Optimal Scenario Reduction Method for Stochastic Programming via Probabilistic Similarity Function

In the scenario-based stochastic programming problems, the computational burden increase as the number of scenarios increases, which involves necessary scenario reduction operations. For the scenario reduction problem with high-dimensional random vector, an optimal reduction framework is presented to eliminate redundant scenarios. In this framework, the concept of probabilistic similarity function is firstly proposed to solve the problem that scenarios cannot be clearly distinguished by traditional distance-based reduction methods in the high-dimensional scenario clustering process. The relative distance under each dimension of scenarios is considered in the computation of probabilistic similarity function, which depends not only on the values of two scenario vectors but also on the overall scenario set. The proposed recursive-type reduction method aims at maximizing the probabilistic similarity between the original scenario set and reduced scenario set. The numerical results demonstrate that our method can exhibit better performance than distance-based methods and have good universality for different stochastic programming problems.