CN109886493B - Logistics system design method based on improved multi-target particle swarm algorithm - Google Patents
Logistics system design method based on improved multi-target particle swarm algorithm Download PDFInfo
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Abstract
The invention provides a logistics system design method based on an improved multi-target particle swarm algorithm, belongs to the field of intelligent logistics application, and mainly solves the problems of low construction cost and high transportation efficiency of a logistics system. The method comprises the steps of firstly describing the construction cost and the transportation efficiency of a logistics system into corresponding objective functions and mathematically describing the form of a solution; secondly, expanding the upper limit and the lower limit of the objective function value by adopting an expansion method, building a grid according to the upper limit and the lower limit, and calculating the grid coordinate of the particles; then, selecting guide particles by adopting a double-distance decision method, generating a next-generation particle swarm by combining a particle swarm formula, and screening out an optimal solution set for storage; and finally, selecting a proper logistics system from the optimal solution set according to the requirements of customers. The logistics system designed by the method can meet the requirements of low construction cost and high transportation efficiency, and has good practical use value.
Description
Technical Field
The invention belongs to the field of intelligent logistics application, and relates to a method for expanding the upper and lower limits of an objective function value and a method for double-distance decision; in particular to a logistics system design method based on a multi-objective particle swarm algorithm of capacity expansion and double distance decision, which can be used for the design of intelligent logistics, traffic hubs and the like.
Background
With the rapid development of intelligent logistics technology, the design of logistics systems is extremely important. The logistics system comprises a plurality of express delivery points and a logistics center, and the design method of the system comprises the steps of firstly selecting a certain number of express delivery points from all the express delivery points as the logistics center, and then distributing the remaining express delivery points to the logistics center. Each express delivery point is only affiliated to one logistics center, the logistics centers are completely connected with each other, and each express delivery point can only be connected through the logistics center, so that the logistics center plays a key role in connecting each express delivery point. At present, the design of logistics systems has become a hotspot of research in the field of intelligent logistics, and especially, the research on the logistics center position has received wide attention from scholars at home and abroad. In view of the design problem of the logistics system, the traditional method only aims at designing the logistics system with low cost, which includes transportation cost between express delivery points and establishment cost of the logistics center, but nowadays, only considering cost cannot satisfy huge market competition, so how to design a low-cost, efficient and fast logistics system has become a challenging subject in the field of intelligent logistics.
Therefore, many domestic and foreign scholars continuously improve and optimize the design scheme of the logistics system and put forward a new theoretical view: mixed integer programming, a double-layer programming model, a fuzzy entropy weight theory and the like, and with the wide application of an intelligent algorithm, a new scheme is provided for solving the problems, such as address selection based on the ant colony algorithm and the like. Most of the methods only consider cost factors (including transportation cost and logistics center construction cost), although other factors are added in some methods, and assigned weight coefficients are distributed to the factors to form a new comprehensive factor, because contradiction constraints possibly exist among the factors, the respective characteristics of the factors cannot be highlighted through mutual integration, so that the whole logistics system cannot be optimized and improved well, and the actual use value of the logistics system is influenced.
The invention content is as follows:
aiming at the problems, the invention provides a logistics system design method based on an improved multi-target particle swarm algorithm, so as to solve the problems of low-cost construction and high-efficiency transportation of a logistics system.
The key technology for realizing the method of the invention is as follows: firstly, describing the construction cost and the transportation time of a logistics system into corresponding objective functions and mathematically describing the form of a solution; secondly, expanding the upper limit and the lower limit of the objective function value in an expansion mode, building a grid by utilizing the upper limit and the lower limit, and calculating grid coordinates of the particles; then, selecting guide particles by adopting a double-distance decision method, generating a next-generation particle swarm by combining a particle swarm formula, and screening out an optimal solution set for storage; and finally, selecting a proper logistics system from the optimal solution set according to the requirements of customers.
