Partial sample average approximation method for chance constrained problems

• Published in: Optimization letters Vol. 13; no. 4; pp. 657 - 672
• Main Authors: Cheng, Jianqiang, Gicquel, Céline, Lisser, Abdel
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019; Springer Verlag
• Subjects: Computational Intelligence; Computer Science; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operations Research; Operations Research/Decision Theory; Optimization; Original Paper; Simulation; Chance constraints; Stochastic programming; Sampling-based method
• ISSN: 1862-4472; 1862-4480
• DOI: 10.1007/s11590-018-1300-8

In this paper, we present a new scheme of a sampling-based method to solve chance constrained programs. The main advantage of our approach is that the approximation problem contains only continuous variables whilst the standard sample average approximation (SAA) formulation contains binary variables. Although our approach generates new chance constraints, we show that such constraints are tractable under certain conditions. Moreover, we prove that the proposed approach has the same convergence properties as the SAA approach. Finally, numerical experiments show that the proposed approach outperforms the SAA approach on a set of tested instances.