Antenna Optimization Algorithm

Surrogate model assisted differential evolution for antenna synthesis (SADEA) is an artificial intelligence (AI) driven antenna design method. It is based on machine learning and evolutionary computation techniques, with the advantages of optimization quality, efficiency, generality and robustness. SADEA carries out global optimization and employs a surrogate model built by statistical learning techniques The method to make surrogate modeling and optimization work harmoniously is critical in such surrogate model-assisted optimization methods. In SADEA, some ideas of the surrogate model-aware evolutionary search framework are borrowed, see [3] and [4].

SADEA uses differential evolution (DE) as the search engine and Gaussian process (GP) machine learning as the surrogate modeling method. For more information, please see [1].

Algorithm Outline


Use the Latin Hypercube sampling (LHS) to generate α design samples from [a,b]d, evaluate all the design samples using EM simulations and then use them to form the initial database. [a,b]d is the search range defined by the user. The value of α is determined self-adaptively.

Iteration steps

  • Select the λ best candidate designs from the database to form a population P. Update the best candidate design obtained so far. The value of λ is determined self-adaptively.

  • Apply the differential evolution current-to-best/1 mutation and binomial crossover operators on P to generate λ child solutions.

  • For each child solution in P, select τ nearest design samples (based on Euclidean distance) as the training data points and construct a local Gaussian process surrogate model. The value of τ is determined self-adaptively.

  • Prescreen the λ child solutions generated before by using the Gaussian process surrogate model with the lower confidence bound prescreening.

  • Carry out an EM simulation to the prescreened best child solution, add this simulated candidate design and its function value to the database.

Stopping criteria

  • The specification(s) is (are) met.

  • The standard deviation of the population is smaller than a threshold and the current best objective function value does not improve for a certain number of iterations. (It is better to be controlled using the figure displaying the convergence trend).

  • The computing budget (the number of EM simulations) is exhausted. Note that the number of EM simulations can be added anytime.


[1] Liu, Bo, Hadi Aliakbarian, Zhongkun Ma, Guy A. E. Vandenbosch, Georges Gielen, and Peter Excell. “An Efficient Method for Antenna Design Optimization Based on Evolutionary Computation and Machine Learning Techniques.” IEEE Transactions on Antennas and Propagation 62, no. 1 (January 2014): 7–18.

[2] Liu, Bo, Alexander Irvine, Mobayode O. Akinsolu, Omer Arabi, Vic Grout, and Nazar Ali. “GUI Design Exploration Software for Microwave Antennas.” Journal of Computational Design and Engineering 4, no. 4 (October 2017): 274–81.

[3] Liu, Bo, Qingfu Zhang, and Georges G. E. Gielen. “A Gaussian Process Surrogate Model Assisted Evolutionary Algorithm for Medium Scale Expensive Optimization Problems.” IEEE Transactions on Evolutionary Computation 18, no. 2 (April 2014): 180–92.

[4] Liu, Bo, Qingfu Zhang, Georges G. E. Gielen, A.Karkar, A.Yakovlev, V.Grout. “SMAS: A Generalized and Efficient Framework for Computationally Expensive Electronic Design Optimization Problems.” Computational Intelligence in Electronic Design, Springer, 2015.

[5] Grout, Vic, Mobayode O. Akinsolu, Bo Liu, Pavlos I. Lazaridis, Keyur K. Mistry, and Zaharias D. Zaharis. “Software Solutions for Antenna Design Exploration: A Comparison of Packages, Tools, Techniques, and Algorithms for Various Design Challenges.” IEEE Antennas and Propagation Magazine 61, no. 3 (June 2019): 48–59.

See Also