A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jo
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A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs Khodakaram Salimifard 1 & Jingpeng Li 2
&
Davood Mohammadi 1 & Reza Moghdani 1
Accepted: 16 October 2020 # The Author(s) 2020
Abstract Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms. Keywords Parallel machine scheduling . Splitting jobs . Wastes . Total tardiness . Multi-objective optimisation . Volleyball premier league
1 Introduction Studying parallel machines are of high importance both theoretically and practically. In terms of theory, it is an extension of the single machine and a particular instance of the flexible flow shop. In terms of practice, it is vitally important for the sake of common parallel resources in the real world, but very difficult to find an optimum solution for the problem. * Jingpeng Li [email protected] Khodakaram Salimifard [email protected] Davood Mohammadi [email protected] Reza Moghdani [email protected] 1
CIIORG, Persian Gulf University, Bushehr 75168, Iran
2
Division of Computer Science and Mathematics, University of Stirling, Stirling, UK
Likewise, decomposition methods used in multi-stage systems sometimes utilize parallel machine techniques. Sometimes the parallel machine scheduling (PMS) is considered as a two-step procedure. First, assigning jobs to available machines. Second, when allocating jobs to machines has been done, the sequence of the jobs needs to be allocated to each machine [1]. Since we cannot consistently find an absolute solution for parallel machines and for most of the criteria, especially those based on tardiness - that don’t have a linear relationship with completion time - the problem is nonpolyn
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