Solving Four Cost Multi-Objective Scheduling Problem Simultaneously


In this paper, we consider single machine scheduling problem (P) to minimize four cost functions, total completion times, total tardiness, maximum tardiness, and maximum earliness. The minimization besed on two types, in the first one we study some special cases including lexigraphical minimization of problem (P). In the second type we minimize four cost functions simultaneously and propose CTTE algorithm ( total completion time, total tardiness, maximum tardiness and maximum earliness) to find the set of "non-dominated solutions" of problem (P), also improve this algorithm by using intensification procedure (IMCTTE) (Imoroved CTTE). Also we propose MOVNS (Multiobjective variable neighborhood search) algorithm based on the variable neighborhood and Intensification Procedure ideas .We compare the proposed algorithms with NSGA2 algorithm. The performance of the proposed algorithms is evaluated on a large set of test problems and the results are compared. The compu- tational results show that IMCTTE algorithm is more efficient than CTTE algorithm in both, number of "non-dominated solutions" and the controbution of "non-dominated solutions" that belong to reference set. Also we find that MOVNS algorithm give better performance than CTTE and IMCTTE algorithms for all problem instancs, and better than NSGA2 specially for small size problems .