Optimization approaches to biological invasions and cancer
Spatio-temporal models have been utilized in a wide range of disciplines to describe and predict spatially explicit processes that change over time. One of the various application areas of spatio-temporal models is ecological studies, specifically invasive species management (ISM) over large landscapes where scarce resources, such as budget, can be a limiting factor for controlling biological invasions. Another application area of spatio-temporal models is cancer treatment, where size, growth, and spread of cancer cells are tracked over time. However, the main challenge with spatio-temporal models is the high complexity of the problem in which model size expands exponentially as spatial and temporal dimensions are increased. Furthermore, incorporating growth and spread dynamics of invasive species, or cancer cells, significantly complicates the problem in terms of its solvability and solution time. In this dissertation, we develop new spatio-temporal mathematical models and optimization-based solution algorithms for determining the optimal strategies to control invasive species and cancer growth. Specifically, we present nonlinear, mixed-integer, and stochastic programming models considering the detailed ecological characteristics of invasive species to analyze their economic impacts. In addition, we develop a spatio-temporal model to determine an optimal breast cancer treatment plan and sequence considering surgery, radiation therapy, and chemotherapy in combination with the optimal dose schedules for chemo- and radiotherapy treatments. In order to increase the solvability of the large-scale problems and reduce the solution time for instances that involve higher spatial and temporal dimensions, we develop linearization approaches and new cutting planes. The results of this dissertation provide practical insights into ISM and cancer treatment planning.
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