Efficient Global Optimization Research Articles

An efficient global optimization algorithm for a class of linear multiplicative problems based on convex relaxation

An efficient global optimization algorithm for a class of linear multiplicative problems based on convex relaxation

Miniaturized design of multi-octave PA using spoof surface plasmon polaritons

Surface Plasmon Polariton (SSPP), which exhibits subwavelength-scaled field confinement, can be realized at microwave frequencies by ultrathin corrugated metallic strips, providing significant potential for circuit and system miniaturization. A number of SSPP units were employed in this study to design input and output matching networks of a multi-octave RF power amplifier (PA) for the purpose of reducing the overall circuit size. The designed SSPP-based PAs were fabricated and demonstrated to have an output power between 39.1 dBm and 41.8 dBm, and a power added efficiency (PAE) ranging between 60.2 % and 69.8 % in the frequency range of 0.8 GHz to 3.1 GHz, with a size of 35.5 mm * 46.7 mm, which achieves a 47 % size reduction compared to the traditional transmission-line based PA. A highly efficient global optimization method, the Bayesian Optimization (BO), was utilized to further enhance performance. SSPP PA's average output power and PAE have been improved by approximately 0.3 dBm and 2.6 %, respectively. Its overall size remains at the same level. With the use of a 20 MHz 5GNR signal, digital pre-distortion (DPD) has been implemented, and the linearity of the PA has been improved.

A dynamic aggregation strategy enhanced efficient global optimization algorithm for solving high-dimensional turbomachinery design problems

ABSTRACT To address challenges effectively in turbomachinery design optimization involving high-dimensional ( d ≥ 30 ) expensive black-box problems, a dedicated Efficient Global Optimization (EGO) algorithm is proposed with dynamic aggregation. This specialized approach efficiently navigates optimization tasks with limited sample evaluations. Specifically, the Dynamic Aggregate Efficient Global Optimization (DA-EGO) algorithm decomposes the original high-dimensional design space into low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite-point for the global search. Most importantly, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. After being validated on 21 benchmark functions ranging from 30 to 90 dimensions, the DA-EGO is used for the optimization of a transonic compressor rotor with 28 variables and a multi-stage compressor optimization with 60 variables. With the above, the effectiveness of the proposed algorithm is well demonstrated.

Size Optimization of Truss Structures Based on Genetic Algorithm by Developing Single-point Crossover with Bit-wise Mutation Using FORTRAN Programming

A truss is a collection of axially loaded structural elements connected through pin joints. Optimization of truss structures indicates the determination of best possible conditions that are necessary for achieving the most economical design in terms of lowest possible weights of the truss elements. According to recent studies, Size, Topology and Shape based optimizations are the three possible independent optimization scopes for finding the optimum weight of a truss. The current study focuses on the size optimization of truss structure and aims to identify the most cost-effective sections of the truss using a powerful evolutionary optimization technique named as Genetic Algorithm (GA). Here single point cross over method and bit wise mutation operator are adopted for expanding the search space with the assigned displacement and stress constraints. Fortran based sub routines are developed for each individual steps of GA such as fitness evaluation, selection, cross-over and mutation. Finaly the complete program is run for validation of its outcome. While comparing with the solution of an existing literature regarding a minimization of objective function having two design variables the outcomes tend to show a good correlation. Further, the study is extended for the weight minimization of two widely used truss having 10 members and 17 members respectively with standard Finite Element Method of analysis. Minimum weight of each truss is obtained via convergence plot and compared with the existing literatures. With this simple but efficient global optimization technique optimum weight of truss structure can easily be achieved.

