State-of-the-art antenna design and optimization (D/O) is increasingly being done using Global Search and Optimization (GSO) algorithms such as Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Differential Evolution (DE), and a plethora of other evolutionary algorithms, among them Central Force Optimization (CFO), which is the subject of this note. CFO analogizes real gravity in the real Universe so that its gravity is usually attractive in nature, that is, “positive”. But in metaphorical CFO space the algorithm designer is free to turn gravity on its head by making it negative, and doing so to a small extent can improve CFO’s exploration of the search space thus providing even better results. This extension is discussed in some detail and applied to a 6-element Yagi-Uda array as an example.
References
[1]
Formato, R.A. (2007) Central Force Optimization: A New Metaheuristic with Applications in Applied Electromagnetics. ProgressInElectromagneticsResearch, 77, 425-491. https://doi.org/10.2528/pier07082403
[2]
Formato, R.A. (2008) Central Force Optimization: A New Nature Inspired Computational Framework for Multidimensional Search and Optimization. In: Krasnogor, N., Nicosia, G., Pavone, M. and Pelta, D., Eds., StudiesinComputationalIntelligence, Springer, 221-238. https://doi.org/10.1007/978-3-540-78987-1_21
[3]
Formato, R.A. (2009) Central Force Optimisation: A New Gradient-Like Metaheuristic for Multidimensional Search and Optimisation. InternationalJournalofBio-InspiredComputation, 1, 217-238. https://doi.org/10.1504/ijbic.2009.024721
[4]
Ding, D.S., Luo, X.P., Chen, J.F., Wang, X.J., Du, P.Y. and Guo, Y.F. (2011) A Convergence Proof and Parameter Analysis of Central Force. JournalofConvergenceInformationTechnology, 6, 16-23.
[5]
Črepinšek, M., Liu, S. and Mernik, M. (2013) Exploration and Exploitation in Evolutionary Algorithms. ACMComputingSurveys, 45, 1-33. https://doi.org/10.1145/2480741.2480752
[6]
Luke, S. (2015) Essentials of Metaheuristics. 2nd Edition. https://cs.gmu.edu/~sean/book/metaheuristics/
[7]
Korošec, P. and Eftimov, T. (2020) Insights into Exploration and Exploitation Power of Optimization Algorithm Using DSC Tool. Mathematics, 8, Article 1474. https://doi.org/10.3390/math8091474
[8]
Cuevas, E., Echavarría, A. and Ramírez-Ortegón, M.A. (2013) An Optimization Algorithm Inspired by the States of Matter That Improves the Balance between Exploration and Exploitation. AppliedIntelligence, 40, 256-272. https://doi.org/10.1007/s10489-013-0458-0
[9]
Green, R.C., Wang, L. and Alam, M. (2012) Training Neural Networks Using Central Force Optimization and Particle Swarm Optimization: Insights and Comparisons. ExpertSystemswithApplications, 39, 555-563. https://doi.org/10.1016/j.eswa.2011.07.046
[10]
Qubati, G.M. and Dib, N.I. (2010) Microstrip Patch Antenna Optimization Using Modified Central Force Optimization. ProgressInElectromagneticsResearchB, 21, 281-298. https://doi.org/10.2528/pierb10050511
[11]
Green, R.C., Wang, L.F. and Alam, M. (2012) Intelligent State Space Pruning with Local Search for Power System Reliability Evaluation. 2012 3rdIEEEPESInnovativeSmartGridTechnologiesEurope (ISGTEurope), Berlin, 14-17 October 2012, 1-8. https://doi.org/10.1109/isgteurope.2012.6465775
[12]
Mahmoud, K.R. (2011) Central Force Optimization: Nelder-Mead Hybrid Algorithm for Rectangular Microstrip Antenna Design. Electromagnetics, 31, 578-592. https://doi.org/10.1080/02726343.2011.621110
[13]
Asi, M. and Dib, N.I. (2010) Design of Multilayer Microwave Broadband Absorbers Using Central Force Optimization. ProgressInElectromagneticsResearchB, 26, 101-113. https://doi.org/10.2528/pierb10090103
[14]
Montaser, A.M., Mahmoud, K.R. and Elmikati, H.A. (2012) Integration of an Opti-Mized E-Shaped Patch Antenna into a Laptop Structure for Bluetooth and Notched-UWB Standards Using Optimization Techniques. AppliedComputationalElectromagneticsSociety, 27, 784.
