Constraint Programming aims at solving hard combinatorial problems, with a computation time increasing in practice exponentially. The methods are today efficient enough to solve large industrial problems, in a generic framework. However, solvers are dedicated to a single variable type: integer or real. Solving mixed problems relies on ad hoc transformations. In another field, Abstract Interpretation offers tools to prove program properties, by studying an abstraction of their concrete semantics, that is, the set of possible values of the variables during an execution. Various representations for these abstractions have been proposed. They are called abstract domains. Abstract domains can mix any type of variables, and even represent relations between the variables. In this work, we define abstract domains for Constraint Programming, so as to build a generic solving method, dealing with both integer and real variables. We also study the octagons abstract domain, already defined in Abstract Interpretation. Guiding the search by the octagonal relations, we obtain good results on a continuous benchmark. We also define our solving method using Abstract Interpretation techniques, in order to include existing abstract domains. Our solver, AbSolute, is able to solve mixed problems and use relational domains. - Exploits the over-approximation methods to integrate AI tools in the methods of CP - Exploits the relationships captured to solve continuous problems more effectively - Learn from the developers of a solver capable of handling practically all abstract domains

This text describes the functions and methodology of abstract domains in constraint programming that apply to both integer and real variables. After a broad assessment of constraint programming, the book covers octagons abstract domain, abstract interpretation techniques, and the application of AbSolute to solve mixed problems and use relational domains. Constraint programming practitioners and students will gain a deeper understanding of solutions to multi-variable problems and their representations.

Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.- Covers the whole field of constraint programming- Survey-style chapters- Five chapters on applications

This book introduces a new logic-based multi-paradigm programming language that integrates logic programming, functional programming, dynamic programming with tabling, and scripting, for use in solving combinatorial search problems, including CP, SAT, and MIP (mixed integer programming) based solver modules, and a module for planning that is implemented using tabling. The book is useful for undergraduate and graduate students, researchers, and practitioners.

This book constitutes the refereed proceedings of the 17th International Conference on Principles and Practice of Constraint Programming, CP 2011, held in Perugia, Italy, September 12-16, 2011. The 51 revised full papers and 7 short papers presented together with three invited talks were carefully reviewed and selected from 159 submissions. The papers are organized in topical sections on algorithms, environments, languages, models and systems, applications such as decision making, resource allocation and agreement technologies.

This book constitutes the proceedings of the First International Conference on Principles and Practice of Constraint Programming, CP '95, held in Cassis near Marseille, France in September 1995. The 33 refereed full papers included were selected out of 108 submissions and constitute the main part of the book; in addition there is a 60-page documentation of the four invited papers and a section presenting industrial reports. Thus besides having a very strong research component, the volume will be attractive for practitioners. The papers are organized in sections on efficient constraint handling, constraint logic programming, concurrent constraint programming, computational logic, applications, and operations research.

This book constitutes the refereed proceedings of the 8th International Conference on Principles and Practice of Constraint Programming, CP 2002, held in Ithaca, NY, USA in September 2002. The 38 revised full papers and 6 innovative application papers as well as the 14 short papers presented toghether with 25 abstracts from contributions to the doctoral program were carefully reviewed and selected from 146 submissions. All current issues in constraint processing are addressed, ranging from theoretical and foundational issues to application in various fields.