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In this paper, a class of combinatorial optimization problems with uncertain objective function costs is considered. The unknown probability distribution for the uncertain cost vector is approximated by an empirical distribution based on an available sample of the cost realizations. The true probability distribution is assumed to lie in a Wasserstein ball centered in the empirical distribution. A solution minimizing the Conditional Value at Risk for a worst probability distribution in the Wasserstein ball is computed. A general method for computing this solution is proposed.

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Solving Wasserstein Distributionally Robust Combinatorial Optimization Problems

  • 会议论文

  • 发表日期：

    2025年

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  • Marcel Jackiewicz,
  • Adam Kasperski,
  • Paweł Zieliński

摘要

In this paper, a class of combinatorial optimization problems with uncertain objective function costs is considered. The unknown probability distribution for the uncertain cost vector is approximated by an empirical distribution based on an available sample of the cost realizations. The true probability distribution is assumed to lie in a Wasserstein ball centered in the empirical distribution. A solution minimizing the Conditional Value at Risk for a worst probability distribution in the Wasserstein ball is computed. A general method for computing this solution is proposed.