Chance-Constrained Optimization: A Review of Mixed-Integer Conic Formulations and Applications

Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we first review recent developments in mixed-integer linear formulations of chance-constrained programs that arise from finite discrete distributions (or sample average approximation). We highlight successful reformulations and decomposition techniques that enable the solution of large-scale instances. We then review active research in distributionally robust CCP, which is a framework to address the ambiguity in the distribution of the random data. The focal point of our review is scalable formulations that can be readily implemented with state-of-the-art optimization software. However, we also discuss alternative approaches and specialized algorithms. Furthermore, we highlight the prevalence of CCPs with a review of applications across multiple domains.