This paper proposes a modified Genetic Programming method for forecasting the mobile telecommunications subscribers’ population. The method constitutes an expansion of the hybrid Genetic Programming (hGP) method improved by the introduction of diffusion models for technological forecasting purposes in the initial population, such as the Logistic, Gompertz, and Bass, as well as the Bi-Logistic and LogInLog. In addition, the aforementioned functions and models expand the function set of hGP. The application of the method in combination with macroeconomic indicators such as Gross Domestic Product per Capita (GDPpC) and Consumer Prices Index (CPI) leads to the creation of forecasting models and scenarios for medium- and long-term level of predictability. The forecasting module of the program has also been improved with the multi-levelled use of the statistical indices as fitness functions and model selection indices. The implementation of the modified-hGP in the datasets of mobile subscribers in the Organisation for Economic Cooperation and Development (OECD) countries shows very satisfactory forecasting performance. 1. Introduction Forecasting is an endogenous process intertwined with the evolution of science. Forecasting methodology is divided into two categories: qualitative and quantitative. Qualitative methods employ the judgment of experts group to produce forecasts . These procedures are mainly applied without using historical data. Quantitative forecasting methods are used when historical data are available as well as the assumption that some of the past patterns will be repeated in the future . There is a variation of quantitative methods such as the time series forecasting which use past trend to forecast the future values of the variable and causal methods that, besides the past trend assumption, also examine the correlation of the variable with other indicators. The adoption of innovative technologies by a society such as the mobile telecommunications adoption has been discussed and some widely used forecasting models have been proposed. The diffusion processes as well as the produced models are described in the literature [3–8]. The most commonly used diffusion models are Gompertz, Logistic, and Bass  which are dynamic models and follow a sigmoid curve against time. In order to follow the overall diffusion process of the mobile wireless penetration in time, we also employ the Bi-Logistic and LogInLog models which are described in the next section of this paper. The parameters of the models have been estimated by regression analysis
S. Konstantinos and S. Vasilios, “A new empirical model for short-term forecasting of the broadband penetration: a short research in Greece,” Modelling and Simulation in Engineering, vol. 2011, Article ID 798960, 10 pages, 2011.
K. Salpasaranis and V. Stylianakis, “A hybrid genetic programming method in optimization and forecasting: a case study of the broadband penetration in OECD countries,” Advances in Operations Research, vol. 2012, Article ID 904797, 32 pages, 2012.
J. Duda and S. Szyd？o, “Collective intelligence of genetic programming for macroeconomic forecasting,” in Proceedings of the Computational Collective Intelligence. Technologies and Applications (ICCCI '11), vol. 6923 of Lecture Notes in Computer Science, pp. 445–454, Springer, Berlin, Germany, 2011.
W. B. Langdon, R. Poli, N. F. McPhee, and J. R. Koza, “Genetic programming: an introduction and tutorial, with a survey of techniques and applications,” Studies in Computational Intelligence, vol. 115, pp. 927–1028, 2008.