A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

HyDesign: a tool for sizing optimization of grid-connected hybrid power plants including wind, solar photovoltaic, and lithium-ion batteries

Abstract. Hybrid renewable power plants consisting of collocated wind, solar photovoltaic (PV), and lithium-ion battery storage connected behind a single grid connection can provide additional value to the owners and society in comparison to individual technology plants, such as those that are only wind or only PV. The hybrid power plants considered in this article are connected to the grid and share electrical infrastructure costs across different generation and storing technologies. In this article, we propose a methodology for sizing hybrid power plants as a nested-optimization problem: with an outer sizing optimization and an internal operation optimization. The outer sizing optimization maximizes the net present values over capital expenditures and compares it with standard designs that minimize the levelized cost of energy. The sizing problem formulation includes turbine selection (in terms of rated power, specific power, and hub height), a wind plant wake loss surrogate, simplified wind and PV degradation models, battery degradation, and operation optimization of an internal energy management system. The problem of outer sizing optimization is solved using a new parallel “efficient global optimization” algorithm. This new algorithm is a surrogate-based optimization method that ensures a minimal number of model evaluations but ensures a global scope in the optimization. The methodology presented in this article is available in an open-source tool called HyDesign. The hybrid sizing algorithm is applied for a peak power plant use case at different locations in India where renewable energy auctions impose a monetary penalty when energy is not supplied at peak hours. We compare the hybrid power plant sizing results when using two different objective functions: the levelized cost of energy (LCoE) or the relative net present value with respect to the total capital expenditure costs (NPV/CH). Battery storage is installed only on NPV/CH-based designs, while the hybrid design, including wind, solar, and battery, only occurs on the site with good wind resources. Wind turbine selection on this site prioritizes cheaper turbines with a lower hub height and lower rated power. The number of batteries replaced changes at the different sites, ranging between two or three units over the lifetime. A significant oversizing of the generation in comparison to the grid connection occurs on all NPV/CH-based designs. As expected LCoE-based designs are a single technology with no batteries.

An EGO-based online model updating method for hybrid simulation

Hybrid simulation combines experimentally testing of physical substructures with computational simulation of numerical substructures to replicate structural responses under earthquakes. When numerical substructure involves parts that are similar to physical substructure, measured responses of physical substructure are often used to update similar parts within numerical substructure, aiming to improve accuracy of seismic assessment. This study proposes an efficient global optimization based approach for online model updating in hybrid simulation (HSMU-EGO) involving multiple key components yet with only one physically tested in laboratory. Kriging meta-model is constructed for the response error between the numerical model for updating and the experimental substructure, while efficient global optimization and optimal Latin hypercube design are integrated for parameter estimation to minimize the response error. Computational simulations are conducted for a simple steel braced frame and a complex concrete continuous bridge to comprehensively evaluate the performance of HSMU-EGO in the presence of constitutive parameter and model errors. The proposed method is demonstrated to effectively and efficiently improve the accuracy of hybrid simulation in almost all cases. Compared with Unscented Kalman Filter (UKF), this proposed HSMU-EGO provides more suitable alternative when prior information is limited for the physical substructure.

Surrogate-based pneumatic and aerodynamic allocation design optimization for flapping-wing micro air vehicles

Determining the mapping relationships between the bionic structures and aerodynamic characteristics of flapping-wing micro air vehicles (FWMAVs), therefore optimizing their comprehensive performances of pneumatic functions and maneuvering capabilities, poses a formidable challenge. In this work, a surrogate-based approach is proposed to tackle the pivotal challenges. Firstly, an experimental surrogate model is established for predicting the pneumatic performances of the flapping wings using multi-fidelity datasets, which incorporates an efficient global optimization strategy for the sample fill-in to enhance predictive precision while minimizing experimental costs. Secondly, to account for the intricate influences of control inputs on aerodynamic characteristics, comprehensive aerodynamic surrogate models are established to precisely anticipate pneumatic performances and torque allocations under different attitude control patterns. Thirdly, by elucidating the mapping relationships between bionic structures and aerodynamic performances, surrogate-based optimizations aim to identify optimal combinations of corresponding parameters of bionic structures, thereby enhancing the pneumatic and toque allocations of the FWMAV. The bionic structures achieve a maximum lift enhancement of 11.5 % and at least a 5.4 % improvement in torque generation through experimental validations. Based on the optimal outcomes of the bionic structure analysis of the FWMAV, a novel prototype family comprising three distinct sub-varieties is successfully fabricated. The findings of our research are hopefully to offer valuable insights for future FWMAV designs and make potential contributions to the advancement of standardized methodologies for evaluating their flight performances.

