Optimal robust optimization approximation for chance constrained optimization problem

被引:24
作者
Li, Zhuangzhi [1 ]
Li, Zukui [1 ]
机构
[1] Univ Alberta, Dept Chem & Mat Engn, Edmonton, AB T6G 2V4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Chance constraint; Robust optimization; Uncertainty set; Optimal approximation; CONVEX APPROXIMATIONS; UNCERTAIN DATA; PROGRAMS;
D O I
10.1016/j.compchemeng.2015.01.003
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
Chance constraints are useful for modeling solution reliability in optimization under uncertainty. In general, solving chance constrained optimization problems is challenging and the existing methods for solving a chance constrained optimization problem largely rely on solving an approximation problem. Among the various approximation methods, robust optimization can provide safe and tractable analytical approximation. In this paper, we address the question of what is the optimal (least conservative) robust optimization approximation for the chance constrained optimization problems. A novel algorithm is proposed to find the smallest possible uncertainty set size that leads to the optimal robust optimization approximation. The proposed method first identifies the maximum set size that leads to feasible robust optimization problems and then identifies the best set size that leads to the desired probability of constraint satisfaction. Effectiveness of the proposed algorithm is demonstrated through a portfolio optimization problem, a production planning and a process scheduling problem. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码:89 / 99
页数:11
相关论文
共 25 条
[1]   Optimizing call center staffing using simulation and analytic center cutting-plane methods [J].
Atlason, Julius ;
Epelman, Marina A. ;
Henderson, Shane G. .
MANAGEMENT SCIENCE, 2008, 54 (02) :295-309
[2]   Robust solutions of Linear Programming problems contaminated with uncertain data [J].
Ben-Tal, A ;
Nemirovski, A .
MATHEMATICAL PROGRAMMING, 2000, 88 (03) :411-424
[3]   Robust solutions of uncertain linear programs [J].
Ben-Tal, A ;
Nemirovski, A .
OPERATIONS RESEARCH LETTERS, 1999, 25 (01) :1-13
[4]  
Bernstein Sergei N., 1937, DOKL AKAD NAUK SSSR, V16, P275
[5]   The price of robustness [J].
Bertsimas, D ;
Sim, M .
OPERATIONS RESEARCH, 2004, 52 (01) :35-53
[6]   The scenario approach to robust control design [J].
Calafiore, Giuseppe C. ;
Campi, Marco C. .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (05) :742-753
[7]   COST HORIZONS AND CERTAINTY EQUIVALENTS - AN APPROACH TO STOCHASTIC-PROGRAMMING OF HEATING OIL [J].
CHARNES, A ;
COOPER, WW ;
SYMONDS, GH .
MANAGEMENT SCIENCE, 1958, 4 (03) :235-263
[8]  
Chebyshev P.L., 1867, J. de Math. Pures et Appliquees, V2, P177
[9]   Robust solutions to uncertain semidefinite programs [J].
El Ghaoui, L ;
Oustry, F ;
Lebret, H .
SIAM JOURNAL ON OPTIMIZATION, 1998, 9 (01) :33-52
[10]   Robust solutions to least-squares problems with uncertain data [J].
ElGhaoui, L ;
Lebret, H .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1997, 18 (04) :1035-1064