An Iterative Problem-Driven Scenario Reduction Framework for Stochastic Optimization with Conditional Value-at-Risk

Abstract: Scenario reduction (SR) alleviates the computational complexity of scenario-based stochastic optimization with conditional value-at-risk (SBSO-CVaR) by identifying representative scenarios to depict the underlying uncertainty and tail risks. Existing distribution-driven SR methods emphasize statistical similarity but often exclude extreme scenarios, leading to weak tail-risk awareness and insufficient problem-specific representativeness. Instead, this paper proposes an iterative problem-driven scenario reduction framework. Specifically, we integrate the SBSO-CVaR problem structure into SR process and project the original scenario set from the distribution space onto the problem space. Subsequently, to minimize the SR optimality gap with acceptable computation complexity, we propose a tractable iterative problem-driven scenario reduction (IPDSR) method that selects representative scenarios that best approximate the optimality distribution of the original scenario set while preserving tail risks. Furthermore, the iteration process is rendered as a mixed-integer program to enable scenario partitioning and representative scenarios selection. And ex-post problem-driven evaluation indices are proposed to evaluate the SR performance. Numerical experiments show IPDSR significantly outperforms existing SR methods by achieving an optimality gap of less than 1% within an acceptable computation time.