If You Can't Beat It, Squash It: Simplify Global Optimization by Evolving Dilation Functions

Optimization problems represent a class of pervasive and complex tasks in Computer Science, aimed at identifying the global optimum of a given objective function. Optimization problems are typically noisy, multi-modal, non-convex, nonseparable, and often non-differentiable. Because of these features, they mandate the use of sophisticated population-based meta-heuristics to effectively explore the search space. Additionally, computational techniques based on the manipulation of the optimization landscape, such as Dilation Functions (DFs), can be effectively exploited to either "compress" or "dilate" some target regions of the search space, in order to improve the exploration and exploitation capabilities of any meta-heuristic. The main limitation of DFs is that they must be tailored on the specific optimization problem under investigation. In this work, we propose a solution to this issue, based on the idea of evolving the DFs. Specifically, we introduce a two-layered evolutionary framework, which combines Evolutionary Computation and Swarm Intelligence to solve the meta-problem of optimizing both the structure and the parameters of DFs. We evolved optimal DFs on a variety of benchmark problems, showing that this approach yields extremely simpler versions of the original optimization problems.