Soft global constraints in constraint optimization and weighted constraint satisfaction.

Leung, Ka Lun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 118-126).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction and Global Constraints --- p.3Chapter 1.2 --- Soft Constraints --- p.4Chapter 1.3 --- Motivation and Goal --- p.5Chapter 1.4 --- Outline of the Thesis --- p.6Chapter 2 --- Background --- p.8Chapter 2.1 --- Constraint Satisfaction Problems --- p.8Chapter 2.1.1 --- Backtracking Tree Search --- p.10Chapter 2.1.2 --- Local Consistency in CSP --- p.11Chapter 2.1.3 --- Constraint Optimization Problem --- p.16Chapter 2.2 --- Weighted Constraint Satisfaction --- p.21Chapter 2.2.1 --- Branch and Bound Search --- p.23Chapter 2.2.2 --- Local Consistency in WCSP --- p.26Chapter 2.3 --- Global Constraints --- p.35Chapter 2.4 --- Flow Theory --- p.37Chapter 3 --- Related Work --- p.39Chapter 3.1 --- Handling Soft Constraints in COPs --- p.39Chapter 3.2 --- Global Constraints --- p.40Chapter 3.2.1 --- Hard Global Constraints --- p.40Chapter 3.2.2 --- Soft Global Constraints --- p.41Chapter 3.3 --- Local Consistency in Weighted CSP --- p.42Chapter 4 --- “Soft as Hard´ح Approach --- p.44Chapter 4.1 --- The General “Soft as Hard´ح Approach --- p.44Chapter 4.2 --- Cost-based GAC --- p.49Chapter 4.3 --- Empirical Results --- p.53Chapter 5 --- Weighted CSP Approach --- p.55Chapter 5.1 --- Strong 0-Inverse Consistency --- p.55Chapter 5.1.1 --- 0-Inverse Consistency and Strong 0-Inverse Consistency --- p.56Chapter 5.1.2 --- Comparison with Other Consistencies --- p.62Chapter 5.2 --- Generalized Arc Consistency Star --- p.65Chapter 5.3 --- Full Directional Generalized Arc Consistency Star --- p.72Chapter 5.4 --- Generalizing EDAC* --- p.78Chapter 5.5 --- Implementation Issues --- p.87Chapter 6 --- Towards A Library of Efficient Soft Global Constraints --- p.90Chapter 6.1 --- The allDifferent Constraint --- p.91Chapter 6.1.1 --- All Interval Series --- p.93Chapter 6.1.2 --- Latin Square --- p.95Chapter 6.2 --- The GCC Constraint --- p.97Chapter 6.2.1 --- Latin Square --- p.100Chapter 6.2.2 --- Round Robin Tournament --- p.100Chapter 6.3 --- The Same Constraint --- p.102Chapter 6.3.1 --- Fair Scheduling --- p.104Chapter 6.3.2 --- People-Mission Scheduling --- p.105Chapter 6.4 --- The Regular Constraint --- p.106Chapter 6.4.1 --- Nurse Rostering Problem --- p.110Chapter 6.4.2 --- Modelling Stretch() Constraint --- p.111Chapter 6.5 --- Discussion --- p.113Chapter 7 --- Conclusion and Remarks --- p.115Chapter 7.1 --- Contributions --- p.115Chapter 7.2 --- Future Work --- p.117Bibliography --- p.11

Hybrid tractability of soft constraint problems

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint problems are a generalisation of the CSP which allow the user to model optimisation problems. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this work, we initiate the study of hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity). We present several novel hybrid classes of soft constraint problems, which include a machine scheduling problem, constraint problems of arbitrary arities with no overlapping nogoods, and the SoftAllDiff constraint with arbitrary unary soft constraints. An important tool in our investigation will be the notion of forbidden substructures.Comment: A full version of a CP'10 paper, 26 page

Global constraints in distributed constraint satisfaction and optimization

Global constraints are an essential component in the efficiency of centralized constraint programming. We propose to include global constraints in distributed constraint satisfaction problem (DisCSP) and distributed constraint optimization problem (DCOP). We detail how this inclusion can be done, considering different representations for global constraints (direct, nested, binary). We explore the relation of global constraints with local consistency (both in the hard and soft cases), in particular, for generalized arc consistency (GAC). We provide experimental evidence of the benefits of global constraints on several benchmarks, both for distributed constraint satisfaction and for distributed constraint optimization. © 2013 The Author.2009-SGR-1434; Generalitat de CatalunyaPeer Reviewe

