Real-world optimization problems often involve uncertainties due to random parameters, leading to stochastic formulations that grow significantly in size as the number of scenarios increases, particularly in two-stage stochastic programming problems. A key challenge is managing the large number of scenarios, which contributes directly to the overall computational complexity. This paper introduces a hybrid scenario reduction method called Variance-weighted K-means with Particle Swarm Optimization (VwK-PSO). This method integrates variance-based analysis, clustering, and metaheuristic optimization to efficiently reduce the problem size while preserving essential stochastic characteristics from a scenario reduction perspective. The proposed method was tested on two case studies: cargo scheduling and aircraft allocation. Experimental results show that VwK-PSO outperforms traditional approaches like K-means clustering and Monte Carlo sampling in terms of solution quality and the Value of Stochastic Solution (VSS). Furthermore, this approach effectively maintains accuracy while significantly reducing computation time compared to the deterministic equivalent method. These findings highlight the effectiveness of VwK-PSO as a practical and scalable tool for addressing stochastic optimization problems, demonstrating that incorporating variable importance into scenario reduction can lead to more efficient and reliable decision-making in uncertain environments.

Keywords

Optimization, Scenario reduction, Particle swarm optimization, Metaheuristic, Two-stage stochastic programming