In order to achieve the above object, the technical scheme of the invention is as follows:
a logistics system design method based on an improved multi-target particle swarm algorithm comprises the following concrete implementation steps:
(1) storing the positions of n express delivery points into X, Y]Wherein X ═ X 1 ,x 2 ,…,x i ,…,x n ],Y＝[y 1 ,y 2 ,…,y i ,…,y n ],x i Abscissa, y, representing the i-th express delivery point i Expressing the ordinate of the ith express point, storing the transportation cost among all express points by using a matrix C, storing the transportation time among the express points by using a matrix T, storing a row vector F of 1 x n at each express point position to establish the cost of a logistics center, and storing a binary column vector H (H) in the express points 1 ,h 2 ,…h i ,…,h n ) The middle elements indicate whether each express point is a logistics center or not, and if h is the logistics center i If the express delivery point i is a logistics center, the number of the logistics centers to be established is represented by p. The solution (i.e. the particle) is an n x n binary matrix, the row (column) of the matrix with the value of 1 on the diagonal is the logistics center, each column in the matrix refers to an express delivery point in the logistics system, and the row with the value of 1 in each column is the number of the logistics center to which the express delivery point belongs. For convenience of use, logistics centers to which all express points in the solution belong are stored in an array hub, subscripts of the array correspond to express point numbers, and for example, hub (i) represents a logistics center to which an express point i belongs;
(2) the objective function of the logistics system is built as follows:
wherein i and j are serial numbers of the express delivery points, k and l are logistics centers to which the express delivery points i and j belong respectively, and the corresponding relation between the express delivery points and the logistics centers is hub. Because of the convenience of transportation between logistics centers, the transportation cost and transportation time between logistics centers are multiplied by a discount factor beta (0 < beta < 1). f. of 1 The first half of (A) is the transportation cost of the whole logistics system, wherein C ik +βC kl +C lj The sum of the transportation cost from the express point i to the logistics center k, from the logistics center k to the logistics center l and from the logistics center l to the express point j is represented as f 1 The second half F x H is the cost of establishing the logistics center; f. of 2 The cargo transportation time of the whole logistics system;
(3) randomly initializing position information of nPOP particles, namely a solution, wherein a position information set of the particles is marked as POP, randomly initializing nPOP speeds, a speed set is marked as V, initializing the maximum iteration times gmax, the external archive capacity nRep, and the division number nGrid of each dimension of grid in a target space, wherein the number of target functions is 2, and the current iteration times are t;
(4) the objective function value for all particles is calculated, indicated at Epa, making each particle individual the best to be itself. Screening Pareto optimal particles and storing the Pareto optimal particles in an external file, recording position information as APOP and recording a corresponding objective function value as Arc;
(5) carrying out grid construction by using particles in an external archive, and then calculating grid coordinates of a midpoint in a target space;
(6) and performing guided particle screening operation by a double-distance decision method. And after the guide particles are selected, updating a formula by utilizing a particle swarm algorithm to generate new particles, then generating a random number r, and carrying out differential variation on the generated new particles when r is greater than 0.8, otherwise, not carrying out variation operation. And if the generated new particle dominates the current particle, replacing the new particle with the corresponding individual optimal particle. The newly generated population replaces the current POP, calculates the objective function of the POP and replaces the current set of Epa. The particle swarm algorithm formula is as follows:
wherein k refers to the kth particle in the particle group, t is the current iteration number, w is a parameter for balancing local search and global search, c 1 、c 2 Is a learning factor, r 1 、r 2 Is a random number between 0 and 1, P k The individual best position of the particle k, G-index directs the position of the particle,
refers to the velocity of particle k at the t-th iteration,
refers to the position of particle k at the t-th iteration;
(7) updating an external archive, namely respectively combining POP and APOP, Epa and Arc, then selecting Pareto optimal particles, updating the previous external archive, and if the number of the particles of the external archive exceeds nRep, performing external archive deletion operation to delete redundant particles;
(8) when t is greater than gmax, outputting Arc and APOP, otherwise, turning to the step (5) to carry out circulation operation;
(9) finally, an appropriate scheme is selected from the external archive according to the requirements of the client.
The invention has the beneficial effects that:
(1) the invention introduces the method of expanding the capacity to expand the grid in the target space, can distribute the points on the upper and lower limit boundaries in the original grid into the new small grid, thus completely preserving the information of the particles corresponding to the boundary points, and improving the diversity of the optimal solution set to a certain extent.
(2) The invention introduces a double-distance decision method to screen corresponding particles, firstly two distances are defined for the particles in each small grid: one is the distance from the corresponding point of the particle function value in the target space to the optimal point of the small grid where the particle function value is currently located, and the distance represents the characteristic that the particle converges on the optimal point of the current small grid, so that the overall diversity is ensured, and the solution set can be uniformly dispersed on the Pareto front edge; the other is the distance from the corresponding point of the particle function value to the ideal point, which reflects the ability of the particle to converge to the ideal point, and helps to improve convergence. And then, the two distances are used for selecting the particles in the external archive, so that the global diversity can be ensured, and the convergence can be improved.
