CN107578199B - Method for solving two-dimensional loading constraint logistics vehicle scheduling problem - Google Patents
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Abstract
The invention discloses a method for solving a two-dimensional loading constraint logistics vehicle scheduling problem. The method comprises the steps of firstly inputting vehicles, fields and tasks into a computer, comprehensively considering customer requirements, time windows, two-dimensional loading constraints, load capacity and customer satisfaction, establishing a vehicle scheduling problem model in multi-target logistics distribution based on the two-dimensional loading constraints, then adopting a two-dimensional loading strategy of an improved minimum horizontal line search algorithm in a cargo loading stage, adopting an improved pheromone updating strategy and a customer transfer probability method in a vehicle path optimization stage, and finally adopting multi-target ant colony optimization to obtain a Pareto optimal solution for vehicle scheduling and transmitting a final scheduling scheme to workers. The invention considers the practical conditions of two-dimensional loading constraint, full-load vehicle distribution and the like, and the method can effectively reduce the number of the vehicles which are put into the system, reduce the no-load rate of the vehicles, improve the customer satisfaction degree and reduce the transportation cost of enterprises.
Description
Technical Field
The invention relates to a method for solving a two-dimensional loading constraint logistics vehicle scheduling problem, and belongs to the technology of LY08 information transmission and processing.
Background
In recent years, with the rapid development of global economy, the logistics industry, as an important service industry of national economy, is rapidly developing in the global scope and gradually becomes an artery and basic industry for the development of national economy, and the development degree of the logistics industry becomes one of important marks for measuring the modernization degree and comprehensive national strength of a country. The logistics is connected with production and consumption, is one of the links of national economy circulation, and the logistics industry also becomes an important department of national economy, is closely related to the life of each person, and has become a research hotspot of each country. In recent decades, the vehicle scheduling problem gradually becomes a research hotspot content in the fields of operational research and combinatorial optimization, the research focus is also from single-factor to multi-factor collaborative consideration, and various scholars perform a great deal of intensive research work on the theory and application of the vehicle scheduling problem and obtain a lot of research results. However, in the current research, only path optimization of a single target, such as the shortest path, is considered, the consideration factor is few, the problem of two-dimensional loading limitation is not solved, and the existing algorithm can not meet the requirement of actual logistics scheduling.
For this reason, an effective vehicle dispatching method is needed for loading the logistics transportation goods and reasonably dispatching and delivering the vehicles.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides the method for solving the problem of the two-dimensional loading constraint logistics vehicle scheduling, which can comprehensively consider the actual situation, effectively reduce the number of the input vehicles, reduce the vehicle idle load rate, improve the customer satisfaction degree and reduce the enterprise transportation cost.
In order to achieve the above purpose, the solution of the invention is as follows:
a method for solving two-dimensional loading constraint logistics vehicle scheduling problem includes inputting information of vehicles, fields, tasks and the like into a computer, establishing a vehicle scheduling problem model in multi-objective logistics distribution based on two-dimensional loading constraint, adopting a two-dimensional loading strategy of an improved minimum horizontal line search algorithm in a cargo loading stage, adopting an improved pheromone updating strategy and a customer transfer probability method in a vehicle path optimization stage, and finally adopting multi-objective ant colony optimization to obtain a Pareto optimal solution of vehicle scheduling and transmitting a final scheduling scheme to workers through a network system. Therefore, the number of the vehicles which are put into the system is effectively reduced, the no-load rate of the vehicles is reduced, the customer satisfaction is improved, and the enterprise transportation cost is reduced.
A method for solving a two-dimensional loading constraint logistics vehicle scheduling problem comprises the following steps:
step 1: inputting information of vehicles, fields, tasks and the like into a computer, and establishing a vehicle scheduling problem model in multi-target logistics distribution based on two-dimensional loading constraint, wherein the model mainly comprises four parts, and basic information comprises position coordinates of customers and distribution centers, basic parameters of the vehicles and basic parameters of goods; the customer requirements are the customer's reservation order and temporary order information; the constraint conditions comprise a soft time window interval, a vehicle loading capacity constraint and a two-position loading constraint; scheduling optimization is mainly to achieve the goals of minimizing transportation cost and maximizing customer satisfaction.
