CN112184099A - Method for optimizing transportation problem based on K-Means clustering and genetic algorithm - Google Patents

Method for optimizing transportation problem based on K-Means clustering and genetic algorithm Download PDF

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CN112184099A
CN112184099A CN202010848889.4A CN202010848889A CN112184099A CN 112184099 A CN112184099 A CN 112184099A CN 202010848889 A CN202010848889 A CN 202010848889A CN 112184099 A CN112184099 A CN 112184099A
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何玲通
李春开
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Anhui Institute of Information Engineering
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Abstract

The invention provides an optimization solution method for transportation problems based on K-Means clustering and genetic algorithm, which comprises the following steps of S1, setting parameters including cluster center population scale N, iteration times T, production place number m and sales place number N; s2, setting m production places and n sales places through a map obtained by an ArcGIS Pro platform, and clustering the sales places by using K-Means; s3, initializing the population, and calculating a cost matrix C by an intelligent hybrid algorithm; s4, setting iteration times; s5, randomly forming double pairings for individuals in the population to form N/2 male parent pairs; s6, crossover operation. The method is different from the traditional linear programming solution, the data are clustered by adopting the K-Means algorithm, the K-Means algorithm can process image and text characteristics, the stability and the flexibility are high, a data set in a numerical form can be processed, and the clustering effect is good.

