A New Framework taking account of Multi-funnel Functions for Real-coded Genetic Algorithms

In this paper, we propose a new framework taking account of multi-funnel functions for Real-coded Genetic Algorithms (RCGAs). In the continuous function optimization, Evolutionary Algorithms (EAs) are one of the most effective optimization methods. However, most conventional EAs, such as RCGAs and CMA-ES, work efficiently on functions with big-valley landscape and they deteriorate on the multi-funnel functions. Innately Split Model (ISM) has been proposed as a framework of GAs for multi-funnel functions and outperforms conventional GAs on this kind of functions. However, ISM is considered to have two problems in terms of efficiency of the search and difficulty of parameter settings. Our framework repeats a search by RCGAs as ISM does and has two effective mechanisms to remedy the two problems of ISM. We conducted experiments on benchmark functions with multi-funnel and big-valley landscapes and our framework outperformed conventional EAs, Multi-start RCGA (MS-RCGA), Multi-start CMA-ES (MS-CMA-ES) and ISM, on the multi-funnel functions. Our framework achieved as good performance as MS-RCGA and MS-CMA-ES on the big-valley function where ISM significantly deteriorates.