A hybrid evolution strategies algorithm for non-permutation flow shop scheduling problems

Flow shop scheduling has garnered significant attention from researchers over the past ten years, establishing itself as a prominent area of study within the field of scheduling. Nevertheless, there exists a paucity of research dedicated to addressing Non-Permutation Flow Shop Scheduling Problems. In this study, a Hybrid Evolution Strategies (HES) is suggested by combining the exploitation ability of Nawaz, Enscore, and Ham (NEH) Heuristic, the exploration ability of Improved Evolution Strategies (IES), and a Local Search Technique to minimize the makespan of NPFSSP. The primary solution is produced through the NEH Heuristic, serving as a foundational solution for the IES. The IES is applied in two stages, in the first stage it improves the permutation sequence found from the NEH heuristic. In the second stage of the IES, the permutation sequence on the first 40% of machines is fixed as found in the first stage. The sequence on the last 60% of machines is altered only so that the makespan is minimized and a good non-permutation sequence is found. Recombination and mutation are the main genetic operators in IES. For recombination in IES, 16 offspring are generated randomly from a single parent. The Quad swap mutation operator is employed in the IES to optimize the utilization of the solution space while minimizing computational time. To prevent trapping in local minima, a Local Search Technique is integrated into the IES algorithm, which guides solutions to less explored areas. Computational analyses indicate that HES exhibits superior performance regarding solution quality, computational efficiency, and robustness.