Abstract
This paper deals with the two-stage hybrid flow shop problem , in which the first stage consists of three machines , the second stage consists of two machines . The aim is to find out the optimal scheduling for n jobs when processing in this environment when the makespan is minimum. Therefore we propose a particle swarm algorithm which consists of a new procedure to calculate the makespan and a new stopping criteria .Also, we added improvement to the proposed algorithm , by using one of the components of the genetic algorithm (crossover operation) in order to obtain initial swarm particles instead of random obtaining. After applying the two algorithms on several problems which were generated randomly by uniform distribution , the results showed that the improved proposed particle swarm algorithm was the best in finding out the optimal scheduling for jobs and in cpu time to reach the solution.
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