Global Optimization Method Research Articles

An efficient zero-order evolutionary method for solving the orbital-free density functional theory problem by direct minimization.

A differential evolution (DE) global optimization method for all-electron orbital-free density functional theory (OF-DFT) is presented. This optimization method does not need information about function derivatives to find extreme solutions. Results for a series of known orbital-free energy functionals are presented. Ground state energies of atoms (H to Ar) are obtained by direct minimization of the energy functional without using either Lagrange multipliers or damping procedures for reaching convergence. Our results are in agreement with previous OF-DFT calculations obtained using the standard Newton-Raphson and trust region methods. Being a zero-order method, the DE method can be applied to optimization problems dealing with non-differentiable functionals or functionals with non-closed forms.

Experiment and simulation of hydrogen oxidation in a high-pressure turbulent flow reactor

Hydrogen oxidation has a complex dependence on pressure. Despite the well-known, reverse S-shape explosion limits, variation of hydrogen oxidation reactivity with pressure has rarely been investigated in a quantitative manner, particularly in the peninsula between the second and third ignition branches when the overall reactivity is low. This work investigates hydrogen oxidation in a turbulent flow reactor at 10 to 48 bar with an inlet temperature of 950 K and an equivalence ratio of 0.03–0.05, which complements our recent study at 1–8 bar in the same reactor (Lu et al. Proc. Combust. Inst. 2021, 243–250). The elevated pressures show a weak promoting effect, in contrast to the strong inhibiting effect at lower pressures in crossing the second ignition branch. Analyzing the hydrogen consumption rates across the pressure range revealed that the reactivity remains at a low level and is barely affected by pressure between 2 and 20 bar, suggesting the existence of a broad low-reactivity valley on the temperature–pressure plane which could be potentially important for practical applications.The measured species-time concentrations, combined with ignition delays selected from the literature, are used to develop a new hydrogen oxidation model focusing on hydrogen autoignition behavior. A comprehensive review of elementary reactions incorporating the latest updates for the rate coefficients is conducted to determine the prior uncertainties. A global optimization method incorporating random sampling and high-dimensional model representation is used to identify the most sensitive reactions and to constrain their uncertainty with the selected experimental targets. An optimized model is then obtained which shows excellent agreement with hydrogen autoignition experiments.

Analog circuit sizing based on Evolutionary Algorithms and deep learning

The use of machine learning-based techniques has expanded to many areas that require optimization. One of such area is Integrated Circuit (IC) design and sizing optimization, where we propose a new framework that combines Deep Neural Networks (DNNs) and Evolutionary Algorithm (EA) for analog IC sizing automation. Our optimization framework incorporates EA, numerical performance evaluation, and DNN models to optimize the analog circuit sizing process. The main steps of the proposed optimization procedure can be summarized as follows: Firstly, we use EA and numerical performance evaluation to increase efficiency and produce highly accurate results for global optimization. Secondly, we incorporate a local search to enhance the performance of global optimization, with DNN models being used to evaluate the performance of analog circuits during this phase. Lastly, we employ DNN model evaluations instead of numerical performance evaluation for ranking candidate designs, which significantly speeds up the local minimum search. These successive steps make our method original and stand out perfectly from existing procedures published in the literature. Our framework is deployed on industrial-scale circuits with strict design specifications. Experimental results demonstrate that it achieves better results and is two times faster in the design process compared to traditional global optimization methods that use sequential SPICE simulation calls for local optimization.

A multi-area intra-day dispatch strategy for power systems under high share of renewable energy with power support capacity assessment

Long-distance power support through High-voltage Direct Current (HVDC) has provided feasible solutions for power dispatch and control problems in multi-area power systems under high share of renewable energy. In this paper, an advanced multi-area intra-day dispatch strategy for power systems with high penetration of renewable energy considering power support capacity is established to increase the accommodation of wind power and enhance the stability of the power system. At first, a novel assessment method of regional active power support capacity is carried out in this paper, which can sufficiently quantify the regional power margin (RPM), the DC dispatchable power (DCDP), and the regional power support distance (RPSD) of a power system. Subsequently, a multi-area intra-day dispatch strategy based on power support capacity analysis is proposed, where constraints on conventional units, wind farms, transmission lines, and RPSD are developed. Finally, to enable the development of the dispatch model, a model predictive control (MPC) scheme is used to update the power support capacity indicators dynamically and improve model reliability. The effectiveness and superiority of the proposed strategy are verified by case studies. Numerical results show a 7.02% cost reduction and overload risk reduction by using the proposed strategy compared to conventional global optimization methods.

