This paper present algorithms for solving a single machine scheduling problem to minimize the sum of total completion times, total tardiness,maxim-um tardiness,and maximum earliness.The single machine total tardiness problem is already NP-hard, so the consider problem is strongly NP-hard, and several algorithms are used to solve it. Branch and bound algorithmwith dominance ruleand local search algorit- hms are proposed for the problem. For the Branch and bound algorithm results- show that using dominance rule improve the performance of the algorithm in both computation times and optimal values,but it need longer times.Thus we tackle the problemof large sizes with local search algorit- hms descent method, simulated annealing and tabusearch. The perfomance of these algorithms is evaluated on a large set of test problems and the results are compared.The computational results show that simulated annealing algorithm and Tabu search algorithm are better than Descent method with preference to simulated annealing algorithm,and show that the three algorithms find optimal or near optimal solutions inreasonable times.
In this paper, we consider 2-machine permutation flow shop scheduling problem with bi-objective of minimizing the makespan (C
max
) and maximum tardiness (T
max
). The aim is to minimize the two objective functions lexicographicaly, which is minimize maximum tardiness subject to that the makespan is optimal. We introduce a Branch and bound algorithm with two dominance conditions to find the optimal solution of the problem for job sequence with up to 14 jobs. For moderate and large sized problems we apply a simulated annealing algorithm to develop a metaheuristic algorithme based on the first level branch and bound and variable neighborhood search. To compare with the original algorithm, numerical experiments provided, the rusults shows the efficiency of the dominance conditions also the efficiency of proposed modification of the original metaheuristic algorithm.
In this paper, we investigate a single machine scheduling problem (SMSP). We try to reach the optimal or near optimal solution which minimize the sum of three objective functions: total completion times, total tardiness and total earliness. Firstly, we solve this problem by Branch and bound algorithm (BAB alg) to find optimal solutions, dominance rules (DR)s are used to improve the performance of BAB alg, the resulting is BABDR, secondly, we solve this problem by simulated annealing algorithm (SA alg) as metaheuristic algorithm (MET alg). It is known that combining MET alg with other algorithms can improve the resulting solutions. In this paper we developed the concept of insertion preselected jobs one by one through all positions of remaining jobs of considered sequence, the proposed MET alg called Insertion Metaheuristic Algorithm (IMA). This procedure improves the performance of SA alg in two directions: in the first one, we use the IMA to generate initial solution for SA alg, in the second one, we use the IMA to improve the solution obtained through the iterations of SA alg. The experiments showed that IMA can improve the performance of SA alg in these two directions.
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