水波优化算法收敛性分析

Convergence Analysis of Water Wave Optimization Algorithm

水波优化(Water Wave Optimization,WWO)算法是一种受浅水波现象启发的新兴进化算法,它通过模拟水波的传播、折射、碎浪等运动机制来在高维解空间中进行高效搜索。该算法已被证明在大量基准测试问题和工程实际问题上优于其它许多前沿的启发式优化算法。从理论上分析了WWO算法的收敛性条件。通过对目标问题和算法参数设置的简化,证明了WWO中任何个体在两种特殊情况下都是收敛的:(1)只执行传播操作;(2)只执行折射操作。这两种情况分别对应两种特殊的适应度变化状态。进行了数值仿真实验,验证了上述两种收敛性条件。

Taking inspiration from the phenomena of water waves tor global optxmlzatxon, water wave opumzntlu （WWO） is a novel evolutionary algorithm which mimics wave motions including propagation, refraction and breaking for effectively searching in a high-dimensional solution space, which has shown promising performance advantage over a variety of state-of-the-art metaheuristic optimization methods on well-known benchmark problems and real-world engi- neering problems. The paper theoretically analyzed the convergence conditions of the WWO algorithm. By simplifying the target problem and the parameter setting of the algorithm, we demonstrated that in WWO any individual can guaran- tee the convergence in two special cases： 1） when only performing the propagation operation and 2） when only perfor- ming the refraction operation, which respectively happen under two special states of fitness changing. The paper also conducted numerical simulations for the two special cases respectively to validate the above convergence conditions.