Abstract
In this paper, a novel global optimization algorithm, named as Maxwell’s equations derived optimization (MEDO), is proposed. Using the Maxwell’s equations to analyse the behaviors of the time-varying current, the Ampere force is obtained from Fleming’s left hand rule. MEDO introduces an ‘Ampere force’ term, which is derived from Maxwell’s equations and is rigorous in physics, to drive the variables to the global optimal solution in the search space. In addition, introducing ‘gravity’ to MEDO can increase the stability of the optimizations. 11 classical benchmarks are tested, and results show that MEDO can always converge to numerical optimal solutions. To evaluate the proposed MEDO in solving the electromagnetic problems, four practical engineering applications are considered including the linear antenna array synthesis, frequency selected surface optimization, numerical dispersion reduction for finite-difference method, and parameters extraction of typical waveform. These examples are significant in electromagnetics, but tough to be solved because of their high dimensionality and strong nonlinearity. Numerical results show that MEDO can outperform several classic optimization methods, like wind driven optimization (WDO) and particle swarm optimization (PSO). Therefore, the electromagnetics-inspired MEDO is robust and of great potential in solving the electromagnetic optimization problems.
Similar content being viewed by others
References
Baldi P. Gradient descent learning algorithm overview: a general dynamical systems perspective. IEEE Trans Neural Netw, 1995, 6: 182–195
Mahony R E, Williamson R C. Prior knowledge and preferential structures in gradient descent learning algorithms. J Machine Learn Res, 2001, 1: 311–355
Wu Y M, Jiang L J, Sha W E I, et al. The numerical steepest descent path method for calculating physical optics integrals on smooth conducting quadratic surfaces. IEEE Trans Antenn Propagat, 2013, 61: 4183–4193
Xu H J, Huang C Q, Pan P, et al. Image retrieval based on multi-concept detector and semantic correlation. Sci China Inf Sci, 2015, 58: 122104
Großhans M, Scheffer T. Solving prediction games with parallel batch gradient descent. In: Proceedings of Joint European Conference on Machine Learning and Knowledge Discovery in Databases, 2015. 152–167
Fan Q, Wu W, Zurada J M. Convergence of batch gradient learning with smoothing regularization and adaptive momentum for neural networks. SpringerPlus, 2016, 5: 295
Si Z, Wen S, Dong B. NOMA codebook optimization by batch gradient descent. IEEE Access, 2019, 7: 117274
Bonnabel S. Stochastic gradient descent on riemannian manifolds. IEEE Trans Automat Contr, 2013, 58: 2217–2229
Mercier Q, Poirion F, Désidéri J A. A stochastic multiple gradient descent algorithm. Eur J Oper Res, 2018, 271: 808–817
Liu Y, Huangfu W, Zhang H, et al. An efficient stochastic gradient descent algorithm to maximize the coverage of cellular networks. IEEE Trans Wirel Commun, 2019, 18: 3424–3436
Tao H, Wu B, Lin X. Budgeted mini-batch parallel gradient descent for support vector machines on spark. In: Proceedings of 2014 20th IEEE International Conference on Parallel and Distributed Systems (ICPADS), 2014. 945–950
Ghadimi S, Lan G, Zhang H. Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization. Math Program, 2016, 155: 267–305
Khirirat S, Feyzmahdavian H R, Johansson M. Mini-batch gradient descent: faster convergence under data sparsity. In: Proceedings of 2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017. 2880–2887
Eberhart R, Kennedy J. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, 1995. 1942–1948
Eberhart R, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, 1995. 39–43
De Jong K. Adaptive system design: a genetic approach. IEEE Trans Syst Man Cybern, 1980, 10: 566–574
Wang Y K, Chen X B. Hybrid quantum particle swarm optimization algorithm and its application. Sci China Inf Sci, 2020, 63: 159201
Sun Z X, Song J J, An Y R. Optimization of the head shape of the CRH3 high speed train. Sci China Technol Sci, 2010, 53: 3356–3364
Storn R, Price K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optimiz, 1997, 11: 341–359
Cui C Y, Jiao Y C, Zhang L, et al. Synthesis of subarrayed monopluse arrays with contiguous elements using a DE algorithm. IEEE Trans Antenn Propagat, 2017, 65: 4340–4345
Xiang S, Xing L N, Wang L, et al. Comprehensive learning pigeon-inspired optimization with tabu list. Sci China Inf Sci, 2019, 62: 070208
Cui Z H, Zhang J J, Wang Y C, et al. A pigeon-inspired optimization algorithm for many-objective optimization problems. Sci China Inf Sci, 2019, 62: 070212
Zhou Y, He F Z, Qiu Y M. Dynamic strategy based parallel ant colony optimization on GPUs for TSPs. Sci China Inf Sci, 2017, 60: 068102
