Multidomain Evolutionary Optimization on Adversarial Link Perturbation in Imbalanced-Size Complex Systems

Real-world complex systems usually share structural characteristics such as the small-world property, power-law distributions, and community structure. Multidomain evolutionary optimization (MDEO) leverages these commonalities to search for optimal solutions in multiple domains simultaneously. However, it still faces challenges in achieving effective cooperation when the networks involved are of highly imbalanced sizes. To address this issue, we propose the harmonized MDEO (HMDEO), in which two graph coarsening strategies are developed to jointly coarsen the large network to a fine level, acting as the bridge between the large network and the small network for knowledge exchange. Following that, we propose a bidirectional optimization framework incorporating two cases: large-to-small and small-to-large, allowing solutions optimized in one domain to be seamlessly transferred to another domain of varied scales. To enhance applicability, we also tailor the measurement of network similarity and the network alignment strategy targeted to imbalanced-size scenarios. The effectiveness of HMDEO is demonstrated through experiments on several pairs of networks of differing scales, where HMDEO outperforms other optimization approaches in addressing adversarial edge perturbation against community detection in complex systems.