Solving four-index transportation problem with the use of a genetic algorithm

Abstract

Background: Under conditions of digital transformation, the effective decision-making process should involve the usage of different mathematical models and methods, one of which is the transportation problem. The transportation problem, as the problem of resource allocation, is applicable in such domains as manufacturing, information technologies, etc. To get more precise solutions, the multi-index transportation problem can be applied, which allows taking into account several variables. Methods: This paper develops an approach for applying the genetic algorithm for solving four-index transportation problems. Results: The steps of the genetic algorithm for solving four-index transportation problems are outlined. The research has proved the steps of the genetic algorithm to be the same for all four-index transportation problem types, except for the first step (initialization), which is described for every type of transportation problem separately. Based on the theoretical results, the program implementation of the genetic algorithm for solving four-index symmetric transportation problems has been developed with the open-source programming language typescript. Conclusions: The paper promotes the application of the genetic algorithm for solving multi-index transportation problems. The investigated problem requires comprehensive studies, specifically, on the influence of change different parameters of the genetic algorithm (population size, the mutation, and crossover rates, etc.) on the efficiency of the algorithm in solving four-index transportation problems.