Abstracting soft constraints: framework, properties, examples

Soft constraints are very and expressive. However, they also are very complex to handle. For this reason, it may be reasonable in several cases to pass to an abstract version of a given soft constraint problem, and then to bring some useful information from the abstract problem to the concrete one. This will hopefully make the search for a solution, or for an optimal solution, of the concrete problem, faster. In this paper we propose an abstraction scheme for soft constraint problems and we study its main properties. We show that processing the abstracted version of a soft constraint problem can help us in finding good approximations of the optimal solutions, or also in obtaining information that can make the subsequent search for the best solution easier. We also show how the abstraction scheme can be used to devise new hybrid algorithms for solving soft constraint problems, and also to import constraint propagation algorithms from the abstract scenario to the concrete one. This may be useful when we don\u27t have any (or any efficient) propagation algorithm in the concrete setting

Solving finite domain constraint hierarchies by local consistency and tree search.

by Hui Kau Cheung Henry.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 107-112).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgments --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Organizations of the Thesis --- p.2Chapter 2 --- Background --- p.4Chapter 2.1 --- Constraint Satisfaction Problems --- p.4Chapter 2.1.1 --- Local Consistency Algorithm --- p.5Chapter 2.1.2 --- Backtracking Solver --- p.8Chapter 2.1.3 --- The Branch-and-Bound Algorithm --- p.10Chapter 2.2 --- Over-constrained Problems --- p.14Chapter 2.2.1 --- Weighted Constraint Satisfaction Problems --- p.15Chapter 2.2.2 --- Possibilistic Constraint Satisfaction Problems --- p.15Chapter 2.2.3 --- Fuzzy Constraint Satisfaction Problems --- p.16Chapter 2.2.4 --- Partial Constraint Satisfaction Problems --- p.17Chapter 2.2.5 --- Semiring-Based Constraint Satisfaction Problems --- p.18Chapter 2.2.6 --- Valued Constraint Satisfaction Problems --- p.22Chapter 2.3 --- The Theory of Constraint Hierarchies --- p.23Chapter 2.4 --- Related Work --- p.26Chapter 2.4.1 --- An Incremental Hierarchical Constraint Solver --- p.28Chapter 2.4.2 --- Transforming Constraint Hierarchies into Ordinary Con- straint System --- p.29Chapter 2.4.3 --- The SCSP Framework --- p.30Chapter 2.4.4 --- The DeltaStar Algorithm --- p.32Chapter 2.4.5 --- A Plug-In Architecture of Constraint Hierarchy Solvers --- p.34Chapter 3 --- Local Consistency in Constraint Hierarchies --- p.36Chapter 3.1 --- A Reformulation of Constraint Hierarchies --- p.37Chapter 3.1.1 --- Error Indicators --- p.37Chapter 3.1.2 --- A Reformulation of Comparators --- p.38Chapter 3.1.3 --- A Reformulation of Solution Set --- p.40Chapter 3.2 --- Local Consistency in Classical CSPs --- p.41Chapter 3.3 --- Local Consistency in SCSPs --- p.42Chapter 3.4 --- Local Consistency in CHs --- p.46Chapter 3.4.1 --- The Operations of Error Indicator --- p.47Chapter 3.4.2 --- Constraint Hierarchy k-Consistency --- p.49Chapter 3.4.3 --- A Comparsion between CHAC and PAC --- p.50Chapter 3.4.4 --- The CHAC Algorithm --- p.52Chapter 3.4.5 --- Time and Space Complexities of the CHAC Algorithm --- p.53Chapter 3.4.6 --- Correctness of the CHAC Algorithm --- p.56Chapter 4 --- A Consistency-Based Finite Domain Constraint Hierarchy Solver --- p.59Chapter 4.1 --- The Branch-and-Bound CHAC Solver --- p.59Chapter 4.2 --- Correctness of the Branch-and-Bound CHAC Solver --- p.61Chapter 4.3 --- An Example Execution Trace --- p.64Chapter 4.4 --- Experiments and Results --- p.66Chapter 4.4.1 --- Experimental Setup --- p.68Chapter 4.4.2 --- The First Experiment --- p.71Chapter 4.4.3 --- The Second Experiment --- p.94Chapter 5 --- Concluding Remarks --- p.103Chapter 5.1 --- Summary and Contributions --- p.103Chapter 5.2 --- Future Work --- p.104Bibliography --- p.10

Semiring-based constraint logic programming

We extend the Constraint Logic Programming (CLP) formalism in order to handle semiring-based constraints. This allows us to perform in the same language both constraint solving and optimization. In fact, constraints based on semirings are able to model both classical constraint solving and more sophisticated features like uncertainty, probability, fuzziness, and optimization. We then provide this class of languages with three equivalent semantics: model-theoretic, fix-point, and proof-theoretic, in the style of classical CLP programs

Empirical evaluation of Soft Arc Consistency algorithms for solving Constraint Optimization Problems

