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2024 | 34 | nr 1 | 211--232
Tytuł artykułu

How to Know it is "the One"? Selecting the Most Suitable Solution from the Pareto Optimal Set. Application to Sectorization

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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. (original abstract)
Rocznik
Tom
34
Numer
Strony
211--232
Opis fizyczny
Twórcy
  • Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal; Faculty of Economics, University of Porto, Porto, Portugal
  • Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal; Polytechnic of Porto, Porto, Portugal
  • Institute for Systems and Computer Engineering, Technology and Science, Porto, Portugal; University of Porto, Porto, Portugal
  • Polytechnic of Porto, Porto, Portugal
Bibliografia
  • [1] Agustín-Blas, L. E., Salcedo-Sanz, S., Jiménez-Fernández, S., Carro-Calvo, L., Del Ser, J., and Portilla- Figueras, J. A. A new grouping genetic algorithm for clustering problems. Expert Systems with Applications 39, 10 (2012), 9695-9703.
  • [2] Angel, S., Parent, J., and Civco, D. L. Ten compactness properties of circles: measuring shape in geography. The Canadian Geographer/Le Géographe canadien 54, 4 (2010), 441-461.
  • [3] Benzarti, E., Sahin, E., and Dallery, Y. Operations management applied to home care services: Analysis of the districting problem. Decision Support Systems 55, 2 (2013), 587-598.
  • [4] Bernábe-Loranca, B., Coello-Coello, C. A., and Osorio-Lama, M. A multiobjective approach for the heuristic optimization of compactness and homogeneity in the optimal zoning. Journal of Applied Research and Technology 10, 3 (2012), 447-457.
  • [5] Bozkaya, B., Erkut, E., and Laporte, G. A tabu search heuristic and adaptive memory procedure for political districting European journal of operational research 144, 1 (2003), 12-26.
  • [6] Branke, J., Deb, K., Dierolf, H., and Osswald, M. Finding knees in multi-objective optimization. In Parallel Problem Solving from Nature - PPSN VIII. 8th International Conference, Birmingham, UK, September 18-22, 2004, X. Yao, E. K. Burke, J. A. Lozano, J. Smith, J. J. Merelo-Guervós, J. A. Bullinaria, J. E. Rowe, P. Tiˇno, A. Kabán and H.-P. Schwefel, Eds., vol. 3242 of Lecture Notes in Computer Science, Springer, Berlin, 2004, pp. 722-731.
  • [7] Brzostowski, J., Roszkowska, E., and Wachowicz, T. Using an analytic hierarchy process to develop a scoring system for a set of continuous feasible alternatives in negotiation. Operations Research and Decisions 22, 4 (2012), 21-40.
  • [8] Camacho-Collados, M., Liberatore, F., and Angulo, J. M. A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector. European Journal of Operational Research 246, 2 (2015), 674-684.
  • [9] Caro, F., Shirabe, T., Guignard, M., and Weintraub, A. School redistricting: Embedding gis tools with integer programming. Journal of the Operational Research Society 55, 8 (2004), 836-849.
  • [10] Crispim, J. A., and de Sousa, J. P. Partner selection in virtual enterprises: a multi-criteria decision support approach. International Journal of Production Research 47, 17 (2009), 4791-4812.
  • [11] Das, A., Mazumder, T. N., and Gupta, A. K. Pareto frontier analyses based decision making tool for transportation of hazardous waste. Journal of Hazardous Materials 227-228 (2012), 341-352.
  • [12] Das, I. On characterizing the "knee" of the Pareto curve based on Normal-Boundary Intersection. Structural Optimization 18, 2-3 (1999), 107-115.
  • [13] de Sousa, F. S., Lima, M. M., Öztürk, E. G., Rocha, P. F., Rodrigues, A. M., Ferreira, J. S., Nunes, A. C., and Oliveira, C. Dynamic sectorization-conceptualization and application. In Innovations in Mechanical Engineering II (Cham, 2022), J. Machado, F. Soares, J. Trojanowska, E. Ottaviano, P. Valášek, D. M. Reddy, E. A. Perondi and Y. Basova, Eds., Lecture Notes in Mechanical Engineering book series, Springer, pp. 293-304.
