ABSTRACT Water Wave Optimisation algorithm (WWO) is a new swarm-based metaheuristic inspired by shallow wave models for global optimisation. In this paper, an enhanced WWO, which combines with multiple assistant strategies (EWWO), is proposed. First, the random opposition-based learning (ROBL) mechanism is introduced to generate the initial population with high quality. Second, a new modified operation is designed and embedded into propagation operation to balance the global exploration and the local exploitation. Third, the covariance matrix self-adaptation evolution strategy (CMA-ES) is employed by the refraction operation to further strengthen the local exploitation. Furthermore, the diversity of the population is maintained in the evolution process by using a crossover operator. The experiment results based on CEC 2017 benchmarks indicate that the EWWO outperforms the state-of-the-art variant algorithms of the WWO and the standard WWO.

中文翻译：

---

基于CMA-ES和基于对立的学习增强的改进水波优化算法

摘要 水波优化算法 (WWO) 是一种新的基于群的元启发式算法，其灵感来自用于全局优化的浅波模型。在本文中，提出了一种结合多种辅助策略（EWWO）的增强型 WWO。首先，引入基于随机对立的学习（ROBL）机制来生成高质量的初始种群。其次，设计了一种新的修改操作并将其嵌入到传播操作中以平衡全局探索和局部开发。第三，折射操作采用协方差矩阵自适应进化策略（CMA-ES）进一步加强局部开发。此外，通过使用交叉算子在进化过程中保持种群的多样性。