Block approach—tabu search algorithm for single machine total weighted tardiness problem

Boejko, Wojciech; Grabowski, J.; Wodecki, Mieczysław

doi:10.1016/j.cie.2005.12.001

Cited by 49 publications

(26 citation statements)

References 20 publications

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“…Let us consider the 10 jobs' instance that is specid in Table 1. Let π = (1,2,3,4,5,6,7,8,9,10). Permutation π has three blocks: T 1 = (1, 2, 3, 4), T 2 = (7), T 3 = (8) and two Dcks: D 1 = (5, 6), D 2 = (9, 10).…”

Section: Ck Of Tardy Jobsmentioning

confidence: 99%

“…, in any permutation of jobs from π E , every job is executed ly in permutation π. Algorithm (AE-block) designating block is included in the work [2].…”

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

“…Considering sequentially π (starting from π (1)) and applyappropriate algorithm AE-block or AT-block (see [2]), we partition π into E and T blocks. Complexity of partition cedure is O(n).…”

Section: Ck Of Tardy Jobsmentioning

confidence: 99%

“…The interchanges are continued until a solution that cannot be improved is obtained, which is a local minimum. To increase the performance of local search algorithms, metaheuristics like tabu search are used [2,7], simulated annealing [23], path relinking [4], genetic algorithms [7], ant colony optimization [9]. A very effective iterated local-search method has been proposed by Kirlik and Oguz [13].…”

Section: Literature Reviewmentioning

confidence: 99%

“…THEOREM 1. [2] Let π ∈ Φ be a permutation with blocks B 1 , B 2 , ..., B m , and let the jobs of each T-block of π are ordered according to the WSPT rule. If the permutation β has been obtained from π by an interchange of jobs that f (β ) < f (π), then in β , at least one job of some block of π was moved before the first or after the last job of this block.…”

Section: Ck Of Tardy Jobsmentioning

confidence: 99%

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Stable scheduling of single machine with probabilistic parameters

Bożejko

Rajba

Wodecki

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. We consider a stochastic variant of the single machine total weighted tardiness problem jobs parameters are independent random variables with normal or Erlang distributions. Since even deterministic problem is NP-hard, it is difficult to find global optimum for large instances in the reasonable run time. Therefore, we propose tabu search metaheuristics in this work. Computational experiments show that solutions obtained by the stochastic version of metaheuristics are more stable (i.e. resistant to data disturbance) than solutions generated by classic, deterministic version of the algorithm.Key words: scheduling, uncertain parameters, tabu search, stability. J = f1, 2, …, ng have to be processed without interruption on a single machine that can handle only one job at a time. All jobs become available for processing at the beginning (time zero). Each job i has an integer processing time p i , a due date d i and a positive weight w i . For a given sequence of jobs (earliest) due date C i , the tardiness T i = maxf0, C i ¡ d i g and the cost w i ¢T i of job i 2 J. The objective is to find a job sequence which minimizes the sum of the costs ∑ n i=1 w i ¢T i . This is a classical problem of scheduling theory. Literature reviewThe total weighted tardiness problem is NP-hard [15]. Enumerative algorithms (which use dynamic programming and branch and bound approaches) for the problem are described in [22,29]. The algorithms are a significant improvement over exhaustive search but they remain laborious and are applicable only to relatively small problems, with the number of jobs not exceeding 50 (80 in a multi-processor computer [29]). The enumerative algorithms mentioned above may require considerable computer resources both in terms of computation times and core storage. Therefore, many algorithms have been proposed to find near optimal schedules in reasonable time.Local search methods start from an initial solution and if repeatedly try to improve the current solution by local changes. The interchanges are continued until a solution that cannot be improved is obtained, which is a local minimum. To increase the performance of local search algorithms, metaheuristics like tabu search are used [2,7], simulated annealing [23], path relinking [4], genetic algorithms [7], ant colony optimization [9]. A very effective iterated local-search method has been proposed by Kirlik and Oguz [13]. The key aspect of the method is its ability to explore an exponential-size neighborhood in polynomial time by a dynamic programming technique.

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Section: Ck Of Tardy Jobsmentioning

confidence: 99%

“…, in any permutation of jobs from π E , every job is executed ly in permutation π. Algorithm (AE-block) designating block is included in the work [2].…”

Section: Computational Complexity Of Executing I-move Is O(n) and O(mentioning

confidence: 99%

Section: Ck Of Tardy Jobsmentioning

confidence: 99%