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Handbook of Combinatorial Optimization pp 929–993Cite as

Data Correcting Approach for Routing and Location in Networks

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Abstract

A data-correcting (DC) algorithm is a branch-and-bound-type algorithm, in which the data of a given problem is “heuristically corrected” at the various stages in such a way that the new instance will be polynomially solvable and its optimal solution is within a prespecified deviation (called prescribed accuracy) from the optimal solution to the original problem. The DC approach is applied to determining exact and approximate global optima of NP-hard problems. DC algorithms are designed for various classes of NP-hard problems including the quadratic cost partition (QCP), simple plant location (SPL), and traveling salesman problems based on the algorithmically defined polynomially solvable special cases. Results of computational experiments on the publicly available benchmark instances as well as on random instances are presented. The striking computational result is the ability of DC algorithms to find exact solutions for many relatively difficult instances within fractions of a second. For example, an exact global optimum of the QCP problem with 80 vertices and 100 % density was found within 0.22 s on a PC with 133-Mhz processor, and for the SPL problem with 200 sites and 200 clients, within 0.2 s on a PC with 733-Mhz processor.

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Acknowledgements

This work was carried out at the Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, and supported by the Ministry of Education and Science of Russian Federation, Grant No. 11.G34.31.0057, and by the Scientific Foundation of the National Research University Higher School of Economics, project “Teachers–Students” No. 11-04-0008.

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  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Boris Goldengorin

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  1. Boris Goldengorin
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Correspondence to Boris Goldengorin .

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  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Goldengorin, B. (2013). Data Correcting Approach for Routing and Location in Networks. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_84

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