Results 1  10
of
15
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 ..."
Abstract

Cited by 35 (3 self)
 Add to MetaCart
(Show Context)
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...
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 ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
(Show Context)
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
Conditional Symmetry Breaking
 Principles and Practice of Constraint Programming  CP 2005, LNCS 3709
, 2005
"... Conditional symmetry arises in a subproblem of a constraint satisfaction problem, where the subproblem satisfies some condition under which additional symetries hold. Typically, the condition is a set of assignments of values to variables, i.e. a partial assignment reached during systematic search ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
(Show Context)
Conditional symmetry arises in a subproblem of a constraint satisfaction problem, where the subproblem satisfies some condition under which additional symetries hold. Typically, the condition is a set of assignments of values to variables, i.e. a partial assignment reached during systematic search. Like unconditional symmetry, conditional symmetry can cause redundancy in a systematic search for solutions. Breaking this symmetry, in addition to breaking unconditional symmetry, is therefore an important part of solving a constraint satisfaction problem effectively. This paper examines three ways in which this can be done: by adding conditional symmetrybreaking constraints, by reformulating the problem to remove the symmetry, and by augmenting the search process to break the conditional symmetry dynamically. 1
A CP Approach to the Balanced Academic Curriculum Problem
, 2007
"... The Balanced Academic Curriculum Problem (BACP) has received little attention in Constraint Programming. Only a few articles deals with this problem with experimental results on the three small instances publicly available in CSPLIB. The present article describes an approach to efficiently solve thi ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The Balanced Academic Curriculum Problem (BACP) has received little attention in Constraint Programming. Only a few articles deals with this problem with experimental results on the three small instances publicly available in CSPLIB. The present article describes an approach to efficiently solve this challenging problem. Optimal solutions are produced on a variety of randomly generated instances which generalize the CSPLIB test cases. This work describes four contributions to the resolution of this problem: a new branching heuristic, the use of dominance relations, experiments on several balance criteria and several search strategies among which an hybridization of Constraint Programming and Local Search.
Progressive Solutions: A Simple but Efficient Dominance Rule for Practical RCPSP
 In Proc. of CPAIOR 2006, the 3 rd Int. Conf. on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, LNCS 3990
, 2006
"... Abstract. This paper addresses the solution of practical resourceconstrained project scheduling problems (RCPSP). We point out that such problems often contain many, in a sense similar projects, and this characteristic can be exploited well to improve the performance of current constraintbased sol ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Abstract. This paper addresses the solution of practical resourceconstrained project scheduling problems (RCPSP). We point out that such problems often contain many, in a sense similar projects, and this characteristic can be exploited well to improve the performance of current constraintbased solvers on these problems. For that purpose, we define the straightforward but generic notion of progressive solution, in which the order of corresponding tasks of similar projects is deduced a priori. We prove that the search space can be reduced to progressive solutions. Computational experiments on two different sets of industrial problem instances are also presented. 1
A constraint programming approach for solving a queueing design and control problem
 INFORMS Journal on Computing
, 2009
"... In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is mini ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closedform expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable runtime. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueingbased problems with constraint programming. 1.
A Generic Method for Identifying and Exploiting Dominance Relations
"... Abstract. Many constraint problems exhibit dominance relations which can be exploited for dramatic reductions in search space. Dominance relations are a generalization of symmetry and conditional symmetry. However, unlike symmetry breaking which is relatively well studied, dominance breaking techniq ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Many constraint problems exhibit dominance relations which can be exploited for dramatic reductions in search space. Dominance relations are a generalization of symmetry and conditional symmetry. However, unlike symmetry breaking which is relatively well studied, dominance breaking techniques are not very well understood and are not commonly applied. In this paper, we present formal definitions of dominance breaking, and a generic method for identifying and exploiting dominance relations via dominance breaking constraints. We also give a generic proof of the correctness and compatibility of symmetry breaking constraints, conditional symmetry breaking constraints and dominance breaking constraints. 1
Solving a stochastic queueing control problem with constraint programming
, 2006
"... Abstract. In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting t ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and a shaving algorithm are presented. Experimental results show that the best constraint programming model, using shaving, is able to find and prove optimal solutions for almost all problem instances within a reasonable runtime, but that an existing heuristic algorithm performs better in terms of solution quality over time. A hybrid method combining the heuristic and the best constraint programming method is shown to perform better than either of these approaches separately. This is the first work of which we are aware that solves a queueing control problem with constraint programming. 1
Constraints (2015) 20:155–182 DOI 10.1007/s1060101491737 Dominance breaking constraints
, 2014
"... © The Author(s) 2014. This article is published with open access at SpringerLink.com Abstract Many constraint problems exhibit dominance relations which can be exploited for dramatic reductions in search space. Dominance relations are a generalization of symmetry and conditional symmetry. However, ..."
Abstract
 Add to MetaCart
(Show Context)
© The Author(s) 2014. This article is published with open access at SpringerLink.com Abstract Many constraint problems exhibit dominance relations which can be exploited for dramatic reductions in search space. Dominance relations are a generalization of symmetry and conditional symmetry. However, unlike symmetry breaking which is relatively well studied, dominance breaking techniques are not very well understood and are not commonly applied. In this paper, we present formal definitions of dominance breaking, and a generic method for identifying and exploiting dominance relations via dominance breaking constraints. We also give a generic proof of the correctness and compatibility of symmetry breaking constraints, conditional symmetry breaking constraints and dominance breaking constraints.
Dominance in Incomplete Solvers for the Multiple Knapsack Problem
"... We investigate incomplete search algorithms in a search space constrained by a dominance criterion. We propose a new genetic algorithm for the Multiple Knapsack Problem (MKP) which searches a space of candidates which are not dominated according to a dominance criterion. We compare the new algorithm ..."
Abstract
 Add to MetaCart
We investigate incomplete search algorithms in a search space constrained by a dominance criterion. We propose a new genetic algorithm for the Multiple Knapsack Problem (MKP) which searches a space of candidates which are not dominated according to a dominance criterion. We compare the new algorithm to previous heuristics for the MKP, as well as alternative algorithms, and show experimentally that our new algorithm yields the best performance on difficult instances where item weights and profits are highly correlated. 1