Multidirection Update-Based Multiobjective Particle Swarm Optimization for Mixed No-Idle Flow-Shop Scheduling Problem

The Mixed No-Idle Flow-shop Scheduling Problem (MNIFSP) is an extension of flow-shop scheduling, which has practical significance and application prospects in production scheduling. To improve the efficacy of solving the complicated multiobjective MNIFSP, a MultiDirection Update (MDU) based Multiobjective Particle Swarm Optimization (MDU-MoPSO) is proposed in this study. For the biobjective optimization problem of the MNIFSP with minimization of makespan and total processing time, the MDU strategy divides particles into three subgroups according to a hybrid selection mechanism. Each subgroup prefers one convergence direction. Two subgroups are individually close to the two edge areas of the Pareto Front (PF) and serve two objectives, whereas the other one approaches the central area of the PF, preferring the two objectives at the same time. The MDU-MoPSO adopts a job sequence representation method and an exchange sequence-based particle update operation, which can better reflect the characteristics of sequence differences among particles. The MDU-MoPSO updates the particle in multiple directions and interacts in each direction, which speeds up the convergence while maintaining a good distribution performance. The experimental results and comparison of six classical evolutionary algorithms for various benchmark problems demonstrate the effectiveness of the proposed algorithm.