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Variable neighborhood search (VNS) algorithm is proposed for scheduling identical parallel machine. The objective is to study the effect of adding a new neighborhood structure and changing the order of the neighborhood structures on minimizing the makespan. To enhance the quality of the final solution, a machine based encoding method and five neighborhood structures are used in VNS. Two initial solution methods which were used in two versions of improved VNS (IVNS) are employed, namely, longest processing time (LPT) initial solution, denoted as HIVNS, and random initial solution, denoted as RIVNS. The proposed versions are compared with LPT, simulated annealing (SA), genetic algorithm (GA), modified variable neighborhood search (MVNS), and improved variable neighborhood search (IVNS) algorithms from the literature. Computational results show that changing the order of neighborhood structures and adding a new neighborhood structure can yield a better solution in terms of average makespan.

mathematical problems in engineering

An Order Effect of Neighborhood Structures in Variable Neighborhood Search Algorithm for Minimizing the Makespan in an Identical Parallel Machine Scheduling