Parameter Tuning Algorithms in Modeling And Simulation
Yıl 2017,
Cilt: 1 Sayı: 2, 58 - 66, 30.06.2017
Rabia Korkmaz Tan
,
Şebnem Bora
Öz
In
this study, parameter optimization studies in modeling and simulations
performed in different areas are examined. The common feature of all works are
the modeling of systems which are difficult to observe their results in real
environment and the problem of setting up large parameter space. The goal is to
reflect the real system of the generated model, and it is necessary to select
the most suitable parameters in the large parameter space. This is an important
issue and is beyond the limits of human problem solving. From the work done, different classifications were developed to
categorize the methods of parameter adjustment and to evaluate the existing
work. This helps model developers to find the algorithm
that produce the optimal solution for the parameter tunning problem that will
arise in future modeling studies.
Kaynakça
- [1] Dobslaw, F., (2010) “A Parameter Tuning Framework for Metaheuristics Based on Design of Experiments and Artificial Neural Networks”, Proceeding of the International Conference on Computer Mathematics and Natural Computing.
[2] Turkay, M., (2006) “Optimization Models and Solution Algorithms, New Frontiers in Total Quality and Strategic Management”, Ed. S. Kingir, Gazi Publishing, Ankara, 309-328.
[3] Akgüç, A.,(2010) “SAYISAL Akışkanlar Dinamiği Problemlerinin Optimizasyon Analizlerinde Kriging Yönteminin Kullanılması”, Master, İstanbul Teknik Üniversetesi, Fen Bilimleri Enstitüsü.
[4] Myers, R., and Hancock, E.R., (2001) Empirical modelling of genetic algorithms, Evolutionary Computation , 9, 461–493.
[5] Taguchi, G. and Yokoyama, T., (2006) Taguchi Methods: Design of Experiments, ASI Press.
[6] Adenso-Diaz, B. and Laguna, M., (2006) Fine-tuning of algorithms using fractional experimental designs and local search, Operations Research, 54, 99–114.
[7] Czarn, A., MacNish, C., Vijayan, K., Turlach, B. and Gupta, R., (2004) “Statistical exploratory analysis of genetic algorithms”, IEEE Transactions on Evolutionary Computation, 8, 405–421.
[8] François, O. and Lavergne, C., (2001) Design of evolutionary algorithms—a statistical perspective, IEEE Transactions on Evolutionary Computation, 5, 129–148.
[9] Ramos, I., Goldbarg, M., Goldbarg, E. and Neto, A., (2005) “Logistic regression for parameter tuning on an evolutionary algorithm”, in: Proceedings of the 2005 IEEE Congress on Evolutionary Computation IEEE Congress on Evolutionary Computation, 2, IEEE Press, Edinburgh, UK,, 1061–1068.
[10] Coy, S.P., Golden, B.L., Runger, G.C. and Wasil, E.A., (2001) “Using experimental design to find effective parameter settings for heuristics”, Journal of Heuristics, 7, 77–97.
[11] Bartz-Beielstein, T., Parsopoulos, K. and Vrahatis, M., (2004) “Analysis of particle swarm optimization using computational statistics”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics, ICNAAM, Ed: Chalkis, Wiley, 34–37.
[12] Lasarczyk, C.W.G., (2007) Genetische programmierung einer algorithmischen chemie, Ph.D. Thesis, Technische Universiteit Dortmund.
[13] Bolme, D.S., Beveridge, J.R. Draper, B.A., Phillips, P.J. and Lui, Y.M., (2011) “Automatically Searching for Optimal Parameter Settings Using a Genetic Algorithm”, Computer Vision Systems - 8th International Conference, {ICVS}, Ed. James L. Crowley and Bruce A. Draper and Monique Thonnat, Springer, Sophia Antipolis, France, 6962, 213-222.
[14] Manuel, F., Franziska, K. and Frank, P., (2006) “Approaches for Resolving the Dilemma between Model Structure Refinement and Parameter Calibration in AgentBased Simulations”, In 5th International Joint Conference on Autonomous Agents and Multiagent Systems.
