Dr. Lakmali Weeraena, Assistant Professor in Mathematics in the UTC Department of Mathematics, has been awarded a 1-year, $8799.00, Faculty Pre-Tenure Enhancement Program (PREP) grant from the Office of Research and Sponsored programs at UTC. Her research interests focus on (1) Developing methods to compute and approximate solutions of multi-objective optimization problems (MOPs); (2) Theoretical analysis resulting from the approximation of solution sets of MOPs; and 3) Develop mathematical models for applications in fields such as engineering, conservation biology, and management. With the support of this grant, Dr. Weerasena will study the multi-objective mathematical models in conservation biology.
Dr. Weerasena’s grant is entitled a multi-objective (MO) optimization approach for designing a connected reserve system for conservation biology. The project consists of an inter-disciplinary effort with a community partner (Reflection Riding Arboretum and Nature Center is a nonprofit arboretum, botanical garden, nature center). Conservation biologists and wildlife managers are challenged with designing protected area networks optimal for biodiversity conservation. Although the protection of extensive wildlands with the full assemblage of native species in large population sizes is the ecologically prudent solution, such targets are unrealistic due to limitations in funds and other resources. The development of conservation prioritization methods is imperative so that limited lands can be eﬀectively used for biodiversity conservation. These prioritization methods should ensure the long-term protection of biological species. In this project Dr. Weerasena develops a multi-objective mathematical model to simultaneously optimize availability of species (plants/animals) and distance between reserve sites by designing a totally connected reserve system subject to a fixed budgetary restriction. The solutions of MOPs is driven by the concept of Pareto optimality. Finding the Pareto set is a challenging task because even if Pareto points can be theoretically characterized, their computation is often computationally expensive. Many MOPs in conservation biology follow a combinatorial structure, thus computing the Pareto set become a challenging task. Therefore, another goal of this project is to develop an efficient algorithm to compute Pareto set of the new model.
This project has substantial educational and outreach components. It will advance understanding both in the philosophy of efficient algorithms in MO and in the application of such theoretical frameworks in real-life problem solving. When selecting students for the project, priority will be given to those from groups underrepresented in STEM.