Abstract
Sectorization problems have significant challenges arising from the many objectives that must be optimised simultaneously. Several methods exist to deal with these many-objective optimisation problems, but each has its limitations. This paper analyses an application of Preference Inspired Co-Evolutionary Algorithms, with goal vectors (PICEA-g) to sectorization problems. The method is tested on instances of different size difficulty levels and various configurations for mutation rate and population number. The main purpose is to find the best configuration for PICEA-g to solve sectorization problems. Performance metrics are used to evaluate these configurations regarding the solutions’ spread, convergence, and diversity in the solution space. Several test trials showed that big and medium-sized instances perform better with low mutation rates and large population sizes. The opposite is valid for the small size instances. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Sectorization consists of grouping the basic units of a large territory to deal with a complex problem involving different criteria. Resectorization rearranges a current sectorization avoiding substantial changes, given a set of conditions. The paper considers the case of the distribution of geographic areas of fire brigades in the north of Portugal so that they can protect and rescue the population surrounding the fire stations. Starting from a current sectorization, assuming the geographic and population characteristics of the areas and the fire brigades’ response capacity, we provide an optimized resectorization considering two objectives: to reduce the rescue time by maximizing the compactness criterion, and to avoid overload situations by maximizing the equilibrium criterion. The solution method is based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). Finally, computational results are presented and discussed. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
This paper explores the problem of sectorization of a parcel delivery service that wants to assign an action region to each of its teams, regarding the number of deliveries scheduled for each zone, so that there is a balanced service amongst sectors, covering contiguous zones, and considering limited capacities for the teams. Besides being relatively easy to model, the available optimization tools and software provide poor results when dimension increases in these types of problems, with computational capacity exceeding. In this paper an integer programming model, combined with an heuristic to return a faster solution, was implemented to solve a sectorization problem in two different situations. The main advantage of the strategy proposed, compared to previous ones, is its simplicity and easy implementation while still returning an optimal solution. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract

Abstract
Sectorization is the division of a large area, territory or network into smaller parts considering one or more objectives. Dynamic sectorization deals with situations where it is convenient to discretize the time horizon in a certain number of periods. The decisions will not be isolated, and they will consider the past. The application areas are diverse and increasing due to uncertain times. This work proposes a conceptualization of dynamic sectorization and applies it to a distribution problem with variable demand. Furthermore, Genetic Algorithm is used to obtain solutions for the problem since it has several criteria; Analytical Hierarchy Process is used for the weighting procedure. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies a complex problem, leading to easier solution approaches to solving the resulting subproblems. Sectors are built with several criteria in mind, such as equilibrium, compactness, contiguity, and desirability, which vary with the applications. Sectorization appears in different contexts: sales territory design, political districting, healthcare logistics, and vehicle routing problems (agrifood distribution, winter road maintenance, parcel delivery). Environmental problems can also be tackled with a sectorization approach; for example, in municipal waste collection, water distribution networks, and even in finding more sustainable transportation routes. This work focuses on sectorization concerning the location of the area's centers and allocating basic units to each sector. Integer programming models address the location-allocation problems, and various formulations implementing different criteria are compared. Methods to deal with multiobjective optimization problems, such as the e-constraint, the lexicographic, and the weighted sum methods, are applied and compared. Computational results obtained for a set of benchmarking instances of sectorization problems are also presented.