[15] Goldsman, D., Nelson, B.L. and Schmeiser B., (1991) “Methods for selecting the best system, in: WSC’91: Proceedings of the 23rd Conference on Winter Simulation”, IEEE Computer Society, Washington, DC, USA, 177–186.
[16] Maron, O. and Moore, A., (1997) The racing algorithm, model selection for lazy learners, in: Artificial Intelligence Review, Kluwer Academic Publishers, Norwell, MA, 11 USA, 193–225.
[17] Manuel, F., Franziska, K. and Frank, P., (2004) Techniques for Analysis and Calibration of Multi-Agent Simulations, Engineering Societies in the Agent World(ESAW), 3451, Ed. Marie Pierre Gleizes and Andrea Omicini and Franco Zambonelli, Springer, 97074 Würzburg, 305-321.
[18] Sallans, B., Pfister, A., Karatzoglou, A. and Dorffner, G., (2003) “Simulation and validation of an integrated markets model”, J. Artificial Societies and Social Simulation, 6, 4.
[19] Brax, N., Andonoff, E. , Gleizes, M. and Glize, P., (2013) “Self-adapted aided decision-making: Application to maritime surveillance”, Proceedings of the 5th International Conference on Agents and Artificial Intelligence (ICAART), Ed. Joaquim Filipe and Ana L. N. Fred, SciTePress, Barcelona, Spain, 419—422.
[20] Lemouzy, S., Camps, V., and Glize, P., (2011) “Principles and properties of a mas learning algorithm: A comparison with standard learning algorithms applied to implicit feedback assessment”, in Proceedings of the 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology(WI-IAT ’11), 02, IEEE Computer Society, Washington, DC, USA, 228–235.
[21] Sahin, Y., EROĞLU, A., (2014) “Kapasite Kısıtlı Araç Rotalama Problemi İçin Metasezgisel Yöntemler”, Bilimsel Yazın Taraması, Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 19, 4, 337-355.
[22] Basak, M.E., Kuntman, A. and Kuntman, H., (2009) “MOS parameter extraction and optimization with genetic algorithm”, Journal of Electrical and Electronics Engineering, Engineering Faculty, Istanbul University, 9, No 2, 1101-1107.
[23] Calvez, B., Hutzler, G., (2005) “Automatic tuning of agent-based models using genetic algorithms”, Proceedings of the 6th International Workshop on Multi-Agent Based Simulation (MABS'05), Ed. Jaime Simao Sichman and Luis Antunes, Springer, Utrecht, The Netherland, 3891, 41-57.
[24] Deliktaş, B., Türker, H.T., Coşkun, H., Bikçe, M., Ve Özdemir, E., (2005) “Genetik Algoritma Parametrelerinin Betonarme Kiriş Tasarımı Üzerine Etkisi”, Bölgesel Jeoloji-Tektonik ve Sismotektonik Deprem Kaynak Mekanizmaları ve Dalga Yayınımı Sempozyumu, Kocaeli.
[25] Imbault, F. and Lebart, K., (2004) A stochastic optimization approach for parameter tuning of support vector machines, ICPR, 597-600.
[26] Salwala, C. Kotrajaras, V. and Horkaew, P., (2010) “Improving Performance for Emergent Environments Parameter Tuning and Simulation in Games Using GPU”, Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on, 2, 37-41.
[27] Saraçoğlu, H. and Demirören, A., (2008) “Parametreleri Genetik Algoritma ile Ayarlanan Bulanık Kontrolör Yardımıyla Otomatik Gerilim Kontrolü”, Elektrik Elektronik-Bilgisayar Mühendisliği 12. Ulusal Kongresi, Eskişehir.
[28] Angeline, P.J., (1995) “Evolution revolution: An introduction to the special track on genetic and evolutionary programming”, IEEE Expert Intelligent Systems and their Applications 10, 6-10.
[29] Greffenstette, J.J., (1986) Optimisation of Control Parameters for Genetic Algorithms, In IEEE Transactions on Systems, Man and Cybernetics, 16, 122–128.
[30] Nannen, V. and Eiben, A.E., (2006) “A method for parameter calibration and relevance estimation in evolutionary algorithms”, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’06), Ed: M. Keijzer, Morgan Kaufmann, San Francisco, 183–190.
