Chance-constrained optimization under limited distributional information: A review of reformulations based on sampling and distributional robustness

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 focus on cases when only limited information on the distribution is available, such as a sample from the distribution, or the moments of the distribution. 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 on scalable formulations that can be readily implemented with state-of-the-art optimization software. Furthermore, we highlight the prevalence of CCPs with a review of applications across multiple domains.