Optimizing Niche Center for Multimodal Optimization Problems

Abstract

Many real-world optimization problems require searching for multiple optimal solutions simultaneously, which are called multimodal optimization problems (MMOPs). For MMOPs, the algorithm is required both to enlarge population diversity for locating more global optima and to enhance refine ability for increasing the accuracy of the obtained solutions. Thus, numerous niching techniques have been proposed to divide the population into different niches, and each niche is responsible for searching on one or more peaks. However, it is often a challenge to distinguish proper individuals as niche centers in existing niching approaches, which has become a key issue for efficiently solving MMOPs. In this article, the niche center distinguish (NCD) problem is treated as an optimization problem and an NCD-based differential evolution (NCD-DE) algorithm is proposed. In NCD-DE, the niches are formed by using an internal genetic algorithm (GA) to online solve the NCD optimization problem. In the internal GA, a fitness-entropy measurement objective function is designed to evaluate whether a group of niche centers (i.e., encoded by a chromosome in the internal GA) is promising. Moreover, to enhance the exploration and exploitation abilities of NCD-DE in solving the MMOPs, a niching and global cooperative mutation strategy that uses both niche and population information is proposed to generate new individuals. The proposed NCD-DE is compared with some state-of-the-art and recent well-performing algorithms. The experimental results show that NCD-DE achieves better or competitive performance on both the accuracy and completeness of the solutions than the compared algorithms.

Knowledge Structure Preserving-Based Evolutionary Many-Task Optimization

“…In our future work, we will further develop the KSP-EA to enhance its performance for solving more difficult MaTOPs. Besides, we will also extend the idea of preserving knowledge structure in solving the real-world MaTOPs with more challenging properties, such as multi-objective [46]- [48], large-scale [49], [50], and multimodal optimization [51]- [53].…”

Optimal Design of an IPMSM for HEVs Using Circular Area Movement Optimization With the Pattern Search Method

“…To verify the performance of the proposed algorithm, the CAMO was applied to two test functions with 11 peaks and 16 peaks and compared with the NGA a widely used conventional optimization algorithm that performs the same multimodal optimization as the proposed algorithm [22], [23], [24], [25]. The test function is as follows:…”

Gene Targeting Differential Evolution: A Simple and Efficient Method for Large-Scale Optimization

“…Since the GT-based modification is only performed on the xbest,g, herein, we choose the DE/best/1 mutation strategy in (2) as the homologous recombination to construct the homologous targeting vector vbest,g. As for the amplification factor F, we directly adopt the setting as 0.5 since it is suggested in many literatures [84] [85]. However, to enhance the parameter diversity, independent parameter is utilized here.…”