Integrating Multi-Criteria Methodology With Symbolic Regression on Loan Modelling in Banking Sector
DOI:
https://doi.org/10.2298/YJOR250615041BKeywords:
Loan modelling, symbolic regression, multi-criteria methodology, banking sectorAbstract
Forecasting loans accurately is essential for the banking sector as it underpins effective risk management, capital allocation, and portfolio optimization. This study aims to model loans in the Turkish banking sector by integrating symbolic regression with multicriteria decision-making methodologies. Monthly data from January 2004 to September 2024, derived from banks’ financial statements, are utilized for the analysis. The optimal parameter configuration for symbolic regression is determined using the TODIM (an acronym in Portuguese for Interative Multi-criteria Decision Making) methodology. The forecasting performance of symbolic regression is evaluated against established models, including Autoregressive Integrated Moving Average (ARIMA), Gaussian Process Regression (GPR), Support Vector Machines (SVM), Neural Networks (NN), Regression Trees (RT), and Long Short-Term Memory (LSTM) network models. The proposed approach is applied across private, public, and foreign banks, as well as the overall banking sector. A significant finding of this study is the identification of a robust relationship between loans and two critical variables: assets and deposits. These results underscore the importance of strengthening deposit mobilization strategies and enhancing asset utilization to effectively grow banks’ loan portfolios.
References
R. C. Merton and Z. Bodie, “A conceptual framework for analyzing the financial environment,” in The Global Financial System: A Functional Perspective, 1st ed., D. B. Crane et al., Eds. Boston, MA, USA: Harvard Business School Press, pp. 3–31, 1995.
C. B. Azolibe, “Banking sector intermediation development and economic growth: Evidence from Nigeria,” Journal of African Business, vol. 23, no. 3, pp. 757–774, 2021, doi: 10.1080/15228916.2021.1926857.
Z. Yakubu and A. Y. Affoi, “An analysis of commercial banks’ credit on economic growth in Nigeria,” Current Research Journal of Economic Theory, vol. 6, no. 1, pp. 11–15, 2014.
W. Yitayew, “The impact of the banking sector on the real economy in Ethiopia: An empirical analysis,” Ph.D. dissertation, Addis Ababa University, Addis Ababa, Ethiopia, 2017.
I. Mallick, “Financial system performance and economic dynamics,” Global Journal of Management and Business Research, vol. 20, no. 9, pp. 23–42, 2020, doi: 10.1007/S11187-005-1996-6.
R. H. Clarida and M. Gertler, “How the Bundesbank conducts monetary policy,” in Reducing Inflation: Motivation and Strategy, 1st ed. Chicago, IL, USA: University of Chicago Press, pp. 363412, 1996.
G. Epstein, Central Banks, Inflation Targeting and Employment Creation. Geneva, Switzerland: International Labour Office, 2007.
J. N. Kallianiotis, “Central banks, monetary policy, and their efficiency,” in Monetary Policy: Perspectives, Strategies and Challenges, H. Ward, Ed. New York, NY, USA: Nova Science Publishers, pp. 82–120, 2017.
A. Cukierman, “Central bank independence and monetary policymaking institutions: Past, present and future,” European Journal of Political Economy, vol. 24, no. 4, pp. 722–736, 2008, doi: 10.1016/j.ejpoleco.2008.07.007.
M. Hellwig, “Liquidity provision, banking, and the allocation of interest rate risk,” European Economic Review, vol. 38, no. 7, pp. 1363–1389, 1994, doi: 10.1016/0014-2921(94)90015-9.
S. O. Fadare, “Banking sector liquidity and financial crisis in Nigeria,” International Journal of Economics and Finance, vol. 3, no. 5, pp. 3–11, 2011, doi: 10.5539/ijef.v3n5p3.
A. Lakstutiene, R. Krusinskas, and J. Platenkoviene, “Economic cycle and credit volume interaction: Case of Lithuania,” Engineering Economics, vol. 22, no. 5, pp. 468–476, 2011, doi: 10.5755/j01.ee.22.5.965.