[31] Nannen, V. and Eiben, A.E., (2007) “Efficient Relevance Estimation and Value Calibration of evolutionary algorithm parameters”, in: IEEE Congress on Evolutionary Computation, 103–110.
[32] Nannen, V. and Eiben, A.E., (2007) “Relevance Estimation and Value Calibration of evolutionary algorithm parameters”, Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI), Ed: M. M. Veloso, Hyderabad, India 1034–1039.
[33] Smit, S.K. and Eiben A.E., (2009) “Comparing parameter tuning methods for evolutionary algorithms”, in: IEEE Congress on Evolutionary Computation, IEEE Press, Ed: Trondheim, 399–406.
[34] Smit, S.K. and Eiben, A.E., (2010) “Beating the ‘world champion’ evolutionary algorithm via REVAC tuning”, in: IEEE Congress on Evolutionary Computation, IEEE Computational Intelligence Society, IEEE Press, Barcelona, Spain, 1–8.
[35] Smit, S.K. and Eiben, A.E., (2010) Parameter tuning of evolutionary algorithms, Applications of Evolutionary Computation, in: Lecture Notes in Computer Science, Ed: generalist vs. specialist, in: C. Di Chio, et al., 6024, 542–551.
[36] Bullnheimer B., Hartl R.F., Strauss C., (1997) “A New Rank Based Version of the Ant System: A Computational Study”, Central European Journal for Operations Research and Economics.
[37] Calvez, B. and Hutzler, G., (2007) “Ant Colony Systems and the Calibration of Multi-Agent Simulations: a New Approach”, Multi-Agents for modelling Complex Systems (MA4CS'07) Satellite Workshop of the European Conference on Complex Systems (ECCS'07), Germany, 16.
[38] Dorigo M. and Gambardella L.M., (1997) Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem, IEEE Transactionson Evolutionary Computation, 1, 1, 53-66.
[39] Gambardella L.M. and Dorigo M., (1995) Ant-Q: “A Reinforcement Learning Approach to the Traveling Salesman Problem”, In Proceedings of the Eleventh International Conference on Machine Learning, Morgan Kaufmann, 252-260.
[40] Maniezzo, V., Colorni, A. and Dorigo, M., (1994) The ant system applied to the quadratic assignment problem, 11, 5, Technical Report IRIDIA/94-28, IRIDIA, Universite Libre de Bruxelles, Belgium.
[41] Stützle T. and Hoos H., (1997) “The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem”, Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC'97).
[42] Stützle T. and Hoos H., (1998) Improvements on the Ant System, Introducing the MAX-MIN Ant System, Artificial Neural Networks and Genetic Algorithms, Springer Verlag, Wien New York.
[43] White T., Pagurek B., Oppacher F., (2000) ASGA Improving the Ant System by Integration with Genetic Algorithms, Systems and Computer Engineering", Carleton University Pres.
[44] Calvez, B. and Hutzler, G., (2007) “Adaptive Dichotomic Optimization: a New Method for the Calibration Of Agent Based Models”, 21st Annual European Simulation and Modelling Conference (ESM 2007), Malta, 415-419.
[45] Banjanovic-Mehmedovic, L. and Karic, S., (2011) Robotic Assembly Replanning Agent Based on Neural Network Adjusted Vibration Parameters, Advances in Reinforcement Learning, Ed. Prof. Abdelhamid Mellouk, InTech.
[46] Doğru, F., (2015) “Güncel Optimizasyon Yöntemleri Kullanılarak Rezidüel Gravite Anomalilerinden Parametre Kestirimi”, Hacettepe Üniversitesi Yerbilimleri Uygulama ve Araştırma Merkezi Bülteni, 36, 1, 31-43, Ankara, 2015
[47] Mcculloch, W. S. and Pitts, W., (1990) A Logical Callculus of The Ideas Immanent in Nervous Activityy, Bulletin of Mothemnticnl Biology, 52, l/2, 99-115.
