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OPTIMIZATION OF PID CONTROLLER USING THE MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM BASED ON DECOMPOSITION

Yıl 2025, Cilt: 28 Sayı: 3, 1143 - 1158, 03.09.2025

Ali Fazıl Uygur

https://doi.org/10.17780/ksujes.1507716

Öz

In control system design, controller parameters need to be adjusted for the controller to show optimum performance. This is usually achieved by solving a “Multi-Objective Optimization Problem” (MOP). In this study, “Proportionality-Integral-Derivative” (PID) controller is considered as the controller and the optimization of the performance objectives selected as the overshoot and rise times of the controller is performed. Although it is possible to adjust the PID parameters by using “Evolutionary Algorithms” (EAs) belonging to the class of population-based optimization algorithms, the computational load of EAs increases when diversity and eliteness are considered for the found solutions. For this reason, an algorithm known as “Decomposition-Based Multi-Objective Evolutionary Algorithm” (MOEA/D) has been preferred instead of EAs for the solution of the optimization problem. With this algorithm, the MOP is addressed by decomposing it into a certain number of single-objective sub-problems over scalarization functions based on the Tchebycheff decomposition. Therefore, instead of a single optimum solution, a set of “Pareto Optimal” (PO) solutions is reached. In this study, the performances of the DC-DC buck converter were evaluated using PID controllers with PO parameter sets obtained with the help of MOEA/D.

Anahtar Kelimeler

Multi-Objective Optimization Evolutionary Algorithms Tchebycheff Decomposition PID Control DC-DC Buck Converter