(3) The invention not only considers the transportation cost between the express delivery point and the logistics center and the cost factor established by the logistics center, but also increases the influence of the transportation time factor on the whole logistics system, forms a new multi-task logistics system, and has more practical application value compared with other single-task objective logistics systems.
Drawings
FIG. 1 is an overall flow diagram of the method of the present invention.
Fig. 2 is a schematic diagram of dual distances.
Fig. 3 is a target space diagram.
FIG. 4 is a target space grid map.
FIG. 5 is a target space grid map after expansion.
Fig. 6 is a schematic diagram of dual distance decision dominance.
FIG. 7 is a 3-stream center logistics system diagram.
FIG. 8 is a 4-stream center logistics system diagram.
FIG. 9 is a 5-stream center logistics system diagram.
Detailed Description
Introduction of theoretical basis
1. Basic concept of multi-target problem
In the formula, X is (X) 1 ,x 2 ,...,x n ) Is a decision variable, n is the dimension of the decision variable, m is the number of objective functions, Ω is the set of decision variables, and Y is the value range of the decision variables, i.e. the target space. In the multi-objective problem, the correlation of Pareto solutions is defined as follows:
definition 1 Pareto governance: solving p, q ∈ omega, if p dominatesq, is marked as
p is a dominant particle, q is a dominated particle, and the following two conditions are satisfied:
definition 2 Pareto optimality: if X is Pareto optimal solution, then
Make it
This is true.
Definition 3 Pareto optimal solution set PS: set of all Pareto optimal solutions in Ω.
Definition 4 Pareto front: PF ═ f (X) | X ∈ PS }.
Definition 5. ideal point R: for R (R) 1 ,r 2 ,...,r m ) Is represented by the formula (I) in which r i ＝min{f i (x) I |, [ x ] belongs to Ω }, i ═ 1,2, … m, and m is the number of objective functions.
Definition 6. optimal points: after the target space is divided into a plurality of small grids, the minimum value point of each dimension in each small grid region is the optimal point of the small grid, as shown in fig. 2, the shaded region is a certain small grid in the target space, and the optimal point in the small grid is point Z.
2. Particle swarm optimization algorithm updating formula
Each particle in the particle swarm algorithm consists of a speed and a position, and an updating formula is as follows:
wherein k refers to the kth particle in the particle group, t is the current iteration number, w is a parameter for balancing local search and global search, c 1 、c 2 Is a learning factor, r 1 、r 2 Is between 0 and 1Random number of (2), P k The individual best position for the current particle k, G-index guides the position of the particle,
refers to the velocity of particle k at the t-th iteration,
refers to the position of the particle k at the t-th iteration.
Secondly, the invention discloses a logistics system design method based on an improved multi-target particle swarm algorithm
Referring to fig. 1, the embodied steps of the present invention include the following.
Step 1, storing the positions of n express delivery points into [ X, Y ]]Wherein X ═ X 1 ,x 2 ,…,x i ,…,x n ]，Y＝[y 1 ,y 2 ,…,y i ,…,y n ]，x i Abscissa, y, representing the i-th express delivery point i Expressing the ordinate of the ith express point, storing the transportation cost among all express points by a matrix C, storing the transportation time among the express points by a matrix T, storing a row vector F of 1 x n in each express point position to establish the cost of a logistics center, and a binary column vector H (H) 1 ,h 2 ,…h i ,…,h n ) The middle elements indicate whether each express point is a logistics center or not, and if h is the logistics center i If the express delivery point i is a logistics center, the number of the logistics centers to be established is represented by p. The solution (i.e. the particle) is an n x n binary matrix, the row (column) of the matrix with the value of 1 on the diagonal is the logistics center, each column in the matrix refers to an express delivery point in the logistics system, and the row with the value of 1 in each column is the number of the logistics center to which the express delivery point belongs. For convenience of use, logistics centers to which all express delivery points in the solution belong are stored in an array hub, subscripts of the array correspond to express delivery point numbers, and for example, hub (i) represents a logistics center to which an express delivery point i belongs. The following solution S is used as an example, in which express points 2, 4 are logistics centers, express points 1, 5 are attached to the logistics center 2, and express point 3 is attached to the logistics center 4. Then storing the schemeIn the final result, hub (1) ═ 2, hub (3) ═ 4, hub (5) ═ 2;
and 2, building a logistics system target function as follows:
wherein i and j are serial numbers of the express delivery points, k and l are logistics centers to which the express delivery points i and j belong respectively, and the corresponding relation between the express delivery points and the logistics centers is hub. Because of the convenience of transportation between logistics centers, the transportation cost and transportation time between logistics centers are multiplied by a discount factor beta (0 < beta < 1). f. of 1 The first half of (A) is the transportation cost of the whole logistics system, wherein C ik +βC kl +C lj The sum of the transportation cost from the express point i to the logistics center k, from the logistics center k to the logistics center l and from the logistics center l to the express point j is represented, f 1 The second half F H is the cost for establishing the logistics center; f. of 2 The cargo transportation time of the whole logistics system;
