Urban underground cable construction is essential for enhancing the reliability of city power grids, yet its high construction costs make planning a worthwhile optimization task. In urban environments, road layouts tightly constrain cable routing. This, on the one hand, renders relation-only models (i.e., those without explicit routes) used in prior work overly simplistic, and on the other hand, dramatically enlarges the combinatorial search space, thereby imposing much higher demands on algorithm design. In this study, we formulate urban cable routing as a connectivity-path co-optimization problem and propose a learning-assisted multi-operator variable neighborhood search (L-MVNS) algorithm. The framework first introduces an auxiliary task to generate high-quality feasible initial solutions. A hybrid genetic search (HGS) and A* serve as the connectivity optimizer and the route-planning optimizer, respectively. Building on these, a multi-operator variable neighborhood search (MVNS) iteratively co-optimizes inter-substation connectivity and detailed routes via three complementary destruction operators, a modified A* repair operator, and an adaptive neighborhood-sizing mechanism. A multi-agent deep reinforcement learning module is further embedded to prioritize promising neighborhoods. We also construct a standardized and scalable benchmark suite for evaluation. Across these cases, comprehensive experiments demonstrate effectiveness and stability: relative to representative approaches, MVNS and L-MVNS reduce total construction cost by approximately 30-50%, with L-MVNS delivering additional gains on larger instances and consistently higher stability.

翻译：城市地下电缆建设对于提升城市电网可靠性至关重要，然而其高昂的建设成本使得规划成为一项值得优化的任务。在城市环境中，道路布局严格约束着电缆布线路径。这一方面使得先前工作中使用的仅考虑连接关系的模型（即不包含显式路径的模型）过于简化，另一方面也极大地扩大了组合搜索空间，从而对算法设计提出了更高的要求。在本研究中，我们将城市电缆布线建模为一个连接性与路径协同优化问题，并提出了一种学习辅助的多算子变邻域搜索（L-MVNS）算法。该框架首先引入一个辅助任务以生成高质量的可行初始解。混合遗传搜索（HGS）和A*算法分别作为连接性优化器和路径规划优化器。在此基础上，多算子变邻域搜索（MVNS）通过三个互补的破坏算子、一个改进的A*修复算子以及一个自适应邻域规模调整机制，迭代地协同优化变电站间的连接性与详细布线路径。进一步嵌入了一个多智能体深度强化学习模块以优先探索有潜力的邻域。我们还构建了一个标准化且可扩展的基准测试集用于评估。在这些案例上，全面的实验证明了算法的有效性和稳定性：相较于代表性方法，MVNS和L-MVNS将总建设成本降低了约30-50%，其中L-MVNS在更大规模实例上实现了额外的收益，并始终表现出更高的稳定性。