Abstract: Clonal Selection Algorithm (CSA) has been widely applied in intelligent computation field, but the theoretical analysis and research works regarding CSA are relatively lacking. In order to enrich the theoretical underpinning of the CSA, the authors abstracted the single-member-based B Cell Algorithm (BCA) from the multi-member-based CSA, and simplified the mathematical model of the CSA. A modified mutation operator in BCA, Contiguous Region Hypermutation Operator (CRHO), was introduced; a Markov chain model of the BCA was proposed; a novel method for the construction of transition matrices for the BCA was given. Consequently, it was proved that the BCA was convergent absolutely. It can be concluded that clonal selection algorithm is convergent, because BCA is an abstract of the generic CSA.

Key words: Clonal Selection Algorithm (CSA), B Cell Algorithm (BCA), Contiguous Region Hypermutation Operator (CRHO), Markov chain model, convergence

摘要： 克隆选择算法(CSA)已经广泛应用于计算智能领域，而针对其理论方面的分析和研究工作相对较少。为了丰富克隆选择算法的理论基础，将含有多个体种群的克隆选择算法抽象为含单个体的B细胞算法（BCA），简化了克隆选择算法的数学模型。给出了在BCA中使用的一种变异算子——连续区域超体变异算子（CRHO）和BCA的Markov链模型，提出了一个新的构造算法的状态跃迁矩阵的方法，证明了BCA的绝对收敛性。由于BCA是一般克隆选择算法的一种抽象，因此可以推断克隆选择算法的收敛性。

关键词: 克隆选择算法, B细胞算法, 连续区域超体变异算子, Markov链模型, 收敛性