Simulated Annealing and Artificial Bee Colony for the Redistricting Process in Mexico

Short abstract: To facilitate the redistricting process in Mexico, the authors designed two optimization algorithms; one is based on simulated annealing, and the other is based on artificial bee colony. In this paper, they describe their methodology and the results they obtained when they used these algorithms. Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that these boundaries fulfill federal and/or state requirements. From 2015 to 2017, the National Electoral Institute of Mexico carried out the redistricting process of all 32 Mexican federal entities using a nonlinear programming model in which population equality and compactness were considered as conflicting objective functions, but other criteria, such as contiguity, travel times between municipalities, and indigenous population, were included as hard constraints. To find high-quality redistricting plans within acceptable time limits, we designed two optimization algorithms; one is based on simulated annealing and the other on artificial bee colony. In this paper, we describe our methodology and the results we obtained when we used these algorithms for this redistricting process.