A note on arithmetic constraint propagation

We consider the resolution by constraint programming of large problems, i.e. involving millions of constraints, which mainly imply arithmetic constraints, like shortest path problems or other related problems. We show that a simple constraint programming model is not competitive with dedicated algorithms (or dedicated constraints). This mainly comes from the propagation mechanism, i.e. the ordering along which the constraints are revised. Thus, we propose a modification of this propagation mechanism integrating the main ideas of the dedicated algorithms. We give some experiments for the shortest path problem and more general problems which confirms the robustness of our approach. Last, we give some results showing that only a few variables are considered more than once during a propagation step

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

Modelling a Maintenance Scheduling Problem with Alternative Resources

Effective management of maintenance in buildings can have a signi cant impact on the total life cycle costs and on the building energy use. Nevertheless, the building maintenance scheduling problem has been infrequently studied. In this paper, we present constraint-based scheduling models for the building maintenance scheduling problem, where each activity has a set of alternative resources. We consider two di erent models, one using basic constraints, and the other using our new and modi fied global constraints, which handle alternative disjunctive resources for each activity to allow propagation before activities are assigned to resources. We evaluate these models on randomly generated problems and show that while the basic model is faster on smaller problems, the global con- straint model scales better

Techniques d'ordonnancement d'atelier et de fournées basées sur la programmation par contraintes

Thèse réalisée en codirection avec l'École Polytechnique de Montréal (CIRRELT)Solving a scheduling problem consists of organizing a set of tasks, that is assigning their starting and ending times and allocating resources such that all constraints are satisfied. In this thesis, we propose new constraint programming approaches for two categories of NP-hard scheduling problems which are validated experimentally by the implementation of a set of new features within the constraint solver choco. In shop scheduling, a set of n jobs, consisting each of m tasks, must be processed on m distinct machines. A machine can process only one task at a time. The processing orders of tasks which belong to a job can vary (global order, order per job, no order). We consider the construction of non-preemptive schedules of minimal makespan. We first propose a study and a classification of different constraint models and search algorithms. Then, we introduce a new flexible approach for these classical problems. A batch processing machine can process several jobs simultaneously as a batch. The starting and ending times of a task are the ones of the batch to which they belong. The studied problem consists of minimizing the maximal lateness for a batch processing machine on which a finite number of tasks of non-identical sizes must be scheduled. The sum of the sizes of the jobs that are in a batch should not exceed the capacity b of the machine. We propose, within this context, a constraint model based on a decomposition of the problem. Then, we define a new optimization constraint based on the resolution of a relaxed problem enhanced by cost-based domain filtering techniques which improves the resolution.Résoudre un problème d'ordonnancement consiste à organiser un ensemble de tâches, c'est-à-dire déterminer leurs dates de début et de fin et leur attribuer des ressources en respectant certaines contraintes. Dans cette thèse, nous proposons de nouvelles approches exactes basées sur la programmation par contraintes pour deux classes de problèmes d'ordonnancement NP-difficiles validées expérimentalement par l'implémentation d'un ensemble de nouvelles fonctionnalités dans le solveur de contraintes choco. Dans un problème d'atelier, n lots sont constitués chacun de m tâches à exécuter sur m machines distinctes. Chaque machine ne peut exécuter qu'une tâche à la fois. La nature des contraintes liant les tâches d'un même lot peut varier (séquencement global ou par lot, pas de séquencement). Le critère d'optimalité étudié est la minimisation du délai total. Nous proposons d'abord une étude et une classification des différents modèles et algorithmes de résolution. Ensuite, nous introduisons une nouvelle approche flexible pour ces problèmes classiques. Une machine à traitement par fournées peut traiter plusieurs tâches en une seule opération, une fournée. Les dates de début et de fin des tâches d'une même fournée sont identiques. Le problème étudié consiste à minimiser le retard algébrique maximal de n tâches de différentes tailles sur une machine de capacité b. Conjointement, la somme des tailles des tâches d'une fournée ne doit pas excéder la capacité b. Nous proposons, dans ce contexte, un modèle basé sur une décomposition du problème. Nous définissons ensuite une nouvelle contrainte pour l'optimisation basée sur une relaxation du problème qui améliore sa résolution

Filtering Rules for Flow Time Minimization in a Parallel Machine Scheduling Problem

International audienceThis paper studies the scheduling of jobs of different families on parallel machines with qualification constraints. Originating from semiconductor manufacturing, this constraint imposes a time threshold between the execution of two jobs of the same family. Otherwise, the machine becomes disqualified for this family. The goal is to minimize both the flow time and the number of disqualifications. Recently, an efficient constraint programming model has been proposed. However, when priority is given to the flow time objective, the efficiency of the model can be improved. This paper uses a polynomial-time algorithm which minimize the flow time for a single machine relaxation where disqualifications are not considered. Using this algorithm one can derived filtering rules on different variables of the model. Experimental results are presented showing the effectiveness of these rules. They improve the competitiveness with the mixed integer linear program of the literature

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Minimizing Flow Time on a Single Machine with Job Families and Setup Times

Publication soumise et acceptée à la conférence Project Management and Scheduling (PMS2020)

Minimizing Flow Time on a Single Machine with Job Families and Setup Times

Publication soumise et acceptée à la conférence Project Management and Scheduling (PMS2020)