  • [14] Deb, K. Multi-Objective Optimization using Evolutionary Algorithms, John Wiley & Sons, 2001.
  • [15] Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 2 (2002), 182-197.
  • [16] Dumedah, G., Berg, A. A., Wineberg, M., and Collier, R. Selecting model parameter sets from a trade-off surface generated from the non-dominated sorting genetic algorithm-II. Water Resources Management 24, 15 (2010), 4469-4489.
  • [17] Farughi, H., Tavana, M., Mostafayi, S., and Santos Arteaga, F. J. A novel optimization model for designing compact, balanced, and contiguous healthcare districts. Journal of the Operational Research Society 71, 11 (2020), 1740-1759.
  • [18] Ferhi, L. A., Sethom, K., and Choubani, F. Toward dynamic 3D sectorization using real traffic profile for green 5G cellular networks. In 2018 International Conference on Advanced Systems and Electric Technologies (IC_ASET) (Hammamet, Tunisia, 2018), IEEE, pp. 227-232.
  • [19] Ferreira, J. C., Fonseca, C. M., and Gaspar-Cunha, A. Methodology to select solutions from the Pareto-optimal set: A comparative study. In GECCO '07: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (London, England, 2007), ACM, pp. 789-796.
  • [20] Florios, K., and Mavrotas, G. Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems. Applied Mathematics and Computation 237 (2014), 1-19.
  • [21] González-Ramírez, R. G., Smith, N. R., Askin, R. G., Miranda, P. A., and Sánchez, J. M. A hybrid metaheuristic approach to optimize the districting design of a parcel company. Journal of Applied Research and Technology 9, 1 (2011), 19-35.
  • [22] Hales, R. O., and García, S. Congress seat allocation using mathematical optimization. Top 27, 3 (2019), 426-455.
  • [23] Ho, W. Integrated analytic hierarchy process and its applications - A literature review. European Journal of Operational Research 186, 1 (2008), 211-228.
  • [24] Hu, F., Yang, S., and Xu, W. A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters. International Journal of Geographical Information Science 28, 7 (2014), 1482-1501.
  • [25] Jurczak, M., Miebs, G., and Bachorz, R. A. Multi-criteria human resources planning optimisation using genetic algorithms enhanced with MCDA. Operations Research and Decisions 32, 4 (2022), 57-74.
  • [26] Kalcsics, J., Nickel, S., and Schröder, M. Towards a unified territorial design approach-applications, algorithms and GIS integration. Top 13, 1 (2005), 1-56.
  • [27] Khan, M., Alhumaima, R. S., and Al-Raweshidy, H. S. QoS-aware dynamic RRH allocation in a self-optimized cloud radio access network with RRH proximity constraint. IEEE Transactions on Network and Service Management 14, 3 (2017), 730-744.
  • [28] Khu, S. T., and Madsen, H. Multiobjective calibration with Pareto preference ordering: An application to rainfall-runoff model calibration. Water Resources Research 41, 3 (2005), W03004.
  • [29] Konak, A., Coit, D. W., and Smith, A. E. Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering & System Safety 91, 9 (2006), 992-1007.
  • [30] Lara-Caballero, A., de-los Cobos-Silva, S. G., Mora-Gutiérrez, R. A., Rincón-García, E. A., Gutiérrez- Andrade, M. Á., and Lara-Velázquez, P. Multiobjective genetic algorithms for reinforcing equal population in congres- sional districts. Mathematical Problems in Engineering 2019 (2019), 2825854.
  • [31] Olivares Benitez, E., Beatríz Bernábe-Loranca, M., Caballero-Morales, S.-O., and Granillo Macias, R. Multi-objective design of balanced sales territories with taboo search: a practical case. International Journal of Supply and Operations Management 8, 2 (2021), 176-193.
  • [32] Önal, H., Wang, Y., Dissanayake, S. T. M., and Westervelt, J. D. Optimal design of compact and functionally contiguous conservation management areas. European Journal of Operational Research 251, 3 (2016), 957-968.