I. M. Banu, “The impact of credit on economic growth in the global crisis context,” Procedia Economics and Finance, vol. 6, pp. 25–30, 2013, doi: 10.1016/S2212-5671(13)00109-3.
R. Stewart, M. Chowdhury, and V. Arjoon, “Interdependencies between regulatory capital, credit extension and economic growth,” Journal of Economics and Business, vol. 117, Art. no. 106010, 2021, doi: 10.1016/j.jeconbus.2021.106010.
H. Bai, “Unemployment and credit risk,” Journal of Financial Economics, vol. 142, no. 1, pp. 127145, 2021, doi: 10.1016/j.jfineco.2021.05.046.
A. Fernandez-Gallardo, “Preventing financial disasters: Macroprudential policy and financial crises,” European Economic Review, vol. 151, Art. no. 104350, 2023, doi: 10.1016/j.euroecorev.2022.104350.
C. Borio, “The financial cycle and macroeconomics: What have we learnt?,” Journal of Banking and Finance, vol. 45, pp. 182–198, 2014, doi: 10.1016/j.jbankfin.2013.07.031.
C. E. Weller, “Financial crises after financial liberalisation: Exceptional circumstances or structural weakness?,” Journal of Development Studies, vol. 38, no. 1, pp. 98–127, 2001, doi: 10.1080/00220380412331322201.
Y. Mimir, E. Sunel, and T. Taşkin, “Required reserves as a credit policy tool,” The B.E. Journal of Macroeconomics, vol. 13, no. 1, pp. 823–880, 2013, doi: 10.1515/bejm-2012-0093.
V. H. T. Nguyen, A. Boateng, and D. Newton, “Involuntary excess reserves, reserve requirements and credit rationing in China,” Applied Economics, vol. 47, no. 14, pp. 1424–1437, 2014, doi: 10.1080/00036846.2014.995362.
M. Brei and R. Moreno, “Reserve requirements and capital flows in Latin America,” Journal of International Money and Finance, vol. 99, Art. no. 102079, 2019, doi: 10.1016/j.jimonfin.2019.102079.
A. Zeynalova, “The impact of credit volume on money supply and economic growth in Azerbaijan: An econometric analysis,” Multidisciplinary Science Journal, vol. 6, no. 1, pp. 1–9, 2023, doi: 10.31893/multiscience.2024004.
A. Ghosh, “Banking-industry specific and regional economic determinants of non-performing loans: Evidence from U.S. states,” Journal of Financial Stability, vol. 20, pp. 93–104, 2015, doi: 10.1016/j.jfs.2015.08.004.
H. O. Makinde, “Implications of commercial bank loans on economic growth in Nigeria (19862014),” Journal of Emerging Trends in Economics and Management Sciences, vol. 7, no. 3, pp. 124136, 2016, doi: 10.10520/EJC196777.
B. N. Ashraf and Y. Shen, “Economic policy uncertainty and banks’ loan pricing,” Journal of Financial Stability, vol. 44, Art. no. 100695, 2019, doi: 10.1016/j.jfs.2019.100695.
K. O. Ochung, “Factors affecting loan repayment among customers of commercial banks in Kenya: A case of Barclays Bank of Kenya,” Ph.D. dissertation, University of Nairobi, Nairobi, Kenya, 2013.
F. P. S. R. Prabowo et al., “Effect of equity to assets ratio (EAR), size, and loan to assets ratio (LAR) on bank performance,” IOSR Journal of Economics and Finance, vol. 9, no. 4, pp. 1–6, 2018, doi: 10.9790/487X-0904010106.
M. Berlin and L. J. Mester, “Deposits and relationship lending,” The Review of Financial Studies, vol. 12, no. 3, pp. 579–607, 1999, doi: 10.1093/rfs/12.3.579.