Description

Method for optimizing transportation problem based on K-Means clustering and genetic algorithm
Technical Field
The invention relates to the technical field of computer data information processing, geographic information systems, network data analysis and graph theory, in particular to a method and a device for optimizing and solving a transportation problem based on K-Means clustering and a genetic algorithm.
Background
In recent years, rapid development of the internet gradually drives prosperous development of logistics transportation industry, how to allocate transportation lines, so that transportation tasks are completed, transportation cost is the lowest, time efficiency is the highest, and transportation optimization problems are problems which people can not encounter in production and life. Therefore, how to optimize the transportation system and the transportation mode of logistics to enable the transportation process to be more scientific and efficient, and the solution for optimizing transportation is obtained, so that the two transportation parties can achieve the effect of cooperative win-win, and the method obviously has important practical significance for saving cost, improving efficiency, realizing benefit and promoting the development of transportation industry, and also has important practical significance for national and economic development of China.
The transportation problem is a special linear programming problem, the application range is extremely wide, however, the traditional transportation optimization method is tedious and tedious, and the time complexity and the space complexity of the traditional algorithm increase exponentially along with the increase of the dimension. For example, the traditional operation method on the table is relatively complicated in solving process and is based on the premise of balancing transportation problems in terms of production and marketing. However, the transportation problem in real life is affected by many factors. The transportation optimization problem is not only related to the cost route, but also related to the time of work and production, weather reasons, climate change, road quality and other human objective factors. How to convert various complex and changeable real transportation scenes into an abstract mathematical model and find an optimal solution is a problem which needs to be solved urgently.
The invention analyzes common practical transportation problems, applies K-Means algorithm and combines with improved dynamic genetic algorithm to process the transportation problems in two stages. A series of steps of clustering, population initialization, crossing, variation and the like are adopted to find a transportation optimization scheme. The cost matrix acquired from the ArcGISPO platform is solved by adopting a genetic algorithm, and the variation in the genetic algorithm applies a dynamic variation rate to accelerate the convergence of the algorithm. And the chromosome generated by the mutation adopts an MC accepted form, so that the algorithm is prevented from falling into local optimization. And carrying out a plurality of iterations through a K-Means clustering algorithm, thereby calculating an optimized solution of the transportation problem.
Therefore, an optimization solution for the transportation problem based on K-Means clustering and a genetic algorithm is provided.
Disclosure of Invention
The invention aims to provide an optimization solution method for transportation problems based on K-Means clustering and a genetic algorithm, which is characterized in that common real transportation problems are analyzed, the K-Means algorithm is applied, the transportation problems are processed in two stages by combining with an improved dynamic genetic algorithm, a series of steps such as clustering, population initialization, crossing, variation and the like are adopted to search a transportation optimization scheme, a cost matrix obtained from an ArcGISPRO platform is solved by the genetic algorithm, the variation in the genetic algorithm applies a dynamic variation rate to accelerate the convergence of the algorithm, chromosomes generated by the variation adopt an MC accepting mode to avoid the algorithm from falling into local optimization, and the K-Means clustering algorithm is used for carrying out a plurality of iterations to calculate the optimization solution method for the transportation problems so as to solve the problems in the background technology.
The invention provides an optimization solution method for a transportation problem based on K-Means clustering and a genetic algorithm, which comprises the following steps:
s1, setting parameters including cluster center population scale N, iteration times T, production place number m and sales place number N;
s2, setting m production places and n sales places through a map obtained by an ArcGISPro platform, and clustering the sales places by using K-Means;
the K-Means clustering algorithm is described as follows:
2.1) selecting some classes or groups, and initializing respective central points, namely randomly selecting K clustering centers;
2.2) calculating the distance dis from each selling place to each cluster center, wherein:
Figure BDA0002644066680000031
s represents a set of clustering centers, represents the jth data in a data set and represents the current clustering number; according to the calculation result, the selling places are assigned to the clustering center range with the closest distance;
2.3) calculating the average value of the clustering centers, and taking the obtained result as a new clustering center;
wherein:
Figure BDA0002644066680000032
2.4) repeating the above operation steps until the change of the clustering center of each type is not large after each iteration, or randomly initializing the center point for multiple times, and then selecting the best result of the operation to finally present a convergence characteristic;
s3, initializing the population; the cost matrix C is calculated by an intelligent hybrid algorithm,
generating an initial population by iterating the following process:
X＝{X1,X2,...,Xn}，
wherein:
Figure BDA0002644066680000033
xi,j≥0n∈{1,2,...,NP}；
the initialization process, namely allocation, has the following basic idea:
3.1) initializing the premise to meet non-negative conditions and balance conditions to generate a population meeting all constraints;
3.2) first selecting x from the distribution matrixijThen assigned a value of xijAs much as possible of the available volume, and then modifying the demand and supply to the production site to ensure equilibrium conditions, the specific operations are as follows:
randomly selecting an xijThe probability of good population generated by random distribution is high,
wherein:
xij＝{ai,bj}，(k-1)/n+1→i,(k-1)％n+1→j (3)
k represents the kth number (1,2,3 … k), and n represents the nth column;
3.3) modification of aiAnd bjThen repeat 3.2) and 3.3) until all data modifications are complete
So far, modified aiAnd bjRespectively as follows:
Figure BDA0002644066680000047
bj＝bj-xij (5)
s4, setting the iteration times T as 1, wherein T belongs to {1, 2.., T };
s5, randomly forming double pairings of individuals in the population to form N/2 male parent pairs, and executing steps S6-S8 for each pair of male parents;
s6, crossover operation, the process is as follows:
6.1) assumptions
Figure BDA0002644066680000041
And
Figure BDA0002644066680000042
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWherein
Figure BDA0002644066680000043
Figure BDA0002644066680000044
The relationship between the two matrices is:
Figure BDA0002644066680000045
Figure BDA0002644066680000046
6.2) decomposing the generated R matrix into
Figure BDA0002644066680000051
And
Figure BDA0002644066680000052
under the condition that R is satisfied1And R2There are a number of situations;
wherein:
R＝R1+R2 (10)
Figure BDA0002644066680000053
Figure BDA0002644066680000054
6.3) generating Cross individuals
Figure BDA0002644066680000055
And
Figure BDA0002644066680000056
Figure BDA0002644066680000057
Figure BDA0002644066680000058
s7 for crossed individuals
Figure BDA0002644066680000059
And
Figure BDA00026440666800000510
performing mutation operations respectively, wherein the process is as follows:
7.1) randomly selecting crosses from the parent matrixP rows and q columns of individuals, creating a submatrix Y ═ Yij)m×n，yijSelected from the values at the intersection of selected rows and columns in the parent matrix. Wherein p is ∈ [2, m ]]，q∈[2,n]；
7.2) generate a new submatrix Y ═ Y'ij)p×q，
Supply of
Figure BDA00026440666800000511
And the need for
Figure BDA00026440666800000512
Determined by the following equation:
Figure BDA00026440666800000513
Figure BDA00026440666800000514
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individuals
Figure BDA0002644066680000061
And
Figure BDA0002644066680000062
s8, selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure BDA0002644066680000063
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure BDA0002644066680000064
And
Figure BDA0002644066680000065
fitness f (X)1)、f(X2)、
Figure BDA0002644066680000066
8.3) if
Figure BDA0002644066680000067