A large number of problems in Artificial Intelligence and other areas of science can be viewed as special cases of constraint satisfaction or optimization problems. Various approaches have been widely studied, including search, propagation, and heuristics. There are still challenging real-world COPs that cannot be solved using current methods. We implemented and compared several consistency propagation algorithms, which include W-AC*2001, EDAC, VAC, and xAC. Consistency propagation is a classical method to reduce the search space in CSPs, and has been adapted to COPs. We compared several consistency propagation algorithms, based on the resemblance between the optimal value ordering and the approximate value ordering generated by them. The results showed that xAC generated value orderings of higher quality than W-AC*2001 and EDAC. We evaluated some novel hybrid methods for solving COPs. Hybrid methods combine consistency propagation and search in order to reach a good solution as soon as possible and prune the search space as much as possible. We showed that the hybrid method which combines the variant TP+OnOff and branch-and-bound search performed fewer constraint checks and searched fewer nodes than others in solving random and real-world COPs

Virtual camera selection using a semiring constraint satisfaction approach

Players and viewers of three-dimensional computer generated games and worlds view renderings from the viewpoint of a virtual camera. As such, determining a good view of the scene is important to present a good game or three-dimensional world. Previous research has developed technologies to nd good positions for the virtual camera, but little work has been done to automatically select between multiple virtual cameras, similar to a human director at a sporting event. This thesis describes a software tool to select among camera feeds from multiple virtual cameras in a virtual environment using semiring-based constraint satisfaction techniques (SCSP), a soft constraint approach. The system encodes a designer's preferences, and selects the best camera feed even in over-constrained or under-constrained environments. The system functions in real time for dynamic scenes using only current information (i.e. no prediction). To reduce the camera selection time the SCSP evaluation can be cached and converted to native code. This SCSP approach is implemented in two virtual environments: a virtual hockey game using a spectator viewpoint, and a virtual 3D maze game using a third person perspective. Comparisons against hard constraints are made using constraint satisfaction problems

Scalable intelligent electronic catalogs

The world today is full of information systems which make huge quantities of information available. This incredible amount of information is clearly overwhelming Internet endusers. As a consequence, intelligent tools to identify worthwhile information are needed, in order to fully assist people in finding the right information. Moreover, most systems are ultimately used, not just to provide information, but also to solve problems. Encouraged by the growing popular success of Internet and the enormous business potential of electronic commerce, e-catalogs have been consolidated as one of the most relevant types of information systems. Nearly all currently available electronic catalogs are offering tools for extracting product information based on key-attribute filtering methods. The most advanced electronic catalogs are implemented as recommender systems using collaborative filtering techniques. This dissertation focuses on strategies for coping with the difficulty of building intelligent catalogs which fully support the user in his purchase decision-making process, while maintaining the scalability of the whole system. The contributions of this thesis lie on a mixed-initiative system which is inspired by observations on traditional commerce activities. Such a conversational model consists basically of a dialog between the customer and the system, where the user criticizes proposed products and the catalog suggests new products accordingly. Constraint satisfaction techniques are analyzed in order to provide a uniform framework for modeling electronic catalogs for configurable products. Within the same framework, user preferences and optimization constraints are also easily modeled. Searching strategies for proposing the adequate products according to criteria are described in detail. Another dimension of this dissertation faces the problem of scalability, i.e., the problem of supporting hundreds, or thousands of users simultaneously using intelligent electronic catalogs. Traditional wisdom would presume that in order to provide full assistance to users in complex tasks, the business logic of the system must be complex, thus preventing scalability. SmartClient is a software architectural model that uses constraint satisfaction problems for representing solution spaces, instead of traditional models which represent solution spaces by collections of single solutions. This main idea is supported by the fact that constraint solvers are extreme in their compactness and simplicity, while providing sophisticated business logic. Different SmartClient architecture configurations are provided for different uses and architectural requirements. In order to illustrate the use of constraint satisfaction techniques for complex electronic catalogs with the SmartClient architecture, a commercial Internet-based application for travel planning, called reality, has been successfully developed. Travel planning is a particularly appropriate domain for validating the results of this research, since travel information is dynamic, travel planning problems are combinatorial, and moreover, complex user preferences and optimization constraints must be taken into consideration

Solving Hierarchical Constraints over Finite Domains with Local Search

National Science and Technology Board (Singapore

Lexicographically-ordered constraint satisfaction problems

We describe a simple CSP formalism for handling multi-attribute preference problems with hard constraints, one that combines hard constraints and preferences so the two are easily distinguished conceptually and for purposes of problem solving. Preferences are represented as a lexicographic order over complete assignments based on variable importance and rankings of values in each domain. Feasibility constraints are treated in the usual manner. Since the preference representation is ordinal in character, these problems can be solved with algorithms that do not require evaluations to be represented explicitly. This includes ordinary CSP algorithms, although these cannot stop searching until all solutions have been checked, with the important exception of heuristics that follow the preference order (lexical variable and value ordering). We describe relations between lexicographic CSPs and more general soft constraint formalisms and show how a full lexicographic ordering can be expressed in the latter. We discuss relations with (T)CP-nets, highlighting the advantages of the present formulation, and we discuss the use of lexicographic ordering in multiobjective optimisation. We also consider strengths and limitations of this form of representation with respect to expressiveness and usability. We then show how the simple structure of lexicographic CSPs can support specialised algorithms: a branch and bound algorithm with an implicit cost function, and an iterative algorithm that obtains optimal values for successive variables in the importance ordering, both of which can be combined with appropriate variable ordering heuristics to improve performance. We show experimentally that with these procedures a variety of problems can be solved efficiently, including some for which the basic lexically ordered search is infeasible in practice