E. Menicucci and G. Paolucci, “The determinants of bank profitability: Empirical evidence from the European banking sector,” Journal of Financial Reporting and Accounting, vol. 14, no. 1, pp. 86115, 2016, doi: 10.1108/JFRA-05-2015-0060.
T. D. Q. Le, “The interrelationship among bank profitability, bank stability, and loan growth: Evidence from Vietnam,” Cogent Business and Management, vol. 7, no. 1, Art. no. 1840488, 2020, doi: 10.1080/23311975.2020.1840488.
S. Dhar and A. Bakshi, “Determinants of loan losses of Indian banks: A panel study,” Journal of Asia Business Studies, vol. 9, no. 1, pp. 17–32, 2015, doi: 10.1108/JABS-04-2012-0017.
Y. Bayar, “Macroeconomic, institutional and bank-specific determinants of non-performing loans in emerging market economies: A dynamic panel regression analysis,” Journal of Central Banking Theory and Practice, vol. 8, no. 3, pp. 95–110, 2019, doi: 10.2478/jcbtp-2019-0026.
F. A. Almaqtari, E. A. Al-Homaidi, M. I. Tabash, and N. H. Farhan, “The determinants of profitability of Indian commercial banks: A panel data approach,” International Journal of Finance and Economics, vol. 24, no. 1, pp. 168–185, 2019, doi: 10.1002/ijfe.1655.
C. Ferreira, “Determinants of non-performing loans: A panel data approach,” International Advances in Economic Research, vol. 28, no. 3, pp. 133–153, 2022, doi: 10.1007/s11294-022-098609.
M. Quade, M. Abel, K. Shafi, R. K. Niven, and B. R. Noack, “Prediction of dynamical systems by symbolic regression,” Physical Review E, vol. 94, Art. no. 012214, 2016, doi: 10.1103/PhysRevE.94.012214.
W. La Cava et al., “Contemporary symbolic regression methods and their relative performance,” in Advances in Neural Information Processing Systems (NeurIPS), vol. 34, 2021.
L. Billard and E. Diday, “Symbolic regression analysis,” in Classification, Data Analysis, and Knowledge Organization. Berlin, Heidelberg: Springer, pp. 281–288, 2002, doi: 10.1007/978-3-64256181-8_31.
G. Kronberger, B. Burlacu, M. Kommenda, S. M. Winkler, and M. Affenzeller, Symbolic Regression. Boca Raton, FL, USA: Chapman and Hall/CRC, 2024, doi: 10.1201/9781315166407.
S. Kousar and N. Kausar, “Multi-criteria decision-making for sustainable agritourism: An integrated fuzzy-rough approach,” Spectrum of Operational Research, vol. 2, no. 1, pp. 134–150, 2025, doi: 10.31181/SOR21202515.
W. Zhang and H. Gao, “Interpretable robust multicriteria ranking with TODIM in generalized orthopair fuzzy settings,” Spectrum of Operational Research, vol. 3, no. 1, pp. 14–28, 2026, doi: 10.31181/SOR31202632.
G. Demir, “Strategic assessment of IoT technologies in healthcare: Grey MCDM approach,” Spectrum of Decision Making and Applications, vol. 2, no. 1, pp. 376–382, 2025, doi: 10.31181/SDMAP21202528.
K. Arman, N. Kundakcı, and A. Katrancı, “Digital innovation performance evaluation of European Union member and candidate countries with IDOCRIW and CRADIS methods,” Spectrum of Decision Making and Applications, vol. 3, no. 1, pp. 364–382, 2026, doi: 10.31181/SDMAP31202650.
E. A. Al-Homaidi, M. I. Tabash, N. H. S. Farhan, and F. A. Almaqtari, “Bank-specific and macroeconomic determinants of profitability of Indian commercial banks: A panel data approach,” Cogent Economics and Finance, vol. 6, no. 1, Art. no. 1548072, 2018, doi: 10.1080/23322039.2018.1548072.
