Abstract
This paper introduces a method for estimating the interregional transportation of certain commodities in those cases where the commodity flows are not readily available and only aggregated flows per origin-destination pair are provided. We use a doubly-constrained gravity model to find a matrix of aggregated flows that is as similar as possible to the available data, in the sense of the standardized root mean square error. This model is calibrated via a real-valued genetic algorithm that uses a combination of global and local searches to find a set of optimal parameters of the deterrence function under study in the gravity model. This method is introduced as an application to estimating the disaggregated flows of ten different products among the fifteen regions of peninsular Spain between 2007 and 2016. After testing several formulations, we conclude that an exponential deterrence function calibrated with data from 2010 is as effective to estimate the flows in this 10-year span as other more complex options, which emphasizes the time transferability of our model.
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References
Arbués, P., Baños, J.F.: A dynamic approach to road freight flows modeling in Spain. Transportation 43(3), 549–564 (2016)
Babri, S., Jørnsten, K., Viertel, M.: Application of gravity models with a fixed component in the international trade flows of coal, iron ore and crude oil. Marit. Econ. Logist. 19(2), 334–351 (2017)
Balcan, D., Colizza, V., Gonçalves, B., Hu, H., Ramasco, J.J., Vespignani, A.: Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl. Acad. Sci. 106(51), 21484–21489 (2009)
Bensassi, S., Márquez-Ramos, L., Martínez-Zarzoso, I., Suárez-Burguet, C.: Relationship between logistics infrastructure and trade: evidence from Spanish regional exports. Transp. Res. Part A Policy Pract. 72, 47–61 (2015)
Bureau of Transportation Statistics (2017a) Freight facts & figures 2017. URL https://www.bts.gov/bts-publications/freight-facts-and-figures/freight-facts-figures-2017-chapter-2-freight-moved, [Online; Accessed 18 June 2018]
Bureau of Transportation Statistics (2017b) Freight facts & figures 2017—Chapter 2: freight moved in domestic and international trade. Table 2-1, Weight of shipments by transportation mode. URL https://www.bts.gov/bts-publications/freight-facts-and-figures/freight-facts-figures-2017-chapter-2-freight-moved, [Online; Accessed 29 Nov 2018]
Cascetta, E., Pagliara, F., Papola, A.: Alternative approaches to trip distribution modelling: a retrospective review and suggestions for combining different approaches. Pap. Reg. Sci. 86(4), 597–620 (2007)
Cascetta, E., Marzano, V., Papola, A.: Multi-regional input-output models for freight demand simulation at a national level. In: Ben-Akiva, M., Meersman, H., Voorde, E.V.D. (eds.) Recent Developments in Transport Modelling: Lessons for the Freight Sector, pp. 93–116. Emerald Group Publishing Limited (2008)
Celik, H.M.: Modeling freight distribution using artificial neural networks. J. Transp. Geogr. 12(2), 141–148 (2004)
Celik, H.M.: Sample size needed for calibrating trip distribution and behavior of the gravity model. J. Transp. Geogr. 18(1), 183–190 (2010)
Celik, H.M., Guldmann, J.M.: Spatial interaction modeling of interregional commodity flows. Socio-Econ. Plan. Sci. 41(2), 147–162 (2007)
Chow, J.Y., Yang, C.H., Regan, A.C.: State-of-the art of freight forecast modeling: lessons learned and the road ahead. Transportation 37(6), 1011–1030 (2010)
Delgado, J.C., Bonnel, P.: Level of aggregation of zoning and temporal transferability of the gravity distribution model: the case of Lyon. J. Transp. Geogr. 51, 17–26 (2016)
Dennett, A., Wilson, A.: A multilevel spatial interaction modelling framework for estimating interregional migration in Europe. Environ. Plan. A 45(6), 1491–1507 (2013)
de Grange, L., Ibeas, A., González, F.: A hierarchical gravity model with spatial correlation: mathematical formulation and parameter estimation. Netw. Spat. Econ. 11(3), 439–463 (2011)
Diplock, G., Openshaw, S.: Using simple genetic algorithms to calibrate spatial interaction models. Geogr. Anal. 28(3), 262–279 (1996)
Dréo, J., Pétrowski, A., Siarry, P., Taillard, E.: Metaheuristics for hard optimization: methods and case studies. Springer, Berlin (2006)
Eurostat (n.d.) Freight transport statistics. URL http://ec.europa.eu/eurostat/statistics-explained/index.php/Freight_transport_statistics, [Online; Accessed 18 June 2018]
Furness, K.: Time function iteration. Traffic Eng. Control 7(7), 458–460 (1965)
Grosche, T., Rothlauf, F., Heinzl, A.: Gravity models for airline passenger volume estimation. J. Air Transp. Manag. 13(4), 175–183 (2007)
Haupt, R.L., Haupt, S.E.: Practical Genetic Algorithms. Wiley (2004)
Havenga, J.H., Simpson, Z.P.: National freight demand modelling: a tool for macrologistics management. Int. J. Logist. Manag. 29(4), 1171–1195 (2018)
