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    A parallel hybrid PSO-GA algorithm for the flexible flow-shop scheduling with transportation
    (Elsevier Ltd, 2022) Amirteimoori, Arash; Mahdavi, Iraj; Solimanpur, Maghsud; Ali, Sadia Samar; Tirkolaee, Erfan Babaee
    In this paper, a Mixed-Integer Linear Programming (MILP) model to simultaneously schedule jobs and transporters in a flexible flow shop system is suggested. Wherein multiple jobs, finite transporters, and stages with parallel unrelated machines are considered. In addition to the mentioned technicalities, the jobs are able to omit one or more stages, and may not be executable by all the machines, and similarly, transportable by all the transporters. To the best of our knowledge, no study in the literature has featured efficacy of the parallel computing in simultaneous scheduling of jobs and transporters in the flexible flow shop system which remarkably shortens run time if the solution approaches are designed accordingly. To this end, we employ Gurobi solver, Parallel Genetic Algorithm (PGA), Parallel Particle Swarm Optimization (PPSO) and hybrid Parallel PSO-GA Algorithm (PPSOGA) to deal with the problem instances. Furthermore, a parallel version of Ant Colony Optimization (ACO) algorithm adapted from the state-of-the-art literature is developed to verify the performance of our suggested solution methods. Using 60 problem instances generated via uniform distribution, the suggested solution approaches are compared against one another. After assessing the results of the computational experiments, it is deduced that PPSOGA algorithm outperforms PGA, PPSO, Parallel Ant Colony Optimization (PACO) and Gurobi solver in terms of the quality of the solutions. The efficiency and run time of the suggested approaches are then assessed through two prominent statistical tests (i.e., Wald and Analysis of Variance (ANOVA)). Eventually, it comes to spotlight that PPSOGA algorithm is computationally rewarding and dependable.