A novel knee-guided algorithm based on frequency analysis for non-cyclic dynamic multiobjective optimization problems

Abstract

In real life, many dynamic multiobjective optimization problems (DMOPs) have both time-varying and non-cyclic properties. Their non-cyclic nature differentiates the dynamics of the problem from all previous moments, and the changes become increasingly complex over time. Therefore, geometric changes in the Pareto-optimal front (PF) are more difficult to track. A novel knee-guided algorithm based on frequency analysis (NKGFA) is designed to solve non-cyclic DMOPs. To identify sufficient feature points to describe the change in PF, a knee-guided prediction strategy based on frequency analysis is proposed. From the perspective of frequency-domain analysis, almost all concave and convex knee points that contain critical feature information on the PF are identified. By predicting the frequency-domain information of the knees, the population’s evolutionary trend is obtained in the frequency-domain space. An interpolation strategy based on approximate frontier manifold construction is proposed to ensure that the population is uniformly distributed on the PF. This strategy established an approximate PF between concave and convex knee points. Moreover, it adaptively interpolated the new individuals in the approximate PF. A non-cyclic dynamic (NCD) benchmark test suite is designed, including PFs with increasingly complex geometric features. The effectiveness of the NKGFA is verified by comparing it with four algorithms in the NCD test suite. The NKGFA performed best on 26, 23, and 29 of the 39 test problems on Inverted Generational Distance (IGD), Schott’s Spacing Metric (SP), and Hypervolume Difference (HVD), respectively.