A method for searching multiple local optimal solutions of nonlinear optimization problems

This paper presents a systematic method for searching multiple local optimal solutions of continuous nonlinear optimization problems. The presented method consists of two major algorithms for searching the solutions. The first part of the algorithms is for a global search, and the second one is for a local search. The effective global search algorithm based on bifurcation theory has been developed to escape from a stability region (basin of attraction) of a stable equilibrium point, and move to another stable equilibrium point via a type I unstable equilibrium point on the stability boundary (basin boundary) using the continuation method. The proposed method is verified by two well-known numerical examples.