Norm minimization-based convex vector optimization algorithms
| buir.advisor | Ulus, Firdevs | |
| dc.contributor.author | Umer, Muhammad | |
| dc.date.accessioned | 2022-09-02T06:58:24Z | |
| dc.date.available | 2022-09-02T06:58:24Z | |
| dc.date.copyright | 2022-08 | |
| dc.date.issued | 2022-08 | |
| dc.date.submitted | 2022-09-01 | |
| dc.department | Department of Industrial Engineering | en_US |
| dc.description | Cataloged from PDF version of article. | en_US |
| dc.description | Thesis (Ph.D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2022. | en_US |
| dc.description | Includes bibliographical references (pages 96-102). | en_US |
| dc.description.abstract | This thesis is concerned with convex vector optimization problems (CVOP). We propose an outer approximation algorithm (Algorithm 1) for solving CVOPs. In each iteration, the algorithm solves a norm-minimizing scalarization for a reference point in the objective space. The idea is inspired by some Benson-type algorithms in the literature that are based on Pascoletti-Serafini scalarization. Since this scalarization needs a direction parameter, the efficiency of these algorithms depend on the selection of the direction parameter. In contrast, our algorithm is free of direction biasedness since it solves a scalarization that is based on minimizing a norm. However, the structure of such algorithms, including ours, has some built-in limitation which makes it difficult to perform convergence analysis. To overcome this, we modify the algorithm by introducing a suitable compact subset of the upper image. After the modification, we have Algorithm 2 in which norm-minimizing scalarizations are solved for points in the compact set. To the best of our knowledge, Algorithm 2 is the first algorithm for CVOPs, which is proven to be finite. Finally, we propose a third algorithm for the purposes of con-vergence analysis (Algorithm 3), where a modified norm-minimizing scalarization is solved in each iteration. This scalarization includes an additional constraint which ensures that the algorithm deals with only a compact subset of the upper image from the beginning. Besides having the finiteness result, Algorithm 3 is the first CVOP algorithm with an estimate of a convergence rate. The experimental results, obtained using some benchmark test problems, show comparable performance of our algorithms with respect to an existing CVOP algorithm based on Pascoletti-Serafini scalarization. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.description.statementofresponsibility | by Muhammad Umer | en_US |
| dc.format.extent | xi, 102 leaves ; 30 cm. | en_US |
| dc.identifier.itemid | B161241 | |
| dc.identifier.uri | http://hdl.handle.net/11693/110486 | |
| dc.language.iso | English | en_US |
| dc.publisher | Bilkent University | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Convex vector optimization | en_US |
| dc.subject | Multiobjective optimization | en_US |
| dc.subject | Approxima-tion algorithm | en_US |
| dc.subject | Scalarization | en_US |
| dc.subject | Norm minimization | en_US |
| dc.title | Norm minimization-based convex vector optimization algorithms | en_US |
| dc.title.alternative | Norm enküçüklemeye dayalı dışbükey vektör eniyileme algoritmaları | |
| dc.type | Thesis | en_US |