Robust optimization: Difference between revisions

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'''Robust optimization''' is a field of [[mathematical optimization]] theory that deals with optimization problems in which a certain measure of robustness is sought against [[uncertainty]] that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution. It is related to, but often distinguished from, [[probabilistic optimization]] methods such as chance-constrained optimization.<ref>https://www{{cite journal | doi=10.mdpi.com3390/1996en15030825 | doi-1073/15/3/825access=free {{Bare| title=Probabilistic Optimization Techniques in Smart Power URLSystem inline| date=August2022 | last1=Riaz | first1=Muhammad | last2=Ahmad | first2=Sadiq | last3=Hussain | first3=Irshad | last4=Naeem | first4=Muhammad | last5=Mihet-Popa | first5=Lucian | journal=Energies | volume=15 | issue=3 | page=825 2024}}</ref><ref>https://people.eecs.berkeley.edu/~elghaoui/Teaching/EE227A/lecture24.pdf {{Bare URL PDF|date=August 2024}}</ref>

== 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 |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==