Local Bubble Dilation Functions: Hypersphere-bounded Landscape Deformations Simplify Global Optimization

Solving optimization problems is one of the most complex and widespread task in Computer Science. In many scenarios, finding the global optimum of a function is hampered by several features that characterize the fitness landscapes, such as noisiness, multi-modality, non-convexity, non-separability, and non-differentiability. In order to facilitate the optimization process, a variety of methods have been proposed to manipulate either the search space or the fitness landscape. Among these, Dilation Functions (DFs) were introduced to expand regions of the search space that are characterized by promising fitness values. In this work, we extend the family of DFs by introducing Local Bubble Dilation Functions (LBDFs), a novel approach that generates local distortions bounded by hyper-spheres. By performing an appropriate mapping of the search space, LBDFs can improve the optimization performance, since they expand and reveal the promising regions around the global optimum, while leaving the rest of the fitness landscape untouched. The additional advantage of LBDFs, with respect to DFs, is that different dilations can be applied to each dimension of the search space, which is useful in the case of asymmetric landscapes. In order to show the benefits of local dilations, we executed several tests on the Michalewicz benchmark function, with different settings for the LBDFs. Our results show that a properly designed LBDF can lead to statistically significant better results than using vanilla optimization. Finally, we investigated the use of LBDFs to facilitate the solution of the parameter estimation problem in Systems Biology by analyzing the landscape related to a stochastic model of enzyme kinetics.