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35
Function Variables for Constraint Programming
, 2003
"... We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable ca ..."
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Cited by 42 (5 self)
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We introduce function variables to constraint programs (CP), variables whose values are one of (exponentially many) possible functions between two sets. Such variables are useful for modelling problems from domains such as configuration, planning, scheduling, etc. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a constraint model expressed using function variables allows for the generation of alternate CP models. Furthermore, we present an extensive theoretical comparison of models of problems involving injective functions supported by asymptotic and empirical studies. Finally, we present and evaluate a practical modelling tool that is based on a highlevel language that supports function variables. The tool helps users explore different alternate CP models starting from a function model that is easy to develop, understand, and maintain.
Dual Models of Permutation Problems
, 2001
"... A constraint satisfaction problem is a permutation problem if it has the same number of values as variables, all variables have the same domain and any solution assigns a permutation of the values to the variables. The dual CSP interchanges the variables and values; the effects of combining both ..."
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Cited by 36 (7 self)
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A constraint satisfaction problem is a permutation problem if it has the same number of values as variables, all variables have the same domain and any solution assigns a permutation of the values to the variables. The dual CSP interchanges the variables and values; the effects of combining both sets of variables in a single CSP are discussed.
Ants can solve Constraint Satisfaction Problems
 IEEE Transactions on Evolutionary Computation
, 2001
"... In this paper we describe a new incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone info ..."
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Cited by 32 (11 self)
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In this paper we describe a new incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone information is used to guide the search, as a heuristic for choosing values to be assigned to variables.
Redundant Modeling for the QUasigroup Completion Problem
 Principles and practice of Constraint Programming (CP03) Lecture Notes in Computer Science
, 2003
"... Abstract. The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs of order 40 could not be solved by pure constraint programming approaches, but could some ..."
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Cited by 15 (1 self)
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Abstract. The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs of order 40 could not be solved by pure constraint programming approaches, but could sometimes be solved by hybrid approaches combining constraint programming with mixed integer programming techniques from operations research. In this paper, we show that the pure constraint satisfaction approach can solve many problems of order 45 in the transition phase, which corresponds to the peak of difficulty. Our solution combines a number of known ideas –the use of redundant modeling [3] with primal and dual models of the problem connected by channeling constraints [13] – with some novel aspects, as well as a new and very effective value ordering heuristic. 1
The designers’ workbench: Using ontologies and constraints for configuration,” in
 SEPTEMBER 2007 Proc. 24th SGAI Int. Conf. Innovative Tech. Appl. Artif. Intell
, 2004
"... Typically, complex engineering artifacts are designed by teams who may not all be located in the same building or even city. Additionally, besides having to design a part of an artifact to be consistent with the specification, it must also be consistent with the company's design standards. The ..."
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Cited by 9 (3 self)
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Typically, complex engineering artifacts are designed by teams who may not all be located in the same building or even city. Additionally, besides having to design a part of an artifact to be consistent with the specification, it must also be consistent with the company's design standards. The Designers ' Workbench supports designers by checking that their configurations satisfy both physical and organisational constraints. The system uses an ontology to describe the available elements in a configuration task. Configurations are composed of features, which can be geometric or nongeometric, physical or abstract. Designers can select a class of feature (e.g. Bolt) from the ontology, and add an instance of that class (e.g. a particular bolt) to their configuration. Properties of the instance can express the parameters of the feature (e.g. the size of the bolt), and also describe connections to other
Removing propagation redundant constraints in redundant modeling
 ACM Transactions on Computational Logic
, 2007
"... A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically ..."
