A New Clustering Approach for Scenario Reduction in Multi-Stochastic Variable Programming

In the scenario-based stochastic programming problem, the solving complexity and computational burden increases as the number of scenarios increase, which involves necessary scenario reduction operations. For the scenario reduction problem with multiple random variables, we present a comprehensive optimal scenario reduction method based on a new optimization framework to eliminate redundant initial scenarios. In this framework, we propose the concept of correlation loss, to solve the problem of serious deviation of correlation in the reduced scenarios. The method uses a corrloss weight to balance the two objectives of the proposed scenario reduction framework. One is to minimize the correlation loss before and after scenario reduction, and the other is to maximize the similarity between the original scenario set and the reduced scenario set. In particular, it has strong universality. Numerical comparative experiments are carried out to evaluate the performance of the method. Application studies to microgrid economic operation optimization are also made to prove the effectiveness of the proposed method.