Multimodal Multi-Objective Flexible Job Shop Scheduling: A Preliminary Study

This paper aims to explore the existence of multimodality in the multi-objective flexible job shop scheduling problem (MOF JSP). Multimodality in real-world problems refers to multiple high-quality solutions to a problem, each with a different approach but achieving the same overall goal. The article briefly introduces the background of flexible shop scheduling problems, focusing on the multimodal characteristics of these problems and the importance of multimodal solutions to shop scheduling. This study highlights existing research gaps in this area through a literature review. A genetic algorithm with a multimodal unarchiving mechanism (NSGA-MSPM) is proposed to explore the multimodality of MOFJSP. The experiment uses benchmark problems in shop scheduling, sets different evaluation counts for each problem, and records the number of optimal target values found by the algorithm, as well as the number of corresponding multi-modal solutions. By randomly selecting individuals and drawing a Gantt chart, this study shows various scheduling arrangements with the same target value, demonstrating the multimodality of MOFJSP. Finally, the paper discusses the limitations of current research methods and outlines future directions, including improvements to the algorithm and its application in a wider context.