Differential Evolution With Domain Transform

Abstract

Although a significant advancement of differential evolution (DE) for global optimization has been witnessed in the past two decades, the problems of premature convergence and stagnation are still open questions that hinder the performance. Both are likely to occur on complicated multi-modal functions, but the phenomena differ. Premature convergence refers to a rapid loss of population diversity when attracted to a local minimum while stagnation happens even though the population is diverse. To deal with these problems, this paper proposes a domain transform (DT) methodology. Different from existing fitness analysis which mainly utilizes the original fitness landscape information, DT yields a transformed fitness landscape with transform operation to the frequency domain and inverse transform operation back to the solution domain, between which the first few highest frequencies are removed. With the deletion operation, the transformed fitness landscape becomes smoother and facilitates the escape from local minima and stagnation on complicated multi-modal functions. Simulation results show that DT significantly improves the population successful update rate and population convergence. The constructed DTDE algorithm consequently exhibits remarkable improvements on the baseline algorithm and outperforms several state-of-the-art DE variants. DT has also been extended for noisy optimization and it performs better than the baseline, the classic resampling method, state-ofthe-art DE variants as well as several popular noisy evolutionary optimization algorithms.