Techniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition

dc.contributor.advisor Boland, Natashia
dc.contributor.author Perini, Tyler Anthony
dc.contributor.committeeMember Savelsbergh, Martin
dc.contributor.committeeMember Dey, Santanu
dc.contributor.committeeMember Van Hentenryck, Pascal
dc.contributor.committeeMember Langville, Amy
dc.contributor.department Industrial and Systems Engineering
dc.date.accessioned 2021-09-15T15:41:31Z
dc.date.available 2021-09-15T15:41:31Z
dc.date.created 2021-08
dc.date.issued 2021-06-17
dc.date.submitted August 2021
dc.date.updated 2021-09-15T15:41:31Z
dc.description.abstract Many real-world applications involve multiple competing objectives, but due to conflict between the objectives, it is generally impossible to find a feasible solution that optimizes all, simultaneously. In contrast to single objective optimization, the goal in multiobjective optimization is to generate a set of solutions that induces the nondominated (ND) frontier. This thesis presents two techniques for multiobjective optimization problems with discrete decision variables. First, the Boxed Line Method is an exact, criterion space search algorithm for biobjective mixed integer programs (Chapter 2). A basic version of the algorithm is presented with a recursive variant and other enhancements. The basic and recursive variants permit complexity analysis, which yields the first complexity results for this class of algorithms. Additionally, a new instance generation method is presented, and a rigorous computational study is conducted. Second, a novel weight space decomposition method for integer programs with three (or more) objectives is presented with unique geometric properties (Chapter 3). The weighted Tchebychev scalarization used for this weight space decomposition provides the benefit of including unsupported ND images but at the cost of convexity of weight set components. This work proves convexity-related properties of the weight space components, including star-shapedness. Further, a polytopal decomposition is used to properly define dimension for these nonconvex components. The weighted Tchebychev weight set decomposition is then applied as a “dual” perspective on the class of multiobjective “primal” algorithms (Chapter 4). It is shown that existing algorithms do not yield enough information for a complete decomposition, and the necessary modifications required to yield the missing information is proven. Modifications for primal algorithms to compute inner and outer approximations of the weight space components are presented. Lastly, a primal algorithm is restricted to solving for a subset of the ND frontier, where this subset represents the compromise between multiple decision makers’ weight vectors.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/65037
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject multiobjective optimization
dc.subject discrete optimization
dc.subject weight set decomposition
dc.subject criterion space search
dc.title Techniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
thesis.degree.level Doctoral
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