A hybrid particle swarm optimization for parallel machine total tardiness scheduling

The parallel machine scheduling problem has received increasing attention in recent years. This research considers the problem of scheduling jobs on parallel machines with a total tardiness objective. In the view of its non-deterministic polynomial-time hard nature, the particle swarm optimization (PSO), which is inspired by the swarming or collaborative behavior of biological populations, is employed to solve the parallel machine total tardiness problem (PMTP). Since it is very hard to directly apply standard PSO to this problem, a new solution representation is designed based on real number encoding, which can conveniently convert the job sequences of PMTP to continuous position values. Moreover, in order to enhance the performance of PSO, we introduce clonal selection algorithm (CSA) into PSO and therefore propose a new CSPSO method. The incorporation of CSA can greatly improve the swarm diversity and avoid premature convergence. We further investigate three parameters of PSO and CSPSO, finding that the parameters have marginal impact on CSPSO, which indicates that CSPSO is a very stable and robust method. The performance of CSPSO is evaluated in comparison with traditional genetic algorithm (GA) and standard PSO on 250 benchmark instances. Experimental results show that CSPSO significantly outperforms GA and PSO, with obtaining the optimal solutions of 237 instances. Additionally, PSO appears more effective than GA.