Kaynakça

  • Abbasi, E., & Naghavi, N. (2017). Offline Auto-Tuning of a PID Controller Using Extended Classifire System (XCS) Algorithm. Journal of Advances in Computer Engineering and Technology, 3, 41–50. https://sanad.iau.ir/Journal/jacet/Article/789011
  • Aref, A., & Cai, H. (2015). A Genetic Algorithm-Based Multi-Objective Optimization for Hybrid Fiber Reinforced Polymeric Deck and Cable System of Cable-stayed Bridges. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s00158-015-1266-4
  • Åström, K. J., & Hägglund, T. (1984). Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica, 20(5), 645–651. https://doi.org/https://doi.org/10.1016/0005-1098(84)90014-1
  • Bandyopadhyay, S., Chakraborty, R., & Maulik, U. (2015). Priority based ∊ dominance: A new measure in multiobjective optimization. Information Sciences, 305, 97–109. https://doi.org/https://doi.org/10.1016/j.ins.2015.01.018
  • Chatterjee, S., & Mukherjee, V. (2016). PID controller for automatic voltage regulator using teaching–learning based optimization technique. International Journal of Electrical Power & Energy Systems, 77, 418–429. https://doi.org/https://doi.org/10.1016/j.ijepes.2015.11.010
  • Cohen, G. H., & Coon, G. A. (1953). Theoretical Consideration of Retarded Control. Journal of Fluids Engineering. https://api.semanticscholar.org/CorpusID:251187413 https://doi.org/10.1115/1.4015451
  • Das, I., & Dennis, J. (1996). Normal-Boundary Intersection: An Alternate Method for Generating Pareto Optimal Points in Multicriteria Optimization Problems. https://doi.org/10.1137/S1052623496307510
  • Deb, K. (2001). Multiobjective Optimization Using Evolutionary Algorithms. Wiley, New York.
  • El-Telbany, M. (2013). Tuning PID Controller for DC Motor: An Artificial Bees Optimization Approach. International Journal of Computer Applications (0975 – 8887), 77, 18–21. https://doi.org/10.5120/13559-1341
  • Grandhi, R. (1992). Structural optimization with frequency constraints - A review. AIAA Journal, 1. https://doi.org/10.2514/3.11928
  • Guenounou, O., Dahhou, B., & Athmani, B. (2012). Optimal design of PID controller by Multi-objective genetic algorithms. International Conference on Computer Related Knowledge (ICCRK’ 2012), 6p. https://hal.science/hal-02947644
  • Hartjes, S., & Visser, H. G. (2016). Efficient trajectory parameterization for environmental optimization of departure flight paths using a genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 231. https://doi.org/10.1177/0954410016648980
  • Hartjes, S., Visser, H. G., & Hebly, S. J. (2010). Optimisation of RNAV noise and emission abatement standard instrument departures. Aeronautical Journal, 114, 757–767. https://doi.org/10.1017/S0001924000004243
  • Hochstrate, N., Naujoks, B., & Emmerich, M. (2007). SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181, 1653–1669. https://doi.org/10.1016/j.ejor.2006.08.008
  • Huang, Y., Li, W., Liang, Z., Xue, Y., & Wang, X. (2018). Efficient business process consolidation: combining topic features with structure matching. Soft Computing, 22. https://doi.org/10.1007/s00500-016-2364-y
  • Jaszkiewicz, A. (2002). Jaszkiewicz, A.: On the Performance of Multiple-Objective Genetic Local Search on the 0/1 Knapsack Problem - A Comparative Experiment. IEEE Trans. on Evolutionary Computation 6, 402-412. Evolutionary Computation, IEEE Transactions On, 6, 402–412. https://doi.org/10.1109/TEVC.2002.802873
  • Joseph, S., & Dada, E. (2018a). Automatic Tuning of Proportional–Integral–Derivative Controller using Genetic Algorithm. 19, 51–57.
  • Joseph, S., & Dada, E. (2018b). Proportional-Integral-Derivative (PID) Controller Tuning For An Inverted Pendulum Using Particle Swarm Optimisation (PSO) Algorithm. 2.
  • Joseph, S., Mishra, M. K., & Omizegba, E. (2011). Automatic Tuning of Proportional-Integral-Derivative (PID) Controller Using Particle Swarm Optimization (PSO) Algorithm. International Journal of Artificial Intelligence & Applications, 2, 25–32. https://doi.org/10.5121/ijaia.2011.2403
  • Katal, N., Kumar, P., & Narayan, S. (2014). Optimal PID controller for coupled-tank liquid-level control system using bat algorithm. 2014 International Conference on Power, Control and Embedded Systems (ICPCES), 1–4. https://doi.org/10.1109/ICPCES.2014.7062818
  • Konstantinidis, A., & Yang, K. (2011). Multi-objective energy-efficient dense deployment in Wireless Sensor Networks using a hybrid problem-specific MOEA/D. Appl. Soft Comput., 11, 4117–4134. https://doi.org/10.1016/j.asoc.2011.02.031
  • Latha, K., Rajinikanth, V., & Surekha, P. (2013). PSO-Based PID Controller Design for a Class of Stable and Unstable Systems. ISRN Artificial Intelligence, 2013. https://doi.org/10.1155/2013/543607
  • Li, K., Kwong, S., Zhang, Q., & Deb, K. (2014). Interrelationship-Based Selection for Decomposition Multiobjective Optimization. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2014.2365354
  • Li, W., Li, K., Guo, L., Huang, Y., & Xue, Y. (2018). A new validity index adapted to fuzzy clustering algorithm. Multimedia Tools and Applications, 77. https://doi.org/10.1007/s11042-017-5550-8
