CN110610239B - Method for solving balanced transportation problem based on dynamic genetic algorithm - Google Patents

Method for solving balanced transportation problem based on dynamic genetic algorithm Download PDF

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CN110610239B
CN110610239B CN201910743305.4A CN201910743305A CN110610239B CN 110610239 B CN110610239 B CN 110610239B CN 201910743305 A CN201910743305 A CN 201910743305A CN 110610239 B CN110610239 B CN 110610239B
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张贵军
李远锋
孙沪增
胡俊
周晓根
秦子豪
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Abstract

A solution to the problem of balanced transportation based on a dynamic genetic algorithm is provided, firstly, parameters are set; 2) setting m producing areas and n selling areas through a map obtained by ArcMap, and calculating a cost matrix through an intelligent hybrid algorithm; initializing a population; judging whether the iteration times is greater than the iteration times; if the iteration times are not more than the set value, entering a loop, otherwise, ending the program; judging whether the iteration times of the cross variation is greater than the iteration times of the cross variation, and if the iteration times is greater than the iteration times, continuing to execute the operation; if the iteration times are less than the iteration times, the loop is exited; crossover, variation and selection, and accepting the results in a Monte Carlo manner. The invention provides a transportation problem solving method based on a dynamic genetic algorithm, which improves the convergence and the real-time performance, and combines ArcMap based on matrix decomposition.

