A heuristic algorithm for districting problems with similarity constraints

Redistricting problems arise when due to evolving attributes, current districts get increasingly inefficient or even infeasible. A typical example are electoral districts of roughly the same population, which after changes in its distribution, become imbalanced. Since the cost of creating entirely new districts, in general, is too high, redistricting problems have two conflicting objectives: to find an improved or optimal solution while keeping the changes to existing districts small. In this paper we propose an efficient heuristic for redistricting problems, which can consider similarity to existing districts together with several other constraints, such as balance, connectedness, and compactness. In an experimental study, we evaluate the contribution of heuristic strategies, the effect of different attribute modification models, and the effect of different similarity metrics on the quality of the redefined districts.