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Using Inference to Reduce Arc Consistency Computation
- PROCEEDINGS OF THE FOURTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE (IJCAI’95
, 1995
"... Constraint satisfaction problems are widely used in artificial intelligence. They involve finding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the co ..."
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Cited by 65 (12 self)
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Constraint satisfaction problems are widely used in artificial intelligence. They involve finding values for problem variables subject to constraints that specify which combinations of values are consistent. Knowledge about properties of the constraints can permit inferences that reduce the cost of consistency checking. In particular, such inferences can be used to reduce the number of constraint checks required in establishing arc consistency, a fundamental constraint-based reasoning technique. A general AC-Inference schema is presented and various forms of inference discussed. A specific algorithm, AC-7, is presented, which takes advantage of a simple property common to all binary constraints to eliminate constraint checks that other arc consistency algorithms perform. The effectiveness of this approach is demonstrated analytically, and experimentally on real-world problems.
Dynamic Ordering for Asynchronous Backtracking on DisCSPs
, 2006
"... An algorithm that performs asynchronous backtracking on distributed CSPs, with dynamic ordering of agents is proposed, ABT DO. Agents propose reorderings of lower priority agents and send these proposals whenever they send assignment messages. Changes of ordering triggers a different computation of ..."
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Cited by 30 (8 self)
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An algorithm that performs asynchronous backtracking on distributed CSPs, with dynamic ordering of agents is proposed, ABT DO. Agents propose reorderings of lower priority agents and send these proposals whenever they send assignment messages. Changes of ordering triggers a different computation of Nogoods. The dynamic ordered asynchronous backtracking algorithm uses polynomial space, similarly to standard ABT. TheABT DO algorithm with three different ordering heuristics is compared to standard ABT on randomly generated DisCSPs. A Nogood-triggered heuristic, inspired by dynamic backtracking, is found to outperform static order ABT by a large factor in run-time and improve the network load.
Symmetry in constraint programming
- Handbook of Constraint Programming
, 2006
"... Symmetry in constraints has always been important but in recent years has become a major research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this problem has been solved, with a numbe ..."
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Cited by 25 (3 self)
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Symmetry in constraints has always been important but in recent years has become a major research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this problem has been solved, with a number of different techniques. As we write, research remains very active for two reasons. First, there are many difficulties in the practical application of the techniques that are known for symmetry exclusion, and overcoming these remain important research problems. Second, the successes achieved in the area so far have encouraged researchers to find new ways to exploit symmetry. In this chapter we cover both these issues, and the details of the symmetry exclusion methods that have been conceived. Figure 10.1: The solution to the puzzle of finding a chess position containing nine queens and a king of each colour, with the rule that no piece is on the same line (row, column or diagonal) as any queen of the opposite colour. Up to symmetry, the solution is unique. 330 10. Symmetry in Constraint Programming To illustrate what we mean by symmetry, we consider the chess puzzle shown in Figure 10.1. The solution to this puzzle is unique “up to symmetry ” [115], but what do
Conflict directed Backjumping for MaxCSPs
- In IJCAI-2007
, 2007
"... Constraint Optimization problems are commonly solved using a Branch and Bound algorithm enhanced by consistency maintenance procedures (Wallace and Freuder 1993; ..."
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Constraint Optimization problems are commonly solved using a Branch and Bound algorithm enhanced by consistency maintenance procedures (Wallace and Freuder 1993;
Non-viability deductions in arc-consistency computation
- in "Proc. of the Nineteenth International Conference on Logic Programming (ICLP 2004)", Lecture Notes in Computer Science, Springer-Verlag, 2004, p. 343–355. Internal Reports
"... Abstract Arc-Consistency (AC) techniques have been used extensively in the study of Constraint Satisfaction Problems (CSP). These techniques are used to simplify the CSP before or during the search for its solutions. Some of the most efficient algorithms for AC computation are AC6++ and AC-7. The no ..."
