FST Graduate Research Topic

Research Topic: Identifying Key Decisions Points in Optimization Spaces
Suggested By: Jason Bernard
Last Update: January 21st, 2026

We have all made decisions and wondered, what if I made a different choice? How would things be different? Often these thoughts coincide with major decisions. For example, we usually do not contemplate the ramifications of having a different breakfast. In this research, we will be examining the decisions points encountered by optimization algorithms while solving a problem. Optimization problems consist of a bounded N-dimensional space where each dimension represents a problem specific, often encoded, element of the solution. An optimization algorithm explores the space by considering different solutions using some heuristic or technique to decide on what solutions to check next to avoid checking all possible solutions. The application of these heuristics or techniques are decision points as choosing to consider one solution means that another will not be explored (at least not right now). Consider the simple case of where the Mth dimension is a binary choice [0,1]. When constructing a candidate solution must choose either 0 or 1 to check meaning the other choice is not checked. While algorithms employ techniques to balance exploration and exploitation, for the most part, choices are made towards utilizing good solutions over bad under a constructivist ideology. Since only those solutions checked provided information on which to act, every choice affects the choices made afterwards, implying as a result that the optimizer will traverse into some of the space where good solutions are expected, and tend to ignore other regions where poor solutions are expected. A key decision point can be defined in a few different ways, and will be one of the first formal steps for this research; however, broadly, it can be described as at which some area of the problem space become statistically unlikely to be explored by the algorithm, and that may still contain promising solutions under typical scenarios (i.e., ignore unrealistic conditions like needle-in-a-haystack solutions). The goal of this is to identify and utilize key decision points towards improving the exploration-exploitation balance without greatly affecting efficiency. If this sounds of interest to you, then contact me. This research is only open to graduate students. You should have an excellent understanding of machine learning, optimization algorithms and problems, and strong analytical skills. Good Python programming skills is helpful as the current library is in Python.