Comparison of Taboo Search Methods for Atomic Cluster Global Optimization with a Basin-Hopping Algorithm.

The basin-hopping algorithm (BHA) allows for the efficient exploration of atomic cluster potential energy surfaces by random perturbations in configuration space, followed by energy minimizations. Here, the taboo search method is incorporated to prevent the search from revisiting recently visited regions of the search space. Two taboo search modes are implemented, one mode resets the search to random coordinates upon encountering the taboo region, while the other simply rejects any proposed move into the taboo region. These two modes are tested and compared on a variety of potential energy surfaces─several clusters where atomic interactions are described by the Lennard-Jones potential, and Au55 where a semi-empirical tight binding potential is used to describe atomic interactions. Some differences in performance between the two taboo search modes were noted for LJ38 and Au55, with the mode that rejects all hops into the taboo region performing better, offering a means to improve the efficiency of the BHA for multifunnel systems. However, both taboo search modes failed to significantly improve performance on multifunnel systems where more than two funnels were present in the system.

Potential of China's national policies on reducing carbon emissions from coal-fired power plants in the period of the 14th Five-Year Plan

Coal-fired power is one of the largest contributors to China's carbon emissions. To promote its national low-carbon transition ambitions, the Chinese government has issued a series of policies to reduce emissions from coal-fired power plants (CFPP) during its 14th Five-Year Plan (2021-2025). This study mainly focuses on the mitigation potential of related national policies, using global optimization methods with double constraints on different policy implementation extents and power supply security under different scheduled views of national new energy developments. Thereby, 81 scenarios are set, and policy simulations till 2025 are conducted, achieving emission reductions ranging from 0.39 Gt to 1.04 Gt across scenarios. Specifically, if all policies are implemented as planned, they can bring significant changes, 0.64 Gt CO2 cumulative reduction and 25 Mt/GWh emitting efficiency improvement. But the simulated emission-changing trend shows that they may not be sufficient for the nation's target of peaking emissions before 2030, while results in higher-extent scenarios indicate that stronger implementation is required for this target. More relevant recommendations are also provided for subsequent sustainability policies on CFPPs in China.

Delayed Deep Deterministic Policy Gradient-Based Energy Management Strategy for Overall Energy Consumption Optimization of Dual Motor Electrified Powertrain

The anxiety-provoking driving range has always been an obstacle to the large-scale popularization of electric vehicles (EVs). To improve the driving range without affecting the driving performance, a Dual-Motor Two-Speed All-Wheel-Drive (DMTS-AWD) electrified powertrain is proposed in this work. The system adopts a motor on the front axle and rear axle, respectively, and the rear motor adopts a two-speed automatic mechanical transmission to improve energy efficiency and dynamic performance. An advanced Delayed Deep Deterministic Policy Gradient (TD3)-based Energy Management Strategy (EMS) is used to pursue better motor working efficiency with consideration of practicability. In addition, a direct control method without complicating the structure of the actor network is proposed to realize mode selection and torque distribution simultaneously, which is a discrete(mode)-continuous (motor torque) hybrid action space. The simulation results show that the energy consumption of DMTS-AWD with TD3-based EMS improves by 6.44% compared to the Single-Motor Single-Speed (SMSS) powertrain, which is comparable to the global optimization method. Moreover, the proposed EMS in this paper has a faster convergence speed and better adaptability compared with the classic Deep Deterministic Policy Gradient (DDPG).

