To improve the performance of the backtracking search optimization algorithm (BSA), a multi-population cooperative evolution strategy guided BSA with hierarchical knowledge (HKBSA) is proposed in this paper. According to the domain knowledge of the candidates in objective space, the population is divided into the dominant population, the ordinary population and the inferior population. The information between the sub-populations has interacted with the evolution processes of the three sub-populations. The individuals in the dominant population are maintained as the optimal solutions and are utilized to guide the evolution of the other two sub-populations. A multi-strategy mutation mechanism is applied to solve non-separable problems. The distribution vector of inferior individuals is constructed by sampling, and a mechanism of the individual generation with feedback is proposed by combining self-learning strategy and elite learning strategy. The convergence of HKBSA is analyzed with the Markov model. Compared with the state-of-the-art BSA variants, HKBSA outperforms other algorithms in terms of the speed of convergence, solution accuracy and stability.

为了提高回溯搜索优化算法（BSA）的性能，提出了一种基于层次知识的多种群协同进化策略指导的BSA（HKBSA）。根据目标空间中候选人的领域知识，将人口分为优势人口，普通人口和劣等人口。亚种群之间的信息已经与这三个亚种群的进化过程相互作用。优势人口中的个体被保持为最优解，并被用来指导其他两个亚群的进化。应用多策略突变机制来解决不可分离的问题。通过抽样构造劣等个体的分布向量，结合自我学习策略和精英学习策略，提出具有反馈的个体生成机制。用Markov模型分析了HKBSA的收敛性。与最新的BSA变体相比，HKBSA在收敛速度，解决方案准确性和稳定性方面均优于其他算法。