Multimodal optimization via dynamically hybrid niching differential evolution

A multimodal optimization problem (MMOP) can be referred to as a single-objective optimization involving multiple global and/or local optima. Solving a MMOP is often a complex task that involves finding as many optimal and accurate solutions as possible in a rough search space and providing more alternative solutions for decision makers. Generally, locating more peaks and improving convergence accuracy are two very challenging tasks. In this paper, a dynamically hybrid niching-based differential evolution (DE) with two archives is proposed to try to solve the MMOPs effectively. The proposed method is referred to as DHNDE, which can be featured as: (i) Two niching techniques, i.e., crowding and speciation, are dynamically used during the run. (ii) A secondary archive is introduced to save the inferior offspring. This archive is integrated into crowding-based DE to promote the diversity. And (iii) an improved neighborhood speciation-based DE (INSDE) is presented to improve the convergence. In INSDE, the extremely similar individuals are identified and removed from population to save the computational resources. Additionally, the optimal solutions are stored into an optimal solution archive to avoid losing them during the run. Based on the proposed dynamically hybrid niching technique, DHNDE can make a good tradeoff between the diversity and the convergence. Of the 20 MMOPs presented in CEC-2013 are chosen as the test suite, the DHNDE can stably find all the global optimal solutions on functions F1–F12. Experimental results indicate that DHNDE provides highly competitive results, especially for the MMOPs with a large number of global optima when comparing with 17 related methods.