One Algorithm to Rule Them All

This report addresses the challenge of determining optimal mentor-mentee pairings for the University of Delaware’s GradLEAP program. Two mathematical models are developed—a linear programming approach solved using the Hungarian Method, and a stable marriage formulation solved via the Gale-Shapley algorithm. Compatibility scores, calculated using responses to a structured survey, incorporate both weighted and uniform criteria such as academic discipline, career interests, and age preferences. A revised survey introduces a Likert scale for ranking preferences, allowing for greater flexibility in determining weights and improving match quality. The performance of both models is evaluated using real and synthetically generated data, with results indicating that the Hungarian Method yields more consistent matches while the Gale-Shapley method is more likely to produce highly compatible pairings. The study also explores classification models using decision trees and random forests, with an eye toward future development of regression-based scoring systems. The final deliverables include a restructured survey, a user-friendly executable program, and documentation for use in future iterations of the GradLEAP program.