In reality, multiple optimal solutions are often necessary to provide alternative options in different occasions. Thus, multimodal optimization is important as well as challenging to find multiple optimal solutions of a given objective function simultaneously. For solving multimodal optimization problems, various differential evolution (DE) algorithms with niching and neighborhood strategies have been developed. In this article, a hypercube-based crowding DE with neighborhood mutation is proposed for such problems as well. It is characterized by the use of hypercube-based neighborhoods instead of Euclidean-distance-based neighborhoods or other simpler neighborhoods. Moreover, a self-adaptive method is additionally adopted to control the radius vector of a hypercube so as to guarantee the neighborhood size always in a reasonable range. In this way, the algorithm will perform a more accurate search in the sub-regions with dense individuals, but perform a random search in the sub-regions with only sparse individuals. Experiments are conducted in comparison with an outstanding DE with neighborhood mutation, namely NCDE. The results show that the proposed algorithm is promising and computationally inexpensive.
A Multi-Angle Hierarchical Differential Evolution Approach for Multimodal Optimization Problems
