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  • 1
    Electronic Resource
    Electronic Resource
    An implementation of Karmarkar's algorithm for linear programming (1989)
    Springer
    Mathematical programming 44 (1989), S. 297-335 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's algorithm ; interior point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality form, which allows for the inexact computation of the algorithm's direction of improvement, resulting in a significant computational advantage. Implementation issues particular to this family of algorithms, such as treatment of dense columns, are discussed. The code is tested on several standard linear programming problems and compares favorably with the simplex codeMinos 4.0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587095
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An interior point algorithm to solve computationally difficult set covering problems (1991)
    Springer
    Mathematical programming 52 (1991), S. 597-618 
    Details
    ISSN: 1436-4646
    Keywords: Integer programming ; interior point method ; Steiner triple systems ; set covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present an interior point approach to the zero–one integer programming feasibility problem based on the minimization of a nonconvex potential function. Given a polytope defined by a set of linear inequalities, this procedure generates a sequence of strict interior points of this polytope, such that each consecutive point reduces the value of the potential function. An integer solution (not necessarily feasible) is generated at each iteration by a rounding scheme. The direction used to determine the new iterate is computed by solving a nonconvex quadratic program on an ellipsoid. We illustrate the approach by considering a class of difficult set covering problems that arise from computing the 1-width of the incidence matrix of Steiner triple systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582907
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  • 3
    Electronic Resource
    Electronic Resource
    A continuous approach to inductive inference (1992)
    Springer
    Mathematical programming 57 (1992), S. 215-238 
    Details
    ISSN: 1436-4646
    Keywords: Inductive inference ; Boolean function synthesis ; satisfiability ; artificial intelligence ; integer programming ; interior point method ; Riemannian geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean functionℱ:{0, 1} n → {0, 1} using outputs obtained by applying a limited number of random inputs to the hidden function. Given this input—output sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used for defining the search region is dynamically modified. Computational results on 8-, 16- and 32-input, 1-output functions are presented. Our implementation successfully identified the majority of hidden functions in the experiment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581082
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  • 4
    Electronic Resource
    Electronic Resource
    Designing and reporting on computational experiments with heuristic methods (1995)
    Springer
    Journal of heuristics 1 (1995), S. 9-32 
    Details
    ISSN: 1572-9397
    Keywords: heuristics ; algorithms ; experimental design ; computational testing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article discusses the design of computational experiments to test heuristic methods and provides reporting guidelines for such experimentation. The goal is to promote thoughtful, well-planned, and extensive testing of heuristics, full disclosure of experimental conditions, and integrity in and reproducibility of the reported results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02430363
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  • 5
    Electronic Resource
    Electronic Resource
    Greedy Randomized Adaptive Search Procedures (1995)
    Springer
    Journal of global optimization 6 (1995), S. 109-133 
    Details
    ISSN: 1573-2916
    Keywords: Combinatorial optimization ; search heuristic ; GRASP ; computer implementation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096763
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  • 6
    Book
    Book
    Parallel processing of discrete optimization problems : DIMACS workshop, April 28-29, 1994; 22 (1995)
    Providence, RI :AMS,
    Details
    Title: Parallel processing of discrete optimization problems : DIMACS workshop, April 28-29, 1994; 22
    Contributer: Pardalos, Panos M. , Resende, Mauricio G. C. , Ramakrishnan, K. G.
    Publisher: Providence, RI :AMS,
    Year of publication: 1995
    Pages: 374 S.
    Series Statement: DIMACS Series in Discrete Mathematics and Theoretical Computer Science 22
    Type of Medium: Book
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  • 7
    Book
    Book
    Metaheuristics /; 86 (2004)
    Boston [u.a.] :Kluwer Acad. Publ.,
    Details
    Title: Metaheuristics /; 86
    Contributer: Resende, Mauricio G. C. , Metaheuristics International Conference 〈4, 2001, Porto〉 , Metaheuristics International Conference 4 Porto 2001.07.16-20 , MIC 2002 4 Porto 2001.07.16-20
    Publisher: Boston [u.a.] :Kluwer Acad. Publ.,
    Year of publication: 2004
    Pages: XIII, 719 S. : , Ill., graph. Darst.
    Series Statement: Applied optimization 86
    ISBN: 1-402-07653-3
    Type of Medium: Book
    Language: Undetermined
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  • 8
    Book
    Book
    Handbook of optimization in telecommunications / (2006)
    [Berlin u.a.] :Springer,
    Details
    Title: Handbook of optimization in telecommunications /
    Contributer: Resende, Mauricio G. C.
    Publisher: [Berlin u.a.] :Springer,
    Year of publication: 2006
    Pages: XXXI, 1134 S. : , graph. Darst.
    ISBN: 0-387-30662-5 , 0-387-30165-8 , 978-0-387-30662-9
    Type of Medium: Book
    Language: English
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