Measuring successful, failed and deceptive exploration of evolutionary algorithms based on attraction basins

This paper introduces a novel direct measure of exploration and exploitation in Evolutionary Algorithms, based on attraction basins—regions of the search space with an attractor toward which neighboring solutions tend to evolve. Each solution can be associated with a particular attraction basin. If a new solution belongs to the same attraction basin as its parent, then the search process is identified as exploitation; otherwise, it is identified as exploration. Four different exploration type definitions were used: successful, failed, deceptive, and successful rejection. These are measured directly at the individual level (without precomputing basins) on six single-objective continuous benchmark problems and a real-world problem using DE/rand/1/bin, JADE, LSHADE, ABC, and TLBO. The results revealed that EAs differentiate themselves in how they handle different types of exploration. The approach outperformed prior basin-based measures in efficiency, and exposed the limitations of diversity-based methods, enabling explicit quantification and control of the balance between exploration and exploitation.