The fourth industrial revolution, driven by the Energy Internet (EI), is having a profound impact on economic development and way of life. With the growth of EI networks, the integration of numerous energy devices poses challenges across different domains. To address this, we propose a self-adaptive NSGA-III algorithm (SA-NSGA-III) for multi-objective optimization of the EI topology, accounting for connectivity, robustness, and operational efficiency. We construct an initial scale-free topology based on real-world EI characteristics and optimize it while preserving its scale-free nature. The method incorporates an adaptive dynamic reference point generation strategy and an adaptive population selection mechanism. Experimental results demonstrate that SA-NSGA-III achieves a 29.5% fitness improvement, outperforming other multi-objective optimization algorithms in both optimization performance and convergence efficiency across various network scales and densities.