Dynamic Multi-Objective Evolutionary Algorithm Based on Spectral Clustering Prediction

To address the challenge of rapidly tracking the new Pareto optimal set (PS) after environmental changes in dynamic multi-objective optimization problems (DMOPs), this paper proposes a dynamic multi-objective evolutionary algorithm (DMOEA) based on spectral clustering prediction (SCP). The algorithm first applies spectral clustering to the PS from historical moments to automatically identify multiple subclasses of the PS. When environmental changes occur, the algorithm uses historical information to predict the centroids and shapes of each subclass, thereby constructing a new initial population. Experimental results on 14 standard dynamic test problems indicate that the proposed SCP-DMOEA outperforms four typical algorithms—PPS, MDP, KTM, and RNN—in handling various change characteristics in most test functions. These characteristics include translation or rotation changes of the PS, correlations between decision variables, and time-varying mixed Pareto optimal fronts (PFs), including variations in convexity and concavity. In particular, SCP-DMOEA also shows superior performance when handling optimization problems with more complex PF changes, such as the position of the PF continuously changes over time, the objective vector oscillates among several modes, and the PFs are discontinuous.