Discarding the parent X1Make the offspring individuals
Figure BDA0002644066680000068
Entering a population; otherwise, the parent individuals X are reserved1；
8.4) if
Figure BDA0002644066680000069
Discarding the parent X2Make the offspring individuals
Figure BDA00026440666800000610
Entering a population; otherwise, the parent individuals X are reserved1Iterating steps S6 to S8 until all the male parent pairs are executed;
s9, if T is T +1, if T is less than or equal to T, go to step S5; otherwise, ending the program and outputting the optimal solution.
Compared with the prior art, the invention has the beneficial effects that:
1. different from the traditional linear programming solution, the data are clustered by adopting a K-Means algorithm, the K-Means algorithm can process image and text characteristics, has higher stability and flexibility, can process data sets in a numerical form, and has good clustering effect;
2. the clustering method enables a central point to be generated in a market population, and the specific idea is that goods are transported to the central point and then transported to other market places near the central point, so that the method greatly shortens the transportation distance, saves the cost and improves the efficiency;
3. the K-Means algorithm can calculate an optimized solution of the transportation problem through a plurality of iterations;
4. solving and optimizing a transportation problem solution by adopting a genetic algorithm;
5. the convergence of the algorithm is improved by adopting a dynamic cross variation and MC receiving mode.
Wherein, the variation applies dynamic variation rate and is randomly distributed, so that the generated population excellence is increased.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of the process of the method for optimizing and solving the transportation problem based on the K-Means clustering and genetic algorithm.
FIG. 2 is a flow chart of a transportation problem process based on the K-Means algorithm.
FIG. 3 is a cross-process flow diagram of a transportation problem solving method based on a dynamic genetic algorithm according to the present invention.
FIG. 4 is a flow chart of the variation process of the transportation problem solving method based on the dynamic genetic algorithm.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the following embodiments, and it should be understood that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", may explicitly or implicitly include one or more of the described features. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise. Furthermore, the terms "mounted," "connected," and "connected" are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Referring to fig. 1 to 4, the present invention provides a technical solution:
the method for optimizing and solving the transportation problem based on the K-Means clustering and the genetic algorithm comprises the following steps of:
s1, setting parameters including cluster center population scale N, iteration times T, production place number m and sales place number N;
s2, setting m production places and n sales places through a map obtained by an ArcGISPro platform, and clustering the sales places by using K-Means;
the K-Means clustering algorithm is described as follows:
2.1) selecting some classes or groups, and initializing respective central points, namely randomly selecting K clustering centers;
2.2) calculating the distance dis from each selling place to each cluster center, wherein:
Figure BDA0002644066680000081
s represents a set of clustering centers, represents the jth data in a data set and represents the current clustering number; according to the calculation result, the selling places are assigned to the clustering center range with the closest distance;
2.3) calculating the average value of the clustering centers, and taking the obtained result as a new clustering center;
wherein:
Figure BDA0002644066680000091
2.4) repeating the above operation steps until the change of the clustering center of each type is not large after each iteration, or randomly initializing the center point for multiple times, and then selecting the best result of the operation to finally present a convergence characteristic;
s3, initializing the population; the cost matrix C is calculated by an intelligent hybrid algorithm,
generating an initial population by iterating the following process:
X＝{X1,X2,...,Xn}，
wherein:
Figure BDA0002644066680000092
xi,j≥0n∈{1,2,...,NP}；
the initialization process, namely allocation, has the following basic idea:
3.1) initializing the premise to meet non-negative conditions and balance conditions to generate a population meeting all constraints;
3.2) first selecting x from the distribution matrixijThen assigned a value of xijAs much as possible of the available volume, and then modifying the demand and supply to the production site to ensure equilibrium conditions, the specific operations are as follows:
randomly selecting an xijThe probability of good population generated by random distribution is high,
wherein:
xij＝{ai,bj}，(k-1)/n+1→i,(k-1)％n+1→j (3)
k represents the kth number (1,2,3 … k), and n represents the nth column;
3.3) modification of aiAnd bjThen repeat 3.2) and 3.3) until all data modifications are complete
Until now. Modified aiAnd bjRespectively as follows:
Figure BDA00026440666800001010
bj＝bj-xij (5)
s4, setting the iteration times T as 1, wherein T belongs to {1, 2.., T };
s5, randomly forming double pairings of individuals in the population to form N/2 male parent pairs, and executing steps S6-S8 for each pair of male parents;
s6, crossover operation, the process is as follows:
6.1) assumptions
Figure BDA0002644066680000101
And
Figure BDA0002644066680000102
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWherein
Figure BDA0002644066680000103
Figure BDA0002644066680000104
The relationship between the two matrices is:
Figure BDA0002644066680000105
Figure BDA0002644066680000106
6.2) decomposing the generated R matrix into
Figure BDA0002644066680000107
And
Figure BDA0002644066680000108
under the condition that R is satisfied1And R2There are a number of situations;
wherein:
R＝R1+R2 (10)
Figure BDA0002644066680000109
Figure BDA0002644066680000111
6.3) generating Cross individuals
Figure BDA0002644066680000112
And
Figure BDA0002644066680000113
Figure BDA0002644066680000114
Figure BDA0002644066680000115
s7 for crossed individuals
Figure BDA0002644066680000116
And
Figure BDA0002644066680000117
performing mutation operations respectively, wherein the process is as follows:
7.1) randomly selecting p rows and q columns of crossed individuals from the parent matrix, and establishing a submatrix Y ═ Yij)m×n，yijSelected from the values at the intersection of selected rows and columns in the parent matrix. Wherein p is ∈ [2, m ]]，q∈[2,n]；
7.2) generate a new submatrix Y ═ Y'ij)p×q，
Supply of
Figure BDA0002644066680000118
And the need for
Figure BDA0002644066680000119
Determined by the following equation:
Figure BDA00026440666800001110
Figure BDA00026440666800001111
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individuals
Figure BDA00026440666800001112
And
Figure BDA00026440666800001113
s8, selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure BDA00026440666800001114
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure BDA00026440666800001115
And
Figure BDA00026440666800001116
fitness f (X)1)、f(X2)、
Figure BDA0002644066680000121
8.3) if
Figure BDA0002644066680000122
Discarding the parent X1Make the offspring individuals
Figure BDA0002644066680000123
Entering a population; otherwise, the parent individuals X are reserved1；
8.4) if
Figure BDA0002644066680000124
Discarding the parent X2Make the offspring individuals
Figure BDA0002644066680000125
Entering a population; otherwise, the parent individuals X are reserved1Iterating steps S6 to S8 until all the male parent pairs are executed;
s9, if T is T +1, if T is less than or equal to T, go to step S5; otherwise, ending the program and outputting the optimal solution.
Has the advantages that:
1. different from the traditional linear programming solution, the data are clustered by adopting a K-Means algorithm, the K-Means algorithm can process image and text characteristics, has higher stability and flexibility, can process data sets in a numerical form, and has good clustering effect;
2. the clustering method enables a central point to be generated in a market population, and the specific idea is that goods are transported to the central point and then transported to other market places near the central point, so that the method greatly shortens the transportation distance, saves the cost and improves the efficiency;
3. the K-Means algorithm can calculate an optimized solution of the transportation problem through a plurality of iterations;
4. solving and optimizing a transportation problem solution by adopting a genetic algorithm;
5. the convergence of the algorithm is improved by adopting a dynamic cross variation and MC receiving mode. Wherein, the variation applies dynamic variation rate and is randomly distributed, so that the generated population excellence is increased.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (4)

