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25
Greedy Randomized Adaptive Search Procedures
, 2002
"... GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phas ..."
Abstract

Cited by 647 (82 self)
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GRASP is a multistart metaheuristic for combinatorial problems, in which each iteration consists basically of two phases: construction and local search. The construction phase builds a feasible solution, whose neighborhood is investigated until a local minimum is found during the local search phase. The best overall solution is kept as the result. In this chapter, we first describe the basic components of GRASP. Successful implementation techniques and parameter tuning strategies are discussed and illustrated by numerical results obtained for different applications. Enhanced or alternative solution construction mechanisms and techniques to speed up the search are also described: Reactive GRASP, cost perturbations, bias functions, memory and learning, local search on partially constructed solutions, hashing, and filtering. We also discuss in detail implementation strategies of memorybased intensification and postoptimization techniques using pathrelinking. Hybridizations with other metaheuristics, parallelization strategies, and applications are also reviewed.
An Algorithm for Large Scale 01 Integer Programming With Application to Airline Crew Scheduling
, 1995
"... We present an approximation algorithm for solving large 01 integer programming problems where A is 01 and where b is integer. The method can be viewed as a dual coordinate search for solving the LPrelaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working t ..."
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Cited by 46 (5 self)
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We present an approximation algorithm for solving large 01 integer programming problems where A is 01 and where b is integer. The method can be viewed as a dual coordinate search for solving the LPrelaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems ...
An Interior Point Algorithm to Solve Computationally Difficult Set Covering Problems
, 1990
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Orbital branching
 in Proceedings of IPCO XII
, 2007
"... Orbital branching is a method for branching on variables in integer programming that reduces the likelihood of evaluating redundant, isomorphic nodes in the branchandbound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an ar ..."
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Cited by 21 (3 self)
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Orbital branching is a method for branching on variables in integer programming that reduces the likelihood of evaluating redundant, isomorphic nodes in the branchandbound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an arbitrary constraint. Many important families of integer programs are structured such that small instances from the family are embedded in larger instances. This structural information can be exploited to define a group of strong constraints on which to base the orbital branching disjunction. The symmetric nature of the problems is further exploited by enumerating nonisomorphic solutions to instances of the small family and using these solutions to create a collection of typically easytosolve integer programs. The solution of each integer program in the collection is equivalent to solving the original large instance. The effectiveness of this methodology is demonstrated by computing the optimal incidence width of Steiner Triple Systems and minimum cardinality covering designs.
A Genetic Algorithm with a NonBinary Representation for the Set Covering Problem
 PROCEEDINGS OF SYMPOSIUM ON OPERATIONS RESEARCH
, 1999
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An Exact Algorithm For The Maximum Stable Set Problem
 Computational Optimization and Application
, 1994
"... We describe a new branchandbound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different nodefixing heuristics are also described. Computational te ..."
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Cited by 12 (2 self)
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We describe a new branchandbound algorithm for the exact solution of the maximum cardinality stable set problem. The bounding phase is based on a variation of the standard greedy algorithm for finding a colouring of a graph. Two different nodefixing heuristics are also described. Computational tests on random and structured graphs and very large graphs corresponding to `reallife' problems show that the algorithm is competitive with the fastest algorithms known so far. 1 Introduction We denote by G = (V; E) an undirected graph. V is the set of nodes and E the set of edges. A stable set is a subset of V such that no two nodes of the subset are pairwise adjacent. The cardinality of a maximum stable set of G will be denoted by ff(G). A clique is a subset of V with the property that all the nodes are pairwise adjacent. A clique covering is a set of disjoint cliques whose union is equal to V ; the cardinality of a minimum clique covering is denoted by `(G), and since at most one nod...
Classification of Orthogonal Arrays by Integer Programming
 JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 138, 8.
, 2006
"... The problem of classifying all isomorphism classes of OA(N, k, s, t)s is shown to be equivalent to finding all isomorphism classes of nonnegative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branchandcut algorithm developed by Margot (20 ..."
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Cited by 10 (1 self)
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The problem of classifying all isomorphism classes of OA(N, k, s, t)s is shown to be equivalent to finding all isomorphism classes of nonnegative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branchandcut algorithm developed by Margot (2002, 2003a, 2003b, 2005) for solving integer programming problems with large symmetry groups is used to find
A biased randomkey genetic algorithm for the steiner triple covering problem
 Optimization Letters
"... Abstract. We present a biased randomkey genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers ..."
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Cited by 10 (9 self)
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Abstract. We present a biased randomkey genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used to evaluate solution procedures for this problem. The new covers for instances A405 and A729 have sizes 335 and 617, respectively. On all other smaller instances our algorithm consistently produces covers of optimal size. 1.