Randomized and rank based differential evolution

Many real world problems which can be assigned to the machine learning domain are inverse problems. The available data is often noisy and may contain outliers, which requires the application of global optimization. Evolutionary Algorithms (EA's) are one class of possible global optimization methods for solving such problems. Within population based EA's, Differential Evolution (DE) is a widely used and successful algorithm. However, due to its differential update nature, given a current population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitnesses of the population. This paper presents a novel extension of DE called Randomized and Rank based Differential Evolution (R2DE) to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the fitnesses. In experiments including non-linear dimension reduction by autoencoders, it is shown that R2DE improves robustness and speed of global convergence. © 2009 IEEE.