randomly initializing position information of nPOP particles, namely a solution, wherein the position information set of the particles is marked as POP, the speed of nPOP is randomly initialized, the speed and the position information of each particle are matrixes of the same type, the speed set is marked as V, the maximum number of initialization iterations gmax, the external archive capacity nRep, the division number nGrid of each dimension of grid in a target space, the number of target functions is 2, and the current iteration number is t;
and 4, calculating the objective function values of all the particles, wherein the objective function values are represented by Epa, and each particle is optimized to be self. Screening Pareto optimal particles and storing the Pareto optimal particles in an external file, recording position information as APOP and recording a corresponding objective function value as Arc;
and 5, carrying out grid building by using the particles in the external file, wherein the upper limit of the function value of all the particles in the external file is marked as CU ═ fu (fu) 1 ,fu 2 ) The lower limit is expressed as CL ═ fl 1 ,fl 2 ) Therein fu 1 And fu 2 Respectively, the maximum of the two objective functions, fl 1 And fl 2 Is the minimum of two objective functions, and the span of the whole grid is DC ═ DC 1 ,dc 2 ) Wherein dc i ＝fu i -fl i And i is 1 and 2. In the conventional method, when a grid is established, CU and CL are used as upper and lower limits of the whole grid, fig. 3 and 4 show a process of mapping corresponding points of particle function values in an external archive in a target space into the grid, grid coordinates of each dimension are counted from 1, and the mapping method uses the following formula:
g (X) is the grid coordinate of the particle, d i The width of each small grid on the ith dimension in the target space is defined, and nGrid is the number of the small grids on each dimension in the target space. However, in the mapped grid, reasonable grid coordinates cannot be assigned to a point on the upper and lower boundary of the grid, and only the point can be randomly assigned to a small grid where a point close to the point is located, so that information contained in a particle corresponding to the point is damaged, and overall diversity is influenced to a certain extent, as shown in fig. 4, a point p 8 The point is located on the lower limit boundary, and the reasonable grid coordinate of the point cannot be directly obtained.
Then, when the mesh is created, the expansion rate a is set to 0.1, and the upper and lower limits of the objective function value of the particles in the external file are expanded to obtain a new upper limit CU ═ (fu' 1 ,fu′ 2 )，fu′ i ＝fu i +α*dc i The new lower limit is CL '═ fl' 1 ,fl′ 2 )，fl′ i ＝fl i -α*dc i And i is 1 and 2, reestablishing the grid according to the new upper limit and the new lower limit, and then calculating the grid coordinates of the midpoint in the target space. After the grid is expanded, the points on the upper and lower limit boundaries in the original grid can be distributed into the new small grid instead of the grid boundary, so that the boundary is completely preservedThe point corresponds to the particle information, thereby improving the diversity of the optimal solution set to a certain extent. As shown in fig. 5, after capacity expansion, the whole target space is divided evenly, and a point p can be seen 8 The grid coordinate is (3,1) which is positioned in the small grid and is conveniently solved;
and 6, conducting guide particle screening operation through a double-distance decision method. After a grid is established in a target space, the particles in the grid are constrained and converged through a small grid, and the uniform grid is beneficial to uniformly dispersing the optimal solution set on a Pareto front edge; and all the particles are close to an ideal point as much as possible, which is beneficial to improving convergence. Based on these two points, two distances are defined for the particles in each small grid: one is the distance d from the corresponding point of the particle function value in the target space to the optimum point of the small grid where the particle function value is currently located 1 ，d 1 The characteristic that the particles are converged at the optimal point of the current small grid is embodied, so that the overall diversity is ensured, and the solution set can be uniformly dispersed on the Pareto front edge; the other is the distance d from the corresponding point of the particle function value to the ideal point R 2 ，d 2 Reflects the ability of the particles to converge to the desired point and helps to improve convergence. The two distances are used for preferentially selecting the particles in the external archive, so that the global diversity can be ensured, and the convergence can be improved. As shown in FIG. 2, a particle function value corresponds to d at point X in the target space 1 And d 2 The value is obtained.
