A memetic algorithm with novel semi-constructive evolution operators for permutation flowshop scheduling problem

Abstract

This paper proposes a memetic algorithm (MA) with novel semi-constructive crossover and mutation operators (MASC) to minimize makespan in permutation flowshop scheduling problem (PFSP). MASC combines the strengths of genetic algorithm (GA), simulated annealing (SA), and Nawaz–Enscore–Ham (NEH) algorithm. The aim is to enhance GA in identifying promising areas in the search space, whose local optima will be subsequently located by SA. This is achieved by means of novel crossover and mutation operators that construct chromosomes by using two different types of genes: static and dynamic genes. MASC is tested on the well-known Taillard’s benchmark instances. The proposed operators are compared with traditional operators. The results show that the proposed operators produce considerable improvements. These improvements reach up to 20.79% in the average relative error of best solution and 11.86% in the average relative error of average solution. MASC is compared with fourteen well-known and state-of-the-art algorithms. These algorithms include MA, whale optimization, ant colony optimization, particle swarm optimization, artificial bee colony, monkey search, and iterated greedy. The results show that MASC outperforms all the compared algorithms except three iterated greedy algorithms. Moreover, the improvement in the average relative error of best solution achieved on the best-so-far MA is 37.92%. Therefore, MASC can be considered as one of the best-so-far methods for PFSP.