联合机会约束问题的鲁棒近似模型

丁然; 李国祥; 李歧强

doi:10.16383/j.aas.2015.e130268

联合机会约束问题的鲁棒近似模型

doi: 10.16383/j.aas.2015.e130268

1.
山东大学控制科学与工程学院济南 250061
2.
山东大学能源与动力工程学院济南 250061

基金项目:

Supported by Shandong Provincial Natural Science Foundation, China (ZR2014FM036)

计量
- 文章访问数: 1559
- HTML全文浏览量: 97
- PDF下载量: 913
- 被引次数: 0
出版历程
- 收稿日期: 2013-10-10
- 修回日期: 2014-12-31
- 刊出日期: 2015-10-20

Robust Approximations to Joint Chance-constrained Problems

1.
School of Control Science and Engineering, Shandong University, Jinan 250061, China;
2.
School of Energy and Power Engineering, Shandong University, Jinan 250061, China

Funds:

Supported by Shandong Provincial Natural Science Foundation, China (ZR2014FM036)

摘要

摘要: 针对联合机会约束优化问题提出了两种新的近似模型. 回顾了CVaR (conditional-value-at-risk 条件风险价值) 、机会约束和鲁棒优化之间的关系之后, 提出了两种新的E((.)+) 的上界, 其中E表示期望, x+ = max(0,x) , 然后以此为基础推出了两种针对独立机会约束问题的近似模型, 并证明了这两种近似模型就是对应相应不确定集合的鲁棒优化模型, 然后推出了针对联合机会约束问题的近似模型. 最后举例对所提出的独立机会约束和联合机会约束的鲁棒近似模型的解进行了对比, 结果说明了所提出方法的有效性.
- 联合机会约束 /
- 鲁棒优化 /
- 不确定集合 /
- 近似
Abstract: Two new approximate formulations to joint chance-constrained optimization problems are proposed in this paper. The relationships of CVaR (conditional-value-at-risk), chance constrains and robust optimization are reviewed. Firstly, two new upper bounds on E(()+) are proposed, where E stands for the expectation and x+=max(0;x), based on which two approximate formu- lations for individual chance-constrained problems are derived. The approximations are proved to be the robust optimization with the corresponding uncertain sets. Then the approximations are extrapolated to joint chance-constrained problem. Finally numerical studies are performed to compare the solutions of individual and joint chance constraints approximations and the results demonstrate the validity of our method.
- Joint chance constraints /
- robust optimization /
- uncertain set /
- approximation

HTML全文

参考文献(15)

[1]	Charnes A, Cooper W W, Symonds G H. Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Management Science, 1958 4(3): 69-83
[2]	[2] Calasfoire G, Ghaoui L E. On distributionally robust chance-constrained linear programs. Journal of Optimization Theory and Applications, 2006, 130(1): 1-22
[3]	[3] Prekopa A. Stochastic Programming. Dordrecht: Kluwer, 1995
[4]	[4] Soyster A L. Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 1973, 21(5): 1154-1157
[5]	[5] Ben-Tal A, Nemirovski A. Robust convex optimization. Operations Research, 1998, 23(4): 769-805
[6]	[6] Ben-Tal A, Nemirovski A. Robust solutions to uncertain programs. Operations Research Letters, 1999, 25(1): 1-13
[7]	[7] Bertsimas D, Sim M. The price of robustness. Operations Research, 2004, 52(1): 35-53
[8]	[8] Bertsimas D, Pachamanova D, Sim M. Robust linear optimization under general norms. Operations Research Letters, 2004, 32(6): 510-516
[9]	[9] Li Z K, Ding R, Floudas C A. A comparative theoretical and computational study on robust counterpart optimization: I. Robust linear optimization and robust mixed integer linear optimization. Industrial and Chemistry Research, 2011, 50(18): 10567-10603
[10]	Li Z K, Tang Q H, Floudas C A. A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Industrial and Chemistry Research, 2012, 51(19): 6769-6788
[11]	Ben-Tal A, Teboulle M. Expected utility, penalty functions and duality in stochastic nonlinear programming. Management Science, 1986, 32(11): 1445-1466
[12]	Chen W Q, Sim M. Goal driven optimization. Operations Research, 2009, 57(2): 342-357
[13]	Chen W Q, Sim M, Sun J, Teo C P. From CVaR to uncertainty set: implications in joint chance constrained optimization. Operations Research, 2010, 58(2): 470-485
[14]	Ang T M M, Lim Y F, Sim M. Robust storage assignment in unit-load warehouses. Operations Research, 2012, 58(1): 2114-2130
[15]	Gounaris C E, Wiesemann W, Floudas C A. The robust capacitated vehicle routing problem under demand uncertainty. Operations Research, 2013, 61(3): 677-693