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16
Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems
, 1998
"... We use a local search method we term Large Neighbourhood Search (LNS) for solving vehicle routing problems. LNS meshes well with constraint programming technology and is analogous to the shuffling technique of jobshop scheduling. The technique explores a large neighbourhood of the current solution ..."
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Cited by 137 (2 self)
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We use a local search method we term Large Neighbourhood Search (LNS) for solving vehicle routing problems. LNS meshes well with constraint programming technology and is analogous to the shuffling technique of jobshop scheduling. The technique explores a large neighbourhood of the current solution by selecting a number of customer visits to remove from the routing plan, and reinserting these visits using a constraintbased tree search. We analyse the performance of LNS on a number of vehicle routing benchmark problems. Unlike related methods, we use Limited Discrepancy Search during the tree search to reinsert visits. We also maintain diversity during search by dynamically altering the number of visits to be removed, and by using a randomised choice method for selecting visits to remove. We analyse the performance of our method for various parameter settings controlling the discrepancy limit, the dynamicity of the size of the removal set, and the randomness of the choice. We demonst...
The Difference AllDifference Makes
 IN PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 1999
"... We perform a comprehensive theoretical and experimental analysis of the use of alldifferent constraints. We prove that generalized arcconsistency on such constraints lies between neighborhood inverse consistency and, under a simple restriction, path inverse consistency on the binary represent ..."
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Cited by 34 (9 self)
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We perform a comprehensive theoretical and experimental analysis of the use of alldifferent constraints. We prove that generalized arcconsistency on such constraints lies between neighborhood inverse consistency and, under a simple restriction, path inverse consistency on the binary representation of the problem. By generalizing the arguments of Kondrak and van Beek, we prove that a search algorithm that maintains generalized arcconsistency on alldifferent constraints dominates a search algorithm that maintains arcconsistency on the binary representation. Our experiments show the practical value of achieving these high levels of consistency. For example, we can solve almost all benchmark quasigroup completion problems up to order 25 with just a few branches of search. These results demonstrate the benefits of using nonbinary constraints like alldifferent to identify structure in problems.
Propositional Satisfiability and Constraint Programming: a Comparative Survey
 ACM Computing Surveys
, 2006
"... Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms ..."
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Cited by 32 (4 self)
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Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, crossfertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a blackbox approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired
Arc Consistency and Quasigroup Completion
 In Proceedings of the ECAI98 workshop on nonbinary constraints
, 1998
"... Quasigroup completion is a recently proposed benchmark constraint satisfaction problem that combines the features of randomly generated instances and highly structured problems. A quasigroup completion problem can be represented as a CSP with n 2 variables, each with a domain of size n. The constr ..."
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Cited by 24 (4 self)
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Quasigroup completion is a recently proposed benchmark constraint satisfaction problem that combines the features of randomly generated instances and highly structured problems. A quasigroup completion problem can be represented as a CSP with n 2 variables, each with a domain of size n. The constraints can be represented either by 2n all different nary constraints or by binary pairwise constraints, giving a constraint graph with 2n cliques of size n. We present a comparison between the two representations and show that the n\Gammaary representation reduces the cost of solving quasigroup completion problems drastically. 1 Introduction Quasigroup completion [GS97b, GS97a, GSC97] is a recently proposed benchmark constraint satisfaction problem that combines the features of randomly generated instances and highly structured problems. A quasigroup is an ordered pair (Q; \Delta), where Q is a set and (\Delta) is a binary operation on Q such that the equations a \Delta x = b and y \Delta...
Programming Constraint Services
, 2002
"... This thesis presents design, application, implementation, and evaluation of computation spaces as abstractions for programming constraint services at a high level. Spaces are seamlessly integrated into a concurrent programming language and make constraintbased computations compatible with concurrenc ..."
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Cited by 18 (0 self)
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This thesis presents design, application, implementation, and evaluation of computation spaces as abstractions for programming constraint services at a high level. Spaces are seamlessly integrated into a concurrent programming language and make constraintbased computations compatible with concurrency through encapsulation. Spaces are applied
Decomposable Constraints
, 2000
"... Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be represented by binary constraints ..."
