Multi-Task Evolutionary Optimization (MTEO), an important field focusing on addressing complex problems through optimizing multiple tasks simultaneously, has attracted much attention. While MTEO has been primarily focusing on task similarity, there remains a hugely untapped potential in harnessing the shared characteristics between different domains to enhance evolutionary optimization. For example, real-world complex systems usually share the same characteristics, such as the power-law rule, small-world property, and community structure, thus making it possible to transfer solutions optimized in one system to another to facilitate the optimization. Drawing inspiration from this observation of shared characteristics within complex systems, we set out to extend MTEO to a novel framework - multi-domain evolutionary optimization (MDEO). To examine the performance of the proposed MDEO, we utilize a challenging combinatorial problem of great security concern - community deception in complex networks as the optimization task. To achieve MDEO, we propose a community-based measurement of graph similarity to manage the knowledge transfer among domains. Furthermore, we develop a graph representation-based network alignment model that serves as the conduit for effectively transferring solutions between different domains. Moreover, we devise a self-adaptive mechanism to determine the number of transferred solutions from different domains and introduce a novel mutation operator based on the learned mapping to facilitate the utilization of knowledge from other domains. Experiments on eight real-world networks of different domains demonstrate MDEO superiority in efficacy compared to classical evolutionary optimization. Simulations of attacks on the community validate the effectiveness of the proposed MDEO in safeguarding community security.

翻译：多任务进化优化（MTEO）作为一个重要领域，致力于通过同时优化多个任务来解决复杂问题，已引起广泛关注。尽管MTEO主要关注任务相似性，但在利用不同领域间的共享特征以增强进化优化方面仍存在巨大潜力。例如，现实世界的复杂系统通常具有相同的特征，如幂律规则、小世界特性和社区结构，这使得将在一个系统中优化的解决方案迁移至另一个系统以促进优化成为可能。受复杂系统内共享特征这一观察的启发，我们着手将MTEO扩展为一个新颖的框架——多领域进化优化（MDEO）。为检验所提MDEO的性能，我们利用一个具有重大安全挑战的组合优化问题——复杂网络中的社区欺骗作为优化任务。为实现MDEO，我们提出了一种基于社区的图相似性度量方法来管理领域间的知识迁移。此外，我们开发了一种基于图表示的网络对齐模型，作为在不同领域间有效迁移解决方案的通道。进一步地，我们设计了一种自适应机制来确定从不同领域迁移的解决方案数量，并引入了一种基于学习映射的新型变异算子，以促进利用来自其他领域的知识。在八个不同领域的真实网络上的实验证明了MDEO在效能上优于经典进化优化方法。对社区攻击的模拟验证了所提MDEO在保护社区安全方面的有效性。