Hybridization of Adaptive Differential Evolution with BFGS

Abstract

Local search (LS) methods start from a point and use the gradient or objective function value to guide the search. Such methods are good in searching the neighborhood of a given solution (i.e., they are good at exploitation), but they are poor in exploration. Evolutionary Algorithms (EAs) are nature inspired populationbased search optimizers. They are good in exploration, but not as good at exploitation as LS methods. Thus, it makes sense to hybridize EAs with LS techniques to arrive at a method which benefits from both and, as a result, have good search ability. Broydon-Fletcher-Goldfarb-Shanno (BFGS) method is a gradient-based LS method designed for nonlinear optimization. It is an efficient, but expensive method. Adaptive Differential Evolution with Optional External Archive (JADE) is an efficient EA. Nonetheless, its performance decreases with the increase in problem dimension. In this paper, we present a new hybrid algorithm of JADE and BFGS, called Hybrid of Adaptive Differential Evolution and BFGS, or DEELS, to solve the unconstrained continuous optimization problems. The performance of DEELS is compared, in terms of the statistics of the function error values with JADE.