杂草算法收敛性分析及其在工程中的应用

Convergence Analysis of Invasive Weed Optimization Algorithm and Its Application in Engineering

摘要:

针对从自然界中杂草的生长繁殖特性演化而来的新型智能优化算法——扩张性杂草进化算法,通过马尔可夫链,分析证明了它的全局收敛性.相比其他启发式算法,其最大优点是基于种群中优秀的个体有指导地进行搜索,且算法中子代个体按正态分布的方式分布于父代个体周围,在进化过程中通过动态调整此正态分布的标准差,使算法在早期与中期充分保持群落的多样性,较其他启发式算法更容易保证对解空间的全面搜索.而在算法的后期加强对优秀个体周围的局部搜索,从而保证算法能够稳健地收敛到全局最优解.典型的复杂机械优化设计算例结果表明,该算法在优化过程中能有效避开局部最优解,快速、有效地收敛到全局最优解.

Abstract:

This paper introduces a novel numerical stochastic optimization algorithm,the invasive weed optimization (IWO),inspired from colonizing weeds,which mimics the robustness,adaptation and randomness of weeds in a simple but effective optimizing algorithm.Its global convergence is analyzed with Markov chain.Compared to other heuristic algorithms,the biggest advantage of IWO is its directed search based on the species of outstanding individuals within the group.Additionally,the offspring individuals are being randomly spread near their parents according to Gauss normal distribution with the standard deviation of the random function adjusted dynamically during the evolution process.Thus,the algorithm explores new areas aggressively to maintain the diversity of the species in the early and middle iterations,and then enhance the local search near optimal individuals in final iterations.Such mechanism ensures the steady convergence of the algorithm to global optimal solution.Simulation results of the optimal design of a typical complex machinery show that IWO algorithm can effectively search global optimum to avoid falling into a local optimal solution.