Fast and Effective Redistricting Optimization via Composite-Move Tabu Search

通过复合移动禁忌搜索实现快速有效的选区划分优化

Abstract: Spatial redistricting is a practical combinatorial optimization problem that demands high-quality solutions, rapid turnaround, and flexibility to accommodate multi-criteria objectives and interactive refinement.

摘要： 空间选区划分是一个实际的组合优化问题，它要求高质量的解决方案、快速的周转时间，以及能够适应多准则目标和交互式优化的灵活性。

A central challenge is the contiguity constraint: enforcing contiguity in integer-programming or heuristic search can severely shrink the feasible neighborhood, weaken exploration, and trap the search in poor local optima.

一个核心挑战是连通性约束：在整数规划或启发式搜索中强制执行连通性，会严重缩小可行邻域，削弱探索能力，并将搜索困在较差的局部最优解中。

We introduce a composite-move Tabu search (CM-Tabu) that systematically expands the feasible neighborhood space in Tabu search while preserving contiguity.

我们引入了一种复合移动禁忌搜索（CM-Tabu），它在保持连通性的同时，系统地扩展了禁忌搜索中的可行邻域空间。

When a boundary unit cannot be reassigned individually without disconnecting its district, our method identifies a minimal set of units that can move together, or a pair of units (or sets of units) that can be switched, as a contiguity-preserving composite move.

当某个边界单元无法在不破坏其所在选区连通性的情况下单独重新分配时，我们的方法会识别出一组可以共同移动的最小单元集合，或者一对可以交换的单元（或单元集合），将其作为一种保持连通性的复合移动。

Candidate single-unit and composite moves are generated in linear time by analyzing each district’s contiguity graph using articulation points and biconnected components.

通过使用关节点和双连通分量分析每个选区的连通图，候选的单单元移动和复合移动可以在线性时间内生成。

Extensive experiments demonstrate that the proposed approach substantially improves solution quality, run-to-run robustness, and computational efficiency relative to traditional Tabu search and other baselines.

大量实验表明，与传统的禁忌搜索和其他基准方法相比，该方法在解的质量、运行稳健性和计算效率方面都有显著提升。

For example, in the Philadelphia case, the approach can consistently attain the theoretical global optimum in population-equality and support multi-criteria trade-offs.

例如，在费城的案例中，该方法能够始终达到人口均衡方面的理论全局最优解，并支持多准则权衡。

CM-Tabu delivers optimization performance suitable for real-world practices and decision-support workflows.

CM-Tabu 提供了适用于现实实践和决策支持工作流的优化性能。