Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions

Abstract

A hybrid method combining two algorithms is proposed for the global optimization of multiminima functions. To localize a “promising area”, likely to contain a global minimum, it is necessary to well “explore” the whole search domain. When a promising area is detected, the appropriate tools must be used to “exploit” this area and obtain the optimum as accurately and quickly as possible. Both tasks are hardly performed through only one method. We propose an algorithm using two processes, each one devoted to one task. Global metaheuristics, such as simulated annealing, tabu search, and genetic algorithms (GAs) are efficient to localize the “best” areas. On the other hand, local search methods are classically available: in particular the hill climbing (e.g. the quasi-Newton method), and the Nelder–Mead simplex search (SS). Therefore we worked out an hybrid method, called continuous hybrid algorithm (CHA), performing the exploration with a GA, and the exploitation with a Nelder–Mead SS. To evaluate the efficiency of CHA, we implemented a set of benchmark functions, and compared our results to the ones supplied by other competitive methods.