  • Li, Y., Peng, Z., Liang, D., Chang, H., & Cai, Z. (2015). Facial age estimation by using stacked feature composition and selection. The Visual Computer, 32. https://doi.org/10.1007/s00371-015-1137-4
  • Li, Y., Wang, G., Nie, L., Wang, Q., & Tan, W. (2017). Distance Metric Optimization Driven Convolutional Neural Network for Age Invariant Face Recognition. Pattern Recognition, 75. https://doi.org/10.1016/j.patcog.2017.10.015
  • Messac, A., Ismail-Yahaya, A., & Mattson, C. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25, 86–98. https://doi.org/10.1007/s00158-002-0276-1
  • Miettinen, K. (1999). Nonlinear Multiobjective Optimization. Springer US. https://books.google.com.tr/books?id=ha_zLdNtXSMC https://doi.org/10.1007/978-1-4615-5563-6
  • Miettinen, K., & Mäkelä, M. (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24, 193–213. https://doi.org/10.1007/s00291-001-0092-9
  • R J, R., & Ananda, C. (2015). PSO tuned PID controller for controlling camera position in UAV using 2-axis gimbal. 128–133. https://doi.org/10.1109/ICPACE.2015.7274930
  • Ribeiro, J. M. S., Santos, M. F., Carmo, M. J., & Silva, M. F. (2017). Comparison of PID controller tuning methods: analytical/classical techniques versus optimization algorithms. 2017 18th International Carpathian Control Conference (ICCC), 533–538. https://doi.org/10.1109/CarpathianCC.2017.7970458
  • Sandoval, D., Soto, I., & Adasme, P. (2015). Control of Direct Current Motor using Ant Colony Optimization. https://doi.org/10.1109/Chilecon.2015.7400356
  • Senberber, H., & Bagis, A. (2017). Fractional PID controller design for fractional order systems using ABC algorithm. 1–7. https://doi.org/10.1109/ELECTRONICS.2017.7995218
  • Singh, K., Vasant, P., Elamvazuthi, I., & Kannan, R. (2015). PID Tuning of Servo Motor Using Bat Algorithm. Procedia Computer Science, 60, 1798–1808. https://doi.org/https://doi.org/10.1016/j.procs.2015.08.290
  • Srinivas, N., & Deb, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation - EC, 2, 221–248. https://doi.org/10.1162/evco.1994.2.3.221
  • Takieldeen, A., Mahmoud, A., & Elsawi, A. (2015). Optimal PID Tuning for DC Motor Speed Controller Based on Genetic Algorithm. International Review of Automatic Control (I.RE.A.CO.), 8, 80–85. https://doi.org/10.15866/ireaco.v8i1.4839
  • Tan, K. C., Khor, E. F., & Lee, T. H. (2005). Multiobjective Evolutionary Algorithms and Applications. https://doi.org/10.1007/1-84628-132-6
  • Trivedi, A., Srinivasan, D., Sanyal, K., & Ghosh, A. (2016). A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition. IEEE Transactions on Evolutionary Computation, PP, 1. https://doi.org/10.1109/TEVC.2016.2608507
  • Visser, H., & Hartjes, S. (2013). Economic and environmental optimization of flight trajectories connecting a city-pair. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 228, 980–993. https://doi.org/10.1177/0954410013485348
  • Vo, D.-T., Duong Gia, D., Ho-Huu, V., & Vu-Do, H. C. (2017). Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Composite Structures, 168. https://doi.org/10.1016/j.compstruct.2017.02.038
  • Waldock, A., & Corne, D. (2011). Multiple objective optimisation applied to route planning. Genetic and Evolutionary Computation Conference, GECCO’11, 1827–1834. https://doi.org/10.1145/2001576.2001821
  • Wang, H., Wang, W., Cui, Z., Zhou, X., Zhao, J., & Li, Y. (2018). A new dynamic firefly algorithm for demand estimation of water resources. Information Sciences, 438. https://doi.org/10.1016/j.ins.2018.01.041
  • Wu, H., Kuang, L., Wang, F., Rao, Q., Gong, M., & Li, Y. (2017). A Multiobjective Box-Covering Algorithm for Fractal Modularity on Complex Networks. Applied Soft Computing, 61. https://doi.org/10.1016/j.asoc.2017.07.034
  • Yadav, S., Verma, S. K., & Nagar, S. K. (2018). Performance enhancement of magnetic levitation system using teaching learning based optimization. Alexandria Engineering Journal, 57(4), 2427–2433. https://doi.org/https://doi.org/10.1016/j.aej.2017.08.016
  • Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731. https://doi.org/10.1109/TEVC.2007.892759
  • Zhang, S., Yang, Z., Xing, X., Gao, Y., Xie, D., & Wong, H.-S. (2017). Generalized Pair-Counting Similarity Measures for Clustering and Cluster Ensembles. IEEE Access, 5, 1. https://doi.org/10.1109/ACCESS.2017.2741221
  • Zhu, Y., Wang, J., & Qu, B. (2014). Multi-objective economic emission dispatch considering wind power using evolutionary algorithm based on decomposition. International Journal of Electrical Power & Energy Systems, 63, 434–445. https://doi.org/10.1016/j.ijepes.2014.06.027
  • Ziegler, B. J. G., & Nichols, N. B. (1942). Optimum Settings for Automatic Controllers. Journal of Fluids Engineering. https://api.semanticscholar.org/CorpusID:41336178 https://doi.org/10.1115/1.4019264
  • Ziegler, J. G., & Nichols, N. B. (1993). Optimum Settings for Automatic Controllers. Journal of Dynamic Systems, Measurement, and Control, 115(2B), 220–222. https://doi.org/10.1115/1.2899060

