Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

TL;DR

This paper develops a new approach for solving distributionally robust chance-constrained binary programs with mean and covariance information, reformulating them as 0-1 SOC programs and enhancing solution efficiency with extended polymatroid inequalities.

Contribution

It introduces a novel reformulation of distributionally robust chance-constrained binary programs as 0-1 SOC programs and develops extended polymatroid inequalities to improve solution algorithms.

Findings

Effective reformulation as 0-1 SOC programs

Enhanced branch-and-cut algorithm with polymatroid inequalities

Demonstrated computational efficiency on bin packing instances

Abstract

We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satisfied probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. We further exploit the submodularity of 0-1 SOC constraints under special and general covariance matrices, and utilize the submodularity as well as lifting to derive extended polymatroid inequalities to strengthen the 0-1 SOC formulations. We incorporate the valid inequalities in a branch-and-cut algorithm for efficiently solving DCBPs. We demonstrate the computational efficacy and solution performance using diverse instances of a chance-constrained bin packing problem.