Multipopulation GA/IWO with Coupled Scale-Free Networks for Solving Flexible Job-Shop Scheduling Problems

In recent years, an increasing number of population-based metaheuristic algorithms have been proposed to solve the flexible job-shop scheduling problem (FJSP) according to its practicality and complexity. Most of these algorithms are single-population-based and hence are very susceptible to becoming trapped in local optimal values. Thus, multipopulation methods are widely used to improve these algorithms, resulting in multipopulation algorithms. These multipopulation algorithms have been widely studied in the context of single-layer complex networks recently. However, coupled networks used to control two (or more) algorithms simultaneously to get a better algorithm are always ignored in literature. Therefore, in this paper, using coupled scale-free networks (with different scaling exponents) to control the genetic algorithm (GA) and the invasive weed optimization (IWO) simultaneously, a multipopulation GA/IWO with coupled scale-free networks (MPGAIWO-SF) is proposed to solve FJSP. Then, we study how some parameters (e.g., subpopulation size, subpopulation number, and scaling exponent) of MPGAIWO-SF affect its performance, which is also ignored in literature. The simulation results illustrate that (1) the performance of MPGAIWO-SF is significantly improved compared with that of GA and IWO; (2) as the subpopulation size increases, the performance of MPGAIWO-SF first becomes better and then remains almost unchanged; (3) as the subpopulation number increases, the performance of MPGAIWO-SF first becomes better and then decreases rapidly; and (4) the performance of MPGAIWO-SF becomes worse slightly as the scaling exponent decreases. Finally, solving more FJSP instances, the MPGAIWO-SF with optimized parameters is compared with other related algorithms to verify its effectiveness.