[48] Cavuslu, M.A., Karakuzu, C. ve Şahin, Ş., (2010) “Parçacık Sürü Optimizasyonu Algoritması ile Yapay Sinir Ağı Eğitiminin FPGA Üzerinde Donanımsal Gerçeklenmesi”, Politeknik Dergisi, 13, 2, 83-92.
Yıl 2017,
Cilt: 1 Sayı: 2, 58 - 66, 30.06.2017
Rabia Korkmaz Tan
,
Şebnem Bora
Kaynakça
- [1] Dobslaw, F., (2010) “A Parameter Tuning Framework for Metaheuristics Based on Design of Experiments and Artificial Neural Networks”, Proceeding of the International Conference on Computer Mathematics and Natural Computing.
[2] Turkay, M., (2006) “Optimization Models and Solution Algorithms, New Frontiers in Total Quality and Strategic Management”, Ed. S. Kingir, Gazi Publishing, Ankara, 309-328.
[3] Akgüç, A.,(2010) “SAYISAL Akışkanlar Dinamiği Problemlerinin Optimizasyon Analizlerinde Kriging Yönteminin Kullanılması”, Master, İstanbul Teknik Üniversetesi, Fen Bilimleri Enstitüsü.
[4] Myers, R., and Hancock, E.R., (2001) Empirical modelling of genetic algorithms, Evolutionary Computation , 9, 461–493.
[5] Taguchi, G. and Yokoyama, T., (2006) Taguchi Methods: Design of Experiments, ASI Press.
[6] Adenso-Diaz, B. and Laguna, M., (2006) Fine-tuning of algorithms using fractional experimental designs and local search, Operations Research, 54, 99–114.
[7] Czarn, A., MacNish, C., Vijayan, K., Turlach, B. and Gupta, R., (2004) “Statistical exploratory analysis of genetic algorithms”, IEEE Transactions on Evolutionary Computation, 8, 405–421.
[8] François, O. and Lavergne, C., (2001) Design of evolutionary algorithms—a statistical perspective, IEEE Transactions on Evolutionary Computation, 5, 129–148.
[9] Ramos, I., Goldbarg, M., Goldbarg, E. and Neto, A., (2005) “Logistic regression for parameter tuning on an evolutionary algorithm”, in: Proceedings of the 2005 IEEE Congress on Evolutionary Computation IEEE Congress on Evolutionary Computation, 2, IEEE Press, Edinburgh, UK,, 1061–1068.
[10] Coy, S.P., Golden, B.L., Runger, G.C. and Wasil, E.A., (2001) “Using experimental design to find effective parameter settings for heuristics”, Journal of Heuristics, 7, 77–97.
[11] Bartz-Beielstein, T., Parsopoulos, K. and Vrahatis, M., (2004) “Analysis of particle swarm optimization using computational statistics”, Proceedings of the International Conference of Numerical Analysis and Applied Mathematics, ICNAAM, Ed: Chalkis, Wiley, 34–37.
[12] Lasarczyk, C.W.G., (2007) Genetische programmierung einer algorithmischen chemie, Ph.D. Thesis, Technische Universiteit Dortmund.
[13] Bolme, D.S., Beveridge, J.R. Draper, B.A., Phillips, P.J. and Lui, Y.M., (2011) “Automatically Searching for Optimal Parameter Settings Using a Genetic Algorithm”, Computer Vision Systems - 8th International Conference, {ICVS}, Ed. James L. Crowley and Bruce A. Draper and Monique Thonnat, Springer, Sophia Antipolis, France, 6962, 213-222.
[14] Manuel, F., Franziska, K. and Frank, P., (2006) “Approaches for Resolving the Dilemma between Model Structure Refinement and Parameter Calibration in AgentBased Simulations”, In 5th International Joint Conference on Autonomous Agents and Multiagent Systems.
[15] Goldsman, D., Nelson, B.L. and Schmeiser B., (1991) “Methods for selecting the best system, in: WSC’91: Proceedings of the 23rd Conference on Winter Simulation”, IEEE Computer Society, Washington, DC, USA, 177–186.
[16] Maron, O. and Moore, A., (1997) The racing algorithm, model selection for lazy learners, in: Artificial Intelligence Review, Kluwer Academic Publishers, Norwell, MA, 11 USA, 193–225.