[15]
Montaser, A.M., Mahmoud, K.R., Abdel-Rahman, A.B. and Elmikati, H.A. (2013) Design Bluetooth and Notched-UWB E-Shape Antenna Using Optimization Techniques. ProgressInElectromagneticsResearchB, 47, 279-295. https://doi.org/10.2528/pierb12101407
[16]
Montaser, A.M., Mahmoud, K.R. and Elmikati, H.A. (2012) B15. Tri-Band Slotted Bow-Tie Antenna Design for RFID Reader Using Hybrid CFO-NM Algorithm. 2012 29thNationalRadioScienceConference (NRSC), Cairo, 10-12 April 2012, 119-126. https://doi.org/10.1109/nrsc.2012.6208515
[17]
Gonzalez, J.E., Amaya, I. and Correa, R., (2013) Design of an Optimal Multi-Layered Electromagnetic Absorber through Central Force Optimization. Progress in Electromagnetics Research Symposium, Stockholm, 12-15 August 2013, 1082.
[18]
Ahmed, E., R. Mahmoud, K., Hamad, S. and T. Fayed, Z. (2013) CFO Parallel Implementation on GPU for Adaptive Beam-Forming Applications. InternationalJournalofComputerApplications, 70, 10-16. https://doi.org/10.5120/12013-8001
[19]
Montaser, A.M., Mahmoud, K.R., Abdel-Rahman, A.B. and Elmikati, H.A. (2013) B10. Design of a Compact Tri-Band Antenna for RFID Handheld Applications Using Optimization Techniques. 2013 30thNationalRadioScienceConference (NRSC), Cairo, 16-18 April 2013, 82-89. https://doi.org/10.1109/nrsc.2013.6587905
[20]
Haghighi, A. and Ramos, H.M. (2012) Detection of Leakage Freshwater and Friction Factor Calibration in Drinking Networks Using Central Force Optimization. WaterResourcesManagement, 26, 2347-2363. https://doi.org/10.1007/s11269-012-0020-6
[21]
Chen, Y.B., Yu, J.Q., Mei, Y.S., Wang, Y.F. and Su, X.L. (2016) Modified Central Force Optimization (MCFO) Algorithm for 3D UAV Path Planning. Neurocomputing, 171, 878-888. https://doi.org/10.1016/j.neucom.2015.07.044
[22]
Abdel-Rahman, A.B., Montaser, A.M. and Elmikati, H.A. (2012) Design a Novel Bandpass Filter with Microstrip Resonator Loaded Capacitors Using CFO-HC Algorithm. The 2ndMiddleEastConferenceonAntennasandPropagation, Cairo, 29-31 December 2012, 1-6. https://doi.org/10.1109/mecap.2012.6618188
[23]
Huan, T.T. and Anh, H.P.H. (2019) Optimal Stable Gait for Nonlinear Uncertain Humanoid Robot Using Central Force Optimization Algorithm. EngineeringComputations, 36, 599-621. https://doi.org/10.1108/ec-03-2018-0154
[24]
Chao, M., Xin, S.Z. and Min, L.S. (2014) Neural Network Ensembles Based on Copula Methods and Distributed Multiobjective Central Force Optimization Algorithm. EngineeringApplicationsofArtificialIntelligence, 32, 203-212. https://doi.org/10.1016/j.engappai.2014.02.009
[25]
Talal, T.M., Attiya, G., Metwalli, M.R., Abd El-Samie, F.E. and Dessouky, M.I. (2020) Satellite Image Fusion Based on Modified Central Force Optimization. MultimediaToolsandApplications, 79, 21129-21154. https://doi.org/10.1007/s11042-019-08471-7
[26]
El-Hoseny, H.M., Abd El-Rahman, W., El-Rabaie, E.M., Abd El-Samie, F.E. and Faragallah, O.S. (2018) An Efficient DT-CWT Medical Image Fusion System Based on Modified Central Force Optimization and Histogram Matching. InfraredPhysics&Technology, 94, 223-231. https://doi.org/10.1016/j.infrared.2018.09.003
[27]
Shaikh, N.F. and Doye, D.D. (2014) A Novel Iris Recognition System Based on Central Force Optimization. InternationalJournalofTomographyandSimulation, 27, 23-34.
[28]
A.khaleel, A.A.J. (2009) Linear Phase Finite-Impulse Response Filter Design Using Central Force Optimization Algorithm. Master of Science (M.Sc.) Electrical Engineering (Thesis), University of Jordan Library. https://theses.ju.edu.jo/Original_Abstract/JUF0706056/JUF0706056.pdf
[29]
Momin, J. and Yang, X-S. (2033) A literature survey of benchmark functions for Global Optimisation Problems. International JournalMathematicalModellingandNumericalOptimization, 4, 150-194.