1. The method for optimizing and solving the transportation problem based on the K-Means clustering and the genetic algorithm is characterized by comprising the following steps of:
s1, setting parameters including cluster center population scale N, iteration times T, production place number m and sales place number N;
s2, setting m production places and n sales places through a map obtained by an ArcGIS Pro platform, and clustering the sales places by using K-Means;
s3, initializing the population, and calculating a cost matrix C by an intelligent hybrid algorithm;
s4, setting iteration times;
s5, randomly forming double pairings for individuals in the population to form N/2 male parent pairs;
s6, cross operation;
s7 for crossed individuals
Figure FDA0002644066670000011
And
Figure FDA0002644066670000012
respectively executing mutation operations;
s8, selecting operation;
and S9, outputting the optimal solution.
2. The method of claim 1, wherein the selling locations are clustered according to step S1, some classes or groups are selected, respective center points are initialized, that is, K cluster centers are randomly selected, the cluster center of each class does not change much after each iteration, or the center points can be randomly initialized for a plurality of times, and then the result with the best operation result is selected to finally show the convergence feature.
3. The method for optimized solution of transportation problem based on K-Means clustering and genetic algorithm as claimed in claim 1, wherein according to step S3, initialization preconditions need to satisfy non-negative condition and equilibrium condition, resulting in population satisfying all constraints.
4. The K-Means clustering and genetic algorithm based optimized solution to the transportation problem according to claim 1 characterized in that according to the step S5, steps S6 to S8 are performed for each pair of composed parents.
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CN113206307A (en) * 2021-05-06 2021-08-03 福建工程学院 Redundancy balancing lithium battery management circuit and method of genetic algorithm combined with K-means clustering
CN113206307B (en) * 2021-05-06 2022-08-09 福建工程学院 Redundancy balancing lithium battery management circuit and method of genetic algorithm combined with K-means clustering

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