The First-Year Seminar Assignment Problem: A Multi-Objective Optimization Approach

Introduction

Introduction Many colleges and universities have a first-year seminar program, serving as a crucial bridge for new students entering higher education. These seminars introduce the rigors of college-level work through writing assignments, research projects, and classroom discussions. As noted by Jaijairam [2016] and Kudrna et al. [2024], first-year seminars enhance students’ academic skills, critical thinking, and intellectual curiosity, while also fostering a sense of community and belonging. These programs often combine the roles of course instructor and academic advisor, providing students with a more personalized and supportive experience.

Seminar topics typically vary annually, encompassing a wide range of disciplines across the institution. Incoming first-year students receive a list of available seminars, along with detailed course descriptions, and are asked to select and prioritize those that best align with their interests and preferences. Institutions then assign students to seminars, balancing student preferences with course capacities.

While students prefer being placed in one of their higher-ranked seminars, faculty aim to ensure that seminar demographics are roughly representative of the entire student body, creating a microcosm of the college.

Note: The information below was created with the assistance of AI.

1. Level of Mathematics
Target Level:
This work is appropriate for upper-level undergraduate students and graduate students in:

Operations Research

Applied Mathematics

Computer Science

Data Science or Industrial Engineering

Justification:

The model involves multi-objective optimization, integer programming, and convex quadratic programming.

The solution strategies include weighted-sum and hierarchical optimization methods.

Requires understanding of linearization, variance calculations, and Pareto optimality.

2. Application Areas
Primary Application Area:

Higher Education Scheduling & Administration, especially for seminar/class assignments balancing preferences and demographics.

Additional Applications:

Operations Research: Assignment and scheduling problems.

Equity and Diversity Planning: Designing inclusive academic environments by balancing gender and international representation.

Public Policy and Resource Allocation: Frameworks for balancing competing priorities.

Software Development: Algorithms embedded in academic registration platforms or institutional research tools.

3. Prerequisites
To fully engage with the article’s content, students should be familiar with:

Linear and Integer Programming

Convex Optimization

Mathematical Modeling Techniques

Python and Optimization Solvers (e.g., Gurobi)

Basic Statistics (especially variance and boxplot interpretation)

Understanding of multi-objective problem-solving concepts like Pareto optimality and trade-offs

4. Subject Matter
Main Themes:

Formulation of a Multi-Objective Optimization Model to assign students to seminars.

Balancing Competing Goals:

Student preferences (modeled as weighted rankings)

Gender diversity

International student representation

Modeling Techniques:

Constraint-based and deviation-based approaches

Squared and absolute differences for demographic balance

Variance minimization for uniformity

Hierarchical and weighted-sum multi-objective methods

Algorithms & Implementation:

Linearization of non-smooth objectives

Python and Gurobi implementation

Comparative evaluation via real data from Dickinson College

Analysis with graphical tools (e.g., boxplots on pp. 29 & 37)

Advanced Topics Introduced:

Handling nonbinary classifications in optimization

Use of symlog plots for visualizing deviations (Figure on p. 39)

Objective prioritization strategies

5. Correlation to Mathematics Standards
Postsecondary/College-Level Standards Alignment:

MAA CRAFTY College-Level Mathematics Curriculum:

Emphasizes modeling real-world problems, use of technology in mathematics, and quantitative reasoning.

NCTM Process Standards (at the pre-college level, still relevant conceptually):

Problem Solving: Modeling the seminar assignment as an optimization problem.

Reasoning and Proof: Validating modeling assumptions and trade-offs.

Connections: Bridging mathematics with administrative planning.

Representation: Visual data (boxplots) and tabular results.

ABET Criteria for Applied Mathematics & Engineering Programs:

Application of mathematics, science, and engineering to solve complex problems.

Use of modern tools and interpretation of data to inform decision-making.