Novel multimodal problems and differential evolution with ensemble of restricted tournament selection

Bo-Yang Qu, Ponnuthurai Nagaratnam Suganthan
2010 IEEE Congress on Evolutionary Computation  
Multi-modal optimization refers to locating not only one optimum but a set of locally optimal solutions. Niching is an important technique to solve multi-modal optimization problems. The ability of discover and maintain multiple niches is the key capability of these algorithms. In this paper, differential evolution with an ensemble of restricted tournament selection (ERTS-DE) algorithm is introduced to perform multimodal optimization. The algorithms is tested on 15 newly designed scalable
more » ... gned scalable benchmark multi-modal optimization problems and compared with the crowding differential evolution (Crowding-DE) in the literature. As shown by the experimental results, the proposed algorithm outperforms the Crowding-DE on the novel scalable benchmark problems. I. INTRODUCTION N real world optimization, many engineering problems can be classified as multi-modal problems, such as classification problems in machine learning [1] and inversion of teleseismic waves [2] . The aim is to locate several globally or locally optimal solutions and then to choose the most appropriate solution considering practical issues. In recent years, evolutionary algorithms (EA) with various niching techniques have been successfully applied to solve multi-modal optimization problems. The earliest niching approach was proposed by Cavicchio [3] . Subsequently, many other niching methods, such as crowding [4] and clearing [5] , have also been proposed. Differential evolution is a very powerful optimization technique compared with other EAs such as genetic algorithms and evolutionary programming. Like other EAs, DE is also a population-based algorithm. Although DE has been proven to be effective in locating one globally optimal solution [6], the basic DE is not efficient for solving multi-modal optimization problems [7] . Some work has been done to extend the DE to solve multi-modal problems [8]- [9] . and showed that Crowding-DE outperformed a DE based fitness sharing algorithm. In this paper, DE with an ensemble of crowding and restricted tournament selection (ECRTS-DE) is proposed and compared with the Crowding-DE on a set of newly designed scalable multi-modal optimization problems. The remainder of this paper is structured as follows. Section II provides a brief overview of differential evolution, crowding and restricted tournament selection as well as the Crowding-DE algorithm. In Section III, the proposed Manuscript
doi:10.1109/cec.2010.5586341 dblp:conf/cec/QuS10a fatcat:mnbcckfgerbjle3hpvbozbpl64