AYRIŞIMA DAYALI ÇOK AMAÇLI EVRİMSEL ALGORİTMA ÜZERİNDEN PID KONTROLCÜ PARAMETRELERİNİN OPTİMİZASYONU

Yıl 2025, Cilt: 28 Sayı: 3, 1143 - 1158, 03.09.2025

Ali Fazıl Uygur

https://doi.org/10.17780/ksujes.1507716

Öz

Kontrol sistemleri tasarımında, kontrolcünün optimum performans göstermesi için, kontrolcü parametrelerinin ayarlanması gerekir. Bu da genellikle bir “Çok Amaçlı Optimizasyon Problemi” (ÇOP)’un çözümüyle gerçekleşir. Bu çalışmada kontrolcü olarak “Orantı-İntegral-Türev” (PID) kontrolcü göz önüne alınmış ve kontrolcünün aşım ve yükselme zamanı olarak seçilen performans amaçlarının optimizasyonu gerçekleştirilmiştir. Her ne kadar popülasyon tabanlı optimizasyon algoritmaları sınıfına ait “Evrimsel Algoritma” (EA)’lar kullanılarak, PID parametrelerinin ayarlanması mümkün olsa da bulunan çözümler için çeşitlilik ve seçkinliğin gözetilmesi halinde EA’ların hesap yükü artmaktadır. Bu sebeple optimizasyon probleminin çözümü için EA’lar yerine “Ayrışıma Dayalı Çok Amaçlı Evrimsel Algoritma” (ÇAEA/A) olarak bilinen bir algoritma tercih edilmiştir. Bu algoritma ile, ÇOP, Tchebycheff ayrışımına dayalı skalerleştirme fonksiyonları üzerinden belli sayıda tek amaçlı alt problemlere ayrıştırılmak suretiyle ele alınmaktadır. Dolayısıyla tek bir optimum çözüm yerine “Pareto Optimal” (PO) çözümler kümesine ulaşılmaktadır. Yapılan çalışmada ÇAEA/A yardımıyla elde edilen PO parametre setlerine sahip PID kontrolcüler kullanılarak DC-DC Azaltan dönüştürücünün sergilediği performanslar değerlendirilmiştir.

Anahtar Kelimeler

Çok Amaçlı Optimizasyon Evrimsel Algoritmalar Tchebycheff ayrışımı PID Kontrol DC-DC Buck Dönüştürücü