The cost of servicing all customers is calculated as:
wherein C represents the total cost of service; c. CijRepresents the cost per unit distance, dijRepresents the distance, x, from client i to client jijkA decision variable representing the vehicle k from customer i to customer j; fkRepresenting the fixed departure cost, y, of each vehiclekA decision variable representing the delivery of vehicle k; c. CwaitCost per unit time, w, representing vehicle waitingi(ti) Indicating that the vehicle has arrived at customer i in advance is a resulting wait time.
The calculation formula of the satisfaction degree of the customer to the service starting time is as follows:
wherein u isi(ti) Representing the satisfaction of customer i; eiRepresents the starting time of the ideal service soft time window of the client i; l isiRepresents the end time of the client i's ideal service soft time window; t is tiIndicating when the vehicle reaches customer i to begin service.
Step 2: on the basis of the model established in the step 1, a multi-objective ant colony optimization algorithm is adopted for scheduling optimization, an integer coding mode is adopted for coding, parameters are initialized, a distribution center is used as the current starting position of ants, all clients are brought into an aggregate table allow to be served, and a Tabu table is emptied.
Wherein, the allow is represented as a set of clients to be served by ants, and each time an ant finishes servicing a client, the client is removed from the allow table; tabu represents the set of clients already served by an ant, and each time an ant has served a client, that client is added to the Tabu table.
And step 3: the ant selects the next service client j from the aggregate table allow at the current position according to a state transition formula, introduces a time width in the construction of a heuristic factor for preferentially serving the client with time urgency, and the ant state transition probability calculation formula is as follows:
wherein the content of the first and second substances,
representing the probability that the ant d transfers from the client i to the client j at the moment t, wherein i is the client or warehouse where the vehicle is located currently, and j is the client which is not yet served; tau isij(t) indicates the pheromone concentration on the path from client i or warehouse to client j at time t; etaij(t) is a distance heuristic function, ηij(t)＝1/dij，dijRepresents the distance from customer i to customer j; thetaij(t) is a time heuristic function, θij(t)＝1/twidthjIndicating the expected degree of transfer, twidth, of client i or warehouse to client j at time tj＝Lj-Ej，EjRepresents the start time, L, of the client j ideal service soft time windowjRepresents the end time of the client j ideal service soft time window; alldThe set of clients to be visited for ant d. Alpha, beta and gamma respectively represent pheromone concentration influence degree factors, distance heuristic function influence degree factors and time heuristic function influence degree factors.
A pseudo-random probability rule is introduced in the ant state transfer process, and the calculation formula is as follows:
wherein r is in [0,1 ]]Random variables subject to uniform distribution; parameter r0Probabilities used to control the transition rules; if r is less than or equal to r0Then find [ tau ] from the customer to be servedij(t)]α·[ηij(t)]β·[θij(t)]γThe largest client is the next service client; if r > r0Then basis
And the next service client is selected according to probability by using a roulette method.
And 4, step 4: loading goods of the customer j by the service customer selected in the step 3 through a two-dimensional loading strategy, if the goods cannot be loaded or are overweight, giving up the service customer j, updating the ant position to a distribution center, distributing a new vehicle, and turning to the step 3; if the load is successful and not overweight, the ant location is updated to client j, client j is transferred from the aggregation table allow to the Tabu, and step 3 is repeated until all clients are serviced.
The two-dimensional loading strategy is specifically as follows:
(1) total area a of items to be loaded for a given customer iiAnd the current remaining area A of the carriageThe residue is leftAnd (3) comparison: if a isi＞AThe residue is leftIf the package can not be loaded, ending; if a isi≤AThe residue is leftThe items of the customer are sorted in reverse order by width and area, and then (2) is performed.
