Finding multiple first order saddle points using a valley adaptive clearing genetic algorithm

Abstract

First order saddle points have important applications in different fields of science and engineering. Some of their interesting applications include estimation of chemical reaction rate, image segmentation, path-planning and robotics navigation. Finding such points using evolutionary algorithms is a field that remains yet to be well investigated. In this paper, we present an evolutionary algorithm that is designed for finding multiple saddle points. In contrast to earlier work [1], we propose a new fitness function that favors 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order saddle points or transition states. In particular, a valley adaptive clearing multi-modal evolutionary optimization approach is proposed to locate and archive multiple solutions by directing the search towards unexplored regions of the search space [2]. Experimental results on benchmark functions and the Lennard Jones Potential are presented to demonstrate the efficacy of the proposed algorithm in locating multiple 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order saddle points.