Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last

We present new filtering algorithms for Disjunctive and Cumulative constraints, each of which improves the complexity of the state-of-theart algorithms by a factor of log n. We show how to perform TimeTabling and Detectable Precedences in linear time on the Disjunctive constraint. Furthermore, we present a linear-time Overload Checking for the Disjunctive and Cumulative constraints. Finally, we show how the rule of Not-first/Not-last can be enforced in quadratic time for the Cumulative constraint. These algorithms rely on the union find data structure, from which we take advantage to introduce a new data structure that we call it time line. This data structure provides constant time operations that were previously implemented in logarithmic time by the Θ-tree data structure. Experiments show that these new algorithms are competitive even for a small number of tasks and outperform existing algorithms as the number of tasks increases. We also show that the time line can be used to solve specific scheduling problems

Explaining Time-Table-Edge-Finding Propagation for the Cumulative Resource Constraint

Abstract. Cumulative resource constraints can model scarce resources in scheduling problems or a dimension in packing and cutting problems. In order to efficiently solve such problems with a constraint programming solver, it is important to have strong and fast propagators for cumulative resource constraints. Time-table-edge-finding propagators are a recent development in cumulative propagators, that combine the current resource profile (time-table) during the edge-finding propagation. The current state of the art for solving scheduling and cutting problems involving cumulative constraints are lazy clause generation solvers, i.e., constraint programming solvers incorporating nogood learning, have proved to be excellent at solving scheduling and cutting problems. For such solvers, concise and accurate explanations of the reasons for propagation are essential for strong nogood learning. In this paper, we develop a time-table-edge-finding propagator for cumulative that explains its propagations. We give results using this propagator in a lazy clause generation system on resource-constrained project scheduling problems from various standard benchmark suites. On the standard benchmark suite PSPLib, we are able to improve the lower bound of about 60 % of the remaining open instances, and close 6 open instances.

Le filtrage des bornes pour les contraintes cumulative et multi-inter-distance

Ce mémoire traite de la résolution de problèmes d’ordonnancement à l’aide de la programmation par contraintes. Il s’intéresse principalement aux contraintes globales et particulièrement à la contrainte cumulative. Il passe en revue les règles permettant de la filtrer et les principaux algorithmes qui les appliquent. Il explique le Edge-Finder de Vilím et son arbre cumulatif. Il propose un algorithme plus performant et plus général pour appliquer les règles découlant du raisonnement énergétique. Le mémoire traite du cas particulier où toutes les tâches sont de durée identique. Pour modéliser efficacement ce type de problèmes, on y conçoit la contrainte multi-inter-distance. L’algorithme d’ordonnancement de López-Ortiz et Quimper est adapté pour réaliser un algorithme qui applique la cohérence de bornes. La contrainte multi-inter-distance s’avère efficace à résoudre le problème de séquençage des atterrissages d’avions du banc d’essai d’Artiouchine et Baptiste.This thesis discusses how to solve scheduling problems using constraint programming. We study global constraints and particularly the Cumulative constraint. We survey its main filtering rules and their state-of-the-art filtering algorithms. We explain the Vilím’s Edge-Finder and its cumulative tree.We introduce a more efficient and more general algorithm that enforces the filtering rules from the energetic reasoning. We study the special case where all tasks have identical processing times. To efficiently model such problems, we introduce the Multi-Inter-Distance constraint. The scheduling algorithm by López-Ortiz and Quimper is adapted to produce a filtering algorithm enforcing bounds consistency. The constraint Multi-Inter-Distance is proved efficient to solve the runway scheduling problem on the benchmark by Artiouchine and Baptiste

Passage à l'échelle pour les contraintes d'ordonnancement multi-ressources

La programmation par contraintes est une approche régulièrement utilisée pour résoudre des problèmes combinatoires d origines diverses. Dans cette thèse nous nous focalisons sur les problèmes d ordonnancement cumulatif. Un problème d ordonnancement consiste à déterminer les dates de débuts et de fins d un ensemble de tâches, tout en respectant certaines contraintes de capacité et de précédence. Les contraintes de capacité concernent aussi bien des contraintes cumulatives classiques où l on restreint la somme des hauteurs des tâches intersectant un instant donné, que des contraintes cumulatives colorées où l on restreint le nombre maximum de couleurs distinctes prises par les tâches. Un des objectifs récemment identifiés pour la programmation par contraintes est de traiter des problèmes de grandes tailles, habituellement résolus à l aide d algorithmes dédiés et de métaheuristiques. Par exemple, l utilisation croissante de centres de données virtualisés laisse apparaitre des problèmes d ordonnancement et de placement multi-dimensionnels de plusieurs milliers de tâches. Pour atteindre cet objectif, nous utilisons l idée de balayage synchronisé considérant simultanément une conjonction de contraintes cumulative et des précédences, ce qui nous permet d accélérer la convergence au point fixe. De plus, de ces algorithmes de filtrage nous dérivons des procédures gloutonnes qui peuvent être appelées à chaque nœud de l arbre de recherche pour tenter de trouver plus rapidement une solution au problème. Cette approche permet de traiter des problèmes impliquant plus d un million de tâches et 64 ressources cumulatives. Ces algorithmes ont été implémentés dans les solveurs de contraintes Choco et SICStus, et évalués sur divers problèmes déplacement et d ordonnancement.Mots-clés : Programmation par contraintes, ordonnancement, cumulatif, passage à l échelle, point fixe, contraintes de ressources multidimensionelles, balayage synchronisé.Constraint programming is an approach often used to solve combinatorial problems in different application areas. In this thesis we focus on the cumulative scheduling problems. A scheduling problem is to determine the starting dates of a set of tasks while respecting capacity and precedence constraints. Capacity constraints affect both conventional cumulative constraints where the sum of the heights of tasks intersecting a given time point is limited, and colored cumulative constraints where the number of distinct colors assigned to the tasks intersecting a given time point is limited. A newly identified challenge for constraint programming is to deal with large problems, usually solved by dedicated algorithms and metaheuristics. For example, the increasing use of virtualized datacenters leads to multi dimensional placement problems of thousand of jobs. Scalability is achieved by using a synchronized sweep algorithm over the different cumulative and precedence constraints that allows to speed up convergence to the fix point. In addition, from these filtering algorithms we derive greedy procedures that can be called at each node of the search tree to find a solution more quickly. This approach allows to deal with scheduling problems involving more than one million jobs and 64 cumulative resources. These algorithms have been implemented within Choco and SICStussolvers and evaluated on a variety of placement and scheduling problems.NANTES-ENS Mines (441092314) / SudocSudocFranceF