(2) Each time the next item I to be loaded is loaded to customer IimComparing the heights of all horizontal lines in the horizontal line set, selecting a horizontal line with the lowest height, and if multiple horizontal line segments have the same height and are the lowest, selecting a horizontal line segment with the leftmost position as the lowest horizontal line Wlow。
(3) Comparing the lowest horizontal line segment with the article I to be containedimWidth w ofimIf W islow≥wimThen I will beimIs placed at the lower left of the lowest horizontal line, and the number and height of the horizontal line set are updated(ii) a If W islow＜wimSearching the sequence of the articles to be packaged of the client i backwards, and selecting the first width in the sequence to be less than or equal to WlowArticle Iim′Is shown byim′Placing at the lower left of the lowest horizontal line, updating the number and height of the horizontal line set, and putting the item Iim′Update the status of (1) to loaded; if no eligible items can be found, the lowest level is raised to be level with a lower level segment of the adjacent levels and the set of levels is updated.
(4) Repeating (3) until the customer I item I can be loadedimAnd updates the set of horizontal lines at that time.
(5) And (4) repeating until all the articles of the customer i are loaded, and obtaining a final horizontal line set.
(6) Selecting the maximum height value I in the horizontal line setmaxAnd comparing with the carriage length L: if H is presentmaxIf the goods of the client i cannot be loaded, updating the horizontal line set to the state before the goods of the client i are not loaded, and ending; if H is presentmaxAnd (5) less than or equal to L, and completing the goods loading of the customer i.
And 5: calculating the information of the total length, the route, the target value and the like of the path taken by each ant in the population, and constructing and updating a non-inferior solution set N according to the domination relationship among the antssetAnd the pheromone on each path needs to be updated, and the minimum threshold value tau of the pheromone is introducedminAnd updating the pheromone concentration table tau of the ant population according to the rule. The rules are as follows:
τij(t+1)＝max(ρ·τij(t)+Δτij,τmin)
wherein rho is the volatilization coefficient of pheromone concentration, and rho belongs to [0,1 ]]；
Pheromone which represents that the d-th ant releases on the path from the client i to the client j; l isdRepresents the total cost of the path, SdRepresents average customer satisfaction; q and P are respectively influence degree factors; delta tauijIs the sum of the concentration of the pathway pheromones.
Step 6: if the iteration number NC does not reach the maximum iteration number NCmaxIf so, the iteration number NC is equal to NC +1, and the step 2 is carried out; otherwise, outputting the non-inferior solution set Nset, and ending. And transmits the final scheduling scheme to the worker through the network system.
Compared with the existing vehicle scheduling method, the method for solving the problem of the two-dimensional loading constraint logistics vehicle scheduling has the following benefits and effects:
(1) aiming at the problems of vehicle path optimization and two-dimensional boxing, the practical conditions such as customer requirements, time windows, two-dimensional loading constraints, load capacity, customer satisfaction and the like are comprehensively considered, so that the calculated result is more accurate and the adaptability is wider;
(2) the two-dimensional loading strategy of the improved minimum horizontal line search algorithm is adopted in the cargo loading stage, so that the number of the thrown vehicles can be effectively reduced, the vehicle no-load rate is reduced, and the vehicle loading rate is improved;
(3) the algorithm obtains a Pareto optimal solution by adopting multi-objective ant colony optimization, and adopts an improved pheromone updating strategy and a customer transfer probability method in a vehicle path optimization stage, so that the customer satisfaction can be effectively improved, and the enterprise transportation cost is reduced.
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FIG. 1 is a flow chart of the present invention.
