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

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