Description

Method for solving balanced transportation problem based on dynamic genetic algorithm
Technical Field
The invention relates to the fields of geographic information data processing, computer application, geography, graph theory and network analysis, in particular to a transportation problem solving method based on a dynamic genetic algorithm.
Background
The transfer of an object from one location to another creates a transport. The research on the transportation problem is generally used for solving the practical problems of how to transport materials, how to optimize expenses, how to make plans, how to arrange personnel and the like in the transportation problem. Particularly, in recent years, logistics is flourishing and developing, the logistics problem provides theoretical basis and practical significance for solving the practical problem, and higher requirements are provided for solving the logistics problem. How to scientifically and effectively organize transportation, save cost, improve transportation quality, realize benefit maximization and the like, and is very important for national and economic development of China.
For transportation per se, the most concerned problem in general is how to save transportation cost, and the transportation problem in reality is not only the shortest path but also simple, and the size of the cost is usually related to a series of operations time, excellent roads, good and bad weather, labor cost rise and fall, climate change difference and the like, which affect the unit cost more or less. How to abstract various complex real scenes into a mathematical model and solve the optimal solution of the model by using a proper method is crucial to the transportation problem.
The transportation problem increases along with the increase of the dimension, and the time complexity and the space complexity of the traditional algorithm increase exponentially, which brings great difficulty to the solution of the problem. Therefore, for the problem of large-scale transportation, intelligent algorithms such as simulated annealing, ant colony algorithm, tabu search, neural network and the like are generally adopted for solving.
Disclosure of Invention
In order to overcome the defects of poor convergence and poor real-time performance of the existing transportation problem solving method, the invention researches the transportation problem and solves the transportation cost problem of dynamic change by using an improved genetic algorithm. And solving the cost matrix acquired from the ArcMap platform by adopting a genetic algorithm. The variation in the genetic algorithm adopts dynamic variation rate, and the convergence of the algorithm can be accelerated. The chromosome generated by the variation adopts a Monte Carlo receiving mode, so that the algorithm is prevented from falling into local optimization. Through a plurality of iterations, the solution of the transportation problem is solved.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a balanced transportation problem solving method based on a dynamic genetic algorithm comprises the following steps:
1) setting parameters: the population scale NP, the iteration times G, the number m of producing places, the number n of selling places and a fitness function adjusting coefficient omega;
2) setting m producing areas and n selling areas through a map obtained by ArcMap, and calculating a cost matrix C through an intelligent hybrid algorithm;
3) initializing the population, and iterating the following process to generate an initial population X ═ X1,X2,...,XNPTherein of
Figure GDA0003285961120000021
Figure GDA0003285961120000022
4) Setting G as 1, where G ∈ {1, 2.
5) Randomly pairing individuals in the population pairwise to form NP/2 male parent pairs; performing steps 6) to 8) for each pair of male parents;
6) the cross operation, the process is as follows:
6.1) assumptions
Figure GDA0003285961120000023
And
Figure GDA0003285961120000024
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWherein mod is the remainder;
Figure GDA0003285961120000025
Figure GDA0003285961120000026
6.2) decomposing the generated R matrix into
Figure GDA0003285961120000027
And
Figure GDA0003285961120000028
wherein
R＝R1+R2 (3)
Figure GDA0003285961120000029
Figure GDA00032859611200000210
6.3) generating the intersectionIndividuals
Figure GDA00032859611200000211
And
Figure GDA00032859611200000212
Figure GDA00032859611200000213
Figure GDA00032859611200000214
7) for crossing individuals
Figure GDA00032859611200000215
And
Figure GDA00032859611200000216
performing mutation operations respectively, wherein the process is as follows:
7.1) randomly selecting p rows and q columns of crossing individuals, and establishing a submatrix Y ═ Yij)p×qWherein p is more than or equal to 2 and less than or equal to m, and q is more than or equal to 2 and less than or equal to n;
7.2) generate a new submatrix Y ═ Y'ij)p×qThe matrix satisfies the following formula:
Figure GDA0003285961120000031
Figure GDA0003285961120000032
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 GDA0003285961120000033
And
Figure GDA0003285961120000034
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure GDA0003285961120000035
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure GDA0003285961120000036
And
Figure GDA0003285961120000037
fitness f (X)1)、f(X2)、
Figure GDA0003285961120000038
8.3) if
Figure GDA0003285961120000039
By using
Figure GDA00032859611200000310
Substitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000311
8.4) if
Figure GDA00032859611200000312
By using
Figure GDA00032859611200000313
Substitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000314
9) iterating the steps 6) to 8) until all the male parent pairs are executed;
10) g is g + 1; if G is less than or equal to G, turning to the step 5); otherwise, ending the program and outputting the optimal solution.
The invention has the following beneficial effects: on one hand, a solution different from the traditional linear programming is adopted, and a genetic algorithm is adopted to solve the transportation problem; on the other hand, the convergence of the algorithm is improved by adopting dynamic variation and a Monte Carlo receiving strategy.
Drawings
FIG. 1 is a flow chart of a transportation problem based on a dynamic genetic algorithm.
FIG. 2 is a cross-process flow diagram of a transportation problem solution based on dynamic genetic algorithm.
FIG. 3 is a flow chart of a variant process of a transportation problem solution based on a dynamic genetic algorithm.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1,2 and 3, a transportation problem solving method based on a dynamic genetic algorithm includes the following steps:
1) setting parameters: the population scale NP, the iteration times G, the number m of producing places, the number n of selling places and a fitness function adjusting coefficient omega;
2) setting m producing areas and n selling areas through a map obtained by ArcMap, and calculating a cost matrix C through an intelligent hybrid algorithm;
3) initializing the population, and iterating the following process to generate an initial population X ═ X1,X2,...,XNPTherein of
Figure GDA0003285961120000041
Figure GDA0003285961120000042
4) Setting G as 1, where G ∈ {1, 2.
5) Randomly pairing individuals in the population pairwise to form NP/2 male parent pairs; performing steps 6) to 8) for each pair of male parents;
6) the cross operation, the process is as follows:
6.1) assumptions
Figure GDA0003285961120000043
And
Figure GDA0003285961120000044
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWhere mod is the remainder
Figure GDA0003285961120000045
Figure GDA0003285961120000046
6.2) decomposing the generated R matrix into
Figure GDA0003285961120000047
And
Figure GDA0003285961120000048
wherein
R＝R1+R2 (3)
Figure GDA0003285961120000049
Figure GDA0003285961120000051
6.3) generating Cross individuals
Figure GDA0003285961120000052
And
Figure GDA0003285961120000053
Figure GDA0003285961120000054
Figure GDA0003285961120000055
7) for crossing individuals
Figure GDA0003285961120000056
And
Figure GDA0003285961120000057
performing mutation operations respectively, wherein the process is as follows:
7.1) randomly selecting p rows and q columns of crossing individuals, and establishing a submatrix Y ═ Yij)p×qWherein p is more than or equal to 2 and less than or equal to m, and q is more than or equal to 2 and less than or equal to n;
7.2) generate a new submatrix Y ═ Y'ij)p×qThe matrix satisfies the following formula:
Figure GDA0003285961120000058
Figure GDA0003285961120000059
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 GDA00032859611200000510
And
Figure GDA00032859611200000511
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure GDA00032859611200000512
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure GDA00032859611200000513
And
Figure GDA00032859611200000514
fitness f (X)1)、f(X2)、
Figure GDA00032859611200000515
8.3) if
Figure GDA00032859611200000516
By using
Figure GDA00032859611200000517
Substitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000518
8.4) if
Figure GDA00032859611200000519
By using
Figure GDA00032859611200000520
Substitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000521
9) iterating the steps 6) to 8) until all the male parent pairs are executed;
10) g is g + 1; if G is less than or equal to G, turning to the step 5); otherwise, ending the program and outputting the optimal solution.
Taking a certain area of Zhejiang as an example, a transportation problem solving method based on a dynamic genetic algorithm comprises the following steps:
1) setting parameters: the population size NP is 20, the iteration number G is 5000, the production place number m is 5, the sales place number n is 8, and the fitness function adjusting coefficient omega is 144;
2) setting 5 producing areas and 8 selling areas through a map obtained by ArcMap, and calculating a cost matrix C through an intelligent hybrid algorithm;
3) initializing the population, and iterating the following process to generate an initial population X ═ X1,X2,...,X20Therein of
Figure GDA0003285961120000061
Figure GDA0003285961120000062
4) Let g be 1, where g ∈ {1, 2.., 5000 };
5) randomly pairing individuals in the population pairwise to form 10 male parent pairs; performing steps 6) to 8) for each pair of male parents;
6) the cross operation, the process is as follows:
6.1) assumptions
Figure GDA0003285961120000063
And
Figure GDA0003285961120000064
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)5×8And R ═ Rij)5×8Where mod is the remainder
Figure GDA0003285961120000065
Figure GDA0003285961120000066
6.2) decomposing the generated R matrix into
Figure GDA0003285961120000067
And
Figure GDA0003285961120000068
wherein
R＝R1+R2 (3)
Figure GDA0003285961120000069
Figure GDA00032859611200000610
6.3) generating Cross individuals
Figure GDA00032859611200000611
And
Figure GDA00032859611200000612
Figure GDA0003285961120000071
Figure GDA0003285961120000072
7) for crossing individuals
Figure GDA0003285961120000073
And
Figure GDA0003285961120000074
performing mutation operations respectively, wherein the process is as follows:
7.1) randomly selecting p rows and q columns of crossing individuals, and establishing a submatrix Y ═ Yij)p×qWherein p is more than or equal to 2 and less than or equal to 5, and q is more than or equal to 2 and less than or equal to 8;
7.2) generate a new submatrix Y ═ Y'ij)p×qThe matrix satisfies the following formula:
Figure GDA0003285961120000075
Figure GDA0003285961120000076
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 GDA0003285961120000077
And
Figure GDA0003285961120000078
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure GDA0003285961120000079
wherein ω is 144 an adjustment factor;
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure GDA00032859611200000710
And
Figure GDA00032859611200000711
fitness f (X)1)、f(X2)、
Figure GDA00032859611200000712
8.3) if
Figure GDA00032859611200000713
By using
Figure GDA00032859611200000714
Substitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000715
8.4) if
Figure GDA00032859611200000716
By using
Figure GDA00032859611200000717
Substitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure GDA00032859611200000718
9) iterating the steps 6) to 8) until all the male parent pairs are executed;
10) g is g + 1; if g is less than or equal to 5000, turning to the step 5); otherwise, ending the program and outputting the optimal solution.
While the foregoing has described the preferred embodiments of the present invention, it will be apparent that the invention is not limited to the embodiments described, but can be practiced with modification without departing from the essential spirit of the invention and without departing from the spirit of the invention.

