A Fuzzy Inference System for the Evaluation of Exploration and Exploitation Capabilities in Metaheuristic Optimization Algorithms

In this paper, we propose the implementation of a Fuzzy Inference System (FIS) for the systematic evaluation of exploration and exploitation capabilities in population-based Metaheuristic Optimization Algorithms (MOAs). Our approach involves an efficient feature extraction scheme applied through different stages of an algorithm’s search process, from which Dimension-Wise Diversity (DD), Average Distance to Global Best (DB), and Fitness Diversity (FD) are extracted and utilized as inputs for the proposed Mamdani-style FIS. These metrics feature zero additional objective function evaluations and are processed in real time by our proposed Mamdani-style inference system using symmetric triangular membership functions. Since the proposed FIS-based evaluation scheme relies on static membership boundaries and elementary min-max aggregation operators, constant time complexity is ensured, which contrasts with the expensive matrix operations that are frequently required in probabilistic models. To validate this framework, a comprehensive experimental design was performed. Such experiments involve testing with MOAs proposing unique and distinctive search strategies, including well-known examples such as Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Grey Wolf Optimizer (GWO), Differential Evolution (DE) and others. Our experiments also consider 14 benchmark functions (chosen by considering scalability and landscape variety) and three operational configurations (which consider varying numbers of decision variables, population size and iterations). Our results not only expose critical differences in exploration/exploitation capabilities among the compared strategies but also allow the visualization of underlying process characteristics, such as convergence speed and repeatability. Our results imply that the most successful MOAs are those which prioritize exploration by no more than 25% percent of the search process, while also manifesting a successful exchange from full exploration to full exploitation by the end of such process, with PSO and DE being among the most consistent examples.