Metaheuristics with restart and learning mechanisms for the no-idle flowshop scheduling problem with makespan criterion

Abstract

The no-idle permutation flowshop scheduling problem (NIPFSP) extends the well-known permutation flowshop scheduling problem, where idle time is not allowed on the machines. This study proposes a new mixed-integer linear programming (MILP) model and a new constraint programming (CP) model for the NIPFSP with makespan criterion. To the best of our knowledge, this study presents a CP model for the NIPFSP for the first time in the literature. We also compare the performance of the proposed MILP and CP models with a well-known MILP model from the literature. Since the studied problem is NP-hard, we also develop a new iterated greedy algorithm with restart and learning mechanisms (IG_RL) and a new iterated local search with restart and learning mechanisms (ILS_RL) as metaheuristics for the problem. In the proposed algorithms, all the parameters are determined by a learning mechanism in a self-adaptive way. Furthermore, a restart mechanism is employed in the proposed IG_RL and ILS_RL algorithms to guarantee the variety of the initial solutions and to assist the algorithm in avoiding the local optima. A variable neighborhood descent procedure is also embedded in the proposed algorithms. We use two well-known benchmark sets, i.e., VRF and Ruiz benchmark suites, to evaluate the performance of proposed solution methods. For almost half of the 240 small VRF instances, optimal results are reported by the MILP and CP models, whereas time-limited model results are reported for the rest. The results on small instances show that the proposed MILP and CP models outperform the MILP model from literature, where the CP model performs better than both MILP models. We compare the performance of the proposed IG_RL and ILS_RL algorithms with the state-of-the-art metaheuristics from the literature on both large VRF instances and Ruiz benchmark instances. The computational results show the effectiveness and superiority of the proposed ILS_RL and IG_RL algorithms for solving the NIPFSP. Primarily, this study improves the current best-known solutions for 102 out of the 250 Ruiz benchmark instances. Additionally, this study reports the NIPFSP results for the well-known VRF benchmark set for the first time in the literature.