The Optimal Transfer Pathway Problem: Optimizing Course Equivalency and Prerequisite Compliance for Seamless Transfer Between Community Colleges and Universities

Abstract

This thesis delves into the Optimal Transfer Pathway (OTP) problem, a pivotal computational challenge in higher education that aims to create efficient transfer roadmaps for students transitioning from community colleges to universities. The OTP problem seeks to minimize total credit hours while ensuring students can earn both associate’s and bachelor’s degrees. We begin by analyzing the computational complexity of the OTP problem, revealing it to be N P -complete and highlighting the inherent difficulty of solving large-scale instances.To tackle this complexity, we first examine the Integer Quadratic Programming (IQP) ap- proach. This approach guarantees an optimal solution but often requires substantial com- putational time, especially for large-scale datasets. This limitation makes the IQP algorithm impractical for real-time applications in student advising and academic planning. In response to these challenges, we introduce the Iterative Course Swapping (ICS) algorithm, a heuristic approach that efficiently generates near-optimal solutions. The ICS algorithm seamlessly integrates degree requirements from both institutions, available courses, articula- tion agreements, and prerequisite information. It produces valid transfer pathways that sat- isfy all degree requirements, respect course prerequisites, and maintain the proper sequence of community college and university courses. Importantly, the ICS algorithm’s time com- plexity is significantly improved over the IQP approach. To evaluate the performance and computational efficiency of both the ICS and IQP algo- rithms, we conducted experiments using real-world data from Pima Community College and the University of Arizona. The results demonstrate that both algorithms significantly improve credit transfer efficiency, leading to higher credit retention rates and reduced time to degree completion. The ICS algorithm excels in computational performance, generating transfer pathways more quickly and effectively than previous approaches, particularly for large datasets. While the IQP algorithm guarantees an optimal solution, developing a trans- fer plan often requires more time, rendering it impractical for large-scale datasets. This trade- off between optimality and computational efficiency highlights the potential of the ICS algo- rithm for real-world applications, where timely solutions are crucial for student advising and academic planning. This research contributes to developing more equitable and efficient transfer systems, ulti- mately facilitating smoother transitions between community colleges and universities. The broader implications include promoting higher graduation rates and reducing student finan- cial burdens. This work lays the foundation for future research in optimizing educational pathways and demonstrates the value of applying computational approaches to complex ed- ucational challenges.