Scenario reduction and scenario tree generation for stochastic programming using Sinkhorn distance

Abstract

Scenario-based stochastic programming is a widely used method for optimization under uncertainty. The solution quality of this approach is dependent on the approximation of the underlying uncertainty distribution. Therefore, the optimal generation of scenarios (or scenario trees) is a pertinent research objective in stochastic programming. In this work, we approach the scenario reduction and scenario tree generation problem through the perspective of optimal transport, specifically entropy-regularized optimal transport. The availability of an iterative procedure to compute the optimal entropy-regularized transport plan between support sets, using the Sinkhorn–Knopp algorithm in lieu of conventional linear programming-based optimal transport, is found to decrease solution time appreciably, with a decrease in memory burden as well. We present algorithms for optimal scenario reduction and multistage scenario tree generation, and illustrate their use through two case studies. We show that the proposed approach generates high-quality scenarios whose use in stochastic programming offers solutions with good accuracy.