Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that combines existing edges with gap transitions, missing but acceptable connections representing links that can be built. This abstraction captures how engineers actually reason about infrastructure: not just what exists, but what can be realized. We present a parametric framework that treats planned connections as first-class transitions, scales to large graphs through efficient candidate filtering, and uses multi-dimensional criteria to decide whether a traversal should continue to be explored or be abandoned. We evaluate the framework through representative scenarios in datacenter circuit design and optical route construction in telecommunication networks, demonstrating conditional feasibility, non-scalarizable trade-offs, and policy calibration capabilities beyond the reach of classical formulations.

翻译：传统路径搜索假设图结构完整且优化指标为标量，然而实际基础设施网络往往不完整且需进行多维评估。本文提出遍历的概念：作为路径的泛化形式，其将现有边与间隙转移相结合——后者指代缺失但可被构建的可行连接。该抽象模型捕捉了工程师对基础设施的实际推理方式：不仅考虑现有连接，更关注可实现的可能性。我们提出一种参数化框架，将规划连接视作一等转移对象，通过高效候选过滤实现大规模图的可扩展处理，并运用多维准则动态判断是否继续探索或放弃当前遍历路径。通过在数据中心电路设计与电信网络光路构建中的典型场景评估，本框架展示了条件可行性、不可标量化权衡及策略校准能力，这些特性均超越了传统建模方法的适用范围。