An adaptive niching method based on multi-strategy fusion for multimodal optimization

Various niching methods have been widely adopted for solving multimodal optimization. However, keeping a balance between exploitation and exploration is still a tough task for designers of multimodal optimization algorithms. An essential niching method is encouraged to deal with optimization problems. In this paper, we proposed an adaptive niching method based on multi-strategy fusion for multimodal optimization. The method changes the traditional way that populations are evaluated in meta-heuristic algorithms. First, a population-entropy based on information theory is proposed as the convergence-maintaining mechanism to track the population status in algorithms. Second, a distribution-radius based on similarity measurement is investigated as the diversity-preserving mechanism to measure the spatial distribution of the optimal solution found. Third, a utility-fitness based on utility theory is adopted to assess the quality of each individual and provide a trade-off between exploitation and exploration. Three strategies are tightly linked and form a closed loop, so that meta-heuristic algorithms equipped with the proposed approach are able to find multiple optimal solutions. The value of population-entropy, the length of distribution-radius, and the evaluation of utility-fitness interact with each other and are adaptively adjusted in each iteration. Meanwhile, our niching method is universal for meta-heuristic algorithms. To illustrate the performance of the proposed method, experiments are conducted using kinds of test functions with different dimensions. The proposed approach is hybrid with different kinds of evolutionary algorithms and swarm intelligence algorithms, including genetic algorithm, differential evolution, particle swarm optimization, brain storm optimization, and artificial bee colony algorithm. The hybrid algorithms are compared with other variants of the standard meta-heuristic algorithms. The validity of the algorithm is analyzed comprehensively. The statistical results show that the hybrid algorithms perform better than other algorithms in both peak ratio and success rate. Then, the hybrid algorithms are verified in practical scheduling problems, and the results show that the algorithms are able to effectively find multiple solutions.