Computational Optimization and Data-Driven Decision Methods
Dr. Francis J. Vasko, Dr. Amy Lu, and Dr. Myung Soon Song conduct research in combinatorial optimization, operations research, and machine learning, with a focus on developing practical computational approaches for solving large-scale decision problems.
Many real-world decision problems can be formulated as binary integer programming problems (BIPP) or related combinatorial optimization models. These problems arise in applications such as logistics planning, resource allocation, facility location, and network design. While such problems are mathematically well-defined, solving them efficiently for large instances typically found in business and industrial applications can be computationally challenging.
Recent research by Dr. Vasko, Dr. Lu, and Dr. Song investigates how modern general-purpose integer programming solvers, such as Gurobi, can be used effectively to solve these problems on standard personal computers. Through extensive computational experiments involving tens of thousands of optimization instances, their research examines the conditions under which exact optimization methods can obtain optimal or near-optimal solutions within acceptable execution times. This makes this work different from that of many other researchers who develop complex metaheuristics that typically do not provide guarantees on solution quality.
These studies show that many binary integer programming problems can be solved to proven optimality using modern solvers with default parameter settings. When default settings are insufficient, carefully tuning solver parameters or adjusting termination tolerances during the solution process can often produce high-quality solutions that are guaranteed to be close to optimal. In some cases, incorporating heuristically generated initial solutions can further improve solver performance. Combining these strategies can provide an effective framework for solving difficult optimization problems in practice.
A central aspect of this research is the use of large-scale computational experiments combined with statistical and machine learning methods to evaluate and understand the performance of different solution approaches. By studying thousands of optimization instances and computational results, this work aims to provide practical guidance for operations research practitioners on how modern optimization software and data-driven methods can be used effectively to solve complex decision problems.
Earlier research by Dr. Vasko and collaborators explored metaheuristic approaches for combinatorial optimization, while more recent work by Dr. Vasko, Dr. Lu, and Dr. Song emphasizes the integration of exact optimization methods, machine learning, computational experimentation, and statistical evaluation of algorithms.
