The student project allocation problem is a well-known constraint satisfaction problem that involves assigning students to projects or supervisors based on a number of criteria. This study investigates the use of population-based strategies inspired from physical phenomena (gravitational search algorithm), evolutionary strategies (genetic algorithm), and swarm intelligence (ant colony optimization) to solve the Student Project Allocation problem for a case study from a real university. A population of solutions to the Student Project Allocation problem is represented as lists of integers, and the individuals in the population share information through population-based heuristics to find more optimal solutions. All three techniques produced satisfactory results and the adapted gravitational search algorithm for discrete variables will be useful for other constraint satisfaction problems. However, the ant colony optimization algorithm outperformed the genetic and gravitational search algorithms for finding optimal solutions to the student project allocation problem in this study.