Abstract

Abstract
Sectorisation refers to dividing a whole into smaller parts, the sectors, to facilitate an activity or achieve some goals. The paper proposes a new matrix form genetic encoding system, called matrix form binary grouping (MFBG), specifically designed for sectorisation and related problems. In MFBG representation, the columns and rows represent sectors and nodes, respectively. As a solution procedure, we followed NSGA-II by contemplating adapted measures for three commonly used criteria (equilibrium, compactness, contiguity) for sectorisation problems. The performance of the MFBG within the NSGA-II is tested from two perspectives: 1) through several experiments on the set of instances; 2) by its comparison with the group-oriented genetic encoding system under the grouping GA. Results showed that the MFBG could find good quality solutions and outperforms the GGA. This confirms that the MFBG is an innovative procedure for dealing with sectorisation problems and an excellent contribution as an alternative encoding technique. © 2023 Inderscience Enterprises Ltd.

Abstract
Sectorization problems, also known as districting or territory design, deal with grouping a set of previously defined basic units, such as points or small geographical areas, into a fixed number of sectors or responsibility areas. Usually, there are multiple criteria to be satisfied regarding the geographic characteristics of the territory or the planning purposes. This work addresses a case study of parcel delivery services in the region of Porto, Portugal. Using knowledge about the daily demand in each basic unit (7-digit postal code), the authors analysed data and used it to simulate dynamically new daily demands according to the relative frequency of service in each basic unit and the statistical distribution of the number of parcels to be delivered in each basic unit. The sectorization of the postal codes is solved independently considering two objectives (equilibrium and compactness) using Non-dominated Sorting Genetic Algorithm-II (NSGA-II) implemented in Python.

Abstract
Sectorization problems refer to dividing a large set, area or network into smaller parts concerning one or more objectives. A decision support system (DSS) is a relevant tool for solving these problems, improving optimisation procedures, and finding feasible solutions more efficiently. This paper presents a new web-based Decision Support System for Sectorization (D3S). D3S is designed to solve sectorization problems in various areas, such as school and health districting,planning sales territories and maintenance operations zones, or political districting. Due to its generic design, D3S bridges the gap between sectorization problems and a state-of-the-art decision support tool. The paper aims to present the generic and technical attributes of D3S by providing detailed information regarding the problem-solution approach (based on Evolutionary Algorithms), objectives (most common in sectorization), constraints, structure and performance.

Abstract
Multi -objective optimization (MOO) considers several objectives to find a feasible set of solutions. Selecting a solution from Pareto frontier (PF) solutions requires further effort. This work proposes a new classification procedure that fits into the analytic hierarchy Process (AHP) to pick the best solution. The method classifies PF solutions using pairwise comparison matrices for each objective. Sectorization is the problem of splitting a region into smaller sectors based on multiple objectives. The efficacy of the proposed method is tested in such problems using our instances and real data from a Portuguese delivery company. A non -dominated sorting genetic algorithm (NSGA-II) is used to obtain PF solutions based on three objectives. The proposed method rapidly selects an appropriate solution. The method was assessed by comparing it with a method based on a weighted composite single -objective function.

Abstract