In this paper, we describe new hybrid genetic algorithm and particle swarm optimization to solve the sum of earliness and the number of tardy job on two-machines flow shop schedule F-2 // (Sigma(n)(k=1) E-K + U-K) problem is NP- hard. The study discusses a hybrid genetic algorithm and particle swarm optimization (HGA-PSO) to tackle the presented mission. Extensive experiments, based on computers, suggest that the proposed mathematical models are efficient in solving flow shop problems with GA solved to n = 3000 while PSO solved to n = 500 job.
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