A Hybrid Differential Evolution Self-Organizing-Map Algorithm for Optimization of Expensive Black-box Functions

Abstract

A hybrid optimization algorithm, DE-SOM, which is a combination of Differential Evolution (DE) and Self Organizing Maps (SOM) is introduced. SOM, an unsupervised learning algorithm, is used to accelerate the convergence of DE. We compare the performance of DE, DE-SOM and Genetic Algorithm (GA) on a suite of 15 widely used benchmark functions. A subset of these benchmark functions are used in higher dimensional (10-D and 30-D) tests. DE-SOM outperforms both DE and GA across all benchmark functions in the test suite by obtaining the same quality of solutions with lower number of function evaluations. In test cases where GA converged with lesser function evaluations, the DE-SOM function value was more optimal. Similar results were obtained for higher dimensional benchmark functions. We also demonstrate the usefulness of this algorithm using an airfoil optimization example problem that involves design for maximum aerodynamic efficiency.