A Multiobjective Optimization Approach to Solve a Par allel Ma chines Scheduling Problem

A multiobjective optimization problem which focuses on par all el machines s ch eduling is considered. T his problem consists ofscheduling n independent jobs on m identical p ar allel m achines w ith release d ates, due dates, and s equence-dependent s etup times.The pre emption of j obs i s for bidden. T he aim i s to m inimize t wo di fferent objectives: makespan and total tardiness. The cont r ibu-tion of this paper i s to propose first a n ew mathematical model for this specific problem. Then, s ince t his problem i s N P h ard i n t hest rong sense, two well-know n approximated methods, NSGA- II and SPE A- II, are a dop te d to s olve it. Exper imental results showthe a dv antages of NSGA- II for t he studied problem. An exact method is then applied to b e compare d w ith NSGA- II algor i thmin order to prove the e fficiency of the for mer. Exper i mental re sults s how t he advantages of NSGA- II for t he studied problem.Computational exper iments show that on all t he tested instances , o ur NSGA- II algor i thm was able to get t he op timal s olutions.