Development of interval and non-interval methods for solving multi-objective optimization problems

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dc.contributorSun, Min
dc.contributorWang, James L.
dc.contributorZhu, Wei
dc.contributorChen, Yuhui
dc.contributorLi, Shuhui
dc.contributor.advisorSun, Min
dc.contributor.authorLiu, Sijie
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2018-07-11T16:49:47Z
dc.date.available2018-07-11T16:49:47Z
dc.date.issued2018
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractMulti-objective optimization problems are pervasive across many diverse disciplines in engineering, economics, management and design where optimal decisions need to be made in the presence of tradeoffs between two or more conflicting objectives with respect to a set of decisions and subject to a set of constraints (Awad and Khanna 2015). The interval method (as a non-scalarization MOP method) is known as a precise and robust tool for optimization that guarantees to capture all points on the Pareto-front (Kubica and Woźniak 2007) . This research investigated the interval and non-interval methods for multi-objective optimization problems with or without constraints. The underlying framework for our improved interval methods are standard Hansen method and Big Cube and Small Cube method. Listed below are some strategies we have developed: a) Twin interval arithmetic is proposed in an effort to improve the quality of estimates for the range of functions. The main use of twin interval arithmetic (TIA) in the improved interval algorithms is to provide an extra choice for the cut-off value in the discarding process. b) Exclusion zone functions are introduced to further reduce variables' intervals which can be added as a reduction step in the standard Hansen method. c) For constrained global optimization problems with two linear constraints, we outlined a steepest descent procedure to locate a feasible sample point within the framework of Hansen method. d) A hybrid BCSC algorithm supported by the three above-mentioned strategies is described in Chapter 3. A refined sampling step is introduced to the BCSC algorithm and this algorithm was marked as original BCSC for comparison in Chapter 3. Numerical results with respect to each strategy are illustrated to show its effectiveness in Chapter 3. Three non-interval multi-objective linear programming (MOLPs) algorithms are presented in Chapter 4. Numerical examples are used to test their effectiveness. Developing their extensions for solving non-linear optimization systems after linearization would be a part of future work.en_US
dc.format.extent159 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0002999
dc.identifier.otherLiu_alatus_0004D_13373
dc.identifier.urihttp://ir.ua.edu/handle/123456789/3684
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleDevelopment of interval and non-interval methods for solving multi-objective optimization problemsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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