Abstract
Redistricting is the process of partitioning a set of basic units into a given number of larger groups for electoral purposes. These groups must follow federal and state requirements to enhance fairness and minimize the impact of manipulating boundaries for political gain. In redistricting tasks, one of the most important criteria is equal population. As a matter of fact, redistricting plans can be rejected when the population deviation exceeds predefined limits. In the literature, there are several methods to balance population among districts. However, further discussion is needed to assess the effectiveness of these strategies. In this paper, we considered two different strategies, mean deviation and overall range. Additionally, a compactness measure is included to design well-shaped districts. In order to provide a wide set of redistricting plans that achieve good trade-offs between mean deviation, overall range, and compactness, we propose four multiobjective metaheuristic algorithms based on NSGA-II and SPEA-II. The proposed strategies were applied in California, Texas, and New York. Numerical results show that the proposed multiobjective approach can be a very valuable tool in any real redistricting process.
Highlights
Alejandro Lara-Caballero,1 Sergio Gerardo de-los-Cobos-Silva,1 Roman Anselmo Mora-Gutierrez,2 Eric Alfredo Rincon-Garcıa,1 Miguel Angel Gutierrez-Andrade,1 and Pedro Lara-Velazquez1
In order to provide a wide set of redistricting plans that achieve good trade-offs between mean deviation, overall range, and compactness, we propose four multiobjective metaheuristic algorithms based on nondominated sorting genetic algorithm II (NSGA-II) and strength Pareto evolutionary algorithm II (SPEA-II). e proposed strategies were applied in California, Texas, and New York
NSGA-II and SPEA-II were designed to produce a set of well spread nondominated solutions. erefore, the algorithms will produce some solutions with low compactness cost their mean deviation and overall range can be affected
Summary
Many real-world scenarios involve simultaneously optimization of several objectives in order to solve a certain problem [26, 27, 28]. In an MOP, the goal is to find the best trade-off solutions, called the Pareto optimal solutions, that are important to a DM. To define the concept of optimality for a multiobjective problem, the following definitions are provided. A feasible solution x∗ ∈ Ω of problem (1) is called a Pareto optimal solution, if and only if there is no other solution y ∈ Ω such that y ≺ x∗. If x∗ is Pareto optimal, z F(x∗) is called as a nondominated point or an efficient point. E Pareto front is the image of the PS in the objective space, which is denoted as PF {F(x) | x ∈ PS}. E main goal when solving an MOP is to provide the DM the so-called Pareto optimal set of Pareto optimal (or nondominated) solutions
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