Modified snake optimizer algorithm for solving the permutation flow shop scheduling problem

Minimising the makespan for large job sets is the goal of the algorithmically intensive NP-hard permutation flow shop scheduling problem (PFSP), which is crucial for real-world applications. Originally designed for continuous optimisation, the snake optimiser is a recently discovered swarm-based metaheuristic that may jeopardise its exploration-exploitation equilibrium in discrete domains, leading to premature convergence. To address this challenge, this work presents a modified snake optimiser (MSO) for (PFSP). To maintain diversity, prevent stagnation, and enhance solution quality, MSO uses three mutation strategies: swap, insertion, and inversion. 120 benchmark instances with job sizes ranging from 20 to 500 are used for extensive research. The results show that MSO performs comparably to well-known algorithms reported in the literature. MSO consistently outperforms its competitors on complex issues, demonstrating its usefulness as a robust approach for PFSP. Deviations from the optimal solutions range from 0.1% to 0.5%, and MSO consistently performs superior.