Scenario tree construction driven by heuristic solutions of the optimization problem

Abstract

We present a new scenario generation process approach driven purely by the out-of-sample performance of a pool of solutions, obtained by some heuristic procedure. We formulate a loss function that measures the discrepancy between out-of-sample and in-sample (in-tree) performance of the solutions. By minimizing such a (usually non-linear, non-convex) loss function for a given number of scenarios, we receive an approximation of the underlying probability distribution with respect to the optimization problem. This approach is especially convenient in cases where the optimization problem is solvable only for a very limited number of scenarios, but an out-of-sample evaluation of the solution is reasonably fast. Another possible usage is the case of binary distributions, where classical scenario generation methods based on fitting the scenario tree and the underlying distribution do not work.