R. Bansal, A. Singh, S. Kumar, and R. Gupta, “Evaluating factors of profitability for the Indian banking sector: A panel regression,” Asian Journal of Accounting Research, vol. 3, no. 2, pp. 236254, 2018, doi: 10.1108/AJAR-08-2018-0026.
D. Yuan, M. A. I. Gazi, I. Harymawan, B. K. Dhar, and A. I. Hossain, “Profitability determining factors of the banking sector: Panel data analysis of commercial banks in South Asian countries,” Frontiers in Psychology, vol. 13, Art. no. 1000412, 2022, doi: 10.3389/fpsyg.2022.1000412.
M. Malede, “Determinants of commercial banks’ lending: Evidence from Ethiopian commercial banks,” European Journal of Business and Management, vol. 6, no. 20, pp. 109–117, 2014.
T. Birhanu, S. B. Deressa, H. Azadi, A.-H. Viira, S. Van Passel, and F. Witlox, “Determinants of commercial bank loan and advance disbursement: The case of private Ethiopian commercial banks,” International Journal of Bank Marketing, vol. 39, no. 7, pp. 1227–1247, 2021, doi: 10.1108/IJBM05-2021-0166.
R. M. Said and M. Mahyoub, “Factors influencing non-performing loans: Empirical evidence from commercial banks in Malaysia,” Pressacademia, vol. 8, no. 3, pp. 160–166, 2021, doi: 10.17261/Pressacademia.2021.1448.
D. Cucinelli, “The impact of non-performing loans on bank lending behavior: Evidence from the Italian banking sector,” Eurasian Journal of Business and Economics, vol. 8, no. 16, pp. 59–71, 2015, doi: 10.17015/ejbe.2015.016.04.
N. Radivojevic and J. Jovovic, “Examining determinants of non-performing loans,” Prague Economic Papers, vol. 26, no. 3, pp. 300–316, 2017, doi: 10.18267/j.pep.615.
J. Kjosevski and M. Petkovski, “Non-performing loans in Baltic states: Determinants and macroeconomic effects,” Baltic Journal of Economics, vol. 17, no. 1, pp. 25–44, 2017, doi: 10.1080/1406099X.2016.1246234.
A. S. Messai and F. Jouini, “Micro and macro determinants of non-performing loans,” International Journal of Economics and Financial Issues, vol. 3, no. 4, pp. 852–860, 2013.
V. Makri, A. Tsagkanos, and A. Bellas, “Determinants of non-performing loans: The case of the Eurozone,” Panoeconomicus, vol. 61, no. 2, pp. 193–206, 2014, doi: 10.2298/PAN1402193M.
G. Jiménez and J. Saurina, “Credit cycles, credit risk, and prudential regulation,” International Journal of Central Banking, vol. 2, no. 2, pp. 65–98, 2006.
L. Abid, M. N. Ouertani, and S. Zouari-Ghorbel, “Macroeconomic and bank-specific determinants of household non-performing loans in Tunisia: A dynamic panel data approach,” Procedia Economics and Finance, vol. 13, pp. 58–68, 2014, doi: 10.1016/S2212-5671(14)00430-4.
A. N. Berger and R. DeYoung, “Problem loans and cost efficiency in commercial banks,” Journal of Banking and Finance, vol. 21, no. 6, pp. 849–870, 1997, doi: 10.1016/S0378-4266(97)00003-4.
G. H. Stern and R. J. Feldman, Too Big to Fail: The Hazards of Bank Bailouts, 1st ed. Lanham, MD, USA: Rowman and Littlefield, 2004, doi: 10.5860/choice.42-1064.
J. Podpiera and L. Weill, “Bad luck or bad management? Emerging banking market experience,” Journal of Financial Stability, vol. 4, no. 2, pp. 135–148, 2008, doi: 10.1016/j.jfs.2008.01.005.
V. Salas and J. Saurina, “Credit risk in two institutional regimes: Spanish commercial and savings banks,” Journal of Financial Services Research, vol. 22, no. 3, pp. 203–224, 2002, doi: 10.1023/A:1019781109676.
