Results 1  10
of
14
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 19 (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
Postponing Branching Decisions
, 2004
"... Solution techniques for Constraint Satisfaction and Optimisation Problems often make use of backtrack search methods, exploiting variable and value ordering heuristics. In this paper, we propose and analyse a very simple method to apply in case the value ordering heuristic produces ties: postponing ..."
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Cited by 5 (1 self)
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Solution techniques for Constraint Satisfaction and Optimisation Problems often make use of backtrack search methods, exploiting variable and value ordering heuristics. In this paper, we propose and analyse a very simple method to apply in case the value ordering heuristic produces ties: postponing the branching decision. To this end, we group together values in a tie, branch on this subdomain, and defer the decision among them to lower levels of the search tree. We show theoretically and experimentally that this simple modification can dramatically improve the efficiency of the search strategy. Although in practise similar methods may have been applied already, to our knowledge, no empirical or theoretical study has been proposed in the literature to identify when and to what extent this strategy should be used.
Decomposition Based Search  a Theoretical And Experimental Evaluation
, 2003
"... In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and domain splitting. subdomains are explored so as to generate, ..."
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Cited by 5 (1 self)
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In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and domain splitting. subdomains are explored so as to generate, according to the heuristic chosen, promising subproblems first.
Improved Filtering for Weighted Circuit Constraints
"... We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1tree relaxation of Held a ..."
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Cited by 4 (1 self)
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We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1tree relaxation of Held and Karp. In addition, we study domain filtering based on an additive bounding procedure that combines the 1tree relaxation with the assignment problem relaxation. Experimental results on Traveling Salesman Problem instances demonstrate that our filtering algorithms can dramatically reduce the problem size. In particular, the search tree size and solving time can be reduced by several orders of magnitude, compared to existing constraint programming approaches. Moreover, for mediumsize problem instances, our method is competitive with the stateoftheart specialpurpose TSP solver Concorde.
A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem
, 2003
"... This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxat ..."
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Cited by 3 (3 self)
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This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.
Exploiting Semidefinite Relaxations in Constraint Programming
 Computers and Operations Research
"... Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In principle, we use the solution of a semidefinite relaxation t ..."
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Cited by 2 (1 self)
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Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In principle, we use the solution of a semidefinite relaxation to guide the traversal of the search tree, using a limited discrepancy search strategy. Furthermore, a semidefinite relaxation produces a bound for the solution value, which is used to prune parts of the search tree. Experimental results on stable set and maximum clique problem instances show that constraint programming can indeed greatly benefit from semidefinite relaxations. 1
CPbased Local Branching
"... Abstract. We propose the integration and extension of the local branching search strategy in Constraint Programming (CP). Local branching is a general purpose heuristic method which searches locally around the best known solution by employing tree search. It has been successfully used in MIP where l ..."
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Abstract. We propose the integration and extension of the local branching search strategy in Constraint Programming (CP). Local branching is a general purpose heuristic method which searches locally around the best known solution by employing tree search. It has been successfully used in MIP where local branching constraints are used to model the neighborhood of an incumbent solution and improve the bound. The integration of local branching in CP is not simply a matter of implementation, but requires a number of significant extensions (concerning the computation of the bound, costbased filtering of the branching constraints, diversification, variable neighbourhood width and search heuristics) and can greatly benefit from the CP environment. In this paper, we discuss how such extensions are possible and provide some experimental results to demonstrate the practical value of local branching in CP. 1
CostBased Filtering for Determining the Pareto Frontier
, 2006
"... Real life problems involve seldom only one criterion, but multiple criteria should be optimised at the same time. The criteria can even be conflicting each other, so the classical techniques used in single criteria optimization cannot be simply reused. Many ideas have been presented in the literatu ..."
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Cited by 1 (1 self)
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Real life problems involve seldom only one criterion, but multiple criteria should be optimised at the same time. The criteria can even be conflicting each other, so the classical techniques used in single criteria optimization cannot be simply reused. Many ideas have been presented in the literature for addressing multiple criteria optimization problems; one of the ideas is to provide the socalled Pareto frontier, i.e., the set of solutions that are not dominated by other feasible solutions. The Pareto frontier provides a lot of information to the decisionmaker, that could be used to select the best preferred solution. On the other hand, finding the Pareto frontier is a timeconsuming task. In singlecriteria optimization, integration of Constraint Programming and Operations Research techniques has often been a successful approach to tackle difficult problems. Information derived by a solver that handles the linear relaxation of the original problem (like lower bounds, reduced costs, dual solution) has been used to improve the bounding and pruning capabilities of a Constraint Programming solver. In this paper, we propose an approach that integrates linear programming in Constraint Programming to speedup the search process in multiplecriteria optimization. We extend a Constraint Programming algorithm for finding the Pareto frontier, integrate it with a linear solver that provides bounds and reduced costs. Promising preliminary experiments show the effectiveness of the approach.
Combinatorial Complexity: Are We on the Right Way?
"... Abstract: We present a hypothetical approach to support existing methods in dealing with combinatorial complexity and describe the application of said approach to some typical combinatorial problems and techniques. ..."
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Abstract: We present a hypothetical approach to support existing methods in dealing with combinatorial complexity and describe the application of said approach to some typical combinatorial problems and techniques.