Modifications for the Differential Evolution Algorithm

Optimising Time-Frequency Distributions: A Surface Metrology Approach

Time-frequency signal processing offers a significant advantage over temporal or frequency-only methods, but representations require optimisation for a given signal. Standard practice includes choosing the appropriate time-frequency distribution and fine-tuning its parameters, usually via visual inspection and various measures-the most commonly used ones are based on the Rényi entropies or energy concentration by Stanković. However, a discrepancy between the observed representation quality and reported numerical value may arise when the filter kernel has greater adaptability. Herein, a performance measure derived from the Abbot-Firestone curve similar to the volume parameters in surface metrology is proposed as the objective function to be minimised by the proposed minimalistic differential evolution variant that is parameter-free and uses a population of five members. Tests were conducted on two synthetic signals of different frequency modulations and one real-life signal. The multiform tiltable exponential kernel was optimised according to the Rényi entropy, Stanković's energy concentration and the proposed measure. The resulting distributions were mutually evaluated using the same measures and visual inspection. The optimiser demonstrated a reliable convergence for all considered measures and signals, while the proposed measure showed consistent alignment of reported numerical values and visual assessments.

A Dynamic Adaptive Weighted Differential Evolutionary Algorithm

This study proposed a dynamic adaptive weighted differential evolution (DAWDE) algorithm to solve the problems of differential evolution (DE) algorithm such as long search time, easy stagnation, and local optimal solution. First, adaptive adjustment strategies of scaling factor and crossover factor are proposed, which are utilized to dynamically balance the global and local search, and avoid premature convergence. Second, an adaptive mutation operator based on population aggregation degree is proposed, which takes population aggregation degree as the amplitude coefficient of the basis vector to determine the influence degree of the optimal individual on the mutation direction. Finally, the Gauss perturbation operator is introduced to generate random disturbance and accelerate premature individuals to jump out of the local optimum. The simulation results show that the DAWDE algorithm can obtain better optimization results and has the characteristics of stronger global optimization ability, faster convergence, higher solution accuracy, and stronger stability compared with other optimization algorithms.