Exploration-Exploitation-Evaluation (EEE): A Framework for Metaheuristic Algorithms in Combinatorial Optimization

We introduce a framework for applying metaheuristic algorithms, such as ant colony optimization (ACO), to combinatorial optimization problems (COPs) like the traveling salesman problem (TSP). The framework consists of three sequential stages: broad exploration of the parameter space, exploitation of top-performing parameters, and uncertainty quantification (UQ) to assess the reliability of results. As a case study, we apply ACO to the TSPLIB berlin52 dataset, which has a known optimal tour length of 7542. Using our framework, we calculate that the probability of ACO finding the global optimum is approximately 1/40 in a single run and improves to 1/5 when aggregated over ten runs.