Based on d 1 And d 2 The dual distance decision method is as follows: the set of the corresponding points of all the particle function values in the target space in a certain small grid is marked as P, d 1 (p i ) And d 2 (p i ) Respectively representing the corresponding points p of the function values of the particles i in the current small grid i D of 1 And d 2 The value is obtained. Corresponding point p of two particle function values in a certain small grid 1 ,p 2 E.g. P, if P 1 ,p 2 The following two conditions are satisfied:
then p is 1 Double distance domination p 2 Memory for recording
p 1 As a dominant point, p 2 Is the dominated point.
The method comprises the steps of conducting screening of guide particles on the basis of a distance decision method, judging the density degree of a small grid according to the number of particles contained in the small grid after the grid is established in a target space, wherein the density degree of the small grid in the target space can reflect the dispersity and diversity of a whole solution set.
In the process of screening guide particles, small grids with smaller density are selected by a roulette method, the smaller density indicates that the particles in the region are more sparse, and the guide particles selected from the region are favorable for guiding the whole particles to the more sparse region on the Pareto frontier so as to increase the diversity of solution sets; after the small grid is determined, d of the function value of each particle in the small grid is calculated 1 、d 2 A value; and finally, screening out dominant particles as guide particles by a double-distance dominant principle, if a plurality of dominant particles exist, selecting Pareto optimal particles according to Pareto optimal definition, and randomly selecting one from the Pareto optimal particles as a guide particle. As shown in fig. 6, taking three particles contained in a small grid as an example, the corresponding points of their function values in the target space are X 1 、X 2 、X 3 By their d 1 、d 2 The value can judge X 1 、X 2 Dominating X 3 But X 1 And X 2 And if the particle is the Pareto optimal, randomly selecting a point from the two points, and taking the particle corresponding to the point as a guide particle.
And after the guide particles are selected, updating a formula by utilizing a particle swarm algorithm to generate new particles, then generating a random number r, and carrying out differential variation on the generated new particles when r is greater than 0.8, otherwise, not carrying out variation operation. And if the generated new particle dominates the current particle, replacing the new particle with the corresponding individual optimal particle. The newly generated population replaces the current POP, calculates the objective function of the POP and replaces the current set of Epa. The particle swarm algorithm formula is as follows:
wherein k refers to the kth particle in the particle group, t is the current iteration number, w is a parameter for balancing local search and global search, c 1 、c 2 Is a learning factor, r 1 、r 2 Is a random number between 0 and 1, P k The individual best position of the particle k, G-index directs the position of the particle,
refers to the velocity of particle k at the t-th iteration,
refers to the position of particle k at the t-th iteration;
and 7, updating the external archive, namely respectively combining POP and APOP, Epa and Arc, then selecting Pareto optimal particles, updating the external archive before updating, and if the number of the particles of the external archive exceeds nRep, performing external archive deletion operation to delete redundant particles, wherein the specific deletion operation is as follows:
when the number of particles in the external archive exceeds its capacity nRep, then a deletion operation needs to be performed on the excess particles. Firstly, selecting small grids with higher density by a roulette method, and deleting particles from the crowded area, which is helpful for the solution set to be uniformly distributed on the Pareto frontier and the diversity to be improved; after the small grid is determined, d of each particle index function value point in the small grid is calculated 1 、d 2 A value of (d); finally, the dominated particle is screened out as the deleted inferior particle by the two distance properties, such as X in FIG. 6 3 The corresponding particle is a poor particle in the current small grid. If a plurality of dominated particles exist, randomly selecting one dominated particle from the plurality of dominated particles as a poor particle, and if the dominated particle does not exist, randomly selecting one dominated particle as a poor particle in the region to delete the poor particle;
and 9, finally, selecting a proper scheme from the external archive according to the requirements of the client.
The effects of the present invention can be further illustrated by the following simulation experiments.
