A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan

It is well known that the flow-shop scheduling problem (FSSP) is a branch of production scheduling and is NP-hard. Now, many different approaches have been applied for permutation flow-shop scheduling to minimize makespan, but current algorithms even for moderate size problems cannot be solved to guarantee optimality. Some literatures searching PSO for continuous optimization problems are reported, but papers searching PSO for discrete scheduling problems are few. In this paper, according to the discrete characteristic of FSSP, a novel particle swarm optimization (NPSO) algorithm is presented and successfully applied to permutation flow-shop scheduling to minimize makespan. Computation experiments of seven representative instances (Taillard) based on practical data were made, and comparing the NPSO with standard GA, we obtain that the NPSO is clearly more efficacious than standard GA for FSSP to minimize makespan.