Kaynakça

  • Abbasi, E., & Naghavi, N. (2017). Offline Auto-Tuning of a PID Controller Using Extended Classifire System (XCS) Algorithm. Journal of Advances in Computer Engineering and Technology, 3, 41–50. https://sanad.iau.ir/Journal/jacet/Article/789011
  • Aref, A., & Cai, H. (2015). A Genetic Algorithm-Based Multi-Objective Optimization for Hybrid Fiber Reinforced Polymeric Deck and Cable System of Cable-stayed Bridges. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s00158-015-1266-4
  • Åström, K. J., & Hägglund, T. (1984). Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica, 20(5), 645–651. https://doi.org/https://doi.org/10.1016/0005-1098(84)90014-1
  • Bandyopadhyay, S., Chakraborty, R., & Maulik, U. (2015). Priority based ∊ dominance: A new measure in multiobjective optimization. Information Sciences, 305, 97–109. https://doi.org/https://doi.org/10.1016/j.ins.2015.01.018
  • Chatterjee, S., & Mukherjee, V. (2016). PID controller for automatic voltage regulator using teaching–learning based optimization technique. International Journal of Electrical Power & Energy Systems, 77, 418–429. https://doi.org/https://doi.org/10.1016/j.ijepes.2015.11.010
  • Cohen, G. H., & Coon, G. A. (1953). Theoretical Consideration of Retarded Control. Journal of Fluids Engineering. https://api.semanticscholar.org/CorpusID:251187413 https://doi.org/10.1115/1.4015451
  • Das, I., & Dennis, J. (1996). Normal-Boundary Intersection: An Alternate Method for Generating Pareto Optimal Points in Multicriteria Optimization Problems. https://doi.org/10.1137/S1052623496307510
  • Deb, K. (2001). Multiobjective Optimization Using Evolutionary Algorithms. Wiley, New York.
  • El-Telbany, M. (2013). Tuning PID Controller for DC Motor: An Artificial Bees Optimization Approach. International Journal of Computer Applications (0975 – 8887), 77, 18–21. https://doi.org/10.5120/13559-1341
  • Grandhi, R. (1992). Structural optimization with frequency constraints - A review. AIAA Journal, 1. https://doi.org/10.2514/3.11928
  • Guenounou, O., Dahhou, B., & Athmani, B. (2012). Optimal design of PID controller by Multi-objective genetic algorithms. International Conference on Computer Related Knowledge (ICCRK’ 2012), 6p. https://hal.science/hal-02947644
  • Hartjes, S., & Visser, H. G. (2016). Efficient trajectory parameterization for environmental optimization of departure flight paths using a genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 231. https://doi.org/10.1177/0954410016648980
  • Hartjes, S., Visser, H. G., & Hebly, S. J. (2010). Optimisation of RNAV noise and emission abatement standard instrument departures. Aeronautical Journal, 114, 757–767. https://doi.org/10.1017/S0001924000004243
  • Hochstrate, N., Naujoks, B., & Emmerich, M. (2007). SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181, 1653–1669. https://doi.org/10.1016/j.ejor.2006.08.008
  • Huang, Y., Li, W., Liang, Z., Xue, Y., & Wang, X. (2018). Efficient business process consolidation: combining topic features with structure matching. Soft Computing, 22. https://doi.org/10.1007/s00500-016-2364-y
  • Jaszkiewicz, A. (2002). Jaszkiewicz, A.: On the Performance of Multiple-Objective Genetic Local Search on the 0/1 Knapsack Problem - A Comparative Experiment. IEEE Trans. on Evolutionary Computation 6, 402-412. Evolutionary Computation, IEEE Transactions On, 6, 402–412. https://doi.org/10.1109/TEVC.2002.802873
  • Joseph, S., & Dada, E. (2018a). Automatic Tuning of Proportional–Integral–Derivative Controller using Genetic Algorithm. 19, 51–57.
