利用最大团问题解空间特殊的结构特征,提出一种基于染色划分构建高维约束指导局部搜索移动方向的改进RLS 算法——RLS-II 算法,该算法提高了局部搜索向最优解靠近的概率.基于吸收态Markov 链理论,建立了RLS 和RLS-II 算法求解最大团问题的数学模型,分析了两种算法的吸收时间,并在77 个标准测试算例上对分析结果进行了实验验证.理论分析及实验结果都表明,染色划分过滤确实能够有效改善RLS 算法的性能,且平均染色组长度越大,性能改进的概率和幅度就越大.

By exploiting the special structure in the solution space of the maximum clique problem (MCP), an improved RLS method, the RLS-II method, is has been created where the neighborhood-moving direction of the local search is guided by the multivariate constraints constructed by the dying partitioning. Therefore, the probability of the local search approaching the optimal solution is increased. Using the absorbing Markov chain theory as a reference, the mathematical models of the RLS and RLS-II algorithms in solving maximum clique problem are constructed and the absorbing time of the two algorithms is analyzed. Moreover, the analytical results are experimentally demonstrated on 77 Benchmark instances. Both the theoretical analysis and simulation results show that the dying partitioning filter can effectively improve the performance of the RLS algorithm. Furthermore, the longer average length of the dying group, the higher probability and amplitude of the performance improvement.