ERGO-II: An Improved Bayesian Optimization Technique for Robust Design With Multiple Objectives, Failed Evaluations, and Stochastic Parameters

Abstract In this work, the efficient robust global optimization (ERGO) method is revisited with the aim of enhancing and expanding its existing capabilities. The original objective of ERGO was to address the computational challenges associated with optimization-under-uncertainty through the use of Bayesian optimization (BO). ERGO tackles robust optimization problems which are characterized by sensitivity in the objective function due to stochasticity in the design space. It does this by concurrently minimizing the mean and variance of the objective in a multi-objective setting. To handle the computational complexity arising from the uncertainty propagation, ERGO exploits the analytical expression of the surrogate model underlying BO. In this study, ERGO is extended to accommodate multiple objectives, incorporate an improved predictive error estimation approach, investigate the treatment of failed function evaluations, and explore the handling of stochastic parameters next to stochastic design variables. To evaluate the effectiveness of these improvements, the enhanced ERGO scheme is compared with the original method using an analytical test problem with varying dimensionality. Additionally, the novel optimization technique is applied to an aerodynamic design problem to validate its performance.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

D 3 PBO: D ynamic D omain D ecomposition-based P arallel B ayesian O ptimization for Large-scale Analog Circuit Sizing

Bayesian optimization (BO) is an efficient global optimization method for expensive black-box functions, but the expansion for high-dimensional problems and large sample budgets still remains a severe challenge. In order to extend BO for large-scale analog circuit synthesis, a novel computationally efficient parallel BO method, D 3 PBO, is proposed for high-dimensional problems in this work. We introduce the dynamic domain decomposition method based on maximum variance between clusters. The search space is decomposed into subdomains progressively to limit the maximal number of observations in each domain. The promising domain is explored by multi-trust region-based batch BO with the local Gaussian process (GP) model. As the domain decomposition progresses, the basin-shaped domain is identified using a GP-assisted quadratic regression method and exploited by the local search method BOBYQA to achieve a faster convergence rate. The time complexity of D 3 PBO is constant for each iteration. Experiments demonstrate that D 3 PBO obtains better results with significantly less runtime consumption compared to state-of-the-art methods. For the circuit optimization experiments, D 3 PBO achieves up to 10× runtime speedup compared to TuRBO with better solutions.

Lower Bounds on the Noiseless Worst-Case Complexity of Efficient Global Optimization

Efficient global optimization is a widely used method for optimizing expensive black-box functions. In this paper, we study the worst-case oracle complexity of the efficient global optimization problem. In contrast to existing kernel-specific results, we derive a unified lower bound for the oracle complexity of efficient global optimization in terms of the metric entropy of a ball in its corresponding reproducing kernel Hilbert space. Moreover, we show that this lower bound nearly matches the upper bound attained by non-adaptive search algorithms, for the commonly used squared exponential kernel and the Matérn kernel with a large smoothness parameter ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}. This matching is up to a replacement of d/2 by d and a logarithmic term logRϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\frac{R}{\\epsilon }$$\\end{document}, where d is the dimension of input space, R is the upper bound for the norm of the unknown black-box function, and ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document} is the desired accuracy. That is to say, our lower bound is nearly optimal for these kernels.

Multi-dimensional flow simulation analysis and kriging-based optimization study on thermodynamic process mechanism of pulse tube refrigerator with displacer