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Cited by 8 (3 self)
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A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with various degrees of constraint propagation for pruning the search space. One common technique to improve the execution efficiency is to add redundant constraints, which are constraints logically implied by others in the problem model. However, some redundant constraints are propagation redundant and hence do not contribute additional propagation information to the constraint solver. Redundant constraints arise naturally in the process of redundant modeling where two models of the same problem are connected and combined through channeling constraints. In this paper, we give general theorems for proving propagation redundancy of one constraint with respect to channeling constraints and constraints in the other model. We illustrate, on problems from CSPlib
Constraint Programming in Practice: Scheduling a Rehearsal Report
, 2003
"... The basic principles of constraint programming (constraint satisfaction problems, search, constraint propagation) are introduced by discussing how constraint programming can be used to solve a specific optimization problem. A set of orchestral pieces is to be rehearsed and the problem requires fi ..."
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Cited by 6 (1 self)
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The basic principles of constraint programming (constraint satisfaction problems, search, constraint propagation) are introduced by discussing how constraint programming can be used to solve a specific optimization problem. A set of orchestral pieces is to be rehearsed and the problem requires finding a sequence that will minimize the time that players are at the rehearsal but not playing, if they arrive for the first piece they are involved in and leave after the last. A constraint programming model of this problem is presented. A similar problem arises in `talent scheduling' in shooting a film; improvements to the basic model are given that allow a larger instance of this kind to be solved.
S.: Assisting domain experts to formulate and solve constraint satisfaction problems
 In: Proc. 15th Internat. Conf. on Knowledge Engineering and Knowledge Management, LNCS No. 4248
, 2006
"... Abstract. Constraint satisfaction is a powerful approach to solving a wide class of problems. However, as many nonexperts have problems formulating tasks as Constraint Satisfaction Problems (CSPs), we have built a number of interfaces for particular kinds of CSPs, including cryptarithmetic problem ..."
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Cited by 4 (0 self)
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Abstract. Constraint satisfaction is a powerful approach to solving a wide class of problems. However, as many nonexperts have problems formulating tasks as Constraint Satisfaction Problems (CSPs), we have built a number of interfaces for particular kinds of CSPs, including cryptarithmetic problems, mapcolouring problems, and scheduling tasks, which ask highly focused questions of the user, c.f., the earlier MOLE/MORE, and SALT knowledge acquisition systems. Information from each of these interfaces is then transformed initially into a structured format which is semantic web compliant and is secondly transformed into the format required by the generic Constraint satisfaction problem solver. When this problem solver is run, the user is either provided with solution(s) or feedback that the problem is underspecified (when many solutions are feasible) or overspecified (when no solution is possible). Effectively the system has 3 distinct phases, namely; information capture, transformation of the information to that suitable for the standard problem solver, and thirdly the solving and user feedback phase. We are planning to analyse in detail a greater range of the CSP tasks, and to produce further UIs to support these tasks. Secondly, we plan to exploit the existence of the intermediary representation which is semantic web compliant, by enhancing the information about tasks with relevant information available from the semantic web. 1
Hybrid modelling for robust solving
 Annals of Operations Research
, 2004
"... ⋆ We would like to thank C. Castro and S. Manzano for providing us with the reallife instances they used in their experiments. The first and the last authors are supported by Science Foundation Ireland. The third author is supported by UKEPSRC grant number GR/N16129. Abstract. We study a balanced ..."
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Cited by 3 (0 self)
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⋆ We would like to thank C. Castro and S. Manzano for providing us with the reallife instances they used in their experiments. The first and the last authors are supported by Science Foundation Ireland. The third author is supported by UKEPSRC grant number GR/N16129. Abstract. We study a balanced academic curriculum problem and an industrial steel mill slab design problem. We show that these problems can be modelled in different ways, using both Integer Linear Programming (ILP) and Constraint Programming (CP) techniques, and consider the utility of each model. We also propose integrating the models to create hybrids that benefit from the complementary strengths of each model. Experimental results show that, especially in the case of hybrid CP/ILP models, the integration significantly increases the domain pruning, and decreases the runtime on many instances. Furthermore, a CP/ILP hybrid model gives a more robust performance in the face of varying instance data. Keywords: Application, Modelling, Integration, Constraint Programming, and Integer Linear Programming.