A genetic algorithm with multi-parent crossover using quaternion representation for numerical function optimization

Finding optimal solutions of a numerical function of more than one independent variable is an important problem with many practical applications including process control systems, data fitting, and engineering designs. Over the last few decades, techniques for solving unconstrained optimization problems have been proposed. Evolutionary Algorithms have emerged as one of the most popular selections for tackling these problems, among which Genetic Algorithms (GAs) are widely used in practice. In recent literature on GAs, a Genetic Algorithm with multi-parent crossover (GA-MPC) was found to be superior over other algorithms. Nevertheless, the GA-MPC still has some difficulties when dealing with separable test issues and convergence to global optima in the high-dimensional search space. Meanwhile, quaternions, which are an extension of complex numbers, can allow algorithms to expand the search space to avoid getting stuck in the local optima. Therefore, this study aims to employ quaternions for representing individuals in the GA-MPC to enhance the effectiveness of the GA-MPC. Experimental results for ten benchmark functions indicated that the GA-MPC using the quaternion representation of individuals improved the quality of solutions compared with the original GA-MPC.