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Generating hard instances for robust combinatorial optimization

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Generating hard instances for robust combinatorial optimization. / Goerigk, M.; Maher, S.J.

In: European Journal of Operational Research, Vol. 280, No. 1, 01.01.2020, p. 34-45.

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Goerigk, M. ; Maher, S.J. / Generating hard instances for robust combinatorial optimization. In: European Journal of Operational Research. 2020 ; Vol. 280, No. 1. pp. 34-45.

Bibtex

@article{0aa04c190ecd4aff967a37085aa3a8d9,
title = "Generating hard instances for robust combinatorial optimization",
abstract = "While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm performance better comparable, and makes reproducing instances unnecessary. Such a benchmark set should contain hard instances in particular, but so far, the standard approach to produce instances has been to sample values randomly from a uniform distribution.In this paper we introduce a new method to produce hard instances for min-max combinatorial optimization problems, which is based on an optimization model itself. Our approach does not make any assumptions on the problem structure and can thus be applied to any combinatorial problem. Using the Selection and Traveling Salesman problems as examples, we show that it is possible to produce instances which are up to 500 times harder to solve for a mixed-integer programming solver than the current state-of-the-art instances.",
keywords = "Robustness and sensitivity analysis, Robust optimization, Problem benchmarking, Problem generation, Combinatorial optimization",
author = "M. Goerigk and S.J. Maher",
year = "2020",
month = jan,
day = "1",
doi = "10.1016/j.ejor.2019.07.036",
language = "English",
volume = "280",
pages = "34--45",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier Science B.V.",
number = "1",

}

RIS

TY - JOUR

T1 - Generating hard instances for robust combinatorial optimization

AU - Goerigk, M.

AU - Maher, S.J.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm performance better comparable, and makes reproducing instances unnecessary. Such a benchmark set should contain hard instances in particular, but so far, the standard approach to produce instances has been to sample values randomly from a uniform distribution.In this paper we introduce a new method to produce hard instances for min-max combinatorial optimization problems, which is based on an optimization model itself. Our approach does not make any assumptions on the problem structure and can thus be applied to any combinatorial problem. Using the Selection and Traveling Salesman problems as examples, we show that it is possible to produce instances which are up to 500 times harder to solve for a mixed-integer programming solver than the current state-of-the-art instances.

AB - While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm performance better comparable, and makes reproducing instances unnecessary. Such a benchmark set should contain hard instances in particular, but so far, the standard approach to produce instances has been to sample values randomly from a uniform distribution.In this paper we introduce a new method to produce hard instances for min-max combinatorial optimization problems, which is based on an optimization model itself. Our approach does not make any assumptions on the problem structure and can thus be applied to any combinatorial problem. Using the Selection and Traveling Salesman problems as examples, we show that it is possible to produce instances which are up to 500 times harder to solve for a mixed-integer programming solver than the current state-of-the-art instances.

KW - Robustness and sensitivity analysis

KW - Robust optimization

KW - Problem benchmarking

KW - Problem generation

KW - Combinatorial optimization

U2 - 10.1016/j.ejor.2019.07.036

DO - 10.1016/j.ejor.2019.07.036

M3 - Journal article

VL - 280

SP - 34

EP - 45

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -