Integer programming: Difference between revisions

Revision as of 07:53, 16 July 2024

Revision as of 03:35, 29 July 2024

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* [[Cashflow matching|Cash flow matching]]

* [[Energy system]] optimization<ref>{{Cite journal|last1=Morais|first1=Hugo|last2=Kádár|first2=Péter|last3=Faria|first3=Pedro|last4=Vale|first4=Zita A.|last5=Khodr|first5=H. M.|date=2010-01-01|title=Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming|url=http://www.sciencedirect.com/science/article/pii/S0960148109001001|journal=Renewable Energy|language=en|volume=35|issue=1|pages=151–156|doi=10.1016/j.renene.2009.02.031|bibcode=2010REne...35..151M |issn=0960-1481|hdl=10400.22/1585|hdl-access=free}}</ref><ref>{{Cite journal|last1=Omu|first1=Akomeno|last2=Choudhary|first2=Ruchi|last3=Boies|first3=Adam|date=2013-10-01|title=Distributed energy resource system optimisation using mixed integer linear programming|url=http://www.sciencedirect.com/science/article/pii/S0301421513003418|journal=Energy Policy|language=en|volume=61|pages=249–266|doi=10.1016/j.enpol.2013.05.009|bibcode=2013EnPol..61..249O |s2cid=29369795 |issn=0301-4215}}</ref>

* [[Unmanned aerial vehicle|UAV]] [[Guidance system|guidance]]<ref>{{Cite book|last1=Schouwenaars|first1=T.|last2=Valenti|first2=M.|last3=Feron|first3=E.|last4=How|first4=J.|title=2005 IEEE Aerospace Conference |chapter=Implementation and Flight Test Results of MILP-based UAV Guidance |date=2005|pages=1–13|doi=10.1109/AERO.2005.1559600|isbn=0-7803-8870-4|s2cid=13447718}}</ref><ref>{{Cite journal|last1=Radmanesh|first1=Mohammadreza|last2=Kumar|first2=Manish|date=2016-03-01|title=Flight formation of UAVs in presence of moving obstacles using fast-dynamic mixed integer linear programming|journal=Aerospace Science and Technology|language=en|volume=50|pages=149–160|doi=10.1016/j.ast.2015.12.021|issn=1270-9638|doi-access=free|bibcode=2016AeST...50..149R }}</ref>

* [[Transit map]] [[Graph drawing|layouting]]<ref>{{cite arXiv |last1=Bast |first1=Hannah |last2=Brosi |first2=Patrick |last3=Storandt |first3=Sabine |date=2017-10-05 |title=Efficient Generation of Geographically Accurate Transit Maps |class=cs.CG |eprint=1710.02226 }}</ref>

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| title = 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9–13, 2018, Prague, Czech Republic

| volume = 107

| year = 2018| doi-access = free

| year = 2018}}</ref> that integer programming can be solved in [[strongly polynomial]] and [[fixed-parameter tractable]] time parameterized by <math>a</math> and <math>d</math>. That is, for some computable function <math>f</math> and some constant <math>k</math>, integer programming can be solved in time <math>f(a,d)n^k</math>. In particular, the time is independent of the right-hand side <math>b</math> and objective function <math>c</math>. Moreover, in contrast to the classical result of Lenstra, where the number <math>n</math> of variables is a parameter, here the number <math>n</math> of variables is a variable part of the input.

==See also==