1. Simulation conditions and parameters
Aiming at the invention, three different logistics systems are designed to test the effect of the invention, namely a 3-logistics center logistics system, a 4-logistics center logistics system and a 5-logistics center logistics system, as shown in figures 7, 8 and 9, a small circle in the figure is an express delivery point, a small square is a logistics center, all the express delivery points are connected with the logistics center to which the express delivery points belong by a line, and all the logistics centers are fully communicated.
Setting basic parameters: popp is 500, nRep is 500, nGrid is 10, a is 0.1, gmax is 1000, and β is 0.7. Since these three logistics systems have two objective functions, the transportation cost C is obtained by multiplying 10 by the euclidean distance between points and rounding off, the road transportation time T is a matrix of n × n, each element is a random number between (0,1), and the diagonal of C and T has a value of 0. The specific parameters of the three logistics systems are as follows:
3-the parameters of the logistics system in the logistics center are as follows: n ═ 20, p ═ 3, X ═ 3, [104.138772039671, 27.9075405335330, -1.21376369914406, 76.1754858683866, 46.8508687849655, 28.5535825270306, 70.4117195721234, 45.7245181673279, 21.7620052223005, -11.7771366479796, 105.753521171260, 101.300762157825, 71.9802867233212, 55.4811941603809, -6.84606567541479, 99.5910302156580, -0.965788166429432, 1.27682695666201, 76.2514343865497, 96.5404803307022], Y ═ 24.8797948152149, -0.659516076836153, 52.5108291501149, 4.37306267615794, 4.43709319045759, 21.5453887120451, 25.3094363645217, 70.1435318255384, 45.5459970340529, 99.9726026875866, 6.13052123313900, 96.9213363449853, 76.4855152510402, 99.0976623909150, 4.46942455525787, 45.6437428197911, 25.1302298566599, 77.2101080844489, 54.4024408715235, 81.1768475820158], F ═ 2243542, 2803144, 2295855, 2986372, 2322686, 2830857, 2240386, 2341551558, 2140532, 2637093, 2746779, 2606777, 24836, 2706939, 0189, 274778, 3014778, 2773310.
4-the parameters of the logistics system in the logistics center are as follows: n ═ 30, p ═ 4, X [,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.
5-the parameters of the logistics system in the logistics center are as follows: n-40, p-5, X-45.8648027495244, 30.5096762099853, 36.0458462551390, 1.00349707013271, 14.1744336018160, 15.5291604623110, 84.0660072855024, 83.9619774840057, 95.1101697641359, -3.44501497449531, 61.6011990938269, 49.7928810223638, 45.0825290075192, 2.00537494121631, 80.4605676340377, 46.8387805091699, 88.4492187717388, 72.8449071123131, -2.34079290766359, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, -66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 66.5608106960060, 3658563256325632563256325638, 365838, 365872, 3665563272, 366556325632563272, 366565563238, 365838, 36655632563272, 3665563256325632563272, 365838, 366556325632563272, 36655632563272, 3665563256325632563272, 366556325632563272, 36655632563272, 3665563256325632563272, 3665563272, 365838, 365829, 365838, 365829, 365838, 365829, 365838, 365829, 365838, 365829, 3665563256325632563256325632563256325632563256325632563256325632563256325632563256325632563272, 365838, 365829, 366556325632563256325632563256325632563256325632563256325632563256325632563256325632563256325632563272, 365829, 366556325632563259, 3665563272, 365838, 36655632563272, 3665563259, 3659, 365838, 365829, 365838, 6491330, 6695471, 6523300, 7014295, 4971931, 5642398, 5868425, 5317470, 4796746, 7004217].
2. Simulation content and experimental result analysis
Experiment 1: 3-logistics center logistics system
3 express delivery points are selected from 20 express delivery points to serve as logistics centers, then the remaining 17 express delivery points are distributed to the three logistics centers, each express delivery point is only affiliated to one logistics center, and all the express delivery points can be mutually contacted through the logistics centers.
The experimental results are as follows: the logistics center to which each express delivery point belongs is hub ═ 8, 9, 9, 19, 8, 9, 9, 19, 19, 19, 8, 9, 19, 9, 9, 19, 19, 9, 9, 19, and the logistics center and express delivery point are distributed as shown in fig. 7, wherein 8, 9, and 19 are logistics centers.
Experiment 2: 4-logistics center logistics system
Selecting 4 express delivery points from 30 express delivery points as logistics centers, and then distributing the remaining 26 express delivery points to the three logistics centers, wherein each express delivery point is only affiliated to one logistics center, and all the express delivery points can be mutually contacted through the logistics centers.