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Cited by 16 (3 self)
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Many constraint satisfaction problems can be naturally and efficiently modelled using nonbinary constraints like the "alldifferent" and "global cardinality" constraints. Certain classes of these nonbinary constraints are "network decomposable" as they can be represented by binary constraints on the same set of variables. We compare theoretically the levels of consistency which are achieved on nonbinary constraints to those achieved on their binary decomposition. We present many new results about the level of consistency achieved by the forward checking algorithm and its various generalizations to nonbinary constraints. We also compare the level of consistency achieved by arcconsistency and its generalization to nonbinary constraints, and identify special cases of nonbinary decomposable constraints where weaker or stronger conditions, than in the general case, hold. We also analyze the cost, in consistency checks, required to achieve certain levels of consistency.
The search for Satisfaction
, 1999
"... In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problem ..."
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Cited by 14 (1 self)
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In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problems with thousands of variables. At the same time, implementations of complete search algorithms like DavisPutnam have been able to solve open mathematical problems. Another factor is the identi cation of hard Sat problems at a phase transition in solubility. A third factor is the demonstration that we can often solve real world problems by encoding them into Sat. There has also seen an improved theoretical understanding of Sat, particularly in the analysis of such phase transition behaviour. This paper reviews the state of the art for research into satis ability, and discuss applications in which algorithms for satis ability have proved successful.
Backtracking Search Algorithms
, 2006
"... There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as var ..."
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Cited by 10 (2 self)
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There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stochastic search algorithms are the topic of Chapter 5. An algorithm for solving a constraint satisfaction problem (CSP) can be either complete or incomplete. Complete, or systematic algorithms, come with a guarantee that a solution will be found if one exists, and can be used to show that a CSP does not have a solution and to find a provably optimal solution. Backtracking search algorithms and dynamic programming algorithms are, in general, examples of complete algorithms. Incomplete, or nonsystematic algorithms, cannot be used to show a CSP does not have a solution or to find a provably optimal solution. However, such algorithms are often effective at finding a solution if one exists and can be used to find an approximation to an optimal solution. Local or stochastic search algorithms are examples of incomplete algorithms. Of the two
Representation and Reasoning with NonBinary Constraints
, 2001
"... Many problems from the \real world" can be eciently expressed as constraint satisfaction problems (CSPs). Most of these can be naturally modelled using nary (or nonbinary) constraints. Representing problems with nary constraints and reasoning with them is therefore very important in constraint sa ..."
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Cited by 3 (0 self)
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Many problems from the \real world" can be eciently expressed as constraint satisfaction problems (CSPs). Most of these can be naturally modelled using nary (or nonbinary) constraints. Representing problems with nary constraints and reasoning with them is therefore very important in constraint satisfaction. However, issues regarding nary constraints have been neglected compared to binary constraints. The reasons were the simplicity of dealing with binary constraints compared to nary and the fact that any nonbinary CSP can be encoded into an equivalent binary. This thesis makes an empirical and theoretical study on representation and solution methods for nary CSPs. The results we present demonstrate the importance of the choice of representation and reasoning techniques in nary problems.
Heuristic Search in Boundeddepth Trees: BestLeafFirst Search
, 2002
"... Many combinatorial optimization and constraint satisfaction problems can be formulated as a search for the best leaf in a tree of bounded depth. When exhaustive enumeration is infeasible, a rational strategy visits leaves in increasing order of predicted cost. Previous systematic algorithms for this ..."
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Cited by 3 (1 self)
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Many combinatorial optimization and constraint satisfaction problems can be formulated as a search for the best leaf in a tree of bounded depth. When exhaustive enumeration is infeasible, a rational strategy visits leaves in increasing order of predicted cost. Previous systematic algorithms for this setting follow a predetermined search order, making strong implicit assumptions about predicted cost and using problemspecific information inefficiently. We introduce a framework, bestleaffirst search (BLFS), that employs an explicit model of leaf cost. BLFS is complete and visits leaves in an order that efficiently approximates increasing predicted cost. Different algorithms can be derived by incorporating different sources of information into the cost model. We show how previous algorithms are special cases of BLFS.