Research On Fireworks Algorithms For Solving Multimodal Optimization Problems

In a large number of practical problems,there are often more than one global optimal solution and multiple local optimal solutions.How to construct an optimization algorithm to solve all global optimal solutions and as many local optimal solutions as possible is called multi-modal optimization problem or multi-modal function optimization problem.Multi-modal optimization problems can be divided into multi-modal single-objective optimization problems and multi-modal multi-objective optimization problems.Fireworks algorithm is a new swarm intelligence algorithm,which can be used to solve many practical optimization problems and has good local search ability.But in recent years,fireworks algorithm has not been applied to solve multi-modal optimization problems.This paper mainly studies the application of fireworks algorithm in multi-modal optimization problems,and it improves the traditional fireworks algorithm,and proposes two new fireworks algorithms to solve multi-modal single-objective optimization problems and multi-modal multi-objective optimization problems respectively.The main work of this paper is summarized as follows.This paper presents a single objective multi-modal optimization algorithm based on fireworks algorithm.In order to maintain the diversity of population and improve the global search ability of fireworks algorithm,this paper applies niche algorithm to fireworks algorithm,designs an adaptive niche radius fireworks algorithm(ANRFWA),and proposes the concept of local optimal dominating space.The local optimal solution is absolutely dominant in its control space.In order to reduce unnecessary iteration,we restrain other fireworks in its control space.We test the algorithm on 20 multi-modal optimization problems with different characteristics.The experimental results show that the ANRFWA performs well on most of the test problems and achieves good global convergence and distribution diversity.In this paper,a fireworks algorithm based on improved crowding distance(ICDFWA)is proposed to solve multi-modal multi-objective optimization problems.Because we need to consider the distribution of solutions in both objective space and decision space,we improve the crowding distance and fireworks selection operator on the basis of the ANRFWA,which makes it suitable for solving multi-modal and multi-objective optimization problems.The proposed algorithm achieves better performance on multi-modal multi-objective test problem set than other advanced multi-modal multi-objective algorithms such as the MO?Ring?SCD ? the Omni-optimizer and the DN-NSGA?.