Differential Evolution With Domain Transform
针对差分进化算法在复杂多峰函数上易早熟收敛或停滞的问题，提出域变换方法，通过频域滤波平滑适应度景观，帮助算法跳出局部最优，显著提升性能。
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 multimodal 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 article 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 multimodal 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-of-the-art DE variants, as well as several popular noisy evolutionary optimization algorithms.