The experimental results are as follows: the logistics center to which each express point belongs is as follows: hub ═ 25, 25, 4, 4, 25, 6, 17, 25, 25, 6, 6, 17, 6, 17, 4, 17, 6, 6, 4, 6, 6, 17, 4, 17, 25, 4, 4, 6, 6, distribution of stream centers and express delivery points is shown in fig. 8, where 4, 6, 17, 25 is the stream center.
Experiment 3: 5-logistics center logistics system
5 express delivery points are selected from 40 express delivery points to serve as logistics centers, then the remaining 35 express delivery points are distributed to the three logistics centers, each express delivery point is only affiliated to one logistics center, and all the express delivery points can be mutually contacted through the logistics centers.
The experimental results are as follows: the logistics center to which each express point belongs is as follows: hub ═ 1, 16, 1, 16, 31, 12, 31, 31, 31, 12, 1, 12, 16, 16, 26, 12, 12, 12, 1, 16, 26, 16, 16, 26, 31, 12, 12, 31, 16, 16, 16, 16, 12, 12, 31, 31, 31, distribution of the logistics center and express delivery point is shown in fig. 9, where 1, 12, 16, 26, 31 is the logistics center.
It is obvious from the experimental result chart that the method of the invention can design different logistics systems with actual use value under the conditions of low cost and high transportation efficiency, can meet the requirements of different users and has good practicability.
Claims (3)
1. A logistics system design method based on an improved multi-target particle swarm algorithm is characterized by comprising the following steps:
(1) storing the positions of n express delivery points into X, Y]Wherein X ═ X 1 ,x 2 ,…,x i ,…,x n ]，Y＝[y 1 ,y 2 ,…,y i ,…,y n ]，x i Abscissa, y, representing the i-th express delivery point i Expressing the ordinate of the ith express point, storing the transportation cost among all express points by using a matrix C, storing the transportation time among the express points by using a matrix T, storing a row vector F of 1 x n at each express point position to establish the cost of a logistics center, and storing a binary column vector H (H) in the express points 1 ,h 2 ,…h i ,…,h n ) Each element in the express delivery system indicates whether each express delivery point is a logistics center or not, and when h is i If the express point i is a logistics center, the number of the logistics centers to be established is represented by p; the solution, namely the particles, is an n x n binary matrix, the row or column of the matrix with the value of 1 on the diagonal is the logistics center, each column in the matrix refers to an express delivery point in the logistics system, and the row with the value of 1 in each column is the serial number of the logistics center to which the express delivery point belongs; storing logistics centers to which all express points in the solution belong in an array hub, wherein subscripts of the array correspond to express point numbers, and hub (i) represents the logistics center to which an express point i belongs;
(2) the objective function of the logistics system is built as follows:
wherein i and j are serial numbers of the express points, k and l are logistics centers to which the express points i and j belong respectively, and the corresponding relation between the express points and the logistics centers is hub; the transportation cost and the transportation time among the logistics centers are multiplied by a discount factor beta, wherein beta is more than 0 and less than 1; f. of 1 The first half of (A) is the transportation cost of the whole logistics system, wherein C ik +βC kl +C lj Express delivery pointThe sum of the transportation fees from the i to the k logistics center, the k to the l logistics center and the l to the j express delivery point, f 1 The second half F H is the cost for establishing the logistics center; f. of 2 The cargo transportation time of the whole logistics system;
(3) randomly initializing position information of nPOP particles, namely a solution, wherein a position information set of the particles is marked as POP, randomly initializing nPOP speeds, a speed set is marked as V, initializing the maximum iteration times gmax, the external archive capacity nRep and the division number nGrid of each dimension of grid in a target space, wherein the number of target functions is 2, and the current iteration times are t;
(4) calculating the objective function values of all the particles, represented by Epa, and making each particle individual optimal to itself; screening Pareto optimal particles and storing the Pareto optimal particles in an external file, recording position information as APOP and recording a corresponding objective function value as Arc;
(5) carrying out grid construction by using particles in an external archive, and then calculating grid coordinates of a midpoint in a target space;
the grid is built according to the following steps:
(2.1) performing mesh building by using the particles in the external file, wherein the upper limit of the function value of all the particles in the external file is marked as CU ═ fu 1 ,fu 2 ) The lower limit is expressed as CL ═ fl 1 ,fl 2 ) Therein fu 1 And fu 2 Respectively, the maximum of the two objective functions, fl 1 And fl 2 Is the minimum of two objective functions, and the span of the whole grid is DC ═ DC 1 ,dc 2 ) Wherein dc i ＝fu i -fl i ，i＝1,2；