Pulse tube refrigerators with active displacers have become increasingly popular due to superior phase shift capability and avoidance of dissipation losses. However, mechanisms of thermodynamic processes within refrigerators due to variations in parameters related to critical structures and operations are not yet clear, making it difficult to optimize the comprehensive performance. In this paper, multi-dimensional flow simulation method instead of one-dimensional simulation method with poor computational accuracy is used to analyze the influence of five key parameters on performance of pulse tube refrigerators with active displacers. An intelligent optimization algorithm combined with efficient Kriging surrogate models is developed for single-objective and multi-objective optimization. Results demonstrate that the mean errors of the Kriging models for cooling capacity, total input power and performance coefficient are 1.81%, 3.94% and 3.37%. The single-objective optimization produces a maximum cooling capacity of 7.29 W and performance coefficient of 7.38%. The combined optimal solution delivers 6.65W in cooling capacity and 7.02% in performance coefficient, obtaining improvements of 150.94% and 75.94%. This study reveals the influence mechanism of key parameters on cooling performance of pulse tube refrigerators with displacers and establishes an efficient global optimization method, which is of great significance for the development of advanced refrigeration technology.

Optimizing Polarization Selective Unidirectional Photoluminescence from Phased‐Array Metasurfaces

AbstractMetasurface‐based optical elements offer a wide design space for miniature and lightweight optical applications. Typically, metasurface optical elements transform an incident light beam into a desired output waveform. Recent demonstrations of light‐emitting metasurfaces highlight the potential for directly producing desired output waveforms via metasurface‐mediated spontaneous emission. In this work, reciprocal finite‐difference time‐domain (FDTD) simulations and machine learning are used to enable the inverse design of highly unidirectional photoluminescent III‐Nitride quantum well metasurfaces capable of directive p‐, s‐, or combined p‐ and s‐ polarized emission at arbitrary angles. In comparison with previous intuition‐guided designs using the same quantum well architectures, the inverse design approach enables new polarization capabilities and experimentally demonstrated improvements in directivity of 54%. An analysis of ways in which the inverse design both validates and contradicts previous intuition‐guided design heuristics is presented. Ultimately, the combination of reciprocal simulations and efficient global optimization (EGO) grants remarkable improvements in emission directivity and results in full control over the polarization and momentum of emitted light, including simultaneous directional emission of s‐ and p‐polarized light.

A machine learning proxy based multi-objective optimization method for low-carbon hydrogen production

With industrial informatization, rich data frameworks provide the possibility of efficient design and global optimization of methane to hydrogen processes. However, the high coupling between mixed variables leads to the difficulty of first-principles modeling (FPM) to capture the optimal Pareto front in infeasible domains. In this paper, a machine learning proxy (MLP) method is proposed to minimize economic, exergy destruction, CO2 emissions, and maximize hydrogen production. First, process simulation as FPM is built using physical properties, energy balance, and reaction kinetics to analyze single variable effects and objective trade-offs. Then, datasets consisting of feed, heat transfer, and design variables are built by sampling the FPM in design and extended spaces. The eXtreme Gradient Boosting (XGBoost) with hyperparameter optimization is built as a proxy FPM, capturing the complex mapping between variables and objectives. Finally, the Pareto front is searched in design and extended spaces by combining the proxy model and genetic algorithm. The proposed method benefits 20.2%, 37.2%, 46.7%, and 2.3% in economic, exergy destruction, CO2 emissions and hydrogen production respectively compared to the heuristic design. XGBoost not only can effectively proxy FPM to capture the complex behavior of reforming techniques, but also can perform better in infeasible domains that are difficult to explore with FPM.

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

Bayesian optimization of gradient trajectory for parallel-transmit pulse design.

Spoke pulses improve excitation homogeneity in parallel-transmit MRI. We propose an efficient global optimization algorithm, Bayesian optimization of gradient trajectory (BOGAT), for single-slice and simultaneous multislice imaging. BOGAT adds an outer loop to optimize kT-space positions. For each position, the RF coefficients are optimized (e.g., with magnitude least squares) and the cost function evaluated. Bayesian optimization progressively estimates the cost function. It automatically chooses the kT-space positions to sample, to achieve fast convergence, often coming close to the globally optimal spoke positions. We investigated the typical features of spokes cost functions by a grid search with field maps comprising 85 slabs from 14 volunteers. We tested BOGAT in this database, and prospectively in a phantom and in vivo. We compared the vendor-provided Fourier transform approach with the same magnitude least squares RF optimizer. The cost function is nonconvex and seen empirically to be piecewise smooth with discontinuities where the underlying RF optimum changes sharply. BOGAT converged to within 10% of the global minimum cost within 30 iterations in 93% of slices in our database. BOGAT achieved up to 56% lower flip angle RMS error (RMSE) or 55% lower pulse energy in phantoms versus the Fourier transform approach, and up to 30% lower RMSE and 29% lower energy in vivo with 7.8 s extra computation. BOGAT efficiently estimated near-global optimum spoke positions for the two-spoke tests, reducing flip-angle RMSE and/or pulse energy in a computation time (˜10 s), which is suitable for online optimization.