Multi sensor fusion methods for state of charge estimation of smart lithium-ion batteries

Multi-dimensional sensing is the key characteristic of next generation smart batteries. But the existing researches on multi-sensor fusion methods haven't focused on algorithm mechanism, the global optimal solution has not been built, the superiority has not been proved theoretically. For the first time, this research built the global optimal structure of multi-sensor fusion state estimation algorithm. Specifically, the state of charge (SoC) estimation problem of lithium iron phosphate (LFP) batteries is studied, cooperating with voltage signal, expansion force (EF) signal is introduced. Firstly, a normalization algorithm is introduced to overcome the drift of EF under different cycles and different pre-tightening force. Secondly, the non-monotonic relationship of LFP battery's EF-SoC curve is addressed with a forced monotone transformation method in the transition areas. Then the global optimal multi-sensor fusion method is built, theoretical reductions are carried out to prove the higher precision of multi-sensor fusion methods compared to single-signal methods. Experiments are conducted to verify the effectiveness of the methods, even under the most serious situations, the fusion methods exhibit powerful correction ability, and the root mean square error can be controlled within 3 %. Moreover, the proposed algorithms shows strong tolerance to error sources.

A review of practice of using evolutionary algorithms for neural network synthesis and training

The object of this research is the application of evolutionary algorithms for the synthesis and training of neural networks. The paper aims to select and review the existing experience on using evolutionary algorithms as competitive methods to conventional approaches in neural network training and creation, and to evaluate such existing solutions for further development of this field. The essence of the obtained results lies in the successful application of genetic algorithms in conjunction with neural networks to optimize parameters, architecture, and weight coefficients of the networks. The genetic algorithms allowed improving the performance and accuracy of neural networks, especially in cases where backpropagation algorithms faced difficulties in finding optimal solutions. These results can be attributed to the fact that genetic algorithms are efficient methods for global optimization in parameter space. They help avoid local minima and discover more reliable and stable solutions. The obtained findings can be practically utilized to enhance the performance and quality of neural networks in various classification and prediction tasks. The use of genetic algorithms enables the selection of optimal weight coefficients, network connections, and identification of significant features from the dataset. However, they come with the limitation of additional time costs for evaluating the entire population according to the selection criteria. It is worth noting that the application of genetic algorithms is not a universal method for all tasks, and the algorithm parameters should be individually tuned for each specific problem. Further research could focus on refining the combination methods of genetic algorithms and neural networks, as well as exploring their application in new domains and tasks.

Efficient Global Optimization of a laidback fan-shaped cooling hole using Large-Eddy Simulation

In the film cooling technique, cold fluid exiting from holes on the surface of the turbine creates a protective film which prevents the ruin of the solid material composing the blades. It is now known that the hole geometry is a key element of this approach and determines the adiabatic film cooling effectiveness. The design of optimal holes which can operate at conditions of high-pressure turbines is, however, a challenge for which several research groups and industrial companies have invested in intensive numerical and experimental campaigns. In the present study, a Large-Eddy Simulation based approach is adopted and demonstrated to be able to optimize the shape of a fan-shaped hole on a flat plate configuration in engine-representative conditions in static conditions, i.e. without rotation. The obtained results target high-pressure vanes and further studies are mandatory to investigate the effect of rotation for the application to turbine blades. This work is purely numerical as no experimental campaign has been done for such hot conditions. Nonetheless, the numerical setup used has been validated in a previously published studies. To do so, four main geometrical parameters defining such a cooling hole shape, namely the depth of the expanded section, the hole inclination angle and the forward as well as the lateral expansion angles are selected as design variables. The Bayesian based Efficient Global Optimization method along with the Expected Improvement as the acquisition function are used to find the maximum surface averaged film cooling effectiveness as the objective function. After nine database enrichment iterations needed to reduce the overall model error, an optimal shape for a given operating condition defined by the blowing and density ratios is obtained. Based on the response surface analysis, the effects of the design parameters on the adiabatic film cooling effectiveness are investigated. Finally, deeper analysis of the flow physics for four shapes is proposed to apprehend the role of the geometrical parameters on the fluid dynamics and on the adiabatic film cooling effectiveness.

Application of conformational space annealing to the protein structure modeling using cryo-EM maps.

