Fuga, a Fuzzy Greedy Algorithm for Redistricting in Mexico

Abstract

Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that the generated districts fulfill federal and state requirements such as contiguity, population equality and compactness. Redistricting is a multi-objective problem which has been proved to be NP-hard. In Mexico, the redistricting process has been done using an aggregation function, considering a weighted sum of the objectives. However, if different weighting factors are used then a set of diverse, high quality solutions can be generated and a new problem arises: which solution should be implemented? In this paper we propose a novel alternative, called FuGA, to select the best solution for the redistricting problem using a fuzzyfication of the objective function. The proposed algorithm was applied in a real case, and its solutions were compared with those produced by VIKOR, a well-known algorithm for decision making. FuGA showed a better performance since it was able to avoid the selection of dominated solutions.