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87
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 209 (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 Constrainedness of Search
 In Proceedings of AAAI96
, 1999
"... We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrain ..."
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Cited by 126 (29 self)
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We propose a definition of `constrainedness' that unifies two of the most common but informal uses of the term. These are that branching heuristics in search algorithms often try to make the most "constrained" choice, and that hard search problems tend to be "critically constrained". Our definition of constrainedness generalizes a number of parameters used to study phase transition behaviour in a wide variety of problem domains. As well as predicting the location of phase transitions in solubility, constrainedness provides insight into why problems at phase transitions tend to be hard to solve. Such problems are on a constrainedness "knifeedge", and we must search deep into the problem before they look more or less soluble. Heuristics that try to get off this knifeedge as quickly as possible by, for example, minimizing the constrainedness are often very effective. We show that heuristics from a wide variety of problem domains can be seen as minimizing the constrainedness (or proxies ...
Bridging the gap between planning and scheduling
 KNOWLEDGE ENGINEERING REVIEW
, 2000
"... Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting orde ..."
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Cited by 115 (12 self)
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Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting ordering problem is hard. In this paper, we give an overview of AI planning and scheduling techniques, focusing on their similarities, differences, and limitations. We also argue that many difficult practical problems lie somewhere between planning and scheduling, and that neither area has the right set of tools for solving these vexing problems.
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
Trying Harder to Fail First
 In: Thirteenth European Conference on Artificial Intelligence (ECAI 98
, 1997
"... Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checki ..."
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Cited by 54 (1 self)
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Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checking which look ahead at the effects of each variable instantiation on those variables not yet instantiated. This heuristic has been explained as an implementation of the failfirst principle, stated by Haralick and Elliott [7], i.e. that the next variable selected should be the one which is most likely to result in an immediate failure. We calculate the probability that a variable will fail when using the forward checking algorithm to solve a class of binary CSPs. We derive a series of heuristics, starting with smallestremainingdomain, based on increasingly accurate estimates of this probability, and predict that if the failfirst principle is sound, the more accurate the estimate the better...
The Constrainedness of Arc Consistency
 in Proceedings of CP97
, 1997
"... . We show that the same methodology used to study phase transition behaviour in NPcomplete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NPcomplete proble ..."
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Cited by 50 (10 self)
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. We show that the same methodology used to study phase transition behaviour in NPcomplete problems works with a polynomial problem class: establishing arc consistency. A general measure of the constrainedness of an ensemble of problems, used to locate phase transitions in random NPcomplete problems, predicts the location of a phase transition in establishing arc consistency. A complexity peak for the AC3 algorithm is associated with this transition. Finite size scaling models both the scaling of this transition and the computational cost. On problems at the phase transition, this model of computational cost agrees with the theoretical worst case. As with NPcomplete problems, constrainedness  and proxies for it which are cheaper to compute  can be used as a heuristic for reducing the number of checks needed to establish arc consistency in AC3. 1 Introduction Following [4] there has been considerable research into phase transition behaviour in NPcomplete problems. Problems from...
Exploiting symmetries within constraint satisfaction search
, 2001
"... Symmetry often appears in realworld constraint satisfaction problems, but strategies for exploiting it are only beginning to be developed. Here, a framework for exploiting symmetry within depthfirst search is proposed, leading to two heuristics for variable selection and a domain pruning procedure ..."
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Cited by 44 (1 self)
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Symmetry often appears in realworld constraint satisfaction problems, but strategies for exploiting it are only beginning to be developed. Here, a framework for exploiting symmetry within depthfirst search is proposed, leading to two heuristics for variable selection and a domain pruning procedure. These strategies are then applied to two highly symmetric combinatorial problems, namely the Ramsey problem and the generation of balanced incomplete block designs. Experimental results show that these generalpurpose strategies can compete with, and in some cases outperform, previous more ad hoc procedures.
Backjumpbased backtracking for constraint satisfaction problems
 Artificial Intelligence
"... The performance of backtracking algorithms for solving nitedomain 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 44 (2 self)
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The performance of backtracking algorithms for solving nitedomain 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.
Random Constraint Satisfaction: theory meets practice
, 1998
"... We study the experimental consequences of a recent theoretical result by Achlioptas et al. that shows that conventional models of random problems are trivially insoluble in the limit. We survey the literature to identify experimental studies that lie within the scope of this result. We then estimate ..."
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Cited by 37 (6 self)
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We study the experimental consequences of a recent theoretical result by Achlioptas et al. that shows that conventional models of random problems are trivially insoluble in the limit. We survey the literature to identify experimental studies that lie within the scope of this result. We then estimate theoretically and measure experimentally the size at which problems start to become trivially insoluble. Our results demonstrate that most (but not all) of these experimental studies are luckily unaffected by this result. We also study an alternative model of random problems that does not suffer from this asymptotic weakness. We show that, at a typical problem size used in experimental studies, this model looks similar to conventional models. Finally, we generalize this model so that we can independently adjust the constraint tightness and density.