Conformational space annealing (CSA), a global optimization method, has been applied to various protein structure modeling tasks. In this paper, we applied CSA to the cryo-EM structure modeling task by combining the python subroutine of CSA (PyCSA) and the fast relax (FastRelax) protocol of PyRosetta. Refinement of initial structures generated from two methods, rigid fitting of predicted structures to the Cryo-EM map and de novo protein modeling by tracing the Cryo-EM map, was performed by CSA. In the refinement of the rigid-fitted structures, the final models showed that CSA can generate reliable atomic structures of proteins, even when large movements of protein domains were required. In the de novo modeling case, although the overall structural qualities of the final models were rather dependent on the initial models, the final models generated by CSA showed improved MolProbity scores and cross-correlation coefficients to the maps. These results suggest that CSA can accomplish flexible fitting and refinement together by sampling diverse conformations effectively and thus can be utilized for cryo-EM structure modeling.

The Visible-Volume Function of a Set of Cameras is Continuous, Piecewise Rational, Locally Lipschitz, and Semi-Algebraic in All Dimensions

The visible-volume function assigns to a configuration of cameras and a flexible environment in a convex room the volume that can be supervised by the cameras. It is of interest to configure the cameras and the environment in such a way that the visible volume is maximized. Some methods of global optimization can take profit from desirable analytic properties of the visible-volume function. Earlier work has only considered this function in dimensions two and three or for static environments implicitly defined by level-set functions. In this paper it is shown, that the visible-volume function for a flexible environment modeled explicitly by a parametrized simplicial complex is continuous, piecewise rational, locally Lipschitz, and semi-algebraic in all dimensions.

Newton’s Method for Global Free Flight Trajectory Optimization

Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton’s method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.

Deep Q-learning to globally optimize a k-D parameter search for medical imaging.

Estimation of the global optima of multiple model parameters is valuable for precisely extracting parameters that characterize a physical environment. This is especially useful for imaging purposes, to form reliable, meaningful physical images with good reproducibility. However, it is challenging to avoid different local minima when the objective function is nonconvex. The problem of global searching of multiple parameters was formulated to be a k-D move in the parameter space and the parameter updating scheme was converted to be a state-action decision-making problem. We proposed a novel Deep Q-learning of Model Parameters (DQMP) method for global optimization which updated the parameter configurations through actions that maximized the Q-value and employed a Deep Reward Network (DRN) designed to learn global reward values from both visible fitting errors and hidden parameter errors. The DRN was constructed with Long Short-Term Memory (LSTM) layers followed by fully connected layers and a rectified linear unit (ReLU) nonlinearity. The depth of the DRN depended on the number of parameters. Through DQMP, the k-D parameter search in each step resembled the decision-making of action selections from 3k configurations in a k-D board game. The DQMP method was evaluated by widely used general functions that can express a variety of experimental data and further validated on imaging applications. The convergence of the proposed DRN was evaluated, which showed that the loss values of six general functions all converged after 12 epochs. The parameters estimated by the DQMP method had relative errors of less than 4% for all cases, whereas the relative errors achieved by Q-learning (QL) and the Least Squares Method (LSM) were 17% and 21%, respectively. Furthermore, the imaging experiments demonstrated that the imaging of the parameters estimated by the proposed DQMP method were the closest to the ground truth simulation images when compared to other methods. The proposed DQMP method was able to achieve global optima, thus yielding accurate model parameter estimates. DQMP is promising for estimating multiple high-dimensional parameters and can be generalized to global optimization for many other complex nonconvex functions and imaging of physical parameters.

Descriptors for binding energies at clusters: The case of nanosilicates as models of interstellar dust grains.

Binding energies of radicals and molecules at dust grain surfaces are important parameters for understanding and modeling the chemical inventory of interstellar gas clouds. While first-principles methods can reliably be used to compute such binding energies, the complex structure and varying sizes and stoichiometries of realistic dust grains make a complete characterization of all adsorption sites exposed by their surfaces challenging. Here, we focus on nanoclusters composed of Mg-rich silicates as models of interstellar dust grains and two adsorbates of particular astrochemical relevance; H and CO. We employ a compressed sensing method to identify descriptors for the binding energies, which are expressed as analytical functions of intrinsic properties of the clusters, obtainable through a single first-principles calculation of the cluster. The descriptors are identified based on a diverse training dataset of binding energies at low-energy structures of nanosilicate clusters, where the latter structures were obtained using a first-principles-based global optimization method. The composition of the descriptors reveals how electronic, electrostatic, and geometric properties of the nanosilicates control the binding energies and demonstrates distinct physical origins of the bond formation for H and CO. The predictive performance of the descriptors is found to be limited by cluster reconstruction, e.g., breaking of internal metal-oxygen bonds, upon the adsorption event, and strategies to account for this phenomenon are discussed. The identified descriptors and the computed datasets of stable nanosilicate clusters along with their binding energies are expected to find use in astrochemical models of reaction networks occurring at silicate grain surfaces.