Propagation des contraintes tables souples Etude pr eliminaire

National audienceWCSP is a framework that has attracted a lot of at- tention during the last decade. In particular, there have been many developments of ltering approaches based on the concept of soft local consistencies such as node consistency (NC), arc consistency (AC), full directio- nal arc consistency (FDAC), existential directional arc consistency (EDAC), virtual arc consistency (VAC) and optimal soft arc consistency (OSAC). Almost all algo- rithms related to these properties have been introduced for binary weighted constraint networks, and most of the conducted experiments typically include constraint networks involving only binary and ternary constraints. In this paper, we focus on extensional soft constraints of large arity. We propose an algorithm to lter such constraints and embed it in PFC-MRDAC.Durant ces dix derni ères ann ées, de nombreuses études ont ét és r éalis ées pour le cadre WCSP (Weighted Constraint Satisfaction Problem). En particulier, ont ét é propos ées de nombreuses techniques de filtrage bas ées sur le concept de coh érence locale souple telle que la co- h érence de n oeud, et surtout la coh érence d'arc souple. Toutefois, la plupart de ces algorithmes ont ét és intro- duits pour le cas des contraintes binaires, et la plupart des exp érimentations ont ét és men ées sur des r éseaux de contraintes comportant uniquement des contraintes binaires et/ou ternaires. Dans cet article, nous nous in- t eressons aux contraintes tables souples de grande arit é. Nous proposons un premier algorithme pour filtrer ces contraintes et nous l'int égrons a PFC-MRDAC

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in the literature that do not require a tree projection to be given, and that either correctly decide whether the given CSP instance is satisfiable, or return that a tree projection actually does not exist. These approaches had not been generalized so far on CSP extensions for optimization problems, where the goal is to compute a solution of maximum value/minimum cost. The paper fills the gap, by exhibiting a fixed-parameter polynomial-time algorithm that either disproves the existence of tree projections or computes an optimal solution, with the parameter being the size of the expression of the objective function to be optimized over all possible solutions (and not the size of the whole constraint formula, used in related works). Tractability results are also established for the problem of returning the best K solutions. Finally, parallel algorithms for such optimization problems are proposed and analyzed. Given that the classes of acyclic hypergraphs, hypergraphs of bounded treewidth, and hypergraphs of bounded generalized hypertree width are all covered as special cases of the tree projection framework, the results in this paper directly apply to these classes. These classes are extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization

Parallelism in Constraint Programming

Writing efficient parallel programs is the biggest challenge of the software industry for the foreseeable future. We are currently in a time when parallel computers are the norm, not the exception. Soon, parallel processors will be standard even in cell phones. Without drastic changes in hardware development, all software must be parallelized to its fullest extent. Parallelism can increase performance and reduce power consumption at the same time. Many programs will execute faster on a dual-core processor than a single core processor running at twice the speed. Halving the speed of a processor can reduce the power consumption up to four times. Hence, parallelism gives more performance per unit of power to efficient programs. In order to make use of parallel hardware, we need to overcome the difficulties of parallel programming. To many programmers, it is easier to learn a handful of small domain-specific programming languages than to learn efficient parallel programming. The frameworks for these languages can then automatically parallelize the program. Automatically parallelizing traditional programs is usually much more difficult. In this thesis, we study and present parallelism in constraint programming (CP). We have developed the first constraint framework that automatically parallelizes both the consistency and the search of the solving process. This allows programmers to avoid the difficult issues of parallel programming. We also study distributed CP with independent agents and propose solutions to this problem. Our results show that automatic parallelism in CP can provide very good performance. Our parallel consistency scales very well for problems with many large constraints. We also manage to combine parallel consistency and parallel search with a performance increase. The communication and load-balancing schemes we developed increase the scalability of parallel search. Our model for distributed CP is orders of magnitude faster than traditional approaches. As far as we know, it is the first to solve standard benchmark scheduling problems

Tractable projection-safe soft global constraints in weighted constraint satisfaction.

Wu, Yi.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 74-80).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Weighted Constraint Satisfaction Problems --- p.3Chapter 1.3 --- Motivation and Goal --- p.4Chapter 1.4 --- Outline of the Thesis --- p.5Chapter 2 --- Background --- p.7Chapter 2.1 --- Constraint Satisfaction Problems --- p.7Chapter 2.1.1 --- Backtracking Tree search --- p.8Chapter 2.1.2 --- Local consistencies in CSP --- p.11Chapter 2.2 --- Weighted Constraint Satisfaction Problems --- p.18Chapter 2.2.1 --- Branch and Bound Search --- p.20Chapter 2.2.2 --- Local Consistencies in WCSP --- p.21Chapter 2.3 --- Global Constraints --- p.31Chapter 3 --- Tractable Projection-Safety --- p.36Chapter 3.1 --- Tractable Projection-Safety: Definition and Analysis --- p.37Chapter 3.2 --- Polynomially Decomposable Soft Constraints --- p.42Chapter 4 --- Examples of Polynomially Decomposable Soft Global Constraints --- p.48Chapter 4.1 --- Soft Among Constraint --- p.49Chapter 4.2 --- Soft Regular Constraint --- p.51Chapter 4.3 --- Soft Grammar Constraint --- p.54Chapter 4.4 --- Max_Weight/Min Weight Constraint --- p.57Chapter 5 --- Experiments --- p.61Chapter 5.1 --- The car Sequencing Problem --- p.61Chapter 5.2 --- The nonogram problem --- p.62Chapter 5.3 --- Well-Formed Parenthesis --- p.64Chapter 5.4 --- Minimum Energy Broadcasting Problem --- p.64Chapter 6 --- Related Work --- p.67Chapter 6.1 --- WCSP Consistencies --- p.67Chapter 6.2 --- Global Constraints . --- p.68Chapter 7 --- Conclusion --- p.71Chapter 7.1 --- Contributions --- p.71Chapter 7.2 --- Future Work --- p.72Bibliography --- p.7