Genetic algorithm with automatic termination and search space rotation

Abstract

In the last two decades, numerous evolutionary algorithms (EAs) have been developed for solving optimization problems. However, only a few works have focused on the question of the termination criteria. Indeed, EAs still need termination criteria prespecified by the user. In this paper, we develop a genetic algorithm (GA) with automatic termination and acceleration elements which allow the search to end without resort to predefined conditions. We call this algorithm “Genetic Algorithm with Automatic Termination and Search Space Rotation”, abbreviated as GATR. This algorithm utilizes the so-called “Gene Matrix” (GM) to equip the search process with a self-check in order to judge how much exploration has been performed, while maintaining the population diversity. The algorithm also implements a mutation operator called “mutagenesis” to achieve more efficient and faster exploration and exploitation processes. Moreover, GATR fully exploits the structure of the GM by calling a novel search space decomposition mechanism combined with a search space rotation procedure. As a result, the search operates strictly within two-dimensional subspaces irrespective of the dimension of the original problem. The computational experiments and comparisons with some state-of-the-art EAs demonstrate the effectiveness of the automatic termination criteria and the space decomposition mechanism of GATR.