Developing novel and efficient binary quadratic optimization methodologies

点击翻译按钮获取中文摘要

Optimization is a branch of Operations Research which appears as an important tool in decision science and in the analysis of physical systems. It has applications in all branches of Science, Engineering and Management. Over the past few decades, the development of modeling and algorithmic techniques of discrete optimization have proved to be very useful in the support of decision making problems in many areas such as, transportation, logistics, banking and manufacturing. Many problems belonging to the family of discrete optimization are still challenging to solve. In fact, the efficiency of existing algorithms is often limited to problems with a small or medium number of decision variables, while most practical cases come with a large number of variables. The long term goal of my discovery research program is to investigate novel and efficient solution methodologies for the class of Binary Quadratic Optimization (BQO) problems and deploy them to solve real life problems of practical large sizes. Indeed, BQO is a special class of discrete optimization, which amounts to optimize a quadratic objective function of binary decision variables subject to a set of linear constraints. Some applications of BQO include portfolio optimization, projects selection, sustainable development, facilities location and vehicle routing problems. BQO problems are known to be very challenging to solve due to the non-linear nature of their objective functions and the discrete nature of their decision variables. The short term goals of my research program will focus on the following three specific research areas: 1) Firstly, I will focus on the development of novel efficient solution methods for some sub-classes of BQO problems for which the existing state-of-the-art solution algorithms can only handle small and medium size problems. I aim to develop a branch-and-cut framework that can handle large scale problems. 2) Secondly, I will investigate the dynamic versions of two practical applications that are specific to some sub-classes of BQO. The aim will then be to propose appropriate optimization models and effective solution algorithms. 3) Finally, the third area of my research program will focus on deploying BQO solution methodologies to problems in energy markets with the specific aim of solving equilibrium problems of large practical sizes. My research program will be expected to serve the research community by providing solution tools for BQO problems that could not be solved previously. It will also serve practioners and the broader society by providing some insights into some societal problems with more realistic considerations. More importantly, I plan to train HQPs with various skill sets that will enable them to pursue a successful career both in research and in industry for further impacts. My priority will be to increase the representativeness of visible minority HQPs into the Operations Research's ecosystem in Canada.