Learning-Assisted Multi-Operator Variable Neighborhood Search for Urban Cable Routing

TL;DR

This work tackles urban underground cable routing by formulating an integrated connectivity-path co-optimization that respects road constraints and capitalizes on trench-sharing. It introduces a learning-assisted multi-operator variable neighborhood search (L-MVNS) with an auxiliary initialization, three destruction operators, a modified A* repair, adaptive neighborhood sizing, and a multi-agent DRL module to prioritize promising neighborhoods. The approach is validated on a standardized lattice benchmark, showing 30–50% cost reductions over relation-only baselines, with L-MVNS delivering additional gains and improved stability on larger instances. Together, these contributions enable more cost-effective, scalable planning of urban cable networks by simultaneously optimizing feeder connectivity and precise routing along road networks.

Abstract

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.

Figures (12)

• Figure 1: Typical topologies of urban MV distribution cable networks: (a) Interconnected network: MV substations are linked by feeders that originate from one HV substation and terminate at another; (b) Ring network: MV substations are linked by feeders that both originate from and terminate at the same HV substation.
• Figure 2: Schematic diagrams of the urban cable routing problem underscore two key points. First, as shown by panel (a) versus panel (b), cables cannot be laid along arbitrary straight-line segments; rather, their paths must adhere strictly to the existing road network topology. Second, as illustrated by panel (c) versus panel (d), planning multiple feeders in parallel along the same road segments can exploit spatial overlap to reduce road-trenching costs, potentially outperforming designs that rely solely on individual shortest-path routes.
• Figure 3: Street layouts and substations for the four built cases, with HV substations as black squares and MV substations as red points.
• Figure 4: The proposed L‑MVNS algorithm comprises three modules: solution initialization, learning-assisted neighborhood generation, and multi-operator variable neighborhood search. The final solution is iteratively refined in the latter two modules.
• Figure 5: The operation diagrams for the three destruction operators: squares indicate HV substations, circles denote MV substations, orange and blue modules signify two independent feeders, gray dotted lines represent removed segments, and orange and blue dotted lines represent newly connected segments.