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15
A greedy randomized adaptive search procedure for the 2partition problem
 Operations Research
, 1994
"... Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search ..."
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Cited by 478 (75 self)
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Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.
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 33 (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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Exploiting orbits in symmetric ilp
 Mathematical Programming
"... This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (wi ..."
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Cited by 22 (0 self)
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This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact kbehrman@andrew.cmu.edu. Mathematical Programming manuscript No. (will be inserted by the editor)
A Genetic Algorithm with a NonBinary Representation for the Set Covering Problem
 PROCEEDINGS OF SYMPOSIUM ON OPERATIONS RESEARCH
, 1999
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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 16 (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.
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 11 (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...
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 7 (7 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.
An Iterated Heuristic Algorithm for the Set Covering Problem
 WAE'98
, 1998
"... The set covering problem is a wellknown NPhard combinatorial optimization problem with wide practical applications. This paper introduces a novel heuristic for the unicost set covering problem. An iterated approximation algorithm (ITEG) based on this heuristic is developed: in the first iterat ..."
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Cited by 5 (0 self)
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The set covering problem is a wellknown NPhard combinatorial optimization problem with wide practical applications. This paper introduces a novel heuristic for the unicost set covering problem. An iterated approximation algorithm (ITEG) based on this heuristic is developed: in the first iteration a cover is constructed, and in the next iterations a new cover is built by starting with part of the best solution so far obtained. The final output of the algorithm is the best solution obtained in all the iterations. ITEG is empirically evaluated on a set of randomly generated problem instances, on instances originated from the Steiner triple systems, and on instances derived from two challenging combinatorial questions by Erdos. The performance of ITEG on these benchmark problems is very satisfactory, both in terms of solution quality (i.e., small covers) as well as in terms of running time.
The design of a 01 integer optimizer and its application in the Carmen system
 European Journal of Operational Research
, 1995
"... We describe the design of an optimizer for 01 integer programming aimed at solving large problems. The algorithm is based on very simple operations giving it a low complexity, and we show that for large set covering problems it can produce very good solutions compared to other methods. This is the ..."
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Cited by 3 (1 self)
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We describe the design of an optimizer for 01 integer programming aimed at solving large problems. The algorithm is based on very simple operations giving it a low complexity, and we show that for large set covering problems it can produce very good solutions compared to other methods. This is the only optimizer in the Carmen system for airline crew scheduling, used by several major European airlines, and we discuss how it has affected the overall design and success of this system. Keywords: 01 integer linear programming, efficient algorithms, set covering, airline crew scheduling. 1 Introduction In this paper I will describe the design of an optimizer for solving large 01 integer programs, and its application in the Carmen system for airline crew scheduling. The design of the optimizer itself has mainly been an academic research project aimed at discrete optimization in general. However, the specific application in mind has been the usually very large optimization problems that a...