D. P. Louzis, A. T. Vouldis, and V. L. Metaxas, “Macroeconomic and bank-specific determinants of non-performing loans in Greece: A comparative study of mortgage, business, and consumer loan portfolios,” Journal of Banking and Finance, vol. 36, no. 4, pp. 1012–1027, 2012, doi: 10.1016/j.jbankfin.2011.10.012.
R. Ranjan and S. C. Dhal, “Non-performing loans and terms of credit of public sector banks in India: An empirical assessment,” Reserve Bank of India Occasional Papers, vol. 24, no. 3, pp. 81–121, 2003.
T. Elshaday, D. Kenenisa, and S. Mohammed, “Determinants of financial performance of commercial banks in Ethiopia: Special emphasis on private commercial banks,” African Journal of Business Management, vol. 12, no. 1, pp. 1–10, 2018, doi: 10.5897/AJBM2017.8470.
M. Karadima and H. Louri, “Non-performing loans in the euro area: Does bank market power matter?,” International Review of Financial Analysis, vol. 72, Art. no. 101593, 2020, doi: 10.1016/j.irfa.2020.101593.
F. A. Mensah and A. B. Adjei, “Determinants of non-performing loans in the Ghanaian banking industry,” Journal of Computational Economics and Econometrics, vol. 5, no. 1, pp. 35–54, 2015, doi: 10.1504/IJCEE.2015.066207.
G. Yang, X. Li, J. Wang, L. Lian, and T. Ma, “Modeling oil production based on symbolic regression,” Energy Policy, vol. 82, pp. 48–61, 2015, doi: 10.1016/j.enpol.2015.02.016.
X. Pan, M. K. Uddin, B. Ai, X. Pan, and U. Saima, “Influential factors of carbon emissions intensity in OECD countries: Evidence from symbolic regression,” Journal of Cleaner Production, vol. 220, pp. 1194–1201, 2019, doi: 10.1016/j.jclepro.2019.02.195.
P. Li, C. Tian, Z. Zhang, M. Li, and Y. Zheng, “Analysis of influencing factors of energy consumption in rural Henan based on symbolic regression method and the Tapio model,” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, vol. 43, no. 2, pp. 160–171, 2021, doi: 10.1080/15567036.2019.1623951.
C. Liu, W. Lyu, W. Zhao, F. Zheng, and J. Lu, “Exploratory research on influential factors of China’s sulfur dioxide emissions based on symbolic regression,” Environmental Monitoring and Assessment, vol. 195, no. 1, Art. no. 41, 2023, doi: 10.1007/s10661-022-10595-7.
L. Stajić, R. Praksová, D. Brkić, and P. Praks, “Estimation of global natural gas spot prices using big data and symbolic regression,” Resources Policy, vol. 95, Art. no. 105144, 2024, doi: 10.1016/j.resourpol.2024.105144.
A. F. Sheta, S. E. M. Ahmed, and H. Faris, “Evolving stock market prediction models using multigene symbolic regression genetic programming,” Artificial Intelligence and Machine Learning, 2015.
P. Orzechowski, W. La Cava, and J. H. Moore, “Where are we now? A large benchmark study of recent symbolic regression methods,” in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), 2018, pp. 1183–1190, doi: 10.1145/3205455.3205539.
C. Wilstrup and J. Kasak, “Symbolic regression outperforms other models for small data sets,” arXiv, 2021, Art. no. arXiv:2103.15147, doi: 10.48550/arXiv.2103.15147.
K. Drachal and M. Pawłowski, “Forecasting selected commodities’ prices with Bayesian symbolic regression,” International Journal of Financial Studies, vol. 12, no. 2, Art. no. 34, 2024, doi: 10.3390/ijfs12020034.
S. Kim et al., “Integration of neural network-based symbolic regression in deep learning for scientific discovery,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 9, pp. 4166–4177, 2021, doi: 10.1109/TNNLS.2020.3017010.
