A Generalized Method for Efficient Global Optimization of Antenna Design

Efficiency improvement is of great significance for simulation-driven antenna design optimization methods based on evolutionary algorithms (EAs). The two main efficiency enhancement methods exploit data-driven surrogate models and/or multi-fidelity simulation models to assist EAs. However, optimization methods based on the latter either need ad hoc low-fidelity model setup or have difficulties in handling problems with more than a few design variables, which is a main barrier for industrial applications. To address this issue, a generalized three stage multi-fidelity-simulation-model assisted antenna design optimization framework is proposed in this paper. The main ideas include introduction of a novel data mining stage handling the discrepancy between simulation models of different fidelities, and a surrogate-model-assisted combined global and local search stage for efficient high-fidelity simulation model-based optimization. This framework is then applied to SADEA, which is a state-of-the-art surrogate-model-assisted antenna design optimization method, constructing SADEA-II. Experimental results indicate that SADEA-II successfully handles various discrepancy between simulation models and considerably outperforms SADEA in terms of computational efficiency while ensuring improved design quality

Steady-State Co-Kriging Models

In deterministic computer experiments, a computer code can often be run at different levels of complexity/fidelity and a hierarchy of levels of code can be obtained. The higher the fidelity and hence the computational cost, the more accurate output data can be obtained. Methods based on the co-kriging methodology Cressie (2015) for predicting the output of a high-fidelity computer code by combining data generated to varying levels of fidelity have become popular over the last two decades. For instance, Kennedy and O\u27Hagan (2000) first propose to build a metamodel for multi-level computer codes by using an auto-regressive model structure. Forrester et al. (2007) provide details on estimation of the model parameters and further investigate the use of co-kriging for multi-fidelity optimization based on the efficient global optimization algorithm Jones et al. (1998). Qian and Wu (2008) propose a Bayesian hierarchical modeling approach for combining low-accuracy and high-accuracy experiments. More recently, Gratiet and Cannamela (2015) propose sequential design strategies using fast cross-validation techniques for multi-fidelity computer codes.;This research intends to extend the co-kriging metamodeling methodology to study steady-state simulation experiments. First, the mathematical structure of co-kriging is extended to take into account heterogeneous simulation output variances. Next, efficient steady-state simulation experimental designs are investigated for co-kriging to achieve a high prediction accuracy for estimation of steady-state parameters. Specifically, designs consisting of replicated longer simulation runs at a few design points and replicated shorter simulation runs at a larger set of design points will be considered. Also, design with no replicated simulation runs at long simulation is studied, along with different methods for calculating the output variance in absence of replicated outputs.;Stochastic co-kriging (SCK) method is applied to an M/M/1, as well as an M/M/5 queueing system. In both examples, the prediction performance of the SCK model is promising. It is also shown that the SCK method provides better response surfaces compared to the SK method

Optimizing Photonic Nanostructures via Multi-fidelity Gaussian Processes

We apply numerical methods in combination with finite-difference-time-domain (FDTD) simulations to optimize transmission properties of plasmonic mirror color filters using a multi-objective figure of merit over a five-dimensional parameter space by utilizing novel multi-fidelity Gaussian processes approach. We compare these results with conventional derivative-free global search algorithms, such as (single-fidelity) Gaussian Processes optimization scheme, and Particle Swarm Optimization---a commonly used method in nanophotonics community, which is implemented in Lumerical commercial photonics software. We demonstrate the performance of various numerical optimization approaches on several pre-collected real-world datasets and show that by properly trading off expensive information sources with cheap simulations, one can more effectively optimize the transmission properties with a fixed budget.Comment: NIPS 2018 Workshop on Machine Learning for Molecules and Materials. arXiv admin note: substantial text overlap with arXiv:1811.0075

mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location

This paper develops mfEGRA, a multifidelity active learning method using data-driven adaptively refined surrogates for failure boundary location in reliability analysis. This work addresses the issue of prohibitive cost of reliability analysis using Monte Carlo sampling for expensive-to-evaluate high-fidelity models by using cheaper-to-evaluate approximations of the high-fidelity model. The method builds on the Efficient Global Reliability Analysis (EGRA) method, which is a surrogate-based method that uses adaptive sampling for refining Gaussian process surrogates for failure boundary location using a single-fidelity model. Our method introduces a two-stage adaptive sampling criterion that uses a multifidelity Gaussian process surrogate to leverage multiple information sources with different fidelities. The method combines expected feasibility criterion from EGRA with one-step lookahead information gain to refine the surrogate around the failure boundary. The computational savings from mfEGRA depends on the discrepancy between the different models, and the relative cost of evaluating the different models as compared to the high-fidelity model. We show that accurate estimation of reliability using mfEGRA leads to computational savings of $\sim$46% for an analytic multimodal test problem and 24% for a three-dimensional acoustic horn problem, when compared to single-fidelity EGRA. We also show the effect of using a priori drawn Monte Carlo samples in the implementation for the acoustic horn problem, where mfEGRA leads to computational savings of 45% for the three-dimensional case and 48% for a rarer event four-dimensional case as compared to single-fidelity EGRA

Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

Efficient Inverse Design of Transonic Airfoils using Variable-Resolution Models and Manifold Mapping

This paper presents an efficient approach for simulation-based inverse design of airfoil shapes using variable-fidelity computational fluid dynamics models and manifold mapping (MM). Inverse design involves determining an airfoil shape fulfilling a given target performance characteristic. In particular, the pressure coefficient distribution is typically used in aerodynamic inverse design. Such a task can be challenging when using computationally expensive simulations. In the context of local optimization, the MM technique searches for a new design in the vicinity of the current design by constructing a fast multi-fidelity model, which is setup by the available evaluations of each of the high- and low-fidelity models at the current design. The MM-based multi-fidelity model predicts the high-fidelity model response at the new design by evaluating the low-fidelity model at the new design and applying the MM mapping. The MM-based multi-fidelity model is embedded within the trust-region algorithm and terminates based on the convergence of the argument, objective, and trust-region radius to yield the optimal design. The MM-based multi-fidelity algorithm only needs one high-fidelity model evaluation per design iteration. The proposed approach is illustrated on the inverse design of airfoils in transonic inviscid flow with the NACA 2412 airfoil as baseline and the pressure distribution of the RAE 2822 airfoil at Mach 0.734 and lift coefficient 0.824 as the target. Using eight B-spline design variables, the results indicate the MM technique is able to reach the target distribution at a low computational cost when compared to derivative-free local search

Variable-fidelity surrogate modelling with kriging

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