An Efficient Linearized Optimization Framework for Designing Balanced and Efficient Degree Plans

Designing balanced and optimized degree plans is a fundamental challenge in higher education, directly impacting student success, graduation rates, and institutional efficiency. This paper presents an innovative framework that addresses this challenge through a two-stage optimization approach. The first stage focuses on selecting a set of courses that maximizes requirement satisfaction while minimizing curriculum complexity, characterized by course cruciality values derived from blocking and delay factors. The second stage utilizes an efficient linearized solution to design semester-level degree plans that balance credit loads and difficulty while respecting hierarchical, prerequisite, and corequisite constraints. Unlike traditional methods, which often struggle with computational inefficiency due to quadratic or absolute-value objectives, our approach employs linearization techniques to reformulate these objectives into scalable, solvable linear forms. The proposed methodology is implemented in a practical application, with visualizations demonstrating its usability and effectiveness. Detailed experiments and time complexity analysis validate the framework's scalability and computational efficiency, even for large academic programs. This work provides an essential tool for educators, advisors, and institutions to generate personalized, real-time degree plans, ultimately enhancing student outcomes and institutional planning capabilities.