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.