Cluster-based framework for metaheuristic empirical similarity

Abstract Numerous metaheuristic search algorithms have been developed due to their effectiveness in solving optimization problems. This has created a need for systematic approaches to classify and compare them to understand their search behaviors better and guide the selection of appropriate algorithms for specific problems. However, common approaches in the literature rely mainly on the theoretical aspects of these algorithms, often not considering how similar algorithms perform in practice. To address this gap, we propose a general framework for analyzing the empirical similarity of metaheuristics using clustering techniques. The framework groups algorithm instances based on their performance profiles and then analyzes the distribution of algorithmic components and parameters across these groups. This approach provides a performance-driven perspective on metaheuristic similarity by grouping algorithm instances with similar performance while also offering insights into how specific algorithmic components and parameters relate to those performance behaviors. To illustrate the framework, we present a baseline implementation and case study involving 36 Particle Swarm Optimization instances, each defined by different combinations of algorithmic components and parameters. Through this case study, the framework identifies clusters based on different performance behaviors and then analyzes the distribution of the algorithmic components and parameters across clusters, revealing component-performance links. These results suggest that the proposed framework offers a structured basis for understanding empirical similarity among metaheuristics, provides a complementary perspective to theoretical classifications, and supports ongoing efforts to map the algorithm design space.