(2.2) the upper and lower limits of the value of the objective function of the particles in the external file are expanded by the expansion ratio α, α being 0.1, and a new upper limit of CU ═ fu' 1 ,fu′ 2 )，fu′ i ＝fu i +α*dc i The new lower limit is CL '═ fl' 1 ,fl′ 2 )，fl′ i ＝fl i -α*dc i I ═ 1,2, the corresponding points in the target space of the particle function values in the external archive are mapped into the grid according to the following formula:
wherein G (X) is the grid coordinate of the particle, d i The width of each small grid on the ith dimension in the target space is defined, nGrid is the number of the small grids on each dimension in the target space, and the grid coordinates of each dimension are counted from 1;
(6) conducting guided particle screening operation through a double-distance decision method; after the guide particles are selected, a particle swarm algorithm is used for updating a formula to generate new particles, then a random number r is generated, when r is larger than 0.8, differential variation is carried out on the generated new particles, otherwise, variation operation is not carried out; when the generated new particle dominates the current particle, replacing the new particle with the corresponding individual optimal particle; the newly generated population replaces the current POP, calculates the objective function of the POP and replaces the current Epa set; the particle swarm algorithm formula is as follows:
wherein k refers to the kth particle in the particle group, t is the current iteration number, w is a parameter for balancing local search and global search, c 1 、c 2 Is a learning factor, r 1 、r 2 Is a random number between 0 and 1, P k Is the individual best position of particle k, G is the position of the guiding particle,
refers to the velocity of particle k at the t-th iteration,
refers to the position of particle k at the t-th iteration;
the double-distance decision method is operated according to the following steps:
(3.1) two distances are defined for the particles in each small grid:one is the distance d from the corresponding point of the particle function value in the target space to the optimum point of the small grid where the particle function value is currently located 1 (ii) a The other is the distance d from the corresponding point of the particle function value to the ideal point 2 ；
(3.2) based on d 1 And d 2 Double distance decision of (2): the set of the corresponding points of all the particle function values in the target space in a certain small grid is marked as P, d 1 (p i ) And d 2 (p i ) Respectively representing the corresponding points p of the function values of the particles i in the current small grid i D of 1 And d 2 A value; corresponding point p of two particle function values in a certain small grid 1 ,p 2 Is e.g. P when P 1 ,p 2 When the following two conditions are satisfied:
then p is 1 Double distance domination p 2 Remember p 1 ＜p 2 ，p 1 As a dominant point, p 2 Is a dominated point;
(7) updating an external archive, namely respectively combining POP and APOP, Epa and Arc, then selecting Pareto optimal particles, updating the previous external archive, and when the number of the particles of the external archive exceeds nRep, performing external archive deletion operation to delete redundant particles;
(8) when t is greater than gmax, outputting Arc and APOP, otherwise, turning to the step (5) to carry out cycle operation;
(9) finally, an appropriate scheme is selected from the external archive according to the requirements of the client.
2. The logistics system design method of claim 1, wherein the guided particle screening of step (6) is performed by the following steps:
(4.1) selecting small grids with small density degree by using a roulette method;
(4.2) after the small grid is determined, d of the function value of each particle in the small grid is calculated 1 And d 2 A value;
and (4.3) finally, screening out dominant particles as guide particles by a double-distance dominant method, when a plurality of dominant particles exist, selecting Pareto optimal particles according to Pareto optimal definitions, and randomly selecting one from the Pareto optimal particles as a guide particle.
3. The logistics system design method of claim 1 or 2, wherein the external archive deletion operation of step (7) is performed according to the following steps:
(5.1) selecting small grids with large density by a roulette method;
(5.2) after the small grid is determined, d of each particle index function value point in the small grid is calculated 1 、d 2 A value of (d);
(5.3) finally, screening the dominated particle as the deleted inferior particle according to the two distance properties; when a plurality of dominated particles exist, one dominated particle is randomly selected from the dominated particles as a poor particle, and when the dominated particle does not exist, one dominated particle is randomly selected in the region as a poor particle to be deleted.
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| CN107992051A (en) * | 2017-12-26 | 2018-05-04 | 江南大学 | Unmanned vehicle paths planning method based on improved multi-objective particle swarm algorithm |
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