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Evolutionary Approaches in Engineering Applications
Published in Om Prakash Jena, Sudhansu Shekhar Patra, Mrutyunjaya Panda, Zdzislaw Polkowski, S. Balamurugan, Industrial Transformation, 2022
Today, the covariance matrix adaptation evolution strategy (CMA-ES) is perceived as a state-of-the-art ES [15, 16]. Several variants of CMA-ES were developed [16] to enhance the efficiency or robustness by different techniques. In the CMA-ES algorithm, the adaptation of the population size or other parameters has been presented in earlier papers [17]. The CMA-ES algorithm employs global weighted recombination for both strategy and object variables, adapts the full covariance matrix for mutation, and, in general, is based on the scheme of the ES(λ,μ). The CMA-ES algorithm can handle poorly scaled functions, and its performance remains invariant under rotation of the search space [15].
Broadband Performance of Lenses Designed with Quasi-Conformal Transformation Optics
Published in Douglas H. Werner, Broadband Metamaterials in Electromagnetics, 2017
Jogender Nagar, Sawyer D. Campbell, Donovan E. Brocker, Xiande Wang, Kenneth L. Morgan, Douglas H. Werner
Figures 6.48a,b show the electric field distribution in the xz-plane for the original cemented doublet and the qTO-derived flattened inhomogeneous metamaterial lens, respectively. The results are nearly identical, with the ideal focal point occurring at the same spot for both lenses. To further verify this, Figs. 6.48c,d show the electric field distributions on the yz-plane (the focal plane). Again, the results are nearly identical. This example shows the accuracy of the qTO process at a single frequency. However, the resulting flattened lens may not be color corrected depending on the dispersive properties of the materials considered. To mitigate this, a numerical optimization alternative to qTO called WFM will be presented, which can effectively transform any general geometry into a continuously varying inhomogeneous metamaterial. In addition, WFM is modular and can enable parallel optimization of a multi-element system. While this approach is extremely powerful and general, its performance depends on the optimization engine chosen. For this section, the Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), a powerful global stochastic optimizer [15,18], will be used. Section 6.5 introduces an approximate but analytical approach explicitly for color correction.
Evolutionary Computing and Swarm Intelligence for Hyper Parameters Optimization Problem in Convolutional Neural Networks
Published in Ali Ahmadian, Soheil Salahshour, Soft Computing Approach for Mathematical Modeling of Engineering Problems, 2021
Senthil kumar Mohan, A John, Ananth kumar Tamilarasan
The lower-dimensional depiction of the original information identifies quickly and shows potential in the hyperparameter space. The values that can be used to perform initializing, optimizing the method for higher-dimensional data. The hyperparameter standard course of action taken place to get optimized with the original input of data. Various methods of optimization of hyperparameters have been used, including the tree of partial evaluators, random search, genetic algorithms, and sequence model-based configuration algorithms (Hinz et al.). The proposed CMA-ES (Co-variance Matrix Adaptation Evolution Strategy) and the CMA-ES for derivative-free optimization and few useful invariance features are also the solutions for parallel assessments (Loshchilov and Hutter 2016).
Implications of subsoil-foundation modelling on the dynamic characteristics of a monitored bridge
Published in Structure and Infrastructure Engineering, 2019
Periklis Faraonis, Anastasios Sextos, Costas Papadimitriou, Eleni Chatzi, Panagiotis Panetsos
The covariance matrix adaptation evolution strategy (CMA-ES) algorithm (Hansen, Müller, & Koumoutsakos, 2003) was selected for the minimisation of the objective function (Equation (1)).(1) The heuristic nature of the algorithm allows tackling of non-conventional optimisation problems (non-linear non-convex black-box optimisation) and can be applied both to unconstrained and bounded constraint continuous optimisation problems. It is a second order approach estimating, within an iterative procedure, a covariance matrix, for convex-quadratic functions closely related to the inverse Hessian. This renders the method applicable to non-separable and/or badly conditioned problems. In contrast to quasi-Newton methods, the CMA-ES neither computes nor uses gradients. Thus, the method is efficiently applied on problems for which the gradients are not available or are inconvenient to compute.
Enhancing the search ability of a hybrid LSHADE for global optimization of interplanetary trajectory design
Published in Engineering Optimization, 2023
Zhe Tang, Lei Peng, Guangming Dai, Panpan Wang, Yuwei Zhao, Haozhe Yang, Zhuoying Pu, Mingcheng Zuo
The covariance matrix adaptation evolution strategy (CMA-ES) is one of the evolution strategies with good performance and wide application range. In particular, CMA-ES very effective on medium scale optimization problems. The main idea of the CMA-ES algorithm is to use the covariance matrix in the normal distribution to adjust and guide the evolution of the algorithm. So the key factor of the algorithm is how to adjust these parameters, especially the step size and covariance matrix. The adjustment idea is to increase the probability that the algorithm produces a better solution.
An improved water wave optimisation algorithm enhanced by CMA-ES and opposition-based learning
Published in Connection Science, 2020
Fuqing Zhao, Lixin Zhang, Yi Zhang, Weimin Ma, Chuck Zhang, Houbin Song
The adaptive covariance matrix evolution strategy (CMA-ES) algorithm is a novel evolutionary algorithm proposed by Hansen, Müller, and Koumoutsakos (2014). CMA-ES is a stochastic evolutionary method that updates and samples population by covariance matrices and evolutionary paths to obtain optimal solutions. During each iteration, individuals are sampled in the Gaussian distribution, and a solution with a desirable fitness is selected to update individuals in the Gaussian distribution. CMA-ES has the characteristics of rotation invariance for solving non-separable and ill-conditioned optimisation problems. In addition, CMA-ES is performed well on complex optimisation problems.