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

TL;DR

To address the lack of standardized benchmarking for metaheuristics solving combinatorial optimization problems, the paper introduces the Exploration--Exploitation--Evaluation (EEE) framework. The authors demonstrate its utility via a case study applying ant colony optimization to the TSPLIB berlin52 TSP, combining Sobol-based parameter space exploration, parametric distribution fitting with AICc model selection for exploitation, and bootstrap-based uncertainty quantification for evaluation. They report a per-run probability of reaching the known optimum of $7542$ around $1/40$, improving to about $1/5$ when results are aggregated over ten runs, highlighting both performance variability and the value of reliability estimates. The work also discusses software-engineering considerations and future directions, including migrating from Hadoop to in-memory parallel platforms and extending the framework to broader metaheuristics and deep learning hyperparameter tuning.

Abstract

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.

Figures (13)

• Figure 1: Comparison of sampling methods
• Figure 2: Optimum path of berlin52
• Figure 3: Summary of a MapReduce job.
• Figure 4: Shortest distance box plots from the Exploitation stage in our EEE framework.
• Figure 5: Q-Q plots from runs of the parameter tuple with index 11.