FIG. 2 is a comparison graph of vehicle dispatch for the method of the present invention and two other methods under different test samples;
FIG. 3 is a Pareto optimal solution set diagram obtained by solving an actual case by the method of the present invention;
FIG. 4 is a schematic diagram of a vehicle dispatching route for solving the actual case sequence by the method of the present invention.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are intended only for the purpose of illustration and not as a definition of the limits of the invention, and that various equivalent modifications of the invention will occur to those skilled in the art upon reading the present specification and are intended to be covered by the appended claims.
The invention provides a method for solving a two-dimensional loading constraint logistics vehicle scheduling problem, which comprises the steps of inputting vehicles, fields and tasks into a computer, establishing a vehicle scheduling problem model in multi-target logistics distribution based on two-dimensional loading constraint, adopting a two-dimensional loading strategy of an improved minimum horizontal line search algorithm in a cargo loading stage, adopting an improved pheromone updating strategy and a customer transfer probability method in a vehicle path optimization stage, and finally adopting multi-target ant colony optimization to obtain a vehicle scheduling Pareto optimal solution and transmitting a final scheduling scheme to workers through a network system. Therefore, the number of the vehicles which are put into the system is effectively reduced, the no-load rate of the vehicles is reduced, the customer satisfaction is improved, and the enterprise transportation cost is reduced.
The technical scheme of the invention is specifically described in three main aspects of a vehicle dispatching model, a two-dimensional loading strategy and a vehicle dispatching algorithm as follows:
(I) multi-objective vehicle scheduling model based on two-dimensional loading constraints
The multi-target Vehicle dispatching Problem based on the two-dimensional loading constraint is a new Problem after the fusion of an Open Vehicle Routing Problem with Time window constraint (OVRPTW) and a two-dimensional packing Problem (2 BPP). Since OVRPTW and 2BPP are NP-hard problems, and how to pack and whether to pack the delivered goods will have great influence on the distribution of the delivery task of the vehicle and the arrangement of the traveling route, their fusion is not a simple extension of the problem condition, but a cross and penetration of the complexity of two aspects on the deeper surface of the delivery process, and the cross changes the essence of the problem to some extent, increases the difficulty of the problem, so that the model and algorithm of the problem will have great change, and the solution of the problem is very challenging.
According to the description of the actual scheduling problem, a model is established by means of a computer, and the model mainly comprises four aspects: the basic information comprises position coordinates of a client and a distribution center, vehicle basic parameters and cargo basic parameters; the customer requirements are the customer's reservation order and temporary order information; the constraint conditions comprise a soft time window interval, vehicle load capacity constraint and two-dimensional loading constraint; scheduling optimization is mainly to achieve the goals of minimizing transportation cost and maximizing customer satisfaction.
Thus, a model problem code is obtained:
(1) position: the distribution center and the customer are represented by N +1 coordinate nodes, 0 representing the number of the distribution center, and the other node numbers representing the number of the customer to be serviced. The distance from index i to index j is dijCost per unit distance of cij。
(2) A distribution center: k identical vehicles providing transport distribution service, each vehicle having a rated load capacity of Qk(K1, 2.. K.) the freight compartment carrying the freight is a rectangle with an area a W × L, and the fixed departure cost of each car is FkAnd i is 0 to denote a distribution center.
