A discrete artificial bee colony algorithm with composite mutation strategies for permutation flow shop scheduling problem

Abstract

The Permutation Flow Shop Scheduling Problem (PFSSP) is an NP-hard problem of wide engineering and theoretical background. In this paper, a kind of discrete artificial bee colony with composite mutation strategies is presented to compensate the defects of the single mutation scheme that is easy to get into the local best for PFSSP, named CDABC. Firstly, to make ABC suitable for PFSSP, we regard each discrete job permutation as a food source and apply discrete operations to generate a new neighbourhood food source for different bees. Secondly, the Nawaz-Enscore-Ham (NEH) heuristic is combined with the random initialization to initialize the population with a certain quality and diversity. Thirdly, the composite mutation strategies are proposed to enable the DABC to solve the permutation flow shop scheduling. Finally, the fast local search is used for enhancing the best individual. Within our knowledge, there are few papers to discuss artificial bee colony algorithm about PFSSP with the objective of minimizing total flow time and maximum lateness of jobs. In this sense, our work can be viewed as a start point for researchers to develop ABC-based algorithms to solve PFSSP. Additionally, simulations and comparisons based on PFSSP benchmarks are carried out, which shows that our algorithm is very competitive. We have also evaluated our algorithm with the well known DMU problems. For the problems with the objective of minimizing makespan, the algorithm CDABC obtains 26 new upper bounds of the 40 instances, and for the problems with the objective of maximum lateness, CDABC obtains 137 new upper bounds of the 160 instances. These new upper bounds can be used for future algorithms to compare their results with ours.