Redistricting optimization with recombination: A local search case study

Abstract

In the U.S., states redraw electoral district boundaries every ten years. Given that redistricting affects political representation at both the state and national levels, it is crucial to prevent the manipulation of district boundaries for political gain. Optimization methods can be valuable tools for promoting transparency and fairness in redistricting. Here we examine a novel local search approach for redistricting that transitions between feasible solutions using Recombination (a recently introduced spanning tree iteration). We compare the performance of multiple local search heuristics using both Recombination and more traditional Flip iterations by optimizing congressional plans for Illinois, Missouri, and Tennessee with respect to several common fairness objectives. We evaluate which heuristic produces the best objective value within limited time periods and generate collections of optimized plans. The Recombination heuristics produced excellent objective values, often far superior to the Flip heuristics; they also maintained more compact district shapes when the objective was not compactness. However, the Flip heuristics converged to a local optimum more quickly and occasionally achieved better solutions than the ReCom heuristics within short time periods. Hence, while the use of Recombination within local search frequently improves solution quality, there are some scenarios for which Flip may be preferable.