Abstract

Robust optimization (RO) has attracted much attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.

摘要

在过去的十年中，稳健的优化（RO）引起了优化社区的广泛关注。RO致力于解决存在不确定性的优化问题：在给定不确定性集中，必须满足所有不确定参数值的设计约束。不确定性集可以建模为确定性集（框，多面体，椭圆体），在这种情况下，可以通过最坏情况分析将RO问题重新表述，也可以将其建模为分布族。RO的挑战是重新制定或近似鲁棒约束，以便将不确定的优化问题转化为可处理的确定性优化问题。大多数重新制定方法都假设稳健约束的线性度或良好形状的不确定性集，这仅代表实际应用的一小部分。