Preprocessing versus search processing for constraint satisfaction problems

A perennial problem in hybrid backtrack CSP search is how much local consistency processing should be done to achieve the best efficiency. This can be divided into two separate questions: (1) how much work should be done before the actual search begins, i.e. during preprocessing? and (2) how much of the same processing should be interleaved with search? At present there are two leading approaches to establishing stronger consistencies than the basic arc consistency maintenance that is done in most solvers. On the one hand there are various kinds singleton arc consistency that can be used; on the other there are several variants of restricted path consistency. To date these have not been compared directly. The present work attempts to do this for a variety of problems, and in so doing, it also provides an empirical evaluation of the preprocessing versus search processing issue. Comparisons are made using the domain/degree and domain/weighted degree variable ordering heuristics. In general, it appears that preprocessing with higher levels of consistency followed by hybrid-AC processing (i.e. MAC) gives the best results, especially when the weighted degree heuristic is used. For problems with n-ary constraints, this difference seems to be even more pronounced. In some cases, higher levels of consistency maintenance established during preprocessing leads to performance gains over MAC of several orders of magnitude

Strong consistencies for weighted constraint satisfaction problems

Cette thèse se focalise sur l'étude de cohérences locales fortes afin de résoudre des problèmes d'optimisation sur des réseaux de fonctions de coûts (ou réseaux de contraintes pondérées). Ces méthodes fournissent le minorant nécessaire pour des approches de type "Séparation-Evaluation". Nous étudions dans un premier temps la cohérence d'Arc virtuelle (VAC), une des plus fortes cohérences d'arcs du domaine, qui est établie via l'établissement de la cohérence d'arc dure dans une séquence de réseaux de contraintes classiques. L'algorithme itératif pour établir VAC est amélioré via l'introduction d'une incrémentalité accrue, exploitant la cohérence d'arc dynamique. La nouvelle méthode est aussi capable de maintenir VAC efficacement pendant la recherche lorsque les réseaux de contraintes pondérées sont dynamiquement modifiés par les opérations de branchement. Dans une seconde partie, nous nous intéressons à des cohérences de domaines plus fortes, inspirées de cohérences similaires dans les réseaux de contraintes classiques (cohérence de chemin inverse, réduite ou Max-réduite). Pour chaque cohérence dure, plusieurs cohérences souples ont été proposées pour les réseaux de contraintes pondérées. Les nouvelles cohérences fournissent un minorant plus fort que celui des cohérences d'arc souples en traitant les triplets de variables connectées deux à deux par des fonctions de coûts binaires. Dans cette thèse, nous étudions les propriétés des nouvelles cohérences, les implémentons et les testons sur une variété de problèmes.This thesis focuses on strong local consistencies for solving optimization problems in cost function networks (or weighted constraint networks). These methods provide the lower bound necessary for Branch-and-Bound search. We first study the Virtual arc consistency, one of the strongest soft arc consistencies, which is enforced by iteratively establishing hard arc consistency in a sequence of classical Constraint Networks. The algorithm enforcing VAC is improved by integrating the dynamic arc consistency to exploit its incremental behavior. The dynamic arc consistency also allows to improve VAC when maintained VAC during search by efficiently exploiting the changes caused by branching operations. Operations. Secondly, we are interested in stronger domain-based soft consistencies, inspired from similar consistencies in hard constraint networks (path inverse consistency, restricted or Max-restricted path consistencies). From each of these hard consistencies, many soft variants have been proposed for weighted constraint networks. The new consistencies provide lower bounds stronger than soft arc consistencies by processing triplets of variables connected two-by-two by binary cost functions. We have studied the properties of these new consistencies, implemented and tested them on a variety of problems

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

Higher-Level Consistencies: Where, When, and How Much

Determining whether or not a Constraint Satisfaction Problem (CSP) has a solution is NP-complete. CSPs are solved by inference (i.e., enforcing consistency), conditioning (i.e., doing search), or, more commonly, by interleaving the two mechanisms. The most common consistency property enforced during search is Generalized Arc Consistency (GAC). In recent years, new algorithms that enforce consistency properties stronger than GAC have been proposed and shown to be necessary to solve difficult problem instances. We frame the question of balancing the cost and the pruning effectiveness of consistency algorithms as the question of determining where, when, and how much of a higher-level consistency to enforce during search. To answer the `where\u27 question, we exploit the topological structure of a problem instance and target high-level consistency where cycle structures appear. To answer the \u27when\u27 question, we propose a simple, reactive, and effective strategy that monitors the performance of backtrack search and triggers a higher-level consistency as search thrashes. Lastly, for the question of `how much,\u27 we monitor the amount of updates caused by propagation and interrupt the process before it reaches a fixpoint. Empirical evaluations on benchmark problems demonstrate the effectiveness of our strategies. Adviser: B.Y. Choueiry and C. Bessier

ESSE 2017. Proceedings of the International Conference on Environmental Science and Sustainable Energy

Environmental science is an interdisciplinary academic field that integrates physical-, biological-, and information sciences to study and solve environmental problems. ESSE - The International Conference on Environmental Science and Sustainable Energy provides a platform for experts, professionals, and researchers to share updated information and stimulate the communication with each other. In 2017 it was held in Suzhou, China June 23-25, 2017

Designing and Optimizing Representations for Non-Binary Constraints

Ph.DDOCTOR OF PHILOSOPH