Measures in the time and frequency domains for fitness landscape analysis of dynamic optimization problems

Dynamic optimization problems (DOPs) have attracted increasing attention in recent years. Analyzing the fitness landscape is essential to understand the characteristics of DOPs and may provide guidance for the algorithm design. Existing measures for analyzing the dynamic fitness landscape, such as the dynamic fitness distance correlation and the severity of change, cannot give a comprehensive evaluation of the landscape and have many disadvantages. In this paper, we used Discrete-time Fourier transform (DTFT) and dynamic time warping (DTW) distance to acquire information of fitness landscape from frequency and time domains. Five measures are proposed, including the stationarity of amplitude change, the keenness, the periodicity, the change degree of average fitness and the similarity. They can reflect the features of fitness landscape from the aspects of outline, keenness, period, fitness value and similarity degree, respectively. These criteria can obtain essential information that cannot be acquired by existing criteria, and do not depend on the distribution of variables, the prior information of solutions and algorithms. To illustrate the performance of the five measures, experiments are conducted based on three types of standard DOPs with a two-peak function. In addition, we also apply these criteria on the test task scheduling problem for illustrating the fairness and adaptability. The experiment results show that these criteria can reflect the change characteristics of dynamic fitness landscape, and are consistent with the theoretical analysis.