http://people.csail.mit.edu/lpk/papers/aij98-pomdp.pdf

Planning and Acting in Partially Observable Stochastic Domains

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)

/pdf/handbook-of-constraint-programming-53srutguo2.pdf

Handbook of Constraint Programming

The past five years have seen dramatic advances in planning algorithms, with an emphasis on propositional methods such as GRAPHPLAN and compilers that convert planning problems into propositional conjunctive normal form formulas for solution using systematic or stochastic SAT methods. Related work, in the context of spacecraft control, advances our understanding of interleaved planning and execution. In this survey, I explain the latest techniques and suggest areas for future research.

/pdf/recent-advances-in-ai-planning-3yrwnp4vs1.pdf

Recent Advances in AI Planning

The formulation of planning as heuristic search with heuristics derived from problem representations has turned out to be a fruitful approach for classical planning. In this paper, we pursue a similar idea in the context planning with incomplete information. Planning with incomplete information can be formulated as a problem of search in belief space, where belief states can be either sets of states or more generally probability distribution over states. While the formulation (as the formulation of classical planning as heuristic search) is not particularly novel, the contribution of this paper is to make it explicit, to test it over a number of domains, and to extend it to tasks like planning with sensing where the standard search algorithms do not apply. The resulting planner appears to be competitive with the most recent conformant and contingent planners (e.g., CGP, SGP, and CMBP) while at the same time is more general as it can handle probabilistic actions and sensing, different action costs, and epistemic goals.

/pdf/planning-with-incomplete-information-as-heuristic-search-in-qvtih3wv9f.pdf

Planning with incomplete information as heuristic search in belief space

http://mapir.isa.uma.es/cgalindo/papers/draft_ras08.pdf

Robot task planning using semantic maps

Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stochastic satisfiability problem, SSAT, which can function for probabilistic domains as SAT does for deterministic domains. It shows the connection between SSAT and well-studied problems in belief network inference and planning under uncertainty, and defines algorithms, both systematic and stochastic, for solving SSAT instances. These algorithms are validated on random SSAT formulae generated under the fixed-clause model. In spite of the large complexity gap between SSAT (PSPACE) and SAT (NP), the paper suggests that much of what we have learned about SAT transfers to the probabilistic domain.

Stochastic Boolean Satisfiability

Classical artificial intelligence planning techniques can operate in large domains but traditionally assume a deterministic universe. Operations research planning techniques can operate in probabilistic domains but break when the domains approach realistic sizes, MAX-PLAN is a new probabilistic planning technique that aims at combining the best of these two worlds, MAX-PLAN converts a planning instance into an E-MAJSAT instance, and then draws on techniques from Boolean satisfiability and dynamic programming to solve the E-MAJSAT instance. E-MAJSAT is an NPPP-complete problem that is essentially a probabilistic version of SAT. MAXPLAN performs as much as an order of magnitude better on some standard stochastic test problems than BURIDAN—a state-of-the-art probabilistic planner—and scales better on one test problem than two algorithms based on dynamic programming.

/pdf/maxplan-a-new-approach-to-probabilistic-planning-4xjqgzp9dv.pdf

MAXPLAN: a new approach to probabilistic planning

Contingent planning under uncertainty via stochastic satisfiability

Probabilistic planning algorithms seek effective plans for large, stochastic domains. MAXPLAN is a recently developed algorithm that converts a planning problem into an E-MAJSAT problem, an NpPP-complete problem that is essentially a probabilistic version of SAT, and draws on techniques from Boolean satisfiability and dynamic programming to solve the E-MAJSAT problem. This solution method is able to solve planning problems at state-of-the-art speeds, but it depends on the ability to store a value for each CNF subformula encountered in the solution process and is therefore quite memory intensive; searching for moderate-size plans even on simple problems can exhaust memory. This paper presents two techniques, based on caching, that overcome this problem without significant performance degradation. The first technique uses an LRU cache to store a fixed number of subformula values. The second technique uses a heuristic based on a measure of subformula difficulty to selectively save the values of only those subformulas whose values are sufficiently difficult to compute and are likely to be reused later in the solution process. We report results for both techniques on a stochastic test problem.

/pdf/using-caching-to-solve-larger-probabilistic-planning-1yds7hn0tq.pdf

Using caching to solve larger probabilistic planning problems

We describe two new probabilistic planning techniques-- c-MAXPLAN and ZANDER--that generate contingent plans in probabilistic propositional domains. Both operate by transforming the planning problem into a stochastic satisfiability problem and solving that problem instead. C-MAXPLAN encodes the problem as an E-MAJSAT instance, while ZANDER encodes the problem as an S-SAT instance. Although S-SAT problems are in a higher complexity class than E-MAJSAT problems, the problem encodings produced by ZANDER are substantially more compact and appear to be easier to solve than the corresponding E-MAJSAT encodings. Preliminary results for ZANDER indicate that it is competitive with existing planners on a variety of problems.

/pdf/contingent-planning-under-uncertainty-via-stochastic-jx6mnjdrgi.pdf

Stephen M. Majercik

Papers

Stochastic Boolean Satisfiability

MAXPLAN: a new approach to probabilistic planning

Contingent planning under uncertainty via stochastic satisfiability

Using caching to solve larger probabilistic planning problems

Contingent planning under uncertainty via stochastic satisfiability