Liu H X, Liu F, Zhang X J, et al. Aircraft conflict resolution method based on hybrid ant colony optimization and artificial potential field. Sci China Inf Sci, 2018, 61: 129103
Bayraktar Z, Komurcu M, Bossard J A, et al. The wind driven optimization technique and its application in electromagnetics. IEEE Trans Antenn Propagat, 2013, 61: 2745–2757
Bayraktar Z, Komurcu M. Adaptive wind driven optimization. In: Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communications Technologies (formerly BIONETICS), 2016. 124–127
Chen G, Yang S, Ren Q, et al. Numerical dispersion reduction approach for finite-difference methods. Electron Lett, 2019, 55: 591–593
Su D L, Xu H, Zhou Z, et al. An improved method of trapezoidal waves time-domain parameters extraction from EMI spectrum. In: Proceedings of 2019 International Applied Computational Electromagnetics Society Symposium (ACES), 2019. 1–2
Paul C R. Inductance: Loop and Partial. Hoboken: John Wiley & Sons, 2011
Maxwell J C. A Dynamical Theory of the Electromagnetic Field. London: Royal Society, 1856
Bevelacqua P J, Balanis C A. Minimum sidelobe levels for linear arrays. IEEE Trans Antenn Propagat, 2007, 55: 3442–3449
Yang S H, Kiang J F. Adjustment of beamwidth and side-lobe level of large phased-arrays using particle swarm optimization technique. IEEE Trans Antenn Propagat, 2014, 62: 138–144
Safaai-Jazi A, Stutzman W L. A new low-sidelobe pattern synthesis technique for equally spaced linear arrays. IEEE Trans Antenn Propagat, 2016, 64: 1317–1324
Rahman S U, Cao Q, Ahmed M M, et al. Analysis of linear antenna array for minimum side lobe level, half power beamwidth, and nulls control using PSO. J Microw Optoelectron Electromagn Appl, 2017, 16: 577–591
Darvish A, Ebrahimzadeh A. Improved fruit-fly optimization algorithm and its applications in antenna arrays synthesis. IEEE Trans Antenn Propagat, 2018, 66: 1756–1766
Goswami B, Mandal D. Nulls and side lobe levels control in a time modulated linear antenna array by optimizing excitations and element locations using RGA. J Microw Optoelectron Electromagn Appl, 2013, 12: 238–255
Keizer W P M N. Element failure correction for a large monopulse phased array antenna with active amplitude weighting. IEEE Trans Antenn Propagat, 2007, 55: 2211–2218
Grewal N S, Rattan M, Patterh M S. A linear antenna array failure correction using firefly algorithm. Progress Electromagn Res M, 2012, 27: 241–254
Muralidharan R, Vallavaraj A, Mahanti G K, et al. QPSO for failure correction of linear array of mutually coupled parallel dipole antennas with desired side lobe level and return loss. J King Saud Univ-Eng Sci, 2017, 29: 112–117
Munk B A. Frequency Selective Surfaces: Theory and Design. Hoboken: John Wiley & Sons, 2005
Kiani G I, Olsson L G, Karlsson A, et al. Cross-dipole bandpass frequency selective surface for energy-saving glass used in buildings. IEEE Trans Antenn Propagat, 2011, 59: 520–525
Lins H W C, Barreto E L F, d’Assunção A G. Enhanced wideband performance of coupled frequency selective surfaces using metaheuristics. Microw Opt Technol Lett, 2013, 55: 711–715
Yee K. Numerical solution of inital boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antenn Propagat, 1966, 14: 302–307
Tam C K W, Webb J C. Dispersion-relation-preserving finite difference schemes for computational acoustics. J Comput Phys, 1993, 107: 262–281
Fornberg B. Classroom note: calculation of weights in finite difference formulas. SIAM Rev, 1998, 40: 685–691
Du Q, Li B, Hou B. Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggeredgrid finite difference scheme. Appl Geophys, 2009, 6: 42–49
Su D L, Xie S, Chen A, et al. Basic emission waveform theory: a novel interpretation and source identification method for electromagnetic emission of complex systems. IEEE Trans Electromagn Compat, 2018, 60: 1330–1339
Shang X, Su D L. Use modified lomb-scargle method to analyze electromagnetic emission spectrum. In: Proceedings of 2015 IEEE 6th International Symposium on Microwave, Antenna, Propagation, and EMC Technologies (MAPE), 2015. 415–420
Acknowledgements
This work was supported by National Military Key Pre-research Project of the 13th Five-Year Plan (Grant No. 41409010101), National Natural Science Foundation of China (Grant Nos. 61427803, 61771032), and Civil Aircraft Projects of China (Grant No. MJ-2017-F-11).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Su, D., Li, L., Yang, S. et al. A new optimization algorithm applied in electromagnetics — Maxwell’s equations derived optimization (MEDO). Sci. China Inf. Sci. 63, 200301 (2020). https://doi.org/10.1007/s11432-020-2927-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-020-2927-2