Tri-objective parallel machine with job splitting and sequence dependent setup times using differential evolution and particle swarm optimization - Warisa Wisittipanich; Nuttachat Wisittipanit (International Journal of Industrial Engineering and Management)
Parallel machines scheduling problems (PMSPs) exist in the industry since most manufacturing operations aim to produce lots of similar products in a defined time period. Some incoming jobs have different sizes and due dates; plus, the production capacity, setup time, job processing time and energy requirement of each machine can be different, possibly due to distinct models and brands. In addition, jobs can be split into sublots and processed independently on any machine; and the setup times of machines also depend on job sequences. As such, the production management involving those machines becomes exceedingly complex, particularly when the problem has multiple objectives. To obtain optimum solutions, it would require complicated mathematical model along with a solver software; however, metaheuristic algorithms might be needed if a problem becomes too large. This study applied two metaheuristic algorithms, namely differential evolution (DE) and particle swarm optimization (PSO) to the tri-objective PMSP with job splitting and sequence dependent setup times (PMSP-JSSDST) in order to obtain solutions with simultaneously minimized makespan, tardiness and total energy consumption. Both algorithms were used to solve the PMSP-JSSDST instances with some small instances being run on a commercial solver for control purpose. Then, the performances of DE and PSO were compared using hypervolume indicator. The results showed that the performances of both algorithms almost matched to those of the commercial solver for the small instances. And for the large instances, DE algorithm offers superior performances compared to those of PSO algorithm, having significantly higher values of the hypervolume indicator.