Climbing Depth-Bounded Discrepancy Search for Solving Hybrid Flow Shop Problems

Abir Ben Hmida (1, 2) , Marie-José Huguet (3) , Pierre Lopez (3) , Mohamed Haouari (2)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 ROI - Unité Recherche Opérationnelle pour l'Industrie
3 LAAS-MOGISA

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.

Mots clés: flow shop scheduling; hybrid flow shops; HFS; discrepancy search methods; climbing depth-bounded discrepancy search; CDDS; lower bounds; LBs; heuristics; parallel machines; local search

Domaines: Recherche opérationnelle [math.OC]

Abir Ben Hmida, Marie-José Huguet, Pierre Lopez, Mohamed Haouari. Climbing Depth-Bounded Discrepancy Search for Solving Hybrid Flow Shop Problems. European Journal of Industrial Engineering, 2007, 1 (2), pp.223-243. ⟨10.1504/EJIE.2007.014110⟩. ⟨hal-00159581⟩