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Abstract

This paper investigates how to adapt some discrepancy-based search methods to solve Hybrid Flow Shop (HFS) problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimizes the makespan. We present here an adaptation of the Depth-bounded Discrepancy Search (DDS) method to obtain near-optimal solutions with makespan of high quality. This adaptation for the HFS contains no redundancy for the search tree expansion. To improve the solutions of our HFS problem, we propose a local search method, called Climbing Depth-bounded Discrepancy Search (CDDS), which is a hybridization of two existing discrepancy-based methods: DDS and Climbing Discrepancy Search. CDDS introduces an intensification process around promising solutions. These methods are tested on benchmark problems. Results show that discrepancy methods give promising results and CDDS method gives the best solutions.

Abstract

In this paper, we introduce a Yet ImprovEd Limited Discrepancy Search (YIELDS), a complete algorithm for solving Constraint Satisfaction Problems. As indicated in its name, YIELDS is an improved version of Limited Discrepancy Search (LDS). It integrates constraint propagation and variable order learning. The learning scheme, which is the main contribution of this paper, takes benefit from failures encountered during search in order to enhance the efficiency of variable ordering heuristic. As a result, we obtain a search which needs less discrepancies than LDS to find a solution or to state a problem is intractable. This method is then less redundant than LDS. The efficiency of YIELDS is experimentally validated, comparing it with several solving algorithms: Depth-bounded Discrepancy Search, Forward Checking, and Maintaining Arc-Consistency. Experiments carried out on randomly generated binary CSPs and real problems clearly indicate that YIELDS often outperforms the algorithms with which it is compared, especially for tractable problems.

Abstract

This paper investigates how to adapt some discrepancy-based search methods to solve Hybrid Flow Shop (HFS) problems in which each stage consists of several identical machines operating in parallel. The objective is to determine a schedule that minimizes the makespan. We present here an adaptation of the Depth-bounded Discrepancy Search (DDS) method to obtain solutions with makespan of high quality. This adaptation for the HFS contains no redundancy for the search tree expansion. To improve the solutions of our HFS problem, we propose a local search method, called CDDS, which is a hybridization of two existing discrepancy-based methods (DDS and Climbing Discrepancy Search). CDDS introduces an intensification process around promising solutions. These methods are tested on benchmark problems. Results show that discrepancy methods give promising results.

Résumé

Cet article s'intéresse aux problèmes d'ordonnancement et à leur analyse par des techniques de propagation de contraintes. Nous proposons une extension de certaines de ces techniques de propagation. Celle-ci est basée sur les déductions temporelles obtenues en recherchant la cohérence de chemins sur le graphe de contraintes considéré comme modèle du problème d'ordonnancement. Des résultats d'expérience montrent que les extensions proposées permettent de contribuer à l'amélioration des résultats sur la borne inférieure de la durée totale d'ordonnancement.

Mots-Clés / Keywords