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Title:REŠEVANJE MEŠANO CELOŠTEVILSKIH NELINEARNIH PROBLEMOV Z DEKOMPOZICIJSKIMI IN RELAKSACIJSKIMI METODAMI
Authors:ID Čuček, Šolasta (Author)
ID Novak Pintarič, Zorka (Mentor) More about this mentor... New window
ID Kravanja, Zdravko (Comentor)
Files:.pdf UN_Cucek_Solasta_2016.pdf (1,74 MB)
MD5: DD5FF18E622168135BC911C396D25762
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FKKT - Faculty of Chemistry and Chemical Engineering
Abstract:Diplomsko delo obravnava razvoj optimizacijskih metod v strukturi mešano celoštevilskega linearnega programiranja in tudi zahtevnejšega mešano celoštevilskega nelinearnega programiranja, katerega razvoj se je začel v šestdesetih letih 20. stoletja. Optimizacijske metode se danes razvijajo zelo hitro, prav tako njihova uporaba v kemijski tehniki, in sicer v sistemski procesni tehniki, ki se neprestano dopolnjuje. Hkrati razvoj optimizacijskih metod predstavlja izziv za znanstvenike na področju matematičnega programiranja, gradbeništva, elektrotehnike, managementa in seveda kemijske tehnologije. Zaradi razvoja optimizacijskih metod sta v diplomskem delu obravnavani dve metodi, in sicer splošna Bendersova dekompozicija in zunanja poenostavitev s sprostitvijo enačb v strukturah mešano celoštevilskega (ne)linearnega programiranja. Prikazana, opisana in rešena sta dva primera za vsako strukturo. Na podlagi števila iteracij je bilo ugotovljeno, da potrebujejo relaksacijske metode manj iteracij in krajši računalniški čas kot izbrana dekompozicijska metoda, s čimer je bila zastavljena hipoteza potrjena.
Keywords:optimizacijske metode, mešano celoštevilsko linearno programiranje, mešano celoštevilsko nelinearno programiranje, splošna Bendersova dekompozicija, modeliranje, procesna sistemska tehnika
Place of publishing:Maribor
Publisher:[Š. Čuček]
Year of publishing:2016
PID:20.500.12556/DKUM-63614 New window
UDC:519.853:66.011(043.2)
COBISS.SI-ID:20334614 New window
NUK URN:URN:SI:UM:DK:2IKJUZYR
Publication date in DKUM:25.10.2016
Views:1734
Downloads:138
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:KTFMB - FKKT
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Secondary language

Language:English
Title:SOLVING MIXED INTEGER NONLINEAR PROBLEMS USING DECOMPOSITION AND RELAXATION METHODS
Abstract:This diploma work deals with the development of optimization methods in the structure of mixed integer linear programming and also more difficult mixed integer nonlinear programming, whose development started in the sixties of the 20th century. Optimization methods are nowadays developing very fast, and also their use in chemical engineering, particularly in process systems engineering, which is constantly advancing. The development of optimization methods at the same time presents a challenge for scientists in the fields of mathematical programming, civil engineering, electrical engineering, management and also chemical engineering. Due to the development of optimization methods, this diploma work deals with two of the methods, General Benders Decomposition and outer approximation with equality relaxation in the structures of mixed integer (non)linear programming. Those two methods are described in more details, and demonstrated by two examples for each structure. It was found, based on the number of iterations that relaxation methods need less iterations and shorter computational time than selected decomposition method. The hypothesis was thus confirmed.
Keywords:optimization methods, mixed integer linear programming, mixed integer nonlinear programming, General Benders decomposition, modelling, process systems engineering


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