A hybrid simheuristic algorithm for solving bi-objective stochastic flexible job shop scheduling problems

The flexible job shop scheduling problem (FJSSP) is a complex optimization challenge that plays a crucial role in enhancing productivity and efficiency in modern manufacturing systems, aimed at optimizing the allocation of jobs to a variable set of machines. This paper introduces an algorithm to tackle the FJSSP by minimizing makespan and total weighted earliness and tardiness under uncertainty. This hybrid algorithm effectively addresses the complexities of stochastic multi-objective optimization by integrating the equilibrium optimizer (EO) as an initial solutions generator, Non-dominated sorting genetic algorithm II (NSGA-II), and simulation techniques. The algorithm's effectiveness is validated by showcasing specific instances and delivering decision results for optimal scheduling across varying levels of uncertainty. Results reveal the algorithm's consistent superiority in managing the complexities of stochastic parameters across various problem scales, achieving lower makespan and improved Pareto front quality compared to existing methods. Particularly notable is the algorithm's faster convergence and robust performance, as validated by the statistical Wilcoxon test, which confirms its reliability and efficacy in handling dynamic scheduling situations. These findings underscore the algorithm's potential in providing flexible, robust solutions. The proposed algorithm's unique balance of exploitative and explorative capabilities within a simulation framework enables effective handling of uncertainty in the FJSSP, offering flexibility and customization that is adaptable to various scheduling environments.