A modified smell agent optimization for global optimization and industrial engineering design problems

Abstract This paper introduces an Improved Smell Agent Optimization Algorithm (mSAO), a new and enhanced metaheuristic designed to tackle complex engineering optimization issues by overcoming the shortcomings of the recently introduced Smell Agent Optimization Algorithm. The proposed mSAO incorporates the jellyfish swarm active–passive mechanism and novel random operator in the elementary SAO. The objective of modification is to improve the global convergence speed, exploration–exploitation behaviour, and performance of SAO, as well as provide a problem-free method of global optimization. For numerical validation, the mSAO is examined using 29 IEEE benchmarks with varying degrees of dimensionality, and the findings are contrasted with those of its basic version and numerous renowned recently developed metaheuristics. To measure the viability of the mSAO algorithm for real-world applications, the algorithm was employed to solve to resolve eight challenges drawn from real-world scenarios including cantilever beam design, multi-product batch plant, industrial refrigeration system, pressure vessel design, speed reducer design, tension/compression spring, and three-bar truss problem. The computational analysis demonstrates the robustness of mSAO relatively in finding optimal solutions for mechanical, civil, and industrial design problems. Experimental results show that the suggested modifications lead to an improvement in solution quality by 10–20% of basic SAO while solving constraint benchmarks and engineering problems. Additionally, it contributes to avoiding local optimal stuck, and premature convergence limitations of SAO and simultaneously.

Training Artificial Neural Networks Using a Global Optimization Method That Utilizes Neural Networks

Perhaps one of the best-known machine learning models is the artificial neural network, where a number of parameters must be adjusted to learn a wide range of practical problems from areas such as physics, chemistry, medicine, etc. Such problems can be reduced to pattern recognition problems and then modeled from artificial neural networks, whether these problems are classification problems or regression problems. To achieve the goal of neural networks, they must be trained by appropriately adjusting their parameters using some global optimization methods. In this work, the application of a recent global minimization technique is suggested for the adjustment of neural network parameters. In this technique, an approximation of the objective function to be minimized is created using artificial neural networks and then sampling is performed from the approximation function and not the original one. Therefore, in the present work, learning of the parameters of artificial neural networks is performed using other neural networks. The new training method was tested on a series of well-known problems, a comparative study was conducted against other neural network parameter tuning techniques, and the results were more than promising. From what was seen after performing the experiments and comparing the proposed technique with others that have been used for classification datasets as well as regression datasets, there was a significant difference in the performance of the proposed technique, starting with 30% for classification datasets and reaching 50% for regression problems. However, the proposed technique, because it presupposes the use of global optimization techniques involving artificial neural networks, may require significantly higher execution time than other techniques.

Globalized Knowledge-Based, Simulation-Driven Antenna Miniaturization Using Domain-Confined Surrogates and Dimensionality Reduction

