基于局部抽象凸支撑面的多模态优化算法

Multimodal optimization based on local abstract convexity support hyperplanes

中文关键词  进化算法  抽象凸  支撑向量  多模态优化  下界估计

英文关键词  evolutionary algorithms  abstract convexity  support vector  multimodal optimization  underestimation

中文摘要

      在基本进化算法框架下, 结合抽象凸理论, 提出一种基于局部抽象凸支撑面的多模态优化算法. 首先, 采用模型变换方法将原优化问题转变为单位单纯形约束条件下的严格递增射线凸松弛问题; 其次, 针对新生成个体的邻域信息构建局部抽象凸支撑面, 并利用局部下界知识动态识别种群模态, 从而减少替换误差, 避免出现早熟现象; 最后, 借助支撑面下降方向进一步实现模态内部的局部增强过程. 数值研究表明, 针对给定的绝大部分测试问题, 提出的算法在精度和可靠性指标方面均优于文中给出的其他算法.

英文摘要

      In the framework of basic evolutionary algorithms, a new multimodal optimization algorithm based on local abstract convexity support hyperplanes is proposed by using the abstract convexity theory. Firstly, the original bound constrained optimization problem is converted to an increasing convex along rays (ICAR) relaxed problem over unit simplex by using the projection transformation method. Secondly, we construct the underestimate support hypeplanes with the information of trial individual neighborhood and make use of the local lower bound to identify the potential niches dynamically, thus reducing the replacement error and avoiding the premature. Finally, with the aid of descendent direction of support hyperplanes, the detected niches will be enhanced at the same time. Experiments had been performed on several benchmark functions. For most of the benchmark functions, the numerical results show the proposed algorithm is capable to provide better and more consistent performance over the existing multimodal algorithms both in accuracy and reliability.