  • Joseph, S., & Dada, E. (2018b). Proportional-Integral-Derivative (PID) Controller Tuning For An Inverted Pendulum Using Particle Swarm Optimisation (PSO) Algorithm. 2.
  • Joseph, S., Mishra, M. K., & Omizegba, E. (2011). Automatic Tuning of Proportional-Integral-Derivative (PID) Controller Using Particle Swarm Optimization (PSO) Algorithm. International Journal of Artificial Intelligence & Applications, 2, 25–32. https://doi.org/10.5121/ijaia.2011.2403
  • Katal, N., Kumar, P., & Narayan, S. (2014). Optimal PID controller for coupled-tank liquid-level control system using bat algorithm. 2014 International Conference on Power, Control and Embedded Systems (ICPCES), 1–4. https://doi.org/10.1109/ICPCES.2014.7062818
  • Konstantinidis, A., & Yang, K. (2011). Multi-objective energy-efficient dense deployment in Wireless Sensor Networks using a hybrid problem-specific MOEA/D. Appl. Soft Comput., 11, 4117–4134. https://doi.org/10.1016/j.asoc.2011.02.031
  • Latha, K., Rajinikanth, V., & Surekha, P. (2013). PSO-Based PID Controller Design for a Class of Stable and Unstable Systems. ISRN Artificial Intelligence, 2013. https://doi.org/10.1155/2013/543607
  • Li, K., Kwong, S., Zhang, Q., & Deb, K. (2014). Interrelationship-Based Selection for Decomposition Multiobjective Optimization. IEEE Transactions on Cybernetics. https://doi.org/10.1109/TCYB.2014.2365354
  • Li, W., Li, K., Guo, L., Huang, Y., & Xue, Y. (2018). A new validity index adapted to fuzzy clustering algorithm. Multimedia Tools and Applications, 77. https://doi.org/10.1007/s11042-017-5550-8
  • Li, Y., Peng, Z., Liang, D., Chang, H., & Cai, Z. (2015). Facial age estimation by using stacked feature composition and selection. The Visual Computer, 32. https://doi.org/10.1007/s00371-015-1137-4
  • Li, Y., Wang, G., Nie, L., Wang, Q., & Tan, W. (2017). Distance Metric Optimization Driven Convolutional Neural Network for Age Invariant Face Recognition. Pattern Recognition, 75. https://doi.org/10.1016/j.patcog.2017.10.015
  • Messac, A., Ismail-Yahaya, A., & Mattson, C. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25, 86–98. https://doi.org/10.1007/s00158-002-0276-1
  • Miettinen, K. (1999). Nonlinear Multiobjective Optimization. Springer US. https://books.google.com.tr/books?id=ha_zLdNtXSMC https://doi.org/10.1007/978-1-4615-5563-6
  • Miettinen, K., & Mäkelä, M. (2002). On scalarizing functions in multiobjective optimization. OR Spectrum, 24, 193–213. https://doi.org/10.1007/s00291-001-0092-9
  • R J, R., & Ananda, C. (2015). PSO tuned PID controller for controlling camera position in UAV using 2-axis gimbal. 128–133. https://doi.org/10.1109/ICPACE.2015.7274930
  • Ribeiro, J. M. S., Santos, M. F., Carmo, M. J., & Silva, M. F. (2017). Comparison of PID controller tuning methods: analytical/classical techniques versus optimization algorithms. 2017 18th International Carpathian Control Conference (ICCC), 533–538. https://doi.org/10.1109/CarpathianCC.2017.7970458
  • Sandoval, D., Soto, I., & Adasme, P. (2015). Control of Direct Current Motor using Ant Colony Optimization. https://doi.org/10.1109/Chilecon.2015.7400356
  • Senberber, H., & Bagis, A. (2017). Fractional PID controller design for fractional order systems using ABC algorithm. 1–7. https://doi.org/10.1109/ELECTRONICS.2017.7995218
  • Singh, K., Vasant, P., Elamvazuthi, I., & Kannan, R. (2015). PID Tuning of Servo Motor Using Bat Algorithm. Procedia Computer Science, 60, 1798–1808. https://doi.org/https://doi.org/10.1016/j.procs.2015.08.290
  • Srinivas, N., & Deb, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation - EC, 2, 221–248. https://doi.org/10.1162/evco.1994.2.3.221