J. R. Koza, “Genetic programming as a means for programming computers by natural selection,” Statistics and Computing, vol. 4, no. 2, pp. 87–112, 1994, doi: 10.1007/BF00175355.
K. Zhang et al., “Neutrosophic management evaluation of insurance companies by a hybrid TODIM–BSC method: A case study of private insurance companies,” Management Decision, vol. 61, no. 2, pp. 363–381, 2023, doi: 10.1108/MD-01-2022-0120.
M. Kommenda, B. Burlacu, G. Kronberger, and M. Affenzeller, “Parameter identification for symbolic regression using nonlinear least squares,” Genetic Programming and Evolvable Machines, vol. 21, no. 4, pp. 471–501, 2020, doi: 10.1007/s10710-019-09371-3.
D. J. Bartlett, H. Desmond, and P. G. Ferreira, “Exhaustive symbolic regression,” IEEE Transactions on Evolutionary Computation, vol. 28, no. 4, pp. 950–964, 2024, doi: 10.1109/TEVC.2023.3280250.
L. Fan, Z. Su, X. Liu, and Y. Wang, “Decomposition-based cross-parallel multiobjective genetic programming for symbolic regression,” Applied Soft Computing, vol. 167, Art. no. 112239, 2024, doi: 10.1016/j.asoc.2024.112239.
N. Makke and S. Chawla, “Interpretable scientific discovery with symbolic regression: A review,” Artificial Intelligence Review, vol. 57, no. 1, Art. no. 2, 2024, doi: 10.1007/s10462-023-10622-0.
G. Yang, X. Li, J. Wang, L. Lian, and T. Ma, “Modeling oil production based on symbolic regression,” Energy Policy, vol. 82, pp. 48–61, 2015, doi: 10.1016/j.enpol.2015.02.016.
L. F. A. M. Gomes and M. M. P. P. Lima, “TODIM: Basics and application to multicriteria ranking of projects with environmental impacts,” Foundations of Computing and Decision Sciences, vol. 16, no. 4, pp. 113–127, 1992.
F. Alali and A. C. Tolga, “Portfolio allocation with the TODIM method,” Expert Systems with Applications, vol. 124, pp. 341–348, 2019, doi: 10.1016/j.eswa.2019.01.054.
Q. Wu et al., “An integrated generalized TODIM model for portfolio selection based on financial performance of firms,” Knowledge-Based Systems, vol. 249, Art. no. 108794, 2022, doi: 10.1016/j.knosys.2022.108794.
B. Aydoğan, M. Olgun, F. Smarandache, and M. Ünver, “A decision-making approach incorporating the TODIM method and sine entropy in q-rung picture fuzzy set settings,” Journal of Applied Mathematics, vol. 2024, pp. 1–17, Jan. 2024, doi: 10.1155/2024/3798588.
Q. Wu, X. Liu, J. Qin, W. Wang, and L. Zhou, “A linguistic distribution behavioral multicriteria group decision-making model integrating extended generalized TODIM and quantum decision theory,” Applied Soft Computing, vol. 98, Art. no. 106757, 2021, doi: 10.1016/j.asoc.2020.106757.
D. Liang, Y. Zhang, Z. Xu, and A. Jamaldeen, “Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality in the Ghanaian banking industry,” Applied Soft Computing, vol. 78, pp. 583–594, 2019, doi: 10.1016/j.asoc.2019.03.006.
F. Zhou and T.-Y. Chen, “A hybrid approach combining AHP with TODIM for blockchain technology provider selection under a Pythagorean fuzzy scenario,” Artificial Intelligence Review, vol. 55, no. 7, pp. 5411–5443, 2022, doi: 10.1007/s10462-021-10128-7.
J. Snoek, H. Larochelle, and R. P. Adams, “Practical Bayesian optimization of machine learning algorithms,” in Advances in Neural Information Processing Systems, vol. 25, pp. 2951–2959, 2012.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Yugoslav Journal of Operations Research

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.