Climbing depth-bounded discrepancy search for solving hybrid flow shop 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 minimises 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 hybridisation of two existing discrepancy-based methods: DDS and Climbing Discrepancy Search (CDS). 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.

Discrepancy search for the flexible job shop scheduling problem

“…Climbing Depth-bounded Discrepancy Search (CDDS) [5] which combines both the CDS and the DDS methods. With this method, one can restrict neighborhoods to be visited by only using discrepancies on variables at the top of the tree (see Algorithm 3).…”

“…Basically, a discrepancy occurs if the choice of a variable does not follow the rank of the ordering heuristic (the initial instantiation). The method stops when a solution is found 5 (if such a solution does exist) or when an inconsistency is detected (the tree is entirely expanded).…”

“…In this paper, we present a new discrepancy-based method, called Climbing Depth-bound Discrepancy Search (CDDS), used initially for solving the hybrid flow shop problem [5].…”

Approches hybrides pour la résolution d'un problème d'ordonnancement industriel /

“…Pour résoudre les problèmes d'ordonnancement, les chercheurs ont longtemps utilisé des approches exactes comme la programmation linéaire, la méthode de séparation et d'évaluation ou encore la programmation dynamique [Blazewicz et al, 1994;Pinedo, 2002;Puchinger et Raidi, 2005;Pelikan et Sastry, 2006;Allahverdi et al, 2008]. Depuis quelques années, des chercheurs ont approché certains problèmes d'ordonnancement avec la programmation par contraintes [LePape, 1994;LePape et Nuijten, 1995;Nuitjen et Aarts, 1996;Pesant et Gendreau, 1996;Baptiste, 1998;Nuijten et Pape, 1998;Shaw, 1998;Harjunkoski et al, 2000;Pinedo, 2002;Hnich et al, 2004;Hmida et al, 2007], et plus particulièrement l'ordonnancement basé sur les contraintes, branche de la programmation par contraintes dédiée aux problèmes d'ordonnancement, qui est une discipline assez jeune [Baptiste et al, 2001]. [Tan et al, 2000;Gagné et al, 2002;Liao et Juan, 2007;Allahverdi et al, 2008].…”

“…Finalement, le CDS (Climbing Discrepancy Search) est une méthode de recherche locale qui adapte la notion de divergence afin de trouver une bonne solution à des problèmes d'optimisation combinatoire . Le CDDS (Climbing Depth-Bounded Discrepancy Search) [Hmida et al, 2007] est une adaptation du CDS qui limite la profondeur de génération des solutions comme le DDS.…”