单纯形免疫算法及其在高维非凸函数优化中的应用

许多工程问题都可以归结为优化问题,而且其目标函数往往是局部最优点的复杂高维非凸函数,传统单一算法一般难以求得全局最优解。在深入分析免疫算法和单纯形法的基础上,将两种算法有机结合,提出单纯形免疫算法。免疫记忆、抽取疫苗、接种疫苗和自适应等免疫机制的引入有助于优良个体和基因的保留和利用,提高算法收敛性;通过反射、扩展、内缩、缩边等操作来改良劣解而调整邻域结构,不断逼近最优解。典型函数优化Benchmark问题的仿真试验表明,提出的单纯形免疫算法比单一算法性能更优,适合于存在许多局部最优点的复杂高维非凸函数优化。

Simplex Immune Hybrid Algorithm and Its Application to Multi-dimensional No-protruding Function Optimization

Optimization can provide solutions for many engineering problems whose objective functions are commonly complex multi-dimensional no-protruding functions with local extremums.Therefore,traditional simplex algorithms cannot always find global optimal solutions for the problems.Based on the in-depth analysis of genetic algorithm and simplex algorithm and with the combination of the two,the paper proposes the simplex immune hybrid algorithm.The introduction of immune mechanisms such as immunity memory,self-adaption,vaccine extraction and inoculability is helpful to the retention and utilization of excellent individuals and genes,enhancing the algorithm′s convergence.The algorithm improves bad solutions and readjusts the structure of adjacent fields and approaches the global optimization using arithmetic operations such as reverberation,extension,inner-shrink and side-shrink.The simulation of the optimization of four Benchmark functions indicates that the simplex immune hybrid algorithm herein is better than simplex algorithm and applicable to the optimization of complicated multi-dimensional no-protruding functions with numerous local extrema.