Genetic Algorithm for multi-product multi-period aggregate production planning and vehicle routing problems with time windows

Abstract

Genetic Algorithm is the search algorithms and optimization methods. The basic concept is based on the mechanisms of evolution and natural selection, according to Darwin’s theory of survival of the fittest. A novel crossover operator is a combination of four crossover operators, including Single point crossover, Two points crossover, Arithmetic crossover, and Scattered crossover, which is called “Stas Crossover”. The most important advantage of Stas crossover is that it provides greater diversity in the choice of methods for creating offspring and increases the opportunity for offspring to directly obtain good genetic information. It presents the performance of the crossover operator, which tests with multi-product and multi-period aggregate production planning problems (APP), provides optimal levels of inventory, backorders, overtime and regular production rates, and other controllable variables, and finally chooses appropriate crossover options. Moreover, Stas crossover in GA was modified to solve the standard Solomon’s benchmark problem instances for vehicle routing problems with time windows (VRPTW) by developing the problem with K-mean clustering. Results from K-mean clustering show that it performs better for minimum distance and average distance than without K-mean clustering. The paths with K-mean clustering are arranged into groups and are orderly, but the paths without K-mean clustering are disordered in terms of location and dispersion characteristics of the customer. After that, the research presents a comparison of the performance of the crossover operator with the instance of the Solomon benchmark, and it is recommended to use the appropriate crossover operator for each type of problem. It has been shown that adding K-mean clustering to the Stas crossover efficiently contributes to its performance. In some instances, the results of Stas crossover are better than the known solutions from previous studies. Furthermore, the proposed research will serve as a guideline for a real-world case study.

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