In differential Evolution (DE) algorithms, a crossover operation filtering variables to be mutated is employed to search the feasible region flexibly, which leads to its successful applications in a variety of complicated optimization problems. To investigate whether the crossover operator of DE is helpful to performance improvement of evolutionary algorithms (EAs), this paper implements a theoretical analysis for the $(1+1)EA_{C}$ and the $(1+1)EA_{CM}$, two variants of the $(1+1)EA$ that incorporate the binomial crossover operator. Generally, the binomial crossover results in the enhancement of exploration and the dominance of transition matrices under some conditions. As a result, both the $(1+1)EA_{C}$ and the $(1+1)EA_{CM}$ outperform the $(1+1)EA$ on the unimodal OneMax problem, but do not always dominate it on the Deceptive problem. Finally, we perform an exploration analysis by investigating probabilities to transfer from non-optimal statuses to the optimal status of the Deceptive problem, and propose adaptive parameter settings to strengthen the promising function of binomial crossover. It suggests that incorporation of the binomial crossover could be a feasible strategy to improve the performances of EAs.
翻译:在不同的进化(DE)算法中,要变异的交叉操作过滤变量用于灵活搜索可行的区域,从而导致在各种复杂的优化问题中成功应用。为了调查DE的交叉操作者是否有助于改进演化算法(EAs),本文件对美元(1+1)和美元(1+1)进行了理论分析,而美元(1+1)和美元(EA ⁇ CM})的两种变式($(1+1)中包含二进制交叉操作者)。一般而言,二进制交叉结果在加强探索和某些条件下过渡矩阵占优势方面产生了结果。结果是,美元(1+1)和美元(1+1)EA ⁇ C}和美元(1+1)对演化算法(EA ⁇ CM})均比美元($1+1)对单式1美元(EAA$)进行理论分析,但不一定在迷惑问题上支配它。最后,我们通过调查从非优化状态向最佳状态转移的概率来进行探索分析,在某些条件下将过渡矩阵矩阵矩阵定位矩阵定位。结果,将改进可行的跨系统化战略的调整后,可以改进硬性战略。