A multimodal butterfly optimization using fitness-distance balance

Due to the multimodal nature of real-world optimization problems, in recent years, there has been a great interest in multi-modal optimization algorithms. Multimodal optimization problems involve identifying multiple local/global optima. Niching techniques have been widely used to tackle multi-modal optimization problems. Most of the existing niching methods either require predefined niching parameters or extra information about the problem space. This paper presents a novel multimodal algorithm based on Butterfly Optimization Algorithm, which is constructed using the Fitness-Distance Balance (FDB) selection method. The purpose of applying the FDB selection method is to discover local/global optima with high potential as a fitness value along with the appropriate distance from solution candidates. Also, a local search scheme is used to enhance the convergence speed of the algorithm. Niching is a technique used in multimodal optimization to maintain diversity among multiple solutions in the population. The minimum distance between the solutions is called a "niche". The proper niching radius is the main challenge for existing approaches. Knowing the problem space helps determine the niche radius. This paper proposes a new multimodal optimization scheme that does not require prior knowledge of the problem space or the niching parameter. Seven state-of-the-art multi-modal optimization algorithms are compared to the multi-modal butterfly optimization algorithm (MBOA) on 16 benchmarks from the CEC 2013 and CEC 2015 competitions to evaluate its performance. Success rate, Number of function evaluations, Success performance, average number of optima found, Success accuracy, Maximum peak ratio, and Run-time performance criteria were measured over 25 runs to assess the efficiency of the proposed method. The experimental results demonstrate that MBOA outperforms other algorithms according to most of the performance criteria.