(3) Customer: n, customer i is a system comprising miSet IT of individual rectangular objectsi，ITiWherein the total weight of all the articles is qiTotal area of aiMth item IimHaving a specific width wimAnd length lim(m＝1，2，...，mi) Let the lower left corner of the carriage top view (with the head down) be the origin of coordinates and the horizontal right and vertical up be coordinate axes, then set item IimLower left corner coordinate (v)im，him)，vim，himRepresenting the horizontal and vertical distances to the origin of coordinates, respectively. The desired soft time window for each client is [ E ]i，Li]The time to the customer's start of service is tiCustomer satisfaction u with Start of service timei(ti) Expressed by a trapezoidal blur function:
the inherent service time of client i is denoted as siWhen the vehicle arrives at the customer i in advance, the vehicle needs to wait, and the waiting time w is generatedi(ti). The cost per unit time of the wait is cwaitThe waiting cost of client i is denoted as wi(ti)×cwait。
The decision variables are defined as follows:
(II) two-dimensional Loading strategy
The reasonable cargo loading method can reduce the transportation cost, optimize the driving route and enable the vehicle scheduling problem to be better solved. Therefore, in the loading stage, a two-dimensional loading strategy based on a minimum horizontal line search algorithm is designed, rectangular cargoes of each client are sequentially loaded into the rectangular compartment, specific constraint conditions are met, and the vehicle loading rate is improved. By combining heuristic experience knowledge, the existing minimum horizontal line search algorithm is guided and improved, and the loading problem in the model is solved closer to reality. The main heuristic experience is: all articles of a client can be transported by only one vehicle, and the total area of the client goods is compared with the residual area of the carriage before loading, so that unnecessary loading is effectively avoided; the articles of a client are sorted in a reverse order according to width and area, so that the generation of infeasible areas is reduced, and the efficiency of backward search matching is improved; the items are placed to the lower left of the lowest level that can be loaded. The loading strategy mainly comprises the following steps:
step 1 Total area a of items to be loaded for a given customer iiAnd the current remaining area A of the carriageThe residue is leftAnd (3) comparison: if a isi＞AThe residue is leftIf the package can not be loaded, ending; if a isi≤AThe residue is leftThe customer's items are sorted in reverse order by width and area, and then step 2 is performed.
Step 2, loading the next article I to be loaded of the customer I each timeimComparing the heights of all horizontal lines in the horizontal line set, selecting a horizontal line with the lowest height, and if multiple horizontal line segments have the same height and are the lowest, selecting a horizontal line segment with the leftmost position as the lowest horizontal line Wlow。
Step 3, comparing the lowest horizontal line segment with the article I to be containedimWidth w ofimIf W islow≥wimThen I will beimPlacing the horizontal line set at the lower left of the lowest horizontal line, and updating the number and the height of the horizontal line set; if W islow＜wimSearching the sequence of the articles to be packaged of the client i backwards, and selecting the first width in the sequence to be less than or equal to WlowArticle Iim′Is shown byim′Placing at the lower left of the lowest horizontal line, updating the number and height of the horizontal line set, and putting the item Iim′Update the status of (1) to loaded; if no eligible items can be found, the lowest level is raised to be level with a lower level segment of the adjacent levels and the set of levels is updated.
Step 4 repeat step 3 until customer I item I can be loadedimAnd updates the set of horizontal lines at that time.
And 5, repeating the step 4 until all the articles of the client i are loaded, and obtaining a final horizontal line set.
Step 6, selecting the maximum height value H in the horizontal line setmaxAnd comparing with the carriage length L: if H is presentmaxIf the goods of the client i cannot be loaded, updating the horizontal line set to the state before the goods of the client i are not loaded, and ending; if H is presentmaxAnd (5) less than or equal to L, and completing the goods loading of the customer i.
(III) vehicle dispatching method
Ant Colony Optimization (ACO) is an emerging Optimization technique and is a simulated evolution algorithm. The ACO is a heuristic bionic evolution system obtained by simulating foraging behaviors of ant colonies in nature, the searching process is a distributed parallel computing mode, the computing capacity and the operating efficiency of the algorithm can be improved, and a heuristic positive feedback mechanism is adopted, so that the algorithm can obtain a global optimal solution.
The vehicle dispatching model simultaneously optimizes a plurality of targets, and the multi-target ant colony optimization algorithm is designed by adopting a Pareto optimal solution to carry out multi-target optimization on the basis of the ant colony optimization algorithm. Generally, when solving the Traveling Salesman Problem (TSP), the ACO algorithm has heuristic factors only related to distance factors. When the next client is selected, on the premise of meeting the vehicle capacity and time window constraints, time precedence preference needs to be considered, and heuristic factors of the time precedence preference are comprehensively determined by factors such as path distance, time window width of the client and the like, so that probability calculation of state transition, updating of pheromones and the like are improved. The improved multi-target ant colony algorithm can keep the diversity of ant colonies in the iterative operation process and also can keep the diversity of Pareto solution sets.
