Grant: Discovery Grants Program - Individual

Given the recent trends in evidence-based and personalized decision making, powerful data-driven modeling approaches are needed to obtain personalized optimal intervention plans for practical engineering problems. We propose developing novel engineering tools based on stochastic dynamic programming and integer programming to address practical decision making problems. While proposed research will be applied to cancer screening and treatment, the main focus is on developing engineering methodology. We will investigate the applications of large-scale stochastic dynamic programming and integer programming methods in cancer screening and treatment. These application areas are rich with operational problems that potentially provide valuable feedback on limitations of the proposed methodologies, thus opening new avenues in these methodological domains. In particular, sequential decision making problems will be formulated as stochastic dynamic programming models (e.g., partially observable Markov decision process models), and deriving structural properties of the optimal solutions, and exploiting those properties to find efficient solution methods for these models will be explored. Moreover, various decomposition schemes will be proposed for the large-scale integer programming formulations encountered in these application problems. Theme 1 of the program will focus on developing novel methods that can overcome modeling and algorithmic challenges in stochastic dynamic programming. We will investigate personalized cancer screening and treatment problems, and test the viability of the proposed solution methods. Using clinical data from the literature and our collaborators, we will apply these methods to determine optimal policies for cancer screening and treatment. The proposed methodology may help develop insights to improve and personalize cancer screening and treatment practices, yielding a significant contribution as cancer is a leading cause of death in Canada. The proposed approach will also improve the engineering knowledge on stochastic dynamic programming for other engineering applications. Theme 2 of the program will explore large-scale discrete optimization models that arise in radiation therapy treatment planning. Specifically, we will investigate fluence map optimization and decomposition in intensity modulated radiation therapy and sector duration optimization in radiosurgery, which lack efficient solution methods for practical instances. We will develop novel optimization models for these problems and explore the effectiveness of new solution methodologies such as decision diagrams. The results will provide valuable planning, scheduling and operational tools for decision makers. The proposed research will be extended to consider more general settings.