Multiple solution search based on hybridization of real-coded evolutionary algorithm and quasi-newton method

Abstract

In recent years, many evolutionary computation methods have been proposed and applied to real-world problems; however, gradient methods are regarded as promising for their capacity to solve problems involving real-coded parameters. Addressing real-world problems should not only involve the search for a single optimal solution, but also a set of several quasi-optimal solutions. Although some methods aiming the search for multiple solutions have been proposed (e.g. Genetic Algorithm with Sharing and Immune Algorithm), these could not render highly optimized solutions to real-coded problems. This paper proposes hybrid algorithms combining real-coded evolutionary computation algorithms and gradient search methods for multiple-solution search in multimodal optimization problems. Furthermore, a new evaluation function of solution candidates with gradient is presented and discussed in order to find quasi-optimal solutions. Two hybrid algorithms are proposed - a hybridization between Immune Algorithm and Quasi-Newton method (IA+QN) and a hybridization between Genetic Algorithm with Sharing and Quasi-Newton method (GA <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</inf> +QN). Experimental results have shown that the pro posed methods can find optimal and quasi-optimal solutions with high accuracy and efficiency even in high-dimensional multimodal benchmark functions. The results have also shown that GA <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</inf> +QN has better performance and higher robustness in terms of parameter configuration than IA+QN.