A Computational Analysis of Optimization Techniques to Solve Assignment Problem

In the field of combinatorial optimization, numerous methods have been developed to address complex problems, including assignment, scheduling, and resource allocation. This paper presents a comparative analysis of seven prominent optimization techniques: Hungarian Algorithm, Greedy Algorithm, Auction Algorithm, Linear Programming, Genetic Algorithm, Simulated Annealing, and Constraint Programming. We evaluate these methods on computational efficiency, scalability, and practical applicability, focusing on assignment problems. The analysis reveals that Hungarian Algorithm, Linear Programming, and Constraint Programming consistently deliver high accuracy across all matrix sizes, making them ideal for scenarios where solution precision is paramount. Conversely, the Greedy Algorithm excels in speed on smaller matrices but suffers from significant time and accuracy issues as matrix size increases. Additionally, while both Constraint Programming and Genetic Algorithm achieve high accuracy, their execution times rise considerably with matrix size, especially for Genetic Algorithm, which becomes impractical for large-scale problems. Thus, Hungarian Algorithm, Linear Programming, and Constraint Programming are optimal for accuracy-focused tasks, while Greedy Algorithm is preferable for smaller, speed-critical cases.