A modified Variable Neighborhood Search for minimizing the makespan on identical parallel machines

Abstract

Variable Neighborhood Search (VNS) is one of the most recent metaheuristics used for problem solving in which a systematic change of neighborhood within a local search is carried out. The idea is to build the best local search and shake operations based on neighbourhood structure available. In this paper, a modified version of VNS algorithm proposed for identical parallel machines scheduling problems with the objective function of minimizing makespan. The proposed VNS algorithm was tested 150 randomly generated problems with different jobs and machines. The results gained by modified VNS (MVNS) algorithm are presented and compared with the both Genetic Algorithm (GA) and Longest Processing Time (LPT) solutions. It is concluded that the MVNS algorithms outperform the both GA and LPT.Keywords: Identical Parallel Machine Scheduling; Makespan; Variable neighboorhood search 1. INTRODUCTION Identical parallel machines scheduling problems (PMS) with the objective function of minimizing makespan (C max ) is one of the best known and NP-hard [I] combinatorial problems. Thus, it is unlikely to obtain the optimal schedule through polynomial time-bounded algorithms. Small size instances of the PMS problem can be solved with reasonable computational time by exact algorithms such as branch-and-bound [2], and the cutting plane algorithm [3]. However, when the problem size increases, the computational time of exact methods grows exponentially. On the other hand heuristic algorithms have generally acceptable time and memory requirements, but do not guarantee optimality of the final solution, that is, a feasible solution is obtained which is likely to be either optimal or near optimal. The well-known longest processing time (LPT) rule of Graham [4] is part of family algorithm knows as list scheduling algorithm. The performance of LPT has been shown very well for the makespan single criteria problem [5]. Later, Coffinan et al. [6] proposed MULTIFIT algorithm that affords the relation between bin-packing and maximum completion time problems . Yue [7] show that the MULTIFIT heuristics is not guaranteed perform better than LPT for any given problem. Gupta and Ruiz-Torres [8] proposed a LISTFIT algorithm that combines the bin packing method used in the MULTIFIT heuristics with multiple lists ofjobs. Their computational results showed that the heuristic out-performs the LPT algorithm, and the MULTIFIT algorithm. Min and Cheng [9] proposed a genetic algorithm (GA) which based on machine code. They indicate that quality of GA's solution has advantage over heuristic procedure and Simulated

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

“…In this section, the results of two versions of the proposed algorithm were compared with LPT [1], SA [17], GA [14], MVNS [21], and IVNS [23] algorithms from the literature. The two versions of the improved variable neighborhood search algorithms "HIVNS1 and RIVNS1" and "HIVNS2 and RIVNS2" were coded in MATLAB R2012a and executed on i5 CPU 5 GHz with 6 GB of RAM.…”

“…Computational results showed that hybridized DPSO (HDPSO) algorithm outperforms both SA and DPSO algorithms. Sevkli and Uysal [21] proposed modified variable neighborhood search (MVNS) which is based on exchange and move neighborhood structures. Computational results demonstrated that the proposed algorithm outperforms both GA and LPT algorithms.…”

Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling

“…The algorithm also employs two neighborhood structures to obtain improved solutions. Sevkli and Uysa [24] proposed a modified variable neighborhood search algorithm with two neighborhood structures for makespan minimization in identical parallel machine scheduling. The authors compared the proposed algorithm with the solutions of both the genetic algorithm and the LPT rule.…”