A hybrid harmony search algorithm with efficient job sequence scheme and variable neighborhood search for the permutation flow shop scheduling problems

摘要

The permutation flow shop scheduling problem (PFSSP), one of the most widely studied production scheduling problems, is a typical NP-hard combinatorial optimization problem. In this paper, a hybrid harmony search algorithm with efficient job sequence mapping scheme and variable neighborhood search (VNS), named HHS, is proposed to solve the PFFSP with the objective to minimize the makespan. First of all, to extend the HHS algorithm to solve the PFSSP effectively, an efficient smallest order value (SOV) rule based on random key is introduced to convert continuous harmony vector into a discrete job permutation after fully investigating the effect of different job sequence mapping schemes. Secondly, an effective initialization scheme, which is based on NEH heuristic mechanism combining with chaotic sequence, is employed with the aim of improving the solution's quality of the initial harmony memory (HM). Thirdly, an opposition-based learning technique in the selection process and the best harmony (best individual) in the pitch adjustment process are made full use of to accelerate convergence performances and improve solution accuracy. Meanwhile, the parameter sensitivity is studied to investigate the properties of HHS, and the recommended values of parameters adopted in HHS are presented. Finally, by making use of a novel variable neighborhood search, the efficient insert and swap structures are incorporated into the HHS to adequately emphasize local exploitation ability. Experimental simulations and comparisons on both continuous and combinatorial benchmark problems demonstrate that the HHS algorithm outperforms the standard HS algorithm and other recently proposed efficient algorithms in terms of solution quality and stability.