Discrete Jaya with refraction learning and three mutation methods for the permutation flow shop scheduling problem

The Permutation Flow Shop Scheduling Problem (PFSSP) is an interesting scheduling problem that has many real-world applications. It has been widely used as a benchmark to prove the efficiency of many discrete optimization algorithms. The DJaya algorithm is a discrete variation of the Jaya algorithm that has been recently proposed for solving discrete real-world problems. However, DJaya may get stuck in a local optima because of some limitations in its optimization operators. In this paper, we propose a new discrete optimization algorithm called Discrete Jaya with Refraction Learning and Three Mutation Methods (DJRL3M) for solving the PFSSP. DJRL3M incorporates five modifications into DJaya. First, it utilizes Refraction Learning (RL), which is a special type of opposition learning, to generate a diverse initial population of solutions. Second, it uses three mutation methods to explore the search space of a problem: DJaya mutation, highly disruptive polynomial mutation and Pitch Adjustment mutation. Third, it employs RL at each iteration to generate the opposite solutions of the best and worst solutions in an attempt to jump out local optima. Fourth, it uses the abandon method at the end of each iteration to discard a predefined percentage of the worst solutions and generate new random solutions. Finally, it uses the smallest position value to determine the correct values of the decision variables in a given candidate solution. The performance of DJRL3M was evaluated and compared with six well-recognized optimization algorithms [(New Cuckoo Search (NCS) (Wang et al. in SC 21:4297–4307, 2017), DJaya (Gao et al. in ITC 49:1944–1955, 2018), Hybrid Harmony Search (HHS) (Zhao et al. in EAAI 65:178-199, 2017), Modified Genetic algorithm (MGA) (Mumtaz et al. in: Advances in Manufacturing Technology XXXII: Proceedings of the 16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, 2018), Generalised Accelerations for Insertion-based Heuristics (GAIbH) (Fernandez-Viagas et al. in EJOR 282:858–872, 2020), Memetic algorithm with novel semi-constructive crossover and mutation operators (MASC) (Kurdi in ASC 94:106548, 2020)] using a set of Taillard’s benchmark instances. The experimental and statistical results show that DJRL3M obtains better performance than the performance of NCS, DJaya, HHS and MGA and exhibits competitive performance compared to the performance of MASC and GAIbH.