Functions for the analysis of exploration and exploitation

Real parameter optimization is one of the most common applications of evolutionary computation. In this study we define a protocol to understand the exploratory and exploitative behaviors of evolutionary algorithms and evaluate two representations on four test functions. The first representation, storing the real parameters in an array, is a standard representation. The second representation, called the walking triangle representation is introduced in this study. This representation is a generative one which models a set of real parameters as the center of mass of a simplex. The generative rules modify the simplex through reflection, scaling, and deformation. It is shown that this representation behaves in a substantially different manner from the standard one and has very different capabilities. On two of the four test problems, one variation of the walking triangle yields an improvement of hundreds orders of magnitude in fitness. This paper suggests that representations themselves are just as important to consider when optimizing evolutionary algorithms for a balance of exploration and exploitation, and further that our system of open-ended test functions can be used to monitor this balance and adjust these considerations accordingly.