The design of contemporary antenna systems encounters multifold challenges, one of which is a limited size. Compact antennas are indispensable for new fields of application such as the Internet of Things or 5G/6G mobile communication. Still, miniaturization generally undermines electrical and field performance. When attempted using numerical optimization, it turns into a constrained problem with costly constraints requiring electromagnetic (EM) simulations. At the same time, due to the parameter redundancy of compact antennas, size reduction poses a multimodal task. In particular, the achievable miniaturization rate heavily depends on the starting point, while identifying a suitable starting point is a challenge on its own. These issues indicate that miniaturization should be addressed using global optimization methods. Unfortunately, the most popular nature-inspired algorithms cannot be applied for solving size reduction tasks because of their inferior computational efficacy and difficulties in handling constraints. This work proposes a novel methodology for the globalized size reduction of antenna structures. Our methodology is a multi-stage knowledge-based procedure, initialized with the detection of the approximate location of the feasible region boundary, followed by the construction of a dimensionality-reduced metamodel and global optimization thereof; the last stage is the miniaturization-oriented local refinement of geometry parameters. For cost reduction, the first stages of the procedure are realized with the use of a low-fidelity EM antenna model. Our approach is verified using four broadband microstrip antennas and benchmarked against multi-start local search as well as nature-inspired methods. Superior size reduction rates are demonstrated for all considered cases while maintaining reasonably low computational costs.

Exploring synchronization and lift suppression in fluid flow around vibrating cylinder: a parallel CFD and global optimization investigation

In this study, we employ a parallel Computational Fluid Dynamics (CFD) code integrated with the VTDIRECT95 algorithm, a parallel deterministic global optimization method, to conduct global optimization for an oscillating circular cylinder. We conduct numerical simulations for the flow at a Reynolds number of 500 within the parameter range of 0.1≤Ax≤0.3 and 0.5fst≤fex≤2.5fst where Ax represents the inline oscillating amplitude, fex denotes the forcing oscillation frequency, and fst corresponds to the frequency of a stationary cylinder. To enhance computational efficiency, a combination of VTdirect and a CFD solver is utilized to efficiently identify the synchronization region, thereby reducing computational resources. The results reveal a significant reduction in the lift coefficient within the synchronized region compared to unsynchronized regimes. Furthermore, the study delves into the underlying flow physics behind synchronization and lift suppression. By synchronizing the shedding of vortices, their detrimental effects are nullified, resulting in a reduction in lift. Moreover, the research examines the influence of three-dimensional (3-D) flow by comparing 2-D and 3-D simulations at two different Reynolds numbers. It demonstrates that accounting for 3-D effects yields more accurate predictions of fluid behavior. Synchronization maps and root mean square (rms) lift coefficient plots illustrate the impact of Reynolds number and movement frequency on lift suppression. The findings indicate that achieving synchronization in 3-D flow necessitates stronger amplitudes and higher frequencies. At higher Reynolds numbers, the wake structures become unstable, leading to intricate vortical patterns. Consequently, the synchronization curve shifts towards higher amplitudes and frequencies in 3-D simulations. Understanding these phenomena is vital for reducing lift force in practical applications. This research significantly contributes to knowledge regarding synchronization and lift suppression in fluid flow around vibrating cylinders.

Design of large-angle distortion-free and spot adjustable LED spot array projector based on microlens array and eyepiece

The spot array projector has long been a challenging and intriguing research focus in the fields of projection and lighting applications. In the current literature, there is a lack of a comprehensive and detailed presentation on the design and analysis method for a spot array generator based on the structure of imaging eyepiece and MLA. We present a novel design and optimization method for a large-angle, distortion-free and spot adjustable LED spot array projector that is composed of an eyepiece, two microlens arrays (MLAs), and a micro-LED array (MLEDA). The eyepiece system is optimized using imaging optical methods to project sub-beams to the target plane with a large angle. The sub-lens of condenser MLA is also optimized using imaging optical methods to refocus the collimating beam and match the numerical aperture (NA) with the eyepiece, and the sub-lens of the collimating MLA is acquired by using simulated annealing (SA) global illumination optics optimization method to achieve collimation and far-field homogenization. The predistortion MLEDA and the MLAs are proposed and implemented by the radial basis function (RBF) interpolation method, which correct the large-angle distortion introduced by the eyepiece. Both near-field and far-field applications can be realized by the proposed system. In the near-field applications, different spot geometries at the near-field target plane can be achieved. In the far-field applications, the power matching of the MLEDA is used to improve far-field uniformity of spot array. Moreover, the predefined-geometry arrangement spot array can be realized in both near and far fields. Two design examples with full field of view (FOV) projection of 80° and 100° are provided to validate the proposed method. Overall, the proposed system offers a promising solution for various applications requiring target identification or 3D calibration.