Constraint satisfaction is a simple but powerful tool. Constraints identify the impossible and reduce the realm of possibilities to effectively focus on the possible, allowing for a natural declarative formulation of what must be satisfied, without expressing how. The field of constraint reasoning has matured over the last three decades with contributions from a diverse community of researchers in artificial intelligence, databases and programming languages, operations research, management science, and applied mathematics. Today, constraint problems are used to model cognitive tasks in vision, language comprehension, default reasoning, diagnosis, scheduling, temporal and spatial reasoning. 

In Constraint Processing, Rina Dechter, synthesizes these contributions, along with her own significant work, to provide the first comprehensive examination of the theory that underlies constraint processing algorithms. Throughout, she focuses on fundamental tools and principles, emphasizing the representation and analysis of algorithms.

·Examines the basic practical aspects of each topic and then tackles more advanced issues, including current research challenges
·Builds the reader's understanding with definitions, examples, theory, algorithms and complexity analysis
·Synthesizes three decades of researchers work on constraint processing in AI, databases and programming languages, operations research, management science, and applied mathematics

Table of Contents

Preface; Introduction; Constraint Networks; Consistency-Enforcing Algorithms: Constraint Propagation; Directional Consistency; General Search Strategies; General Search Strategies: Look-Back; Local Search Algorithms; Advanced Consistency Methods; Tree-Decomposition Methods; Hybrid of Search and Inference: Time-Space Trade-offs; Tractable Constraint Languages; Temporal Constraint Networks; Constraint Optimization; Probabilistic Networks; Constraint Logic Programming; Bibliography

Constraint Processing

Kaizen: The key to Japan‚s competitive success

Scheduling, vehicle routing and timetabling are all examples of constraint problems, and methods to solve them rely on the idea of constraint propagation and search. This book meets the need for a modern, multidisciplinary introduction to the field that covers foundations and applications. Written by Krzysztof Apt, an authority on the subject, it will be welcomed by graduate students and professionals. With the insertion of constraint techniques into programming environments, new developments have accelerated the solution process. Constraint programming combines ideas from artificial intelligence, programming languages, databases, and operational research.

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Principles of constraint programming

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

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Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

http://cepac.cheme.cmu.edu/pasilectures/henning/EJOR-BrailsfordSmith.pdf

Constraint satisfaction problems: Algorithms and applications

The materials management group at any hospital is responsible for ensuring that their inventory policies provide a good service in delivering products. The group also needs to be aware of their own costs for distribution, in terms of the frequency of delivery. With future changes to the hospital’s infrastructure, function and size, the group require that these policies are reviewed and prepared for the changes taking place. For this, inventory policy models need to be built and used to anticipate the effect of these changes. Due to the importance of many products, high service levels are essential, yet there are often space and delivery constraints, limiting the amount of stock which can be held and delivered at each location. We present in this paper a new constraint-based model for determining optimal stock levels for all products at a storage location, with restrictions on space, delivery and criticality of items taken into account. We validate this model on sterile and bulk items in a real-life setting of an intensive care unit within Cork University Hospital, Ireland.

Optimal inventory policy within hospital space constraints

The comparative performance of Integer Programming (IP) and Constraint Logic Programming (CLP) is explored by examining a number of models for four different combinatorial optimization applications. Computational results show contrasting behavior for the two approaches, and an analysis of performance with respect to problem and model characteristics is presented. The analysis shows that tightness of formulation is of great benefit to CLP where effective search reduction results in problems that can be solved quickly. In IP, if the linear feasible region does not identify the corresponding integer polytope, the problem may be difficult to solve. The paper identifies other characteristics of model behavior and concludes by examining ways in which IP and CLP may be incorporated within hybrid solvers.

Properties of Some Combinatorial Optimization Problemsand Their Effect on the Performance of Integer Programming and Constraint Logic Programming

Generalised Assignment Problems (GAP), traditionally solved by Integer Programming techniques, are addressed in the light of current Constraint Programming methods. A scheduling application from manufacturing, based on a modified GAP, is used to examine the performance of each technique under a variety of problem characteristics. Experimental evidence showed that, for a set of assignment problems, Constraint Logic Programming (CLP) performed consistently better than Integer Programming (IP). Analysis of the CLP and IP processes identified ways in which the search was effective. The insight gained from the analysis led to an Integer Programming approach with significantly improved performance. Finally, the issue of collaboration between the two contrasting approaches is examined with respect to ways in which the solvers can be combined in an effective manner.

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Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem

'Constraint programming' (CP) is a powerful tool for problem solving However, to obtain maximum benefit from CP, programmers require significant knowledge and experience We describe a new approach where Case-Based Reasoning is used to help write good constraint programs Our approach provides the potential for the full range of CBR advantages to be brought to bear on the task of automating constraint programming

This work has received support from Science Foundation Ireland under Grant 00/PI1/C075

Using case-based reasoning to write constraint programs

Many decision problems can be modelled as adversarial constraint satisfaction, which allows us to integrate methods from AI game playing. In particular, by using the idea of opponents, we can model both collaborative problem solving, where intelligent participants with different agendas must work together to solve a problem, and multi-criteria optimisation, where one decision maker must balance different objectives. In this paper, we focus on the case where two opponents take turns to instantiate constrained variables, each trying to direct the solution towards their own objective. We represent the process as game-tree search. We develop variable and value ordering heuristics based on game playing strategies. We examine the performance of various algorithms on general-sum graph colouring games, for both multi-participant and multi-criteria optimisation.

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James Little

Papers

Optimal inventory policy within hospital space constraints

Properties of Some Combinatorial Optimization Problemsand Their Effect on the Performance of Integer Programming and Constraint Logic Programming

Constraint Logic Programming and Integer Programming approaches and their collaboration in solving an assignment scheduling problem

Using case-based reasoning to write constraint programs

Adversarial constraint satisfaction by game-tree search