We are pleased to congratulate Mindaugas Kepalas, the new Doctor of Natural Sciences in the field of Informatics, who has successfully defended his doctoral dissertation “Searching for Global Solutions of Constrained Location Problems.”
Dr Mindaugas Kepalas and Prof. Dr Julius Žilinskas
The dissertation investigates complex constrained location problems and proposes new, efficient algorithms for real-world spatial placement tasks. The research focuses on three main mathematical models: equal-area Voronoi tessellation, net-constrained clustering, and the multi-Weber problem with physical obstacles.
Key results include:
- For the constrained equal-area Voronoi problem, the proposed algorithm finds high-quality solutions for instances with up to 50 Voronoi points.
- For net-constrained clustering, the branch-and-bound algorithm solves problems that are infeasible for commercial solvers – reducing computation time from years to approximately one hour.
- For the multi-Weber problem with barriers, the algorithm successfully finds global solutions for some instances for the first time.
These findings have practical applications in infrastructure planning, logistics, engineering, and other areas requiring optimal placement of objects. Notably, this dissertation is the first to report global solutions for such classes of constrained location problems at this scale, marking a significant contribution to the field of global optimization.
The dissertation was conducted during 2020–2025 at the Faculty of Mathematics and Informatics, Vilnius University, which carries out doctoral studies in informatics, informatics engineering, and mathematics science fields.
Scientific Supervisor – Prof. Dr Julius Žilinskas.
Dissertation Defense Board:
Academician Prof. Dr Olga Kurasova – Chairperson (Vilnius University)
Assoc. Prof. Dr Algirdas Lančinskas (Vilnius University)
Prof. Dr Audris Mockus (University of Tennessee, USA)
Prof. Dr Remigijus Paulavičius (Vilnius University)
Prof. Dr Dmitrij Šešok (Vilnius Gediminas Technical University)
1 April 2026