紧凑型遗传算法的研究进展
A Step Forward in Studying the Compact Genetic Algorithm
摘要：
紧凑型遗传算法（cGA）是一种分布估计算法，它不使用传统的重组和变异算子，而是根据父种群的概率模型来产生后代种群。cGA只需要少量的内存;因此，它在内存受限的应用中可能非常有用。本文介绍了一个理论框架，研究cGA的收敛性的观点，其中，我们建模的cGA的马尔可夫过程和近似的行为，使用常微分方程（ODE）。然后，我们证明了相应的常微分方程收敛到局部最优，并停留在那里。因此，我们得出结论，cGA将收敛到局部最优的功能进行优化。
英文摘要：
The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.
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