[30]
Formato, R.A. (2021) Central Force Optimization with Gravity < 0, Elitism, and Dynamic Threshold Optimization: An Antenna Application, 6-Element Yagi-Uda Arrays. WirelessEngineeringandTechnology, 12, 53-82. https://doi.org/10.4236/wet.2021.124004
[31]
Formato, R.A. (2021) Six-Element Yagi Array Designs Using Central Force Optimization with Pseudo Random Negative Gravity. WirelessEngineeringandTechnology, 12, 23-51. https://doi.org/10.4236/wet.2021.123003
[32]
Lisboa, A.C., Vieira, D.A.G., Vasconcelos, J.A., Saldanha, R.R. and Takahashi, R.H.C. (2009) Monotonically Improving Yagi-Uda Conflicting Specifications Using the Dominating Cone Line Search Method. IEEETransactionsonMagnetics, 45, 1494-1497. https://doi.org/10.1109/tmag.2009.2012688
Formato, R.A. (2017) Determinism in Electromagnetic Design & Optimization-Part II: BBP-Derived π Fractions for Generating Uniformly Distributed Sampling Points in Global Search and Optimization Algorithms. Forum for Electromagnetic Research Methods and Application Technologies, 19, Article No. 10. http://www.e-fermat.org/
[35]
De Rainville, F., Gagné, C., Teytaud, O. and Laurendeau, D. (2012) Evolutionary Optimization of Low-Discrepancy Sequences. ACMTransactionsonModelingandComputerSimulation, 22, 1-25. https://doi.org/10.1145/2133390.2133393
[36]
De Rainville, F., Gagné, C., Teytaud, O. and Laurendeau, D. (2009) Optimizing Low-Discrepancy Sequences with an Evolutionary Algorithm. Proceedingsofthe 11thAnnual Conference onGeneticand Evolutionary Computation, Canada, 8-12 July 2009, 1491-1498. https://doi.org/10.1145/1569901.1570101
[37]
Pant, M., Thangaraj, R., Grosan, C. and Abraham, A. (2008) Improved Particle Swarm Optimization with Low-Discrepancy Sequences. 2008 IEEECongressonEvolutionaryComputation (IEEEWorldCongressonComputationalIntelligence), Hong Kong, 1-6 June 2008, 3011-3018. https://doi.org/10.1109/cec.2008.4631204
[38]
Imamichi, T., Numata, H., Mizuta, H. and Ide, T. (2011) Nonlinear Optimization to Generate Non-Overlapping Random Dot Patterns. Proceedings of the 2011 Winter Simulation Conference (WSC), Phoenix, AZ, 11-14 December 2011, 2414-2425.
[39]
Alabduljabbar, A.A., Milanovi, J.V. and Al-Eid, E.M. (2008) Low Discrepancy Sequences Based Optimization Algorithm for Tuning PSSs. Proceedings of the 10th International Conference on Probablistic Methods Applied to Power Systems, Rincon, 25-29 May 2008, 1-9.
[40]
Krykova, I. (2003) Evaluating of Path-Dependent Securities with Low Discrepancy Methods. M.S. Thesis (Financial Mathematics), Worcester Polytechnic Institute.
[41]
Jørgensen, K. (2008) Himalaya Options: An Analysis of Pricing Himalaya Options in a Monte Carlo and Quasi‐Random Monte Carlo framework. Master’s Thesis, Aarhus University.
[42]
Bailey, D., Borwein, P. and Plouffe, S. (1997) On the Rapid Computation of Various Polylogarithmic Constants. MathematicsofComputation, 66, 903-913. https://doi.org/10.1090/s0025-5718-97-00856-9
[43]
Formato, R.A. (2017) Determinism in Electromagnetic Design & Optimization-Parts I & II. ForumforElectromagneticResearchMethodsandApplicationTechnologies, 19, Article No. 9. https://efermat.github.io/
[44]
Sörensen, K. (2013) Metaheuristics—The Metaphor Exposed. InternationalTransactionsinOperationalResearch, 22, 3-18. https://doi.org/10.1111/itor.12001
[45]
Aranha, C., and Campelo, F. (2023) Lessons from the Evolutionary Computation Bestiary. Artificial Life, 29, 421-432. https://github.com/fcampelo/EC-Bestiary
[46]
van der Corput, J.G. (1935) Verteilungsfunktionen. Proceedings Nederlandse Akademie van Wetenschappen, 38, 813-821.
[47]
Halton, J.H. (1960) On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals. NumerischeMathematik, 2, 84-90. https://doi.org/10.1007/bf01386213
[48]
Li, W.T., Shi, X.W., Hei, Y.Q., Liu, S.F. and Zhu, J. (2010) A Hybrid Optimization Algorithm and Its Application for Conformal Array Pattern Synthesis. IEEETransactionsonAntennasandPropagation, 58, 3401-3406. https://doi.org/10.1109/tap.2010.2050425
[49]
Pehlivanoglu, Y.V. (2013) A New Particle Swarm Optimization Method Enhanced with a Periodic Mutation Strategy and Neural Networks. IEEETransactionsonEvolutionaryComputation, 17, 436-452. https://doi.org/10.1109/tevc.2012.2196047