Is provided with
Representing the probability of ant d transitioning from client i, which is the current client or warehouse of the vehicle, to client j, which is an unserviced client, at time t. For the priority service of the client with time urgency, the time width tWidth is introduced in the construction of the heuristic factorj＝Lj-EjThe calculation formula is as follows:
wherein, tauij(t) indicates the pheromone concentration on the path from client i or warehouse to client j at time t; etaij(t) is a distance heuristic function, ηij(t)＝1/dij；θij(t) is a time heuristic function, θij(t)＝1/twidthjThe heuristic function represents the desirability of the transfer of client i or warehouse to client j at time t. alldIs an antd set of clients to be accessed.
Introducing a pseudo-random probability rule in the ant state transfer process to overcome the defect of slow ant state transfer speed, wherein the rule is as follows:
wherein r is in [0,1 ]]Subject to uniformly distributed random variables, parameter r0To control the probability of the transition rule. If r is less than or equal to r0Then find [ tau ] from the customer to be servedij(t)]α·[ηij(t)]β·[θij(t)]γThe largest client is the next service client; if r > r0Then basis
And using roulette to select the next service client by probability.
To avoid too large a difference in pheromone concentration on the path, a pheromone minimum threshold τ is introducedminAnd the algorithm is prevented from falling into local optimization too early. Pheromones on all paths gradually volatilize, and the pheromones are left after an ant walks through one path, and after the ant completes one cycle, the pheromones on all paths need to be updated according to the following rules:
τij(t+1)＝max(ρ·τij(t)+Δτij,τmin)
wherein rho is the volatilization coefficient of pheromone concentration, and rho belongs to [0,1 ]]；
Pheromone L representing release of the d-th ant on the path from client i to client jdRepresents the total cost of the path, SdRepresenting average customer satisfaction, Q and P being respectively influence degree factors; delta tauijIs the sum of the concentration of the pathway pheromones.
The vehicle dispatching algorithm mainly comprises the following steps:
step 1, initializing parameters, and coding in an integer coding mode.
And 2, taking the current starting position of the ants as the distribution center, bringing all clients into the service-waiting collection table allow, and emptying the Tabu.
And 3, selecting the next service client j from the aggregate table allow at the current position by the ant according to the state transfer formula, and loading the goods of the client j by adopting a two-dimensional loading strategy:
(1) if the ant can not be loaded or is overweight, the service client j is abandoned, the ant position is updated to the distribution center, a new vehicle is distributed, and the step 3 is carried out.
(2) If the load is successful and not overweight, the ant location is updated to client j, client j is transferred from the aggregation table allow to the Tabu, and step 3 is repeated until all clients are serviced.
And 4, calculating information such as the total length, the route, the target value and the like of the path taken by each ant in the population, and constructing and updating a non-inferior solution set Nset according to the dominance relation among the ants.
And 5, updating the pheromone concentration table tau of the ant population according to a formula.
Step 6, if the iteration number NC does not reach the maximum iteration number NCmaxIf so, the iteration number NC is equal to NC +1, and the step 2 is carried out; otherwise, outputting the non-inferior solution set Nset, and ending.
In order to compare the effects of the scheduling optimization method, a genetic algorithm (a), a mixed particle swarm algorithm (B) and the scheduling optimization method (C) provided herein are respectively adopted to reform three different types of examples C101, R101 and RC101 of a standard Solomon example library, the three types of examples are repeatedly operated, and an average result is obtained, and the obtained operation conditions are as shown in fig. 2: the comparison of the results shows that the number of the vehicles is basically the same as the running time of the algorithm, the running distance is greatly reduced, and the customer satisfaction is slightly improved. In general, the algorithm herein is apparently due to the other two algorithms. In addition, an example was solved for population size of 50 and number of iterations of 200, and the results are shown in fig. 3 and 4: pareto optimal solutions are set to (2413.9, 0.57), (2429.1, 0.60), (2478.3, 0.64), (2544.0, 0.72), (2682.1, 0.76), (2835.9, 0.79), as shown in fig. 3 below. The scheduling routes for respectively selecting 2 target vectors are shown in fig. 4 below.
