### Abstract

This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing the true distribution with a high statistical guarantee. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive program, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature on three applications. Numerical results illustrate the effectiveness of our approach.

Language | English (US) |
---|---|

Pages | 111-134 |

Number of pages | 24 |

Journal | Computational Management Science |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2018 |

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### Keywords

- Copositive programming
- Distributionally robust optimization
- Semidefinite programming
- Wasserstein metric

### Cite this

**A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming.** / Xu, Guanglin; Burer, Samuel.

Research output: Contribution to journal › Article

*Computational Management Science*, vol. 15, no. 1, pp. 111-134. https://doi.org/10.1007/s10287-018-0298-9

}

TY - JOUR

T1 - A data-driven distributionally robust bound on the expected optimal value of uncertain mixed 0-1 linear programming

AU - Xu, Guanglin

AU - Burer, Samuel

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing the true distribution with a high statistical guarantee. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive program, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature on three applications. Numerical results illustrate the effectiveness of our approach.

AB - This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from the observed samples and containing the true distribution with a high statistical guarantee. The problem of interest is to investigate the bound on the expected optimal value over the Wasserstein ambiguity set. Under standard assumptions, we reformulate the problem into a copositive program, which naturally leads to a tractable semidefinite-based approximation. We compare our approach with a moment-based approach from the literature on three applications. Numerical results illustrate the effectiveness of our approach.

KW - Copositive programming

KW - Distributionally robust optimization

KW - Semidefinite programming

KW - Wasserstein metric

UR - http://www.scopus.com/inward/record.url?scp=85040698959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040698959&partnerID=8YFLogxK

U2 - 10.1007/s10287-018-0298-9

DO - 10.1007/s10287-018-0298-9

M3 - Article

VL - 15

SP - 111

EP - 134

JO - Computational Management Science

T2 - Computational Management Science

JF - Computational Management Science

SN - 1619-697X

IS - 1

ER -