Adaptive Niche Radius Fireworks Algorithm for Multi-modal Function Optimization

In recent years, many multi-modal optimization algorithms have been proposed to find not only the one optimal solution but all global optimums of the problem. In solving multi-modal optimization problems, conventional fireworks algorithms only consider the global optima of the problem, but ignore the local optima. In this paper, inspired by the niching theory, a novel adaptive radius fireworks algorithm (ANRFWA) which introduces the concept of dominating space of local optima is proposed to solve multi-modal optimization problems. Local optima is absolutely dominant in its dominating space, we directly eliminate other fireworks in its dominating space in case of unnecessary iteration. We have tested a large number of multimodal optimization problems, and the ANRFWA performs well in solving most of them. Compared with the previous fireworks algorithm, the ANRFWA can find more global optima, and it is not inferior to some well-known evolutionary algorithms.