Optimization of the Second Target Station cold source moderators using an automated workflow

The Second Target Station (STS) at the US Department of Energy’s Oak Ridge National Laboratory is designed to become the world’s highest peak-brightness spallation source of cold neutrons. Successful completion of the STS, which is currently in the preliminary design phase, will provide transformative new capabilities to examine novel materials for future technologies. At STS, neutrons will be generated by spallation reactions in a solid tungsten target. They will be moderated and thermalized in two cold (20 K) para-hydrogen moderators. Careful optimization of these moderators is essential to the project’s success. To find optimal moderator designs, an advanced optimization workflow integrates high-fidelity neutronics calculations using the Monte Carlo N-Particle (MCNP) transport code MCNP6.2 with state-of-the-art optimization algorithms in the Dakota optimization toolkit. For each design iteration, a parametrized solid CAD geometry is generated in Creo and automatically converted into an unstructured mesh geometry by Attila 4MC for the neutronics calculation with MCNP. Iterations repeat until optimal designs are found. This paper presents the results of a sensitivity and optimization study for the cylindrical and tube moderators. Both moderators can be optimized for maximum peak brightness, maximum time-integrated brightness, or any combination between these extremes. Maximum peak brightness is achieved by using smaller optimal dimensions of the moderators, whereas maximum time-integrated brightness is achieved by using larger dimensions. A Pareto front details the designs that optimally balance both brightness metrics. The Pareto front can be found in only 40–110 iterations with 4–5 design parameters when using the efficient global and Pareto-set optimization algorithms in Dakota. Additionally, important engineering constraints can be taken into account, such as the coupling between the cylindrical moderator radius and aluminum vessel wall thicknesses required to ensure structural integrity of the vessels. This interaction has a significant impact on the resulting optimal designs. Our new, highly efficient, fully automated optimization workflow will be used to optimize additional STS components in the future and can be adopted for design and optimization studies at other experimental neutron and accelerator facilities.

Impact Identification Based on Surrogate-assisted Efficient Global Optimisation

Model-based methods have gained significant attention as an on-line tool for impact diagnosis in composite structures. These methods involve the development of a mathematical model that simulates impact dynamics and identifies impact characteristics by minimizing the differences between predicted and actual responses. However, the associated optimisation process is often computationally demanding and time-consuming. Traditional heuristic algorithms like the genetic algorithm may necessitate thousands of impact simulations to achieve convergence. To address the challenge of computational efficiency in model-based methods, this study introduces the surrogate-assisted efficient global optimisation algorithm to solve the minimization problem for impact identification. The proposed approach leverages the efficient global optimisation framework, which utilizes a Kriging meta-model to capture the relationships among impact location, impact force (design variables), and response differences (objective function). By iteratively infill sampling using the generalized expected improvement criterion, a suitable balance between exploration and exploitation is maintained during the optimisation process. This ensures effective search in the design space. Additionally, local surrogates for impact location and impact peak force are constructed to adaptively bound these design variables within feasible ranges. This bounding technique narrows down the search space and accelerates convergence. The validity of the proposed method is demonstrated on the finite element model of a composite plate using impact force history obtained from experiments as input excitation. The results illustrate that the proposed method accurately identifies impacts with fewer than 100 impact simulations, highlighting its efficiency and effectiveness. By leveraging surrogate models and efficient search strategies, the proposed algorithm significantly reduces the computational burden while ensuring precise and reliable impact identification.