采用最优混合的进化算法收敛复杂性的理论透视
Theoretical Perspective of Convergence Complexity of Evolutionary Algorithms Adopting Optimal Mixing
摘要：
最优混合进化算法（OMEAs）以其鲁棒性强、所需种群规模小、函数求值次数少等优点受到广泛关注。本文通过研究OMEA中的变异算子最优混合（OM）的机理，研究了OMEA在单层和双层掩模下的性能和行为。对于单层掩模的情况，所需的人口规模是从初始供应的角度来推导，而收敛时间是通过分析子解生长的进展。然后，通过估计执行评估的概率，NFE是渐近有界的理性概率。对于双层口罩的情况下，经验结果表明，所需的人口规模是成正比的交叉竞争的程度和结果从一层口罩的情况下。导出的模型还表明，人口规模决定于初始供应时，采用不相交的面具，高选择压力施加的OM使子问题的组成对NFE的影响很小，和人口规模的要求，两层面具的反向增长概率增加。
英文摘要：
The optimal mixing evolutionary algorithms (OMEAs) have recently drawn much attention for their robustness, small size of required population, and efficiency in terms of number of function evaluations (NFE). In this paper, the performances and behaviors of OMEAs are studied by investigating the mechanism of optimal mixing (OM), the variation operator in OMEAs, under two scenarios -- one-layer and two-layer masks. For the case of one-layer masks, the required population size is derived from the viewpoint of initial supply, while the convergence time is derived by analyzing the progress of sub-solution growth. NFE is then asymptotically bounded with rational probability by estimating the probability of performing evaluations. For the case of two-layer masks, empirical results indicate that the required population size is proportional to both the degree of cross competition and the results from the one-layer-mask case. The derived models also indicate that population sizing is decided by initial supply when disjoint masks are adopted, that the high selection pressure imposed by OM makes the composition of sub-problems impact little on NFE, and that the population size requirement for two-layer masks increases with the reverse-growth probability.
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