[17] Manuel, F., Franziska, K. and Frank, P., (2004) Techniques for Analysis and Calibration of Multi-Agent Simulations, Engineering Societies in the Agent World(ESAW), 3451, Ed. Marie Pierre Gleizes and Andrea Omicini and Franco Zambonelli, Springer, 97074 Würzburg, 305-321.
[18] Sallans, B., Pfister, A., Karatzoglou, A. and Dorffner, G., (2003) “Simulation and validation of an integrated markets model”, J. Artificial Societies and Social Simulation, 6, 4.
[19] Brax, N., Andonoff, E. , Gleizes, M. and Glize, P., (2013) “Self-adapted aided decision-making: Application to maritime surveillance”, Proceedings of the 5th International Conference on Agents and Artificial Intelligence (ICAART), Ed. Joaquim Filipe and Ana L. N. Fred, SciTePress, Barcelona, Spain, 419—422.
[20] Lemouzy, S., Camps, V., and Glize, P., (2011) “Principles and properties of a mas learning algorithm: A comparison with standard learning algorithms applied to implicit feedback assessment”, in Proceedings of the 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology(WI-IAT ’11), 02, IEEE Computer Society, Washington, DC, USA, 228–235.
[21] Sahin, Y., EROĞLU, A., (2014) “Kapasite Kısıtlı Araç Rotalama Problemi İçin Metasezgisel Yöntemler”, Bilimsel Yazın Taraması, Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 19, 4, 337-355.
[22] Basak, M.E., Kuntman, A. and Kuntman, H., (2009) “MOS parameter extraction and optimization with genetic algorithm”, Journal of Electrical and Electronics Engineering, Engineering Faculty, Istanbul University, 9, No 2, 1101-1107.
[23] Calvez, B., Hutzler, G., (2005) “Automatic tuning of agent-based models using genetic algorithms”, Proceedings of the 6th International Workshop on Multi-Agent Based Simulation (MABS'05), Ed. Jaime Simao Sichman and Luis Antunes, Springer, Utrecht, The Netherland, 3891, 41-57.
[24] Deliktaş, B., Türker, H.T., Coşkun, H., Bikçe, M., Ve Özdemir, E., (2005) “Genetik Algoritma Parametrelerinin Betonarme Kiriş Tasarımı Üzerine Etkisi”, Bölgesel Jeoloji-Tektonik ve Sismotektonik Deprem Kaynak Mekanizmaları ve Dalga Yayınımı Sempozyumu, Kocaeli.
[25] Imbault, F. and Lebart, K., (2004) A stochastic optimization approach for parameter tuning of support vector machines, ICPR, 597-600.
[26] Salwala, C. Kotrajaras, V. and Horkaew, P., (2010) “Improving Performance for Emergent Environments Parameter Tuning and Simulation in Games Using GPU”, Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on, 2, 37-41.
[27] Saraçoğlu, H. and Demirören, A., (2008) “Parametreleri Genetik Algoritma ile Ayarlanan Bulanık Kontrolör Yardımıyla Otomatik Gerilim Kontrolü”, Elektrik Elektronik-Bilgisayar Mühendisliği 12. Ulusal Kongresi, Eskişehir.
[28] Angeline, P.J., (1995) “Evolution revolution: An introduction to the special track on genetic and evolutionary programming”, IEEE Expert Intelligent Systems and their Applications 10, 6-10.
[29] Greffenstette, J.J., (1986) Optimisation of Control Parameters for Genetic Algorithms, In IEEE Transactions on Systems, Man and Cybernetics, 16, 122–128.
[30] Nannen, V. and Eiben, A.E., (2006) “A method for parameter calibration and relevance estimation in evolutionary algorithms”, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’06), Ed: M. Keijzer, Morgan Kaufmann, San Francisco, 183–190.
[31] Nannen, V. and Eiben, A.E., (2007) “Efficient Relevance Estimation and Value Calibration of evolutionary algorithm parameters”, in: IEEE Congress on Evolutionary Computation, 103–110.
