基于状态空间模型进化算法的全局收敛性分析

基于状态空间模型进化算法(SEA)是一种新颖的实数编码进化算法，在工程优化问题中具有广阔的应用前景。为了完善SEA的理论体系，促进SEA在工程优化问题中的应用研究，利用齐次有限Markov链对SEA的全局收敛性进行分析， 证明了SEA不是全局收敛的。通过限定SEA状态进化矩阵内元素的取值范围，同时引入弹力搜索得到改进型弹力状态空间模型进化算法（MESEA）。分析结果表明，弹力搜索能提高SEA的搜索效率。最后得到了MESEA全局收敛的结论，为算法在工程优化问题中的应用提供了理论依据。

Global convergence analysis of evolutionary algorithm based on state-space model

Evolutionary Algorithm based on State-space model (SEA) is a new evolutionary algorithm using real strings, and it has broad application prospects in engineering optimization problems. Global convergence of SEA was analyzed by homogeneous finite Markov chain to improve the theoretical system of SEA and promote the application research in engineering optimization problems of SEA. It was proved that SEA is not global convergent. Modified Elastic Evolutionary Algorithm based on State-space model (MESEA) was presented by limiting the value ranges of elements in state evolution matrix of SEA and introducing the elastic search. The analytical results show that search efficiency of SEA can be enhanced by introducing elastic search. The conclusion that MESEA is global convergent is drawn, and it provides theory basis for the application of algorithm in engineering optimization problems.