  • [33] Öztürk, E., Rocha, P., Sousa, F., Lima, M., Rodrigues, A. M., Ferreira, J. S., Nunes, A. C., Lopes, C., and Oliveira, C. An application of preference-inspired co-evolutionary algorithm to sectorization. In Innovations in Mechatronics Engineering II, J.Machado, F. Soares, J. Trojanowska, S. Yildirim, J. Vojtˇešek, P. Rea, B. Gramescu and O. O. Hrybiuk, Eds., Lecture Notes in Mechanical Engineering book series, Springer, 2017, pp. 257-268.
  • [34] Öztürk, E. G., Rodrigues, A. M., and Ferreira, J. S. A new matrix form genetic encoding for balanced, compact and connected sectorization through NSGA-II. International Journal of Multicriteria Decision Making 9, 3 (2023), 250-279.
  • [35] Öztürk, E. G., Rodrigues, A. M., and Ferreira, J. S. Using AHP to deal with sectorization problems. In Proceedings of the 4th European International Conference on Industrial Engineering and Operations Management (IEOM), (Rome, Italy, 2021), IEOM Society International, pp. 460-471.
  • [36] Perrier, N., Langevin, A., and Campbell, J. F. The sector design and assignment problem for snow disposal operations. European Journal of Operational Research 189, 2 (2008), 508-525.
  • [37] Prischink, M., Kloimüllner, C., Biesinger, B., and Raidl, G. R. Districting and routing for security control. In Hybrid Metaheuristics. Proceedings of the 10th International Workshop, HM 2016 - Plymouth, UK, June 8-10, 2016 (Cham, 2016), M. J. Blesa, C. Blum, A. Cangelosi, V. Cutello, A. Di Nuovo, M. Pavone and E.-G.i Talbi, Eds., vol. 9668 of Lecture Notes in Computer Science, Springer, pp. 87-103.
  • [38] Richter, A., Ng, K. T. W., and Karimi, N. The role of compactness distribution on the development of regionalized waste management systems. Journal of Cleaner Production 296 (2021), 126594.
  • [39] Ríos-Mercado, R. Z., and Bard, J. F. An exact algorithm for designing optimal districts in the collection of waste electric and electronic equipment through an improved reformulation. European Journal of Operational Research 276, 1 (2019), 259-271.
  • [40] Rodrigues, A. M., and Ferreira, J. S. Sectors and routes in solid waste collection. In Operational Research. IO 2013 - XVI Congress of APDIO - Bragança, Portugal, June 3-5, 2013 (Cham, 2015), J. P. Almeida, J. F. Oliveira, A. A. Pinto, Eds., vol. 4 of CIM Series in Mathematical Sciences, Springer, pp. 353-375.
  • [41] Rudenko, O., and Schoenauer, M. A steady performance stopping criterion for pareto-based evolutionary algorithms. In 6th International Multi-Objective Programming and Goal Programming Conference (Hammamet, Tunisia, 2004).
  • [42] Saaty, R. W. The analytic hierarchy process-what it is and how it is used. Mathematical Modelling 9, 3-5 (1987), 161-176.
  • [43] Saaty, T. L. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 3 (1977), 234-281.
  • [44] Saaty, T. L. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill International Book Co., New York, 1980.
  • 45] Tavares-Pereira, F., Figueira, J. R., Mousseau, V., and Roy, B. Multiple criteria districting problems. Annals of Operations Research 154, 1 (2007), 69-92.
  • [46] Thomas, J., and Chaudhari, N. S. A new metaheuristic genetic-based placement algorithm for 2D strip packing. Journal of Industrial Engineering International 10, 1 (2014), 47.
  • [47] Thorndike, R. L. Who belongs in the family? Psychometrika 18, 4 (1953), 267-276.
  • [48] Vanneschi, L., Henriques, R., and Castelli, M. Multi-objective genetic algorithm with variable neighbourhood search for the electoral redistricting problem. Swarm and Evolutionary Computation 36 (2017), 37-51.
  • [49] Wong, C. S. Y., Sundaram, S., and Sundararajan, N. CDAS: A cognitive decision-making architecture for dynamic airspace sectorization for efficient operations. IEEE Transactions on Intelligent Transportation Systems 20, 5 (2019), 1659-1668.
  • [50] Zhang, K., Yan, H., Zeng, H., Xin, K., and Tao, T. A practical multi-objective optimization sectorization method for water distribution network. Science of the Total Environment 656 (2019), 1401-1412.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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