Fast and Effective Redistricting Optimization via Composite-Move Tabu Search

2026-05-11 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Advanced, extended

Summary

A novel Composite-Move Tabu search (CM-Tabu) method has been developed to enhance spatial redistricting optimization, addressing the challenge of maintaining contiguity constraints while expanding the feasible search neighborhood. Traditional methods often limit exploration by only allowing single-unit reassignments or simple swaps, which can trap searches in poor local optima. CM-Tabu systematically identifies minimal sets of units that can move together, or pairs of units/sets that can be switched, as contiguity-preserving composite moves. This approach generates candidate moves in linear time by analyzing each district's contiguity graph using articulation points and biconnected components. Extensive experiments, including a 1,000-run study on Iowa congressional redistricting and a multi-criteria Philadelphia City Council case study, demonstrate that CM-Tabu substantially improves solution quality, run-to-run robustness, and computational efficiency, consistently outperforming traditional Tabu search and other baselines. For instance, in the Iowa case, the median population deviation decreased by 84% (from 2,627 to 371) with sub-second runtime.

Key takeaway

For AI Scientists and Research Scientists developing spatial optimization algorithms, the CM-Tabu approach offers a robust solution to the persistent challenge of contiguity constraints. By systematically expanding the feasible move set through composite moves, your models can achieve significantly higher solution quality and reliability, as demonstrated by the 84% reduction in median population deviation in the Iowa case study. Consider integrating this contiguity-preserving neighborhood expansion into your trajectory-based metaheuristics to escape local optima more effectively and support multi-criteria decision-making workflows.

Key insights

Expanding the feasible neighborhood with composite moves significantly improves spatial optimization under contiguity constraints.

Principles

• Contiguity constraints limit search space in spatial optimization.
• Composite moves can expand feasible neighborhoods efficiently.
• Analyzing graph connectivity identifies contiguity-preserving moves.

Method

The CM-Tabu method generates contiguity-preserving composite moves and switches in linear time using articulation points and biconnected components, then integrates these into a Tabu search algorithm for robust spatial optimization.

In practice

• Apply CM-Tabu for political redistricting.
• Use for school districting or service territory design.
• Incorporate multi-criteria objectives like population equality and compactness.

Topics

• Composite-Move Tabu Search
• Spatial Redistricting
• Contiguity Constraint
• Combinatorial Optimization
• Graph Algorithms

Best for: Research Scientist, AI Scientist, Consultant

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.