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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...
Increasing Constraint Propagation by Redundant Modeling: an Experience Report
 CONSTRAINTS
, 1999
"... This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of ..."
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Cited by 68 (8 self)
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This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as submodels. Channeling constraints allow the submodels to cooperate during constraint solving by propagating constraints freely amongst the submodels. This extra level of pruning and propagation activities becomes the source of execution speedup. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and wellknown nqueens problem, while the second case study applies our method in the design and construction of a reallife ...
MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems
 In Proceedings of the Second International Conference on Principles and Practice of Constraint Programming
, 1996
"... . In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often le ..."
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Cited by 40 (3 self)
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. In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FCCBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks. 1 Introducti...
Backjumpbased Backtracking for Constraint Satisfaction Problems
 Artificial Intelligence
, 2002
"... The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques ..."
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Cited by 37 (2 self)
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The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques use constraint propagation algorithms to avoid such deadends altogether. This survey describes a number of lookback variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space. The last portion of the paper gives an overview of lookahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.
A Tutorial on Constraint Programming
 University of Leeds
, 1995
"... A constraint satisfaction problem (CSP) consists of a set of variables; for each variable, a finite set of possible values (its domain); and a set of constraints restricting the values that the variables can simultaneously take. A solution to a CSP is an assignment of a value from its domain to ever ..."
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Cited by 30 (3 self)
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A constraint satisfaction problem (CSP) consists of a set of variables; for each variable, a finite set of possible values (its domain); and a set of constraints restricting the values that the variables can simultaneously take. A solution to a CSP is an assignment of a value from its domain to every variable, in such a way that every constraint is satisfied. Many problems arising in O.R., in particular scheduling, timetabling and other combinatorial problems, can be represented as CSPs. Constraint programming tools now exist which allow CSPs to be expressed easily, and provide standard strategies for finding solutions. This tutorial is intended to give a basic grounding in constraint satisfaction problems and some of the algorithms used to solve them, including the techniques commonly used in constraint programming tools. In particular, it covers arc and path consistency; simple backtracking and forward checking, as examples of search algorithms; and the use of heuristics to guide the...
Dual Modelling of Permutation and Injection Problems
 Journal of Artificial Intelligence Research
, 2004
"... When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many ..."
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Cited by 30 (9 self)
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general...
Interchangeability Supports Abstraction and Reformulation for Constraint Satisfaction
 In Proceedings of Symposium on Abstraction, Reformulation and Approximation (SARA'95
, 1995
"... Abstraction and reformulation are fundamental, powerful ideas in artificial intelligence, but they have not had a great deal of application in the area of constraint satisfaction. The obvious way to implement abstraction in a constraint satisfaction context is to simplify the problem by removing con ..."
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Cited by 29 (1 self)
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Abstraction and reformulation are fundamental, powerful ideas in artificial intelligence, but they have not had a great deal of application in the area of constraint satisfaction. The obvious way to implement abstraction in a constraint satisfaction context is to simplify the problem by removing constraints, and then use the solutions to the simplified problem to guide the search for a solution to the original problem. In a sense, local search, hill climbing methods use this approach, while giving up completeness guarantees. The problem for a complete method is that a simplified problem may be trivial (recent work on locating hard problems suggests that hard problems may cluster on narrow ridges in problem space). Thus there may be too many solutions to the simplified problem to be useful. The Cartesian product representation and interchangeability techniques provide ways of working with compact representations of large sets of solutions.
Backtracking algorithms for constraint satisfaction problems
, 1999
"... Over the past twenty veyears many backtracking algorithms have been developed for constraint satisfaction problems. This survey describes the basic backtrack search within the search space framework and then presents a number of improvements developed in the past two decades, including lookback met ..."
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Cited by 28 (6 self)
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Over the past twenty veyears many backtracking algorithms have been developed for constraint satisfaction problems. This survey describes the basic backtrack search within the search space framework and then presents a number of improvements developed in the past two decades, including lookback methods such asbackjumping, constraint recording, backmarking, and lookahead methods such as forward checking and dynamic variable ordering. 1
Suggestion Strategies for ConstraintBased Matchmaker Agents
 In Principles and Practice of Constraint Programming  CP98
, 1998
"... In this paper we describe a paradigm for contentfocused matchmaking, based on a recently proposed model for constraint acquisitionandsatisfaction. Matchmaking agents are conceived as constraintbased solvers that interact with other, possibly human, agents (Clients or Customers). The Matchmaker pro ..."
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Cited by 26 (13 self)
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In this paper we describe a paradigm for contentfocused matchmaking, based on a recently proposed model for constraint acquisitionandsatisfaction. Matchmaking agents are conceived as constraintbased solvers that interact with other, possibly human, agents (Clients or Customers). The Matchmaker provides potential solutions ("suggestions") based on partial knowledge, while gaining further information about the problem itself from the other agent through the latter's evaluation of these suggestions. The dialog between Matchmaker and Customer results in iterative improvement of solution quality, as demonstrated in simple simulations. We also show empirically that this paradigm supports "suggestion strategies " for finding acceptable solutions more efficiently or for increasing the amount of information obtained from the Customer. This work also indicates some ways in which the tradeoff between these two metrics for evaluating performance can be handled. Introduction Intelligent matchm...
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...