Advanced Multi-Objective Optimization for Green Flow Shop Scheduling: Addressing Uncertainty with a Simheuristic NSGA-II Approach

This study focuses on advancing Green Flow Shop Scheduling Problems under uncertain conditions. Unlike previous studies that have primarily examined the problem with one or two optimization goals, the present study adopts a realistic approach by considering three objectives: (1) minimizing makespan, (2) increasing machine reliability through preventive maintenance (PM), and (3) optimizing total energy consumption. The decision variables of this study are the sequence of jobs, production rate, and preventive maintenance time. Due to the NP-hard nature of the problem, along with stochastic machine breakdowns, maintenance, and processing times, a simheuristic approach is employed. Accordingly, two advanced algorithms NSGA-II and MOPSO are proposed to solve the presented model. The performance of these algorithms is evaluated using key metrics such as MID (Mean Ideal Deviation), RAS (Reliability Assessment Score), and SNS (Solution Non-dominance Score) to identify the best solutions. Furthermore, a comparative analysis is conducted to examine the performance of each algorithm, and various numerical experiments are carried out to study scenarios with different scales of jobs and machines, including small, medium, and large cases.