Robust optimization: Difference between revisions

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== History ==

The origins of robust optimization date back to the establishment of modern [[decision theory]] in the 1950s and the use of '''worst case analysis''' and [[Wald's maximin model]] as a tool for the treatment of severe uncertainty. It became a discipline of its own in the 1970s with parallel developments in several scientific and technological fields. Over the years, it has been applied in [[statistics]], but also in [[operations research]],<ref>{{cite journal|last=Bertsimas|first=Dimitris|author2=Sim, Melvyn |title=The Price of Robustness|journal=Operations Research|year=2004|volume=52|issue=1|pages=35–53|doi=10.1287/opre.1030.0065|hdl=2268/253225 |s2cid=8946639 |hdl-access=free}}</ref> [[electrical engineering]],<ref>{{Cite journal |last1=Giraldo |first1=Juan S. |last2=Castrillon |first2=Jhon A. |last3=Lopez |first3=Juan Camilo |last4=Rider |first4=Marcos J. |last5=Castro |first5=Carlos A. |date=July 2019 |title=Microgrids Energy Management Using Robust Convex Programming |url=https://ieeexplore.ieee.org/document/8424876 |journal=IEEE Transactions on Smart Grid |volume=10 |issue=4 |pages=4520–4530 |doi=10.1109/TSG.2018.2863049 |bibcode=2019ITSG...10.4520G |s2cid=115674048 |issn=1949-3053}}</ref><ref name="VPP Robust 2015">{{Cite journal| title = The design of a risk-hedging tool for virtual power plants via robust optimization approach | journal= Applied Energy | date = October 2015 | doi = 10.1016/j.apenergy.2015.06.059 | author = Shabanzadeh M | volume = 155 | pages = 766–777 | last2 = Sheikh-El-Eslami | first2 = M-K |last3 = Haghifam | first3 = P|last4 = M-R| bibcode= 2015ApEn..155..766S }}</ref><ref name="RO2015">{{Cite book| pages= 1504–1509 | date = July 2015 | doi = 10.1109/IranianCEE.2015.7146458 | author = Shabanzadeh M | last2 = Fattahi | first2 = M | title= 2015 23rd Iranian Conference on Electrical Engineering | chapter= Generation Maintenance Scheduling via robust optimization | isbn= 978-1-4799-1972-7 | s2cid= 8774918 }}</ref> [[control theory]],<ref>{{cite journal|last=Khargonekar|first=P.P.|author2=Petersen, I.R. |author3=Zhou, K. |title=Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory|journal=IEEE Transactions on Automatic Control|volume=35|issue=3|pages=356–361|doi=10.1109/9.50357|year=1990}}</ref> [[finance]],<ref>[https://books.google.com/books?id=p6UHHfkQ9Y8C&dq=economics%20robust%20optimization&pg=PR11 Robust portfolio optimization]</ref> [[Investment management|portfolio management]]<ref>Md. Asadujjaman and Kais Zaman, "Robust Portfolio Optimization under Data Uncertainty" 15th National Statistical Conference, December 2014, Dhaka, Bangladesh.</ref> [[logistics]],<ref>{{cite journal|last=Yu|first=Chian-Son|author2=Li, Han-Lin |title=A robust optimization model for stochastic logistic problems|journal=International Journal of Production Economics|volume=64|issue=1–3|pages=385–397|doi=10.1016/S0925-5273(99)00074-2|year=2000}}</ref> [[manufacturing engineering]],<ref>{{cite journal|last=Strano|first=M|title=Optimization under uncertainty of sheet-metal-forming processes by the finite element method|journal=Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture|volume=220|issue=8|pages=1305–1315|doi=10.1243/09544054JEM480|year=2006|s2cid=108843522}}</ref> [[chemical engineering]],<ref>{{cite journal|last=Bernardo|first=Fernando P.|author2=Saraiva, Pedro M. |title=Robust optimization framework for process parameter and tolerance design|journal=AIChE Journal|year=1998|volume=44|issue=9|pages=2007–2017|doi=10.1002/aic.690440908|bibcode=1998AIChE..44.2007B |hdl=10316/8195|hdl-access=free}}</ref> [[medicine]],<ref>{{cite journal|last=Chu|first=Millie|author2=Zinchenko, Yuriy |author3=Henderson, Shane G |author4= Sharpe, Michael B |title=Robust optimization for intensity modulated radiation therapy treatment planning under uncertainty|journal=Physics in Medicine and Biology|year=2005|volume=50|issue=23|pages=5463–5477|doi=10.1088/0031-9155/50/23/003|pmid=16306645|bibcode=2005PMB....50.5463C |s2cid=15713904 }}</ref> and [[computer science]]. In [[engineering]] problems, these formulations often take the name of "Robust Design Optimization", RDO or "Reliability Based Design Optimization", RBDO.

== Example 1==

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*{{cite journal | last1 = Bertsimas | first1 = D. | last2 = Sim | first2 = M. | year = 2003 | title = Robust Discrete Optimization and Network Flows | journal = Mathematical Programming | volume = 98 | issue = 1–3| pages = 49–71 | doi=10.1007/s10107-003-0396-4| citeseerx = 10.1.1.392.4470 | s2cid = 1279073 }}

*{{cite journal | last1 = Bertsimas | first1 = D. | last2 = Sim | first2 = M. | year = 2006 | title = Tractable Approximations to Robust Conic Optimization Problems Dimitris Bertsimas | journal = Mathematical Programming | volume = 107 | issue = 1| pages = 5–36 | doi=10.1007/s10107-005-0677-1| citeseerx = 10.1.1.207.8378 | s2cid = 900938 }}

*{{cite journal | last1 = Chen | first1 = W. | last2 = Sim | first2 = M. | year = 2009 | title = Goal Driven Optimization | journal = Operations Research | volume = 57 | issue = 2| pages = 342–357 | doi=10.1287/opre.1080.0570 | url = http://scholarbank.nus.edu.sg/handle/10635/43946 }}

*{{cite journal | last1 = Chen | first1 = X. | last2 = Sim | first2 = M. | last3 = Sun | first3 = P. | last4 = Zhang | first4 = J. | year = 2008 | title = A Linear-Decision Based Approximation Approach to Stochastic Programming | journal = Operations Research | volume = 56 | issue = 2| pages = 344–357 | doi=10.1287/opre.1070.0457}}

*{{cite journal | last1 = Chen | first1 = X. | last2 = Sim | first2 = M. | last3 = Sun | first3 = P. | year = 2007 | title = A Robust Optimization Perspective on Stochastic Programming | journal = Operations Research | volume = 55 | issue = 6| pages = 1058–1071 | doi=10.1287/opre.1070.0441 | url = http://scholarbank.nus.edu.sg/handle/10635/44052 }}

*{{cite journal | last1 = Dembo | first1 = R | year = 1991 | title = Scenario optimization | journal = Annals of Operations Research | volume = 30 | issue = 1| pages = 63–80 | doi=10.1007/bf02204809| s2cid = 44126126 }}

* Dodson, B., Hammett, P., and Klerx, R. (2014) ''Probabilistic Design for Optimization and Robustness for Engineers'' John Wiley & Sons, Inc. {{ISBN|978-1-118-79619-1}}