[32] Nannen, V. and Eiben, A.E., (2007) “Relevance Estimation and Value Calibration of evolutionary algorithm parameters”, Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI), Ed: M. M. Veloso, Hyderabad, India 1034–1039.
[33] Smit, S.K. and Eiben A.E., (2009) “Comparing parameter tuning methods for evolutionary algorithms”, in: IEEE Congress on Evolutionary Computation, IEEE Press, Ed: Trondheim, 399–406.
[34] Smit, S.K. and Eiben, A.E., (2010) “Beating the ‘world champion’ evolutionary algorithm via REVAC tuning”, in: IEEE Congress on Evolutionary Computation, IEEE Computational Intelligence Society, IEEE Press, Barcelona, Spain, 1–8.
[35] Smit, S.K. and Eiben, A.E., (2010) Parameter tuning of evolutionary algorithms, Applications of Evolutionary Computation, in: Lecture Notes in Computer Science, Ed: generalist vs. specialist, in: C. Di Chio, et al., 6024, 542–551.
[36] Bullnheimer B., Hartl R.F., Strauss C., (1997) “A New Rank Based Version of the Ant System: A Computational Study”, Central European Journal for Operations Research and Economics.
[37] Calvez, B. and Hutzler, G., (2007) “Ant Colony Systems and the Calibration of Multi-Agent Simulations: a New Approach”, Multi-Agents for modelling Complex Systems (MA4CS'07) Satellite Workshop of the European Conference on Complex Systems (ECCS'07), Germany, 16.
[38] Dorigo M. and Gambardella L.M., (1997) Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem, IEEE Transactionson Evolutionary Computation, 1, 1, 53-66.
[39] Gambardella L.M. and Dorigo M., (1995) Ant-Q: “A Reinforcement Learning Approach to the Traveling Salesman Problem”, In Proceedings of the Eleventh International Conference on Machine Learning, Morgan Kaufmann, 252-260.
[40] Maniezzo, V., Colorni, A. and Dorigo, M., (1994) The ant system applied to the quadratic assignment problem, 11, 5, Technical Report IRIDIA/94-28, IRIDIA, Universite Libre de Bruxelles, Belgium.
[41] Stützle T. and Hoos H., (1997) “The MAX-MIN Ant System and Local Search for the Traveling Salesman Problem”, Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC'97).
[42] Stützle T. and Hoos H., (1998) Improvements on the Ant System, Introducing the MAX-MIN Ant System, Artificial Neural Networks and Genetic Algorithms, Springer Verlag, Wien New York.
[43] White T., Pagurek B., Oppacher F., (2000) ASGA Improving the Ant System by Integration with Genetic Algorithms, Systems and Computer Engineering", Carleton University Pres.
[44] Calvez, B. and Hutzler, G., (2007) “Adaptive Dichotomic Optimization: a New Method for the Calibration Of Agent Based Models”, 21st Annual European Simulation and Modelling Conference (ESM 2007), Malta, 415-419.
[45] Banjanovic-Mehmedovic, L. and Karic, S., (2011) Robotic Assembly Replanning Agent Based on Neural Network Adjusted Vibration Parameters, Advances in Reinforcement Learning, Ed. Prof. Abdelhamid Mellouk, InTech.
[46] Doğru, F., (2015) “Güncel Optimizasyon Yöntemleri Kullanılarak Rezidüel Gravite Anomalilerinden Parametre Kestirimi”, Hacettepe Üniversitesi Yerbilimleri Uygulama ve Araştırma Merkezi Bülteni, 36, 1, 31-43, Ankara, 2015
[47] Mcculloch, W. S. and Pitts, W., (1990) A Logical Callculus of The Ideas Immanent in Nervous Activityy, Bulletin of Mothemnticnl Biology, 52, l/2, 99-115.
[48] Cavuslu, M.A., Karakuzu, C. ve Şahin, Ş., (2010) “Parçacık Sürü Optimizasyonu Algoritması ile Yapay Sinir Ağı Eğitiminin FPGA Üzerinde Donanımsal Gerçeklenmesi”, Politeknik Dergisi, 13, 2, 83-92.