, if not, the customer is served by the vehicle, if so, randomly selecting one vehicle from the rest vehicles, judging whether the vehicle is overloaded again, and so on until the customer is allocated to a certain vehicle;
step 3.4, sequentially distributing the remaining clients of the new sequence to the remaining vehicles according to the method, wherein the sequence of the clients distributed to the vehicles is the sequence of the vehicle service clients;
step 4, evaluating all individuals by adopting the target function as a fitness function;
and step 5, selecting and cross-operating: the specific process is as follows:
step 5.1, determining the cross probability Pc, wherein the Pc is a random floating point number between 0 and 1, randomly selecting two individuals A and B in the population to generate a random floating point number ri between 0 and 1, and if r is the random floating point number riiIf the number of individuals in the population is less than Pc, performing cross operation, and sequentially performing the steps 5.2-5.6, otherwise, not performing cross operation, randomly selecting two individuals again, and judging whether to perform cross operation or not until all the individuals in the population are selected;
step 5.2, generating a random natural number between 1 and H, representing the numbers of two individual chromosomes to be subjected to crossover operation, and recording the numbers as a and b, wherein a is equal to b;
step 5.3, respectively storing the client genes shared by the chromosomes a and b into a gene bank FabIn (1), unique client genes are respectively stored in the gene bank FaAnd FbPerforming the following steps;
step 5.4, exchanging client genes of the chromosome a and the chromosome b in sequence;
step 5.5, traverse the client genes of chromosomes other than chromosome a in individual A and combine them with FbComparing the genes in (1), and deleting all common genes; then, the same operation is carried out on the individual B in the same way;
step 5.6, randomly select FaInserting one client gene into other random positions behind the vehicle gene of any chromosome in the individual A, judging whether the overload exists, if so, randomly inserting the client gene into the next chromosome, and judging the overload again until FaIf the gene is empty, all genes are distributed; by analogy, the same operation is carried out on the individual B;
step 6, mutation operation: the variation is divided into two types, one type is insertion variation, and some genes on one chromosome are inserted into other chromosomes to help the communication between the chromosomes; the other is rearrangement mutation, which rearranges the customer genes on the chromosome to generate better customer service sequence, and the specific process is as follows:
step 6.1, insertion mutation: the specific process is as follows:
step 6.1.1 setting the mutation probability Pe，PeIs a random floating point number between 0 and 1, the first gene of each individual chromosome representing the vehicle does not generate variation, and for each other customer gene of the chromosome, a random floating point number r between 0 and 1 is generatediIf r isiLess than PeStoring the gene into a variant gene library G, and correspondingly deleting the corresponding client gene in the original chromosome; if r isiGreater than or equal to PeThen the gene is not mutated, i.e. does not make any changes; by analogy, the client genes of all chromosomes in the individual execute the above operations;
step 6.1.2, randomly selecting one client gene in G, inserting the client gene into other random positions behind the vehicle genes of any chromosome of an individual, judging whether the client gene is overloaded or not, if so, randomly inserting the client gene into the next chromosome, and judging overload again until the G is empty, namely all the client genes in the G are distributed;
step 6.2, rearrangement mutation: the specific process is as follows:
step 6.2.1, aiming at each chromosome in an individual, generating two random natural numbers between 2 and the length of the chromosome, wherein the larger value is named as max, and the smaller value is named as min;
6.2.2, inverting the client gene from the number min to max in the chromosome, and adjusting the client gene from 456 to 654;
step 6.2.3, calculating the fitness of the chromosome before and after inversion, if the fitness after rearrangement is smaller, storing the rearrangement operation, otherwise, not inverting the chromosome;
6.3, performing mutation operation on each individual in the population;
step 7, performing neighborhood search on each individual in the population by using an improved extremum optimization algorithm, wherein the specific process is as follows:
step 7.1, defining fitness lambda of each node i in the chromosome except the vehicle geneiThe following were used:
λi＝(d(yimin，yi)+d(yi，yimin2))-(d(yi-1，yi)+d(yi，yi+1)) (3)
wherein, yiminAnd yimin2Respectively represent distance clients yiNearest customer and second nearest customer, d (y)i-1，yi) Representing node yi-1And yiThe distance between them;
step 7.2, according to the formula
Selecting a client gene i to be subjected to neighborhood search, wherein r is more than or equal to 1 and less than or equal to t, the client gene is represented in the sequence of fitness, r is 1 and represents the client gene with the minimum fitness, r is t and represents the client gene with the maximum fitness, t is the number of the client genes in the chromosome, tau is a coefficient which can be adjusted and is more than or equal to 0, and p (r) represents the probability that the gene with the r-th fitness is selected;
step 7.3, according to the formula
Selecting adjacent node j of client gene for neighborhood search, wherein s represents that the client gene is close to the s of the client gene i to be neighborhood searched, s is 1 represents that the client gene is closest to the client gene i for neighborhood search, s is 2 represents close to the 2 nd of the client gene i, and the like, h represents the total number of all genes on the chromosome, including the client gene and the vehicle gene, mu is an adjustable coefficient which is more than or equal to 0, and p(s) tableShowing the probability that the gene closest to the gene ith is selected;
7.4, redistributing the selected customer gene i for neighborhood search and the adjacent gene j thereof, exploring a larger space, wherein the redistribution mainly comprises the following six conditions:
(1) the same yard customer is moved; when the customer genes i and j belong to different routes but are served by the same distribution center, one customer is redistributed from one route to another route;
(2) exchanging the same parking lot route part; when the client genes i and j belong to different routes but are served by the same distribution center, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(3) exchanging clients in the same parking lot; when the client genes i and j are on the same route, the client genes i and j are interchanged;
(4) different yards of customers move; when the customer genes i and j belong to different routes and are served by different distribution centers, one customer is redistributed from one route to another route;
(5) exchanging the route parts of different yards; when the client genes i and j belong to different routes and are served by different distribution centers, randomly selecting a section of route on one route, wherein the length of the section of route is random, and exchanging the section of route with a route with the same length on the other route;
(6) exchanging the vehicle yards; and when the client genes i and j belong to different parking lots, the parking lots of the two routes are exchanged.
