Parallel path relinking method for the single machine total weighted tardiness problem with sequence-dependent setups

Bożejko, Wojciech

doi:10.1007/s10845-009-0253-2

Cited by 31 publications

(15 citation statements)

References 16 publications

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“…Pinedo, 1995;Bozejko, 2010) applied to the pairs of individuals, denoted as S 1 and S 2 , obtained by the n-tournament procedure, or to both o springs obtained after crossover if it has been carried out.…”

Section: Improvement Methodsmentioning

confidence: 99%

Single machine interfering jobs problem with flowtime objective

González

2015

J Intell Manuf

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)>IJH=?J Interfering jobs problems (or multi agents scheduling problems) are an emergent topic in the scheduling literature. In these decision problems, two or more sets of jobs have to be scheduled, each one with its own criteria. More speci cally, we focus on a problem in which jobs belonging to two sets have to be scheduled in a single machine in order to minimize the total owtime of the jobs in one set, while the total owtime of the jobs in the other set should not exceed a given constant ϵ. This problem is known to be weakly NP-hard, and a Dynamic Programming (DP) algorithm has been proposed to nd optimal solutions.In this paper, we rst analyse the distribution of solutions of the problem in order to establish its empirical hardness. Next, a novel encoding scheme and a set of properties associated to the neighbourhood of this scheme are presented. These properties are used to develop both exact and approximate methods, i.e. a branch and bound (B&B) method, several constructive heuristics, and di erent versions of a genetic algorithm (GA). The computational experience carried out shows that the proposed B&B is more e cient than the existing DP algorithm. The results also show the advantages of the proposed encoding scheme, as the approximate methods yield close-to-optimum solutions for big-sized instances where exact methods are not feasible.Scheduling interfering jobs two-agent scheduling problem total owtime single machine

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Section: Improvement Methodsmentioning

confidence: 99%

Single machine interfering jobs problem with flowtime objective

González

2015

J Intell Manuf

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“…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%

“…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%

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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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“…A real-time fuzzy expert system to schedule parts for a flexible manufacturing system was suggested by Chan et al [34]. Bozejko [20] dealt with the parallel path relinking method for the singlemachine TWT problem with sequence-dependent setups.…”

Section: Introductionmentioning

confidence: 99%