CN110610239A - 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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CN110610239A
CN110610239A CN201910743305.4A CN201910743305A CN110610239A CN 110610239 A CN110610239 A CN 110610239A CN 201910743305 A CN201910743305 A CN 201910743305A CN 110610239 A CN110610239 A CN 110610239A
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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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Zhejiang University of Technology ZJUT
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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.
Technical Field
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
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) assumptionsAndis two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWherein mod is the remainder;
6.2) decomposing the generated R matrix intoAndwherein
R＝R1+R2 (3)
6.3) generating Cross individualsAnd
7) for crossing individualsAndperforming 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)m×nWherein 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:
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individualsAnd
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individualsAndfitness f (X)1)、f(X2)、
8.3) ifBy usingSubstitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
8.4) ifBy usingSubstitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
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
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) assumptionsAndis two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWhere mod is the remainder
6.2) decomposing the generated R matrix intoAndwherein
R＝R1+R2 (3)
6.3) generating Cross individualsAnd
7) for crossing individualsAndperforming 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)m×nWherein 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:
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individualsAnd
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individualsAndfitness f (X)1)、f(X2)、
8.3) ifBy usingSubstitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
8.4) ifBy usingSubstitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
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
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) assumptionsAndis two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)5×8And R ═ Rij)5×8Where mod is the remainder
6.2) decomposing the generated R matrix intoAndwherein
R＝R1+R2 (3)
6.3) generating Cross individualsAnd
7) for crossing individualsAndperforming 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:
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individualsAnd
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
wherein ω is 144 an adjustment factor;
8.2) calculating parent individuals X respectively1、X2And progeny individualsAndfitness f (X)1)、f(X2)、
8.3) ifBy usingSubstitution of X1Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
8.4) ifBy usingSubstitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
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
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) assumptionsAndis two randomly selected parent individuals, and two temporary matrixes D ═ D are establishedij)m×nAnd R ═ Rij)m×nWhere mod is the remainder;
6.2) decomposing the generated R matrix intoAndwherein
R＝R1+R2 (3)
6.3) generating Cross individualsAnd
7) for crossing individualsAndperforming 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)m×nWherein 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:
7.3) converting the submatrix Y '═ Y'ij)p×qReplacing elements at corresponding positions of the crossed individual construction submatrix to generate offspring individualsAnd
8) selecting operation, the process is as follows:
8.1) designing a fitness function:
wherein ω is an adjustment coefficient;
8.2) calculating parent individuals X respectively1、X2And progeny individualsAndfitness f (X)1)、
8.3) ifBy usingSubstitution of X1Entering a population; otherwise, replace by probability, replace probabilityThe following were used:
8.4) ifBy usingSubstitution of X2Entering a population; otherwise, replacing according to the probability, wherein the replacement probability is as follows:
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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