和声搜索算法探索能力研究及其修正

Exploration ability study of harmony search algorithm and its modification

和声搜索算法(harmony search,HS)的一大缺点是它容易陷入局部最优.针对此缺点,深入研究了近期文献中所提出的步长(bw)调整方法.首先具体分析了和声搜索算法即兴创作过程的探索能力,而后推导出在不对称区间下即兴创作过程的探索能力与各参数的关系,并进一步讨论了bw对探索能力和算法收敛的影响,证明了方差期望和均值期望所组成的迭代方程的迭代收敛充分性.基于这些分析和证明,提出一种修正和声搜索算法(modified harmony search,MHS),并分析了参数和声记忆库大小(harmony memory size,HMS)、基音调整概率(pitch adjusting rate,PAR)及和声记忆库的考虑概率(harmony memory considering rate,HMCR)对MHS优化性能的影响.数值仿真结果表明MHS算法优于HS及最新文献所报道的8种改进HS算法,具有良好的优化性能.

Harmony search （HS） algorithm often generates solutions that are only local optimal. To conquer this disad- vantage, the distance bandwidth adjusting methods that were proposed in recent publications are deeply studied. At first, the exploration ability of HS improvisation is investigated. Secondly, the relationship between improvisation exploration and each parameter under asymmetric interval is deduced. Finally, the effects of the parameter bw on the exploration ability and convergence of HS are discussed, and the iterative convergence sufficiency of the iteration equation which consists of variance expectation and mean expectation is theoretically proven. Based on the above analyses and proof, a modified har- mony search （MHS） algorithm is proposed. The effects of the key parameters HMS, PAR and HMCR on the performance of MHS algorithm are also discussed in detail. Experimental results demonstrated that the proposed MHS algorithm has better performance than HS and the other eight state-of-the-art HS variants that were recently proposed.