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基因表达式编程算法(或称基因表达式程序设计)的基因型/表现型双实体为之带来许多不同于传统演化算法的优势,但建立其Markov模型时,我们须在两者之间作出权衡.为简化遗传算子概率结构的分析,本文以基因型空间为搜索空间,研究一类GEP在宽松条件下的收敛性.首先,针对由基因型-表现型映射所致的多峰适应值函数,重构带精英保留策略的GEP的Markov链模型转移矩阵.然后,通过建立依概率收敛速度的精确表达式、估计其上界,证明了算法依均值收敛、几乎必然收敛甚至完全收敛至全局最优值.与之前的严格假设下的若干结论相比,本文的模型更匹配算法的特性,收敛性结论更强且最优状态子集更小.另外,上述精确表达式也可以推广至自适应演化算法.
The genotype / phenotype double entity of the gene expression programming algorithm brings many advantages over the traditional evolutionary algorithms, but when it comes to establishing its Markov model, we have to make a difference between the two Tradeoffs.To simplify the analysis of the probability structure of genetic operators, this paper uses the genotype space as the search space to study the convergence of a class of GEP under relaxed conditions.First, according to the multi-peak fitness caused by genotype-phenotype mapping Function to reconstruct the Markov chain model transfer matrix of GEP with elitist retention strategy.And then, by setting exact expression of probability convergence rate, the upper bound is estimated, which proves that the algorithm converges by mean, almost converges or even completely converges to the global The optimal value.Compared with the previous conclusions under certain strict assumptions, the model in this paper is more suitable for the characteristics of the algorithm, the convergence conclusion is stronger and the subset of the optimal state is smaller.In addition, the above exact expression can also be extended to Adapt to evolutionary algorithm.