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

Table of Contents

Foreword (Ugo Montanari) 
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) 
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) 
Chapter 3. Constraint Propagation (Christian Bessiere) 
Chapter 4. Backtracking Search Algorithms (Peter van Beek) 
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) 
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons) 
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) 
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith) 
Part II : Extensions, Languages, and Applications

Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) 
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) 
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) 
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) 
Chapter 17. Constraints over Structured Domains
(Carmen Gervet) 
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings) 
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) 
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

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Handbook of Constraint Programming

In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover exploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application.

The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power -- exceeding the capabilities of current planning technology -- and presents a number of important challenges to the research community.

/pdf/pddl2-1-an-extension-to-pddl-for-expressing-temporal-1u955z1r8x.pdf

PDDL2.1: an extension to PDDL for expressing temporal planning domains

Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory.

This paper presents an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to describe performance criteria, in the functions used to describe state transitions and observations, and in the relationships among features used to describe states, actions, rewards, and observations.

Specialized representations, and algorithms employing these representations, can achieve computational leverage by exploiting these various forms of structure. Certain AI techniques-- in particular those based on the use of structured, intensional representations--can be viewed in this way. This paper surveys several types of representations for both classical and decision-theoretic planning problems, and planning algorithms that exploit these representations in a number of different ways to ease the computational burden of constructing policies or plans. It focuses primarily on abstraction, aggregation and decomposition techniques based on AI-style representations.

/pdf/decision-theoretic-planning-structural-assumptions-and-121uyk4rmj.pdf

Decision-theoretic planning: structural assumptions and computational leverage

https://www.cs.toronto.edu/~sheila/2542/s14/A1/bonetgeffner-heusearch-aij01.pdf

Planning as heuristic search

Planning is a notoriously hard combinatorial search problem. In many interesting domains, current planning algorithms fail to scale up gracefully. By combining a general, stochastic search algorithm and appropriate problem encodings based on propositional logic, we are able to solve hard planning problems many times faster than the best current planning systems. Although stochastic methods have been shown to be very effective on a wide range of scheduling problems, this is the first demonstration of its power on truly challenging classical planning instances. This work also provides a new perspective on representational issues in planning.

Pushing the envelope: planning, propositional logic, and stochastic search

http://www.cs.toronto.edu/~fbacchus/Papers/tlplanaij.pdf

Using temporal logics to express search control knowledge for planning

In planning, goals have traditionally been viewed as specifying a set of desirable final states. Any plan that transforms the current state to one of these desirable states is viewed to be correct. Goals of this form are limited in what they can specify, and they also do not allow us to constrain the manner in which the plan achieves its objectives. We propose viewing goals as specifying desirable sequences of states, and a plan to be correct if its execution yields one of these desirable sequences. We present a logical language, a temporal logic, for specifying goals with this semantics. Our language is rich and allows the representation of a range of temporally extended goals, including classical goals, goals with temporal deadlines, quantified goals (with both universal and existential quantification), safety goals, and maintenance goals. Our formalism is simple and yet extends previous approaches in this area. We also present a planning algorithm that can generate correct plans for these goals. This algorithm has been implemented, and we provide some examples of the formalism at work. The end result is a planning system which can generate plans that satisfy a novel and useful set of conditions.

/pdf/planning-for-temporally-extended-goals-3oc2mne0fm.pdf

Planning for temporally extended goals

In this paper, we present a powerful framework for describing, storing, and reasoning about infinite temporal information. This framework is an extension of classical relational databases. It represents infinite temporal information by generalized tuples defined by linear repeating points and constraints on these points. We prove that relations formed from generalized tuples are closed under the operations of relational algebra. A characterization of the expressiveness of generalized relations is given in terms of predicates definable in Presburger arithmetic. Finally, we provide some complexity results.

Handling infinite temporal data

Planning control rules for reactive agents

Over the years increasingly sophisticated planning algorithms have been developed. These have made for more efficient planners, but unfortunately these planners still suffer from combinatorial explosion. Indeed, recent theoretical results demonstrate that such an explosion is inevitable. It has long been acknowledged that domain independent planners need domain dependent information to help them plan effectively. In this work we describe how natural domain information, of a “strategic” nature, can be expressed in a temporal logic, and then utilized to effectively control a forward-chaining planner. There are numerous advantages to our approach, including a declarative semantics for the search control knowledge; a high degree of modularity (the more search control knowledge utilized the more efficient search becomes); and an independence of this knowledge from the details of the planning algorithm. We have implemented our ideas in the TLPLAN system, and have been able to demonstrate its remarkable effectiveness in a wide range of planning domains.

/pdf/using-temporal-logic-to-control-search-in-a-forward-chaining-59gmzxu7b8.pdf

Froduald Kabanza

Papers

Using temporal logics to express search control knowledge for planning

Planning for temporally extended goals

Handling infinite temporal data

Planning control rules for reactive agents

Using temporal logic to control search in a forward chaining planner