Modified Differential Evolution Variants with Local Search Operator to Solve Combinatorial Optimization Problems

Abstract

Differential Evolution (DE) is a global optimization algorithm, which is known for its simplicity, robustness, and efficiency. Though DE was designed to solve optimization problems in continuous domain, it has made remarkable efficiency in discrete domain also by incorporating relevant mapping and local search approaches. However, still DE is not free from the issues of stagnation and premature convergence. This paper presents a set of modified DE variants incorporating changes to its mutation component and adding the 2-OPT local search approach for updating the population. This approach is an attempt to improve the exploration and exploitation capabilities of DE algorithm without any additional evaluation. Three different variants of discrete DE algorithms were proposed and experimented. One best variant out of these three proposed variants was used to extend the study to compare the DE with proposed modified mutation logic with state-of-the-art classical optimization algorithms. The proposed DE variant presented in this paper is an attempt to study and analyze the exploration and exploitation nature of DE on solving the combinatorial optimization problems. The classical traveling salesman problem (TSP) was taken for experiments to evaluate the performance of the proposed DE variants. The empirical and the statistical results obtained are presented in this paper.