多元优化算法的渐近性分析
On asymptotic property of multivariant optimization algorithm

本文提出了一种多元化智能个体分工明确、协同合作的超启发式智能优化算法—–多元优化算法. 多元优化算法通过交替的全局、局部搜索迭代对解空间搜索以逐渐逼近全局最优解. 搜索个体按照分工不同可以分为全局搜索个体(全局元)和局部搜索个体(局部元). 全局元负责对整个解空间进行全局搜索以快速找到较优潜在解区域, 局部搜索元负责对各个潜在解区域进行局部搜索以提高解的质量. 该算法具有两个特点: 分工明确的搜索策略不需要考虑均衡全局搜索和局部搜索, 能够保证局部搜索能力的同时加强全局搜索以避免陷入局部最优解; 全局、局部交替搜索保证了算法对全局最优解的渐近性. 本文从理论上证明了算法的渐近性并且基于复杂多模态测试函数比较了几个优秀的进化算法. 实验结果表明多元优化算法在渐近性方面优于其他几个比较的算法.
We propose a meta-heuristic intelligent optimization algorithm named as multivariant optimization algorithm, in which intelligent searchers have specific and defined roles in cooperation. To obtain the global optimal solution gradually, we search the solution space through alternate iterations of global exploration and local exploitation. According to different responsibilities, the searchers (atoms) can be divided into two kinds: the global atoms and the local ones. The global atoms explore the whole solution space to locate the potential areas rapidly. The local atoms exploit each potential area to improve the quality of the solution found by the global atom. The algorithm has two characters: on the one hand, the search strategy with clear division of responsibilities eliminates the need of balancing global exploration and local exploitation, which helps the global exploration to escape from local traps while ensuring the local exploitation. On the other hand, the alternate iterations of global exploration and local exploitation guarantee the asymptotic behavior of algorithm. The asymptotic property of multivariant optimization algorithm is proved theoretically. Extensive comparisons with some outstanding evolutionary algorithms are carried out based on eight complex multi-modal benchmark functions. Results show that this multivariant optimization algorithm is superior to the compared algorithms in asymptotic property.