Centroidal Spatial-Temporal Topological Tensor-Based for Evolutionary Dynamic Multi-objective Optimization

Existing dynamic multi-objective optimization algorithms often face challenges when predicting the initial population for a new environment, as they rely on exploring relationships across all historical populations. This approach can be hindered by potential correlations between solutions, making it difficult to extract meaningful information across different environments. Additionally, the accumulation of historical solutions often leads to reduced computational efficiency in subsequent predictions. To address these issues, this paper proposes a novel framework based on centroid spatial-temporal topological tensors. The algorithm leverages the observation that centroids from the same cluster exhibit topological similarity over time, enabling the construction of centroid tensors to capture population characteristics in each environment. A block Hankel tensor auto-regressive integrated moving average (ARIMA) model is then used to predict centroids for the next environment, followed by a boundary generation strategy to generate new solutions. Experimental results on various benchmarks demonstrate the framework’s competitiveness with existing prediction-based dynamic multi-objective evolutionary algorithms.