Claims (4)
1. A method for solving a two-dimensional loading constraint logistics vehicle scheduling problem is characterized by comprising the following steps:
step 1: establishing a vehicle scheduling problem model in multi-target logistics distribution based on two-dimensional loading constraint; the input of the model comprises position coordinates of a client and a distribution center, vehicle basic parameters, goods basic parameters, a predetermined order of the client and temporary order information; the constraint conditions comprise a soft time window interval, vehicle load capacity constraint and two-dimensional loading constraint; the scheduling optimization aims to achieve the minimum total transportation cost and the maximum customer satisfaction;
step 2: on the basis of the model established in the step 1, scheduling optimization is carried out by adopting a multi-objective ant colony optimization algorithm, parameters are initialized, a distribution center is taken as the starting position of an ant, all clients are brought into a collection table allow representing the clients to be served by the ant, the collection table allow comprises position coordinates of the clients, order information and goods basic parameters in an order, and a taboo table Tabu representing the client collection served by the ant is emptied; whenever an ant has served a client, remove the client from the aggregate table allow; every time an ant finishes servicing a client, adding the client to a Tabu;
and step 3: the ant selects the next service client j from the collection table all at the current position according to a state transition formula;
and 4, step 4: loading goods of the customer j by the service customer selected in the step 3 through a two-dimensional loading strategy, if the goods cannot be loaded or are overweight, giving up the service customer j, updating the ant position to a distribution center, distributing a new vehicle, and turning to the step 3; if the loading is successful and not overweight, updating the ant position to the client j, transferring the client j from the collection table allow to the Tabu, and repeating the step 3 until all the clients are completely served;
and 5: calculating the total length, the route, the target value and other information of the path taken by each ant in the ant population to generate a scheduling solution space; the target values include the transportation cost and customer satisfaction for each ant;
step 6: constructing and updating a non-inferior solution set Nset according to the dominance relation among all ants;
and 7: updating an pheromone concentration table of the ant population according to rules;
and 8: if the updated iteration number NC does not reach the maximum iteration number NCmaxIf so, the iteration number NC is equal to NC +1, and the step 2 is carried out; otherwise, outputting a non-inferior solution set Nset;
the two-dimensional loading strategy in the step 4 comprises the following steps:
step 4.1: total area a of items to be loaded for a given customer iiAnd the current remaining area A of the carriageThe residue is leftAnd (3) comparison: if a isi＞AThe residue is leftIf the package can not be loaded, ending; if a isi≤AThe residue is leftSorting the articles of the customer in a reverse order according to width and area, and then executing step 4.2;
step 4.2: each time the next item I to be loaded is loaded to customer IimComparing the heights of all horizontal lines in the horizontal line set, selecting a horizontal line with the lowest height, and if multiple horizontal line segments have the same height and are the lowest, selecting a horizontal line segment with the leftmost position as the lowest horizontal line Wiow；
Step 4.3: comparing the lowest horizontal line segment with the article I to be containedimWidth w ofimIf W islow≥wimThen I will beimPlacing the horizontal line set at the lower left of the lowest horizontal line, and updating the number and the height of the horizontal line set; if W islow＜wimSearching the sequence of the articles to be packaged of the client i backwards, and selecting the first width in the sequence to be less than or equal to WlowArticle Iim′Is shown byim′Placing at the lower left of the lowest horizontal line, updating the number and height of the horizontal line set, and putting the item Iim′Update the status of (1) to loaded; if the qualified article can not be found, lifting the lowest horizontal line to be level with a section with lower height in the adjacent horizontal lines, and updating the horizontal line set;