7.5, executing a neighborhood search strategy for each individual in the population, wherein in the executing process, the solution after each neighborhood search must be a feasible solution and meets the requirements of vehicle capacity constraint and the like, otherwise, performing neighborhood search again until the maximum search times G;
step 7.6, receiving a solution of neighborhood search according to a simulated annealing strategy, which comprises the following specific steps:
calculating a solution f (x ') after neighborhood searching according to formula (1), wherein x' represents a vehicle route after neighborhood searching,if f (x')<f (x), accepting the solution of the neighborhood search, otherwise, using probability exp (- (f (x') -f (x))/Tg) Accepting a solution, T, of a neighborhood searchgRepresents the temperature at the g-th iteration;
step 8, calculating the fitness of all individuals in the population according to the formula (1), namely calculating the objective function value of the route corresponding to the individual;
and 9, selecting: according to individual fitness, selecting individuals with better fitness with probability, reserving excellent genes thereof, and realizing population evolution, wherein the specific process is as follows:
step 9.1, according to the formula
Transforming the fitness of the individual, wherein fkDenotes the fitness of the individual before transformation, fkIndication of fitness after transformation, fmaxDenotes the maximum fitness of the individual in the population, fminRepresenting the minimum fitness of individuals in the population, and gamma represents the average fixed cost of vehicle use;
step 9.2, selecting the individuals according to the probability, wherein the larger the fitness of the individuals is, the larger the probability reserved by the selection is, and the specific process is as follows:
step 9.2.1, calculate the sum of fitness F ═ Σ F for all individualskiRelative probability P of individual iri＝fki' F, cumulative probability of individual i Pci＝∑Pri；
Step 9.2.2, generating a random floating point number r between 0 and 1iIf r isiLess than PciThen the first individual in the population is selected, otherwise the selection can be made Pc(i-1)＜ri≤PciThe ith individual in the establishment;
step 9.3, repeatedly executing the step 9.2 for NP times, wherein NP individuals form a new population;
step 10, elite preservation: the optimal individuals in the population are stored, the population is ensured to evolve towards the correct direction without the phenomenon of degeneration, and the specific process is as follows:
let the optimal individual in the initial population be GbEvery time an evolution is carried out, G isbComparing with fitness of all individuals in the population if individual GbIf the fitness value is more optimal, G is usedbReplacing the individuals with the worst fitness value in the population, otherwise, GbReplaced by the best individual in the population;
step 11, one iteration is completed, the iteration time g is g +1, and the current temperature T isg＝T*q；
Step 12, judging whether a termination condition is met, wherein the termination condition is that the iteration time G reaches the maximum iteration time MaxGen or GbKeeping the number Nu of times that the fitness value is kept unchanged to reach the specified number Kbest, if the number Nu of times is met, continuing to execute the step 13, and if the number Nu of times that the fitness value is kept unchanged is not met, returning to execute the step 5;
step 13, outputting the individuals GbAnd its fitness value fGbWherein the first position of each chromosome is a vehicle gene and the back is a customer gene;
step 14, for the optimal individual GbInterpretation, GbIs [ N +1, a, f, …, b; n +2, d, c, …, e; …, respectively; n + H-1, g, k, …, H; n + H, j, i, …, m](ii) a Wherein [ a, b, …, k, …, m, …]Representing N customers, (N +1) to (N + H) representing H vehicles, according to the result GbArranging the vehicle N +1 to sequentially serve the customers a, f, … and b, finally returning to the original yard, arranging the vehicle N +2 to sequentially serve the customers d, c, … and e, finally returning to the original yard, …, arranging the vehicle N + H-1 to sequentially serve the customers g, k, … and H, finally returning to the original yard, arranging the vehicle N + H to sequentially serve the customers j, i, … and m, and finally returning to the original yard, wherein the total cost of the vehicles scheduled and distributed at this time is fGb。
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