A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Un...A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.展开更多
文摘最小负载着色问题(minimum load coloring problem,MLCP)源于构建光通信网络的波分复用(wavelength division multiplexing,WDM)技术,是一个被证明的NP完全问题.由于NP完全问题有着随问题规模呈指数增长的解空间,因此启发式算法常被用来解决这类问题.在对国内外相关工作的深入分析基础上得知,现有的多类求解MLCP问题的启发式算法中局部搜索算法表现是最好的.研究针对当前求解MLCP问题的局部搜索算法在数据预处理和邻域空间搜索上的不足,提出了两点相应的优化策略:一是在数据的预处理阶段,提出一度顶点规则来约简数据的规模,进而减小MLCP问题的搜索空间;二是在算法的邻域空间搜索阶段,提出两阶段多重选择策略(twostage best from multiple selections,TSBMS)来帮助局部搜索算法在面对不同规模的邻域空间时可以高效地选择一个高质量的邻居解,它有效地提高了局部搜索算法在处理不同规模数据时的求解表现.将这个优化后的局部搜索算法命名为IRLTS.采用74个经典的测试用例来验证IRLTS算法的有效性.实验结果表明,无论最优解还是平均解,IRLTS算法在大多数测试用例上都明显优于当前表现最好的3个局部搜索算法.此外,还通过实验验证了所提策略的有效性以及分析了关键参数对算法的影响.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.
