{"647763":{"#nid":"647763","#data":{"type":"event","title":"PhD Defense by Tyler Perini","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003EThesis Title:\u0026nbsp;\u003C\/strong\u003ETechniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAdvisor:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Natashia Boland, School of Industrial and Systems Engineering, Georgia Tech\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee Members:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Martin Savelsbergh, School of Industrial and Systems Engineering, Georgia Tech\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Santanu Dey, School of Industrial and Systems Engineering, Georgia Tech\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Pascal Van Hentenryck, School of Industrial and Systems Engineering, Georgia Tech\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Amy Langville, Department of Mathematics, The College of Charleston\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EDate and Time:\u0026nbsp;\u0026nbsp;\u003C\/strong\u003EJune 9\u003Csup\u003Eth\u003C\/sup\u003E, 2021 8:00 PM\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EMeeting URL:\u0026nbsp;\u003C\/strong\u003E\u003Ca href=\u0022https:\/\/bluejeans.com\/2975069046\u0022\u003Ehttps:\/\/bluejeans.com\/2975069046\u003C\/a\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ESummary:\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EMany real-world applications involve multiple\u0026nbsp; 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 \u003Cem\u003Eset\u003C\/em\u003E of solutions that induces the \u003Cem\u003Enondominated (ND) frontier\u003C\/em\u003E. This thesis presents two techniques for multiobjective optimization problems with discrete decision variables.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EFirst,\u003C\/strong\u003E 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.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ESecond,\u003C\/strong\u003E 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.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EFinally,\u003C\/strong\u003E the weighted Tchebychev weight set decomposition is then applied as a \u0026ldquo;dual\u0026rdquo; perspective on the class of multiobjective \u0026ldquo;primal\u0026rdquo; 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\u0026#39; weight vectors.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cbr \/\u003E\r\n\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Techniques for Multiobjective Optimization with Discrete Variables: Boxed Line Method and Tchebychev Weight Set Decomposition "}],"uid":"27707","created_gmt":"2021-05-27 13:43:05","changed_gmt":"2021-05-27 13:43:05","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2021-06-09T21:00:00-04:00","event_time_end":"2021-06-09T23:00:00-04:00","event_time_end_last":"2021-06-09T23:00:00-04:00","gmt_time_start":"2021-06-10 01:00:00","gmt_time_end":"2021-06-10 03:00:00","gmt_time_end_last":"2021-06-10 03:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}