f911090d-c38b-4df4-b9f1-dbf66a5e82f820210203080636701wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON COMPUTERS1109-275010.37394/23205http://wseas.org/wseas/cms.action?id=40262720202720201910.37394/23205.2020.19http://wseas.org/wseas/cms.action?id=23186Geographically Separating Sectors in Multi-Objective Location-RoutingProblemsAydinTeymourifarInesc Tec - Institute for Systems and Computer Engineering, Technology and Science, R. Dr. Roberto Frias, Porto, PortugalAna MariaRodriguesCeos.pp - Center for Organizational and Social Studies Porto Polytechnic, R. Jaime Lopes Amorim S/n, 4465-004 São Mamede De Infesta, Porto, PortugalJose SoeiroFerreiraFeup - Faculty of Engineering, University of Porto S/n, R. Dr. Roberto Frias, 4200-465 Porto, PortugalThis paper deals with multi-objective location-routing problems (MO-LRPs) and follows a sectorizationapproach, which means customers are divided into different sectors, and a distribution centre is opened for eachsector. The literature has considered objectives such as minimizing the number of opened distribution centres,the variances of compactness, distances and demands in sectors. However, the achievement of these objectivescannot guarantee the geographical separation of sectors. In this sense, and as the geographical separation ofsectors can have significant practical relevance, we propose a new objective function and solve a benchmarkof problems with the non-dominated sorting genetic algorithm (NSGA-II), which finds multiple non-dominatedsolutions. A comparison of the results shows the effectiveness of the introduced objective function, since, in thenon-dominated solutions obtained, the sectors are more geographically separated when the values of the objectivefunction improve.4152020415202098102https://www.wseas.org/multimedia/journals/computers/2020/a265105-056.pdf10.37394/23205.2020.19.13https://www.wseas.org/multimedia/journals/computers/2020/a265105-056.pdf10.1016/j.ejor.2005.06.074Barreto, S., Ferreira, C., Paixão, J., & Santos, B. S. Using clusteringanalysis in a capacitated location-routing problem. European Journalof Operational Research, 179(3) (2007), 968–977.Chen, C., Qiu, R., & Hu, X. The location-routing problem with fulltruckloads in low-carbon supply chain network designing. Mathematical Problems in Engineering, 2018 (2018).Davies, D. L., & Bouldin, D. W. A cluster separation measure. IEEEtransactions on pattern analysis and machine intelligence, (2) (1979),224–227.10.1109/4235.996017Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. A fast andelitist multiobjective genetic algorithm: NSGA-II. IEEE transactionson evolutionary computation, 6(2) (2002), 182–197.10.1007/s10479-020-03559-yDugošija, D., Savić, A., & Maksimović, Z. A new integer linear programming formulation for the problem of political districting. Annalsof Operations Research, (2020), 1–17.10.1007/bf02023807Laporte, G., Nobert, Y., & Arpin, D. An exact algorithm for solving a capacitated location-routing problem. Annals of Operations Research, 6(9) (1986), 291–310.10.1016/j.ejor.2006.04.004Nagy, G., & Salhi, S. Location-routing: Issues, models and methods.European journal of operational research, 177(2) (2007), 649–672.10.1016/j.simpat.2019.102064Oudouar, F., Lazaar, M., & El Miloud, Z. A novel approach based onheuristics and a neural network to solve a capacitated location routing problem. Simulation Modelling Practice and Theory, 100 (2020),102064.Prodhon, C., & Prins, C. A survey of recent research on locationrouting problems. European Journal of Operational Research, 238(1)(2014), 1–17.Rodrigues, A. M., & Ferreira, J. S. (a). Measures in sectorization problems. In Operations research and big data, Springer, Cham,(2015), 203–211.Rodrigues, A. M., & Ferreira, J. S. (b). Sectors and routes in solidwaste collection. In Operational Research, Springer, Cham, (2015),353–375.10.1002/net.21597Rodrigues, A. M., & Ferreira, J. S. (c). Waste collection routinglimited multiple landfills and heterogeneous fleet. Networks, 65(2)(2015), 155–165.10.13189/ujam.2018.060302Teymourifar, A., Ozturk, G., & Bahadir, O. A Comparison betweenTwo Modified NSGA-II Algorithms for Solving the Multi-objectiveFlexible Job Shop Scheduling Problem. Universal Journal of AppliedMathematics, 6(3) (2018), 79–93.