This research extends a two-phase algorithm for parallel job scheduling problem by considering earliness and tardiness as multi-objective functions. Here, it is also assumed that the jobs may use more than one machine at the same time, which is known as parallel job scheduling. In the first phase, jobs are grouped into job sets according to their machine requirements. For this, here, a heuristic algorithm is proposed for coloring the associated graph. In the second phase, job sets will be sequenced as a single machine scheduling problem. In this stage, for sequencing the job sets which are obtained from the first phase, a discrete algorithm is proposed, which comprises two well-known metaheuristics. In the proposed hybrid algorithm, the genetic algorithm operators are used to discretize the particle swarm optimization algorithm. An extensive numerical study shows that the algorithm is very efficient for the instances which have different structures so that the proposed algorithm could balance exploration and exploitation and improve the quality of the solutions, especially for large-sized test problems.
