Evolving Dilation Functions for Parameter Estimation

Global optimization problems are among the most complex and widespread tasks in Computer Science. The capability of finding the global optimum is often hindered by many features-e.g., multi-modality, noisiness and non-differentiability-of the fitness landscape related to the problem. To overcome such issues, Dilation Functions (DFs) can be used to perform problem-dependent manipulations of the fitness landscape to 'expand' promising regions and 'compress' less promising regions. Since in many real-world scenarios the knowledge of the problem characteristics to handcraft tailored DFs is lacking, two automatic approaches to evolve ad-hoc DFs have been proposed and assessed on benchmark problems. One approach is a two-layered method that leverages an Evolution Strategies (ES) and a self-Tuning variant of Particle Swarm optimization to evolve a DF. The other approach uses Genetic Programming (GP) to evolve a set of tailored DFs for each dimension of the search space. In this work, we introduce Evolutionary LBDFs (EvLBDFs), a novel approach based on ES to evolve Local Bubble Dilation Functions, a family of DFs that locally dilate hyper-spherical bounded regions of the search space. Moreover, we compare these approaches to solve the Parameter Estimation (PE) problems of two bio-chemical systems. Our results highlight that all three approaches evolved DFs that simplified the PE landscapes. The GP-based approach outperformed the other approaches on the PE problem with the higher number of kinetic parameters to infer.