Boolean satisfiability is probably the most studied of the combinatorial optimization/search problems. Significant effort has been devoted to trying to provide practical solutions to this problem for problem instances encountered in a range of applications in electronic design automation (EDA), as well as in artificial intelligence (AI). This study has culminated in the development of several SAT packages, both proprietary and in the public domain (e.g. GRASP, SATO) which find significant use in both research and industry. Most existing complete solvers are variants of the Davis-Putnam (DP) search algorithm. In this paper we describe the development of a new complete solver, Chaff which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy. Chaff has been able to obtain one to two orders of magnitude performance improvement on difficult SAT benchmarks in comparison with other solvers (DP or otherwise), including GRASP and SATO.

/pdf/chaff-engineering-an-efficient-sat-solver-2ima1ekzuu.pdf

Chaff: engineering an efficient SAT solver

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

https://ira.lib.polyu.edu.hk/bitstream/10397/1269/1/SetupSurvey-2006%28June-19%29.pdf

A survey of scheduling problems with setup times or costs

One of the most important features of current state-of-the-art SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We re-examine the learning techniques used in various SAT solvers and propose an array of new learning schemes. Extensive experiments with real world examples show that the best performing new learning scheme has at least a 2/spl times/ speedup compared with learning schemes employed in state-of-the-art SAT solvers.

/pdf/efficient-conflict-driven-learning-in-a-boolean-12te839wng.pdf

Efficient conflict driven learning in a boolean satisfiability solver

http://egon.cheme.cmu.edu/Papers/BatchReviewMendezGrossmann.pdf

State-of-the-art review of optimization methods for short-term scheduling of batch processes

Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems Hence the development of Constraint-Based Scheduling as a field of study The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques Following the principles of Constraint Programming, the book consists of three distinct parts: The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsible for the "hardness" of the scheduling problem Chapters 6, 7, and 8 are dedicated to the resolution of several scheduling problems These examples illustrate the use and the practical efficiency of the constraint propagation methods of the previous chapters They also show that besides constraint propagation, the exploration of the search space must be carefully designed, taking into account specific properties of the considered problem (eg, dominance relations, symmetries, possible use of decomposition rules) Chapter 9 mentions various extensions of the model and presents promising research directions

Constraint - based scheduling : applying constraint programming to scheduling problems

Given a set of resources with given capacities, a set of activities with given processing times and resource requirements, and a set of temporal constraints between activities, a “pure” scheduling problem consists of deciding when to execute each activity, so that both temporal constraints and resource constraints are satisfied. Most scheduling problems can easily be represented as instances of the constraint satisfaction problem (Kumar, 1992): given a set of variables, a set of possible values (domain) for each variable, and a set of constraints between the variables, assign a value to each variable, so that all the constraints are satisfied.

/pdf/constraint-based-scheduling-5diz9hh32c.pdf

Constraint-based scheduling

We study the problem of minimizing the weighted number of late jobs to be scheduled on a single machine when processing times are equal In this paper, we show that this problem, as well as its preemptive variant, are strongly polynomial When preemption is not allowed (1∣pj=p, rj∣ΣwjUj), the problem can be solved in O(n7) In the preemptive case, (1∣pj=p, pmtn, rj ∣ΣwjUj), the problem can be solved in O(n10) Both algorithms are based upon dynamic programming Copyright © 1999 John Wiley & Sons, Ltd

Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times

This paper shows that the use of satisfiability tests and time-bound adjustments based on energetic reasoning and global operations can enhance the efficiency of branch and bound procedures for optimally solving the hybrid flow shop scheduling problem. Procedures to use energetic reasoning and extended forms of global adjustment techniques are described and are empirically evaluated. Computational results show that the proposed approaches outperform the best known procedures to optimally solve the hybrid flow shop problem.

Solving hybrid flow shop problem using energetic reasoning and global operations

In recent years, constraint satisfaction techniques have been successfully applied to ’’disjunctive‘‘ scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of ’’cumulative‘‘ scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between ’’highly disjunctive‘‘ and ’’highly cumulative‘‘ problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n^2) ’’edge-finding‘‘ algorithm for cumulative resources (where n is the number of activities requiring the same resource) and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to highly cumulative problems. In the end, we also propose a refined version of the ’’edge-finding‘‘ algorithm for cumulative resources which, despite its worst case complexity in O(n^3), performs very well on highly cumulative instances.

Philippe Baptiste

Papers

Constraint - based scheduling : applying constraint programming to scheduling problems

Constraint-based scheduling

Polynomial time algorithms for minimizing the weighted number of late jobs on a single machine with equal processing times

Solving hybrid flow shop problem using energetic reasoning and global operations

Constraint Propagation and Decomposition Techniques forHighly Disjunctive and Highly Cumulative Project Scheduling Problems