An assessment of diverse discretization strategies for particle swarm optimization in flow shop scheduling

Abstract

This paper examines the effectiveness and impact of different discretization methods used to transform continuous solution representations into integer values when addressing discrete optimization problems with originally continuous algorithms. Ten discretization methods from the literature are adapted and evaluated across five flow shop scheduling problems encompassing diverse objective functions, namely makespan, flowtime, idle and waiting times, total quadratic completion time, and completion time variance, thus covering just-in-time, non-regular, and trade-off performance criteria. Particle Swarm Optimization is employed as the common metaheuristic framework for implementing and comparing these discretization strategies. The computational results are assessed using analysis of variance (ANOVA), Tukey’s statistical test, and performance profiles. The findings indicate that while discretization methods such as Largest Order Value, Mapping Method, Random-Key, and Great Value Priority achieve superior performance depending on the objective function, the Backward Transformation method consistently underperforms. This study provides an updated comparative evaluation of discretization methods in flow shop scheduling contexts and offers practical insights for selecting effective discretization strategies when applying continuous metaheuristics to discrete optimization problems.