Exploring Genetic Algorithms and the Greedy Algorithm: A Comparative Study on Solving Stable Marriage Problems

The Stable Marriage Problem (SMP) is a fundamental combinatorial optimization problem with real-world applications in market design, medical residency assignments, and college admissions. This paper presents a comparative study of three computational approaches: the Genetic Algorithm (GA), the Greedy Algorithm, and the Deferred Acceptance Algorithm (DAA). GA employs evolutionary techniques to enhance matching quality, using selection, crossover, and mutation to iteratively refine solutions. The Greedy Algorithm quickly selects locally optimal solutions, prioritizing immediate improvements but often leading to instability. DAA, a structured iterative matching process, ensures stability by following a proposal-acceptance mechanism. Experimental results demonstrate that GA achieves superior solution quality but at a higher computational cost, the Greedy Algorithm offers efficiency but risks instability, and DAA guarantees stability but does not maximize preference satisfaction. These findings provide insights into the trade-offs between computational efficiency and match quality in SMP applications, offering a foundation for future research into hybrid algorithms that balance stability, efficiency, and preference satisfaction.