Homaifar, A., Qi, C.X., Lai, S.H.: Constrained optimization via genetic algorithms. Simulation 62(4), 242–253 (1994)
Jebari, K., Madiafi, M.: Selection methods for genetic algorithms. Int. J. Emerg. Sci. 3(4), 333–344 (2013)
Jin, P.J., Cebelak, M., Yang, F., Zhang, J., Walton, C.M., Ran, B.: Location-based social networking data: exploration into use of doubly constrained gravity model for origin-destination estimation. Transp. Res. Rec. 2430(1), 72–82 (2014)
Kapur, J.N.: Maximum-Entropy Models in Science and Engineering. Wiley, Hoboken (1989)
Kim, C., Choi, C.G., Cho, S., Kim, D.: A comparative study of aggregate and disaggregate gravity models using seoul metropolitan subway trip data. Transp. Plan. Technol. 32(1), 59–70 (2009)
Knudsen, D.C., Fotheringham, A.S.: Matrix comparison, goodness-of-fit, and spatial interaction modeling. Int. Reg. Sci. Rev. 10(2), 127–147 (1986)
Kompil, M., Celik, H.M.: Modelling trip distribution with fuzzy and genetic fuzzy systems. Transp. Plan. Technol. 36(2), 170–200 (2013)
Lenormand, M., Huet, S., Gargiulo, F., Deffuant, G.: A universal model of commuting networks. PLoS ONE 7(10), e45985 (2012)
Lenormand, M., Bassolas, A., Ramasco, J.J.: Systematic comparison of trip distribution laws and models. J. Transp. Geogr. 51, 158–169 (2016)
Mao, S., Demetsky, M.J.: Calibration of the gravity model for truck freight flow distribution. Pennsylvania Transportation Institute, Pennsylvania State University, Technical Report (2002)
Martínez, L.M., Viegas, J.M.: A new approach to modelling distance-decay functions for accessibility assessment in transport studies. J. Transp. Geogr. 26, 87–96 (2013)
McArthur, D.P., Kleppe, G., Thorsen, I., Ubøe, J.: The spatial transferability of parameters in a gravity model of commuting flows. J. Transp. Geogr. 19(4), 596–605 (2011)
Ministerio de Fomento - Secretaría General Técnica (2016) Los Transportes y las Infraestructuras. Informe anual 2015. URL https://www.fomento.gob.es/AZ.BBMF.Web/documentacion/pdf/M-642_2015.pdf, [Online; Accessed 15 July 2019]
Ministerio de Fomento de España (2008) Estudio de costes del transporte de mercancías por carretera. URL https://www.fomento.gob.es/NR/rdonlyres/D12A4405-3DE8-4D87-8F06-8CED0E11DD3E/40278/EstudioCostesMercanciasCarreteraoctubre2008.pdf, [Online; Accessed 18 June 2018]
Mozolin, M., Thill, J.C., Usery, E.L.: Trip distribution forecasting with multilayer perceptron neural networks: a critical evaluation. Transp. Res. Part B Methodol. 34(1), 53–73 (2000)
Openshaw, S.: Neural network, genetic, and fuzzy logic models of spatial interaction. Environ. Plan. A 30(10), 1857–1872 (1998)
Ortúzar J. de D., Willumsen, L.G.: Modelling Transport. Wiley, Hoboken (2011)
Pooler, J.: An extended family of spatial interaction models. Prog. Hum. Geogr. 18(1), 17–39 (1994)
Richards, F.: A flexible growth function for empirical use. J. Exp. Bot. 10(2), 290–301 (1959)
Shrewsbury, J.S.: Calibration of trip distribution by generalised linear models. New Zealand Transport Agency Research Report, 473 (2012)
Stefanouli, M., Polyzos, S.: Gravity vs radiation model: two approaches on commuting in Greece. Transp. Res. Procedia 24, 65–72 (2017)
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Tang, L., Xiong, C., Zhang, L.: Spatial transferability of neural network models in travel demand modeling. J. Comput. Civ. Eng. 32(3), 04018010 (2018)
Tobler, W.R.: A computer movie simulating urban growth in the Detroit region. Econ. Geogr. 46(sup1), 234–240 (1970)
Venkatraman, S., Yen, G.G.: A generic framework for constrained optimization using genetic algorithms. IEEE Trans. Evol. Comput. 9(4), 424–435 (2005)
Wikimedia Commons: File:Comunidades autónomas de España.svg — Wikimedia Commons, the free media repository. URL https://commons.wikimedia.org/w/index.php?title=File:Comunidades_aut%C3%B3nomas_de_Espa%C3%B1a.svg&oldid=236275380, [Online; Accessed 29 Nov 2018] (2017)
Williams, I.: A comparison of some calibration techniques for doubly constrained models with an exponential cost function. Transp. Res. 10(2), 91–104 (1976)
Wilson, A.G.: A family of spatial interaction models, and associated developments. Environ. Plan. A 3(1), 1–32 (1971)
Wong, S.C., Wong, C., Tong, C.: A parallelized genetic algorithm for the calibration of lowry model. Parallel Comput. 27(12), 1523–1536 (2001)
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Javier Rubio-Herrero: Literature search and review, manuscript writing, statistical tests, and optimization methods. Jesús Muñuzuri: Literature search and review, manuscript writing.
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Rubio-Herrero, J., Muñuzuri, J. Indirect estimation of interregional freight flows with a real-valued genetic algorithm. Transportation 48, 257–282 (2021). https://doi.org/10.1007/s11116-019-10050-6
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DOI: https://doi.org/10.1007/s11116-019-10050-6