Developing novel and efficient binary quadratic optimization methodologies

最优化是运筹学的一个分支，是决策科学和物理系统分析的重要工具。它适用于科学、工程和管理的所有分支。在过去的几十年里，离散优化的建模和算法技术的发展已被证明是非常有用的，在许多领域，如运输，物流，银行和制造业的决策问题的支持。许多问题属于离散优化的家庭仍然是具有挑战性的解决。事实上，现有算法的效率通常仅限于具有少量或中等数量的决策变量的问题，而大多数实际情况下具有大量的变量。我的发现研究计划的长期目标是调查新颖和有效的解决方法的类二次优化（BQO）的问题，并部署它们来解决实际的大规模的真实的生活问题。实际上，BQO是一类特殊的离散优化，它相当于优化一组线性约束下的二元决策变量的二次目标函数。BQO的一些应用包括投资组合优化，项目选择，可持续发展，设施选址和车辆路径问题。由于BQO问题的目标函数的非线性和决策变量的离散性，BQO问题的求解具有很大的挑战性。我的研究计划的短期目标将集中在以下三个具体的研究领域：1）首先，我将专注于开发新的有效的解决方法，为一些子类的BQO问题，现有的国家的最先进的解决方案的算法只能处理小型和中型的问题。我的目标是开发一个可以处理大规模问题的分支和切割框架。 2)其次，我将研究特定于BQO的一些子类的两个实际应用程序的动态版本。目标是提出适当的优化模型和有效的求解算法。3)最后，我的研究计划的第三个领域将集中在部署BQO解决方案的方法，以解决大规模的实际规模的均衡问题的具体目标，在能源市场的问题。我的研究计划将有望通过为以前无法解决的BQO问题提供解决方案工具来服务于研究社区。它还将为从业者和更广泛的社会提供一些更现实的考虑，对一些社会问题的见解。更重要的是，我计划培训具有各种技能的HQP，使他们能够在研究和行业中追求成功的职业生涯，以产生进一步的影响。我的首要任务是增加可见少数HQP的代表性，使其进入加拿大运筹学的生态系统。

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.