Hybrid Particle Swarm Optimization with Genetic Operators and Cauchy Distribution for Flexible Job-shop Scheduling Problem

Flexible job-shop scheduling problem (FJSP) has been well known as one of the most difficult NP-hard combinatorial optimization problems. This problem FJSP is an extension of job-shop scheduling problem (JSP) which is to create a sequence of operations satisfying the precedence relationship together with assignment of time and resources for each operation. Thus, the FJSP model is closer to the real factory situation and greater complexity than JSP model due to the need to determine the assignment of operations to machines. This paper proposes a hybrid particle swarm optimization (PSO) algorithm combined with genetic algorithm (GA) and Cauchy distribution to solve the flexible job shop scheduling problem. The objective is to find a job sequence that minimizes the makespan. The hybrid PSO combined with GA is based on the particle swarm optimization for creating operation sequences and assign operations on machines, and for improving by the genetic operators such as crossover and mutation to update particles. Finally, the proposed method is illustrated with a numerical example and numerical experiment results show that the effectiveness of the approach by the hybrid PSO combined with GA and Cauchy distribution (PSO + GA with CD).