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Abstract Arc-Consistency (AC) techniques have been used extensively in the study of Constraint Satisfaction Problems (CSP). These techniques are used to simplify the CSP before or during the search for its solutions. Some of the most efficient algorithms for AC computation are AC6++ and AC-7. The novelty of these algorithms is that they satisfy the so-called four desirable properties for AC computation. The main purpose of these interesting properties is to reduce as far as possible the number of constraint checks during AC computation while keeping a reasonable space complexity. In this paper we prove that, despite providing a remarkable reduction in the number of constraint checks, the four desirable properties do not guarantee a minimal number of constraint checks. We therefore refute the minimality claim in the paper introducing these properties. Furthermore, we propose a new desirable property for AC computation and extend AC6++ and AC-7 to consider such a property. We show theoretically and experimentally that the new property provides a further substantial reduction in the number of constraint checks. 1
Conflict based Backjumping for Constraints Optimization Problems
"... Abstract. Constraints Optimization problems are commonly solved using a Branch and Bound algorithm enhanced by a consistency maintenance procedures [WF93] [LM96,LMS99,LS04]. All these algorithms traverse the search space in a chronological order and gain their efficiency from the quality of the cons ..."
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Abstract. Constraints Optimization problems are commonly solved using a Branch and Bound algorithm enhanced by a consistency maintenance procedures [WF93] [LM96,LMS99,LS04]. All these algorithms traverse the search space in a chronological order and gain their efficiency from the quality of the consistency maintenance procedure. The present study introduces Conflict-based Backjumping (CBJ) in Branch and Bound algorithms. The proposed algorithm maintains Conflict Sets which include only assignments whose replacement can lead to a better solution and backtracks according to these sets. CBJ can be added to Branch and Bound which uses the most advanced consistency maintenance heuristics, NC ∗ and AC∗. The experimental evaluation of of B&B CBJ on random Max-CSPs shows that the performance of the algorithms are improved by a large factor. 1
Organized by
, 2005
"... (Soft 2005) continues the series of workshops on soft constraints that were held in conjunction with the previous CP conferences. The aim of this workshop is to provide a forum where researchers in this area can exchange ideas, discuss new developments and explore possible future directions. As in 2 ..."
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(Soft 2005) continues the series of workshops on soft constraints that were held in conjunction with the previous CP conferences. The aim of this workshop is to provide a forum where researchers in this area can exchange ideas, discuss new developments and explore possible future directions. As in 2004, Soft 2005 extends its scope to include formalisms and techniques for dealing with preferences. Preferences are ubiquitous in real life; most problems are over-constrained and would not be solved if we insist all their requirements to be strictly met. Instead, many practical problems can be naturally described via preferences rather than hard statements. The idea of using soft constraints provides an effective way to extend the conventional framework of constraints to support the concept of preferences. In parallel to the framework of soft constraints, other frameworks for expressing preferences have been proposed and developed in recent years in AI and other related fields. These diverse frameworks have different features and have led to many results. For example, both qualitative and quantitative preference
Retroactive Ordering for Dynamic Backtracking
"... Abstract. Dynamic Backtracking (DBT) is a well known algorithm for solving Constraint Satisfaction Problems. In DBT, variables are allowed to keep their assignment during backjump, if they are compatible with the set of eliminating explanations. A previous study has shown that when DBT is combined w ..."
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Abstract. Dynamic Backtracking (DBT) is a well known algorithm for solving Constraint Satisfaction Problems. In DBT, variables are allowed to keep their assignment during backjump, if they are compatible with the set of eliminating explanations. A previous study has shown that when DBT is combined with variable ordering heuristics it performs poorly compared to standard Conflictdirected Backjumping (CBJ) [1]. The special feature of DBT, keeping valid elimination explanations during backtracking, can be used for generating a new class of ordering heuristics. In the proposed algorithm, the order of already assigned variables can be changed. Consequently, the new class of algorithms is termed Retroactive DBT. In the proposed algorithm, the newly assigned variable can be moved to a position in front of assigned variables with larger domains and as a result prune the search space more effectively. The experimental results presented in this paper show an advantage of the new class of heuristics and algorithms over standard DBT and over CBJ. All algorithms tested were combined with forward-checking and used a Min-Domain heuristic. 1
