Multimodal optimization aims to find and maintain as many global and local optima of a function as possible. Niching techniques based on multi-populations and clustering proved to be efficient for tackling multimodal optimization problems. The main focus of this work is to enhance the diversity of the population and improve the global search ability to locate more optima. A Double-Layer-Clustering Speciation Differential Evolution (DLCSDE) algorithm for multimodal optimization is proposed. We also show how the DLCSDE can be improved by integrating with a self-adaptive strategy to form the Self-adaptive DLCSDE (SDLCSDE). Based on speciation, first layer clustering divides the entire population into multiple subpopulations to locate global and local optima. The seeds from each species then form a sub-population to search globally during the second layer clustering to find peaks missed during the first layer clustering search process. To test the performance, both DLCSDE and SDLCSDE are compared with 17 state-of-art niching algorithms on 29 multimodal problems with different dimensions. The experiment results demonstrate that both the proposed algorithms outperform or perform comparably to the 17 niching algorithms on all the test functions.

多峰优化旨在发现并保持尽可能多的函数全局和局部最优。事实证明，基于多种群和聚类的小生境技术对于解决多峰优化问题非常有效。这项工作的主要重点是增强种群的多样性并提高全球搜索能力以找到更多的最佳状态。提出了一种用于多峰优化的双层集群物种差异演化算法。我们还展示了如何通过与自适应策略集成以形成自适应DLCSDE（SDLCSDE）来改进DLCSDE。基于物种形成，第一层聚类将整个种群分为多个子种群，以定位全局和局部最优值。然后，来自每个物种的种子会形成一个子种群，以便在第二层聚类期间进行全局搜索，以查找在第一层聚类搜索过程中遗漏的峰。为了测试性能，将DLCSDE和SDLCSDE两者与针对29个具有不同维度的多峰问题的17种最新小生境算法进行了比较。实验结果表明，所提算法在全部测试功能上均优于或优于17种小算法。