step 4.4: repeat step 4.3 until item I can be loadedimAnd updating the current horizontal line set;
step 4.5: repeating the step 4.4 until all the articles of the client i are loaded to obtain a final horizontal line set;
step 4.6: selecting the maximum height value H in the horizontal line setmaxAnd comparing with the carriage length L: if H is presentmaxIf the goods of the client i cannot be loaded, updating the horizontal line set to the state before the goods of the client i are not loaded, and ending; if H is presentmaxLess than or equal to L, completing the goods loading of the customer i;
in step 7, the rules are as follows:
τij(t+1)＝max(ρ·τij(t)+Δτij，τmin)
wherein rho is the volatilization coefficient of pheromone concentration, and rho belongs to [0,1 ]]；
Pheromone which represents that the d-th ant releases on the path from the client i to the client j; l isdRepresents the total cost of the path, SdRepresents average customer satisfaction; q and P are respectively influence degree factors; delta tauijIs the sum of the concentration of the pathway pheromones; tau isminIndicating the pheromone minimum threshold.
2. The method for solving the two-dimensional loading constraint logistics vehicle scheduling problem according to claim 1, wherein the vehicle scheduling problem model in step 1 comprises:
the cost of servicing all customers is calculated as:
wherein c represents the total cost of service; c. CijRepresents the cost per unit distance, dijRepresents the distance, x, from client i to client jijkA decision variable representing the vehicle k from customer i to customer j; fkRepresenting the fixed departure cost, y, of each vehiclekA decision variable representing the delivery of vehicle k; c. CwaitCost per unit time, w, representing vehicle waitingi(ti) Indicating that the vehicle has arrived at customer i ahead of time is a resulting wait time; k represents that k vehicles with the same number provide transportation delivery service; the distribution center and the customers are represented by N +1 coordinate nodes, and 0 represents the reference number of the distribution center;
the decision variables are defined as follows:
the calculation formula of the satisfaction degree of the customer to the service starting time is as follows:
wherein u isi(ti) Representing the satisfaction of customer i; eiRepresenting the ideal service of client iThe start time of the soft time window; l isiRepresents the end time of the client i's ideal service soft time window; t is tiIndicating when the vehicle reaches customer i to begin service.
3. The method as claimed in claim 1, wherein the ant state transition probability calculation formula in step 3 is:
wherein the content of the first and second substances,
representing the probability that the ant d transfers from the client i to the client j at the moment t, wherein i is the client or the distribution center where the vehicle is located currently, and j is the client which is not yet served; tau isij(t) indicates the pheromone concentration on the route from the client i or the distribution center to the client j at the time t; r isij(t) is a distance heuristic function, ηij(t)＝1/dij，dijRepresents the distance from customer i to customer j; thetaij(t) is a time heuristic function, θij(t)＝1/twidthjIndicating the desired degree of transition, twidth, from customer i or the distribution center to customer j at time tj＝Lj-Ej，EjRepresents the start time, L, of the client j ideal service soft time windowjRepresents the end time of the client j ideal service soft time window; alldA set of clients to be visited for ant d; alpha, beta and gamma respectively represent pheromone concentration influence degree factors, distance heuristic function influence degree factors and time heuristic function influence degree factors.
4. The method as claimed in claim 3, wherein the ant state transition probability calculation formula incorporates a pseudo-random probability rule, and the calculation formula is:
wherein r is in [0,1 ]]Random variables subject to uniform distribution; parameter r0Probabilities used to control the transition rules; if r is less than or equal to r0Then find [ tau ] from the customer to be servedij(t)]α·[rij(t)]β·[θij(t)]γThe largest client is the next service client; if r > r0Then basis
And the next service client is selected according to probability by using a roulette method.
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