  • Takieldeen, A., Mahmoud, A., & Elsawi, A. (2015). Optimal PID Tuning for DC Motor Speed Controller Based on Genetic Algorithm. International Review of Automatic Control (I.RE.A.CO.), 8, 80–85. https://doi.org/10.15866/ireaco.v8i1.4839
  • Tan, K. C., Khor, E. F., & Lee, T. H. (2005). Multiobjective Evolutionary Algorithms and Applications. https://doi.org/10.1007/1-84628-132-6
  • Trivedi, A., Srinivasan, D., Sanyal, K., & Ghosh, A. (2016). A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition. IEEE Transactions on Evolutionary Computation, PP, 1. https://doi.org/10.1109/TEVC.2016.2608507
  • Visser, H., & Hartjes, S. (2013). Economic and environmental optimization of flight trajectories connecting a city-pair. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 228, 980–993. https://doi.org/10.1177/0954410013485348
  • Vo, D.-T., Duong Gia, D., Ho-Huu, V., & Vu-Do, H. C. (2017). Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Composite Structures, 168. https://doi.org/10.1016/j.compstruct.2017.02.038
  • Waldock, A., & Corne, D. (2011). Multiple objective optimisation applied to route planning. Genetic and Evolutionary Computation Conference, GECCO’11, 1827–1834. https://doi.org/10.1145/2001576.2001821
  • Wang, H., Wang, W., Cui, Z., Zhou, X., Zhao, J., & Li, Y. (2018). A new dynamic firefly algorithm for demand estimation of water resources. Information Sciences, 438. https://doi.org/10.1016/j.ins.2018.01.041
  • Wu, H., Kuang, L., Wang, F., Rao, Q., Gong, M., & Li, Y. (2017). A Multiobjective Box-Covering Algorithm for Fractal Modularity on Complex Networks. Applied Soft Computing, 61. https://doi.org/10.1016/j.asoc.2017.07.034
  • Yadav, S., Verma, S. K., & Nagar, S. K. (2018). Performance enhancement of magnetic levitation system using teaching learning based optimization. Alexandria Engineering Journal, 57(4), 2427–2433. https://doi.org/https://doi.org/10.1016/j.aej.2017.08.016
  • Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731. https://doi.org/10.1109/TEVC.2007.892759
  • Zhang, S., Yang, Z., Xing, X., Gao, Y., Xie, D., & Wong, H.-S. (2017). Generalized Pair-Counting Similarity Measures for Clustering and Cluster Ensembles. IEEE Access, 5, 1. https://doi.org/10.1109/ACCESS.2017.2741221
  • Zhu, Y., Wang, J., & Qu, B. (2014). Multi-objective economic emission dispatch considering wind power using evolutionary algorithm based on decomposition. International Journal of Electrical Power & Energy Systems, 63, 434–445. https://doi.org/10.1016/j.ijepes.2014.06.027
  • Ziegler, B. J. G., & Nichols, N. B. (1942). Optimum Settings for Automatic Controllers. Journal of Fluids Engineering. https://api.semanticscholar.org/CorpusID:41336178 https://doi.org/10.1115/1.4019264
  • Ziegler, J. G., & Nichols, N. B. (1993). Optimum Settings for Automatic Controllers. Journal of Dynamic Systems, Measurement, and Control, 115(2B), 220–222. https://doi.org/10.1115/1.2899060
Toplam 49 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Elektrik Mühendisliği (Diğer)
Bölüm Elektrik Elektronik Mühendisliği
Yazarlar

Ali Fazıl Uygur 0000-0002-1049-4927

Yayımlanma Tarihi 3 Eylül 2025
Gönderilme Tarihi 30 Haziran 2024
Kabul Tarihi 11 Temmuz 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 28 Sayı: 3

Kaynak Göster

APA Uygur, A. F. (2025). AYRIŞIMA DAYALI ÇOK AMAÇLI EVRİMSEL ALGORİTMA ÜZERİNDEN PID KONTROLCÜ PARAMETRELERİNİN OPTİMİZASYONU. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 28(3), 1143-1158. https://doi.org/10.17780/ksujes.1507716
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