Claims (1)

1. A balanced transportation problem solving method based on a dynamic genetic algorithm is characterized by comprising the following steps: the transportation problem solving method based on the dynamic genetic algorithm comprises the following steps:
1) setting parameters: the population scale NP, the iteration times G, the number m of producing places, the number n of selling places and a fitness function adjusting coefficient omega;
2) setting m producing areas and n selling areas through a map obtained by ArcMap, and calculating a cost matrix C through an intelligent hybrid algorithm;
3) initializing the population, and iterating the following process to generate an initial population X ═ X1,X2,...,XNPTherein of
Figure FDA0003285961110000011
4) Setting G as 1, where G ∈ {1, 2.
5) Randomly pairing individuals in the population pairwise to form NP/2 male parent pairs; performing steps 6) to 8) for each pair of male parents;
6) the cross operation, the process is as follows:
6.1) assumptions
Figure FDA0003285961110000013
And
Figure FDA0003285961110000014
is two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWhere mod is the remainder;
Figure FDA0003285961110000015
Figure FDA0003285961110000016
6.2) decomposing the generated R matrix into
Figure FDA0003285961110000017
And
Figure FDA0003285961110000018
wherein
R＝R1+R2 (3)
Figure FDA0003285961110000019
Figure FDA00032859611100000110
6.3) generating Cross individuals
Figure FDA00032859611100000111
And
Figure FDA00032859611100000112
Figure FDA00032859611100000113
Figure FDA0003285961110000021
7) for crossing individuals
Figure FDA0003285961110000022
And
Figure FDA0003285961110000023
performing mutation operations respectively, wherein the process is as follows:
7.1) randomizationSelecting p rows and q columns of crossed individuals, and establishing a submatrix Y ═ Yij)p×qWherein p is more than or equal to 2 and less than or equal to m, and q is more than or equal to 2 and less than or equal to n;
7.2) generate a new submatrix Y ═ Y'ij)p×qThe matrix satisfies the following formula:
Figure FDA0003285961110000024
Figure FDA0003285961110000025
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 FDA0003285961110000026
And
Figure FDA0003285961110000027
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
Figure FDA0003285961110000028
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individuals
Figure FDA0003285961110000029
And
Figure FDA00032859611100000210
fitness f (X)1)、f(X2)、
Figure FDA00032859611100000211
8.3) if
Figure FDA00032859611100000212
By using
Figure FDA00032859611100000213
Substitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure FDA00032859611100000214
8.4) if
Figure FDA00032859611100000215
By using
Figure FDA00032859611100000216
Substitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
Figure FDA00032859611100000217
9) iterating the steps 6) to 8) until all the male parent pairs are executed;
10) g is g + 1; if G is less than or equal to G, turning to the step 5); otherwise, ending the program and outputting the optimal solution.
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