Surrogate Algorithm Research Articles

Rapid Optimization of Active Disturbance Rejection Controller Parameters for Quadrotor UAVs Using Kriging Surrogate Modeling

The Active Disturbance Rejection Controller (ADRC), celebrated for its superior resistance to interference, presents itself as an exemplary solution for the development of control systems that are designed to accommodate substantial changes in payload weight for quadrotor Unmanned Aerial Vehicles (UAVs) and to endure robust side winds along with other challenging operational scenarios. Despite the inherent complexity due to the numerous parameters required for the configuration of the ADRC, an innovative method utilizing the Kriging surrogate optimization algorithm has been introduced to automate and expedite the generation of these controller parameters. The development of the ADRC begins with the dynamics model of the quadrotor UAV, followed by the identification of key design parameters. These parameters are then rapidly optimized through the Kriging surrogate optimization algorithm. The controller’s effectiveness is confirmed by implementing the ADRC on Pixhawk flight control hardware, with a comparative analysis of the attitude response under various operating conditions, thereby validating the ADRC’s superior anti-disturbance performance.

An optimized surrogate model and algorithm with rapid multi-parameter processing capability for antenna design

A methodology based on an optimized surrogate model and Non-dominated Sorting Genetic Algorithm III(NSGA-III) algorithm is proposed to address the long design cycle issues that conventional antennas encounter, with fast multiple parameters processing capability. A Temporal Convolutional Network (TCN) network model with high fitting efficiency and a simple structure is first developed as a surrogate model for antenna performance prediction, taking antenna dimensional parameters as input and outputting the reflection coefficient (S11) and gain of the antenna. Then, an adaptive NSGA-III algorithm with enhanced search efficiency is presented. By combing it with the prior TCN surrogate model, the parameter optimization for a 5G millimeter-wave antenna design is realized. Results show that the proposed method achieves a remarkable reduction in Mean Squared Error (MSE) by 12.489 % and 3.277 % respectively, while also presents a decreased running time by 2.670 % and 70.419 % respectively, as compared to the Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory (BiLSTM) network models. The proposed method can rapidly and accurately perform the optimization task of multiple antenna parameters, demonstrating its feasibility and effectiveness for antenna applications requiring wide bandwidth, low loss and high gain.

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories.

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Multi-Objective Optimization of the Seawall Cross-Section by DYCORS Algorithm

The purpose of this research is to develop a new method for automatically optimizing the seawall cross-section with composite slopes and a berm, considering both overtopping discharge and construction cost. Minimizing these competing multi-objectives is highly challenging due to the intricate geometry of seawalls. In this study, the surrogate model optimization algorithm DYCORS (Dynamic COordinate search using Response Surface models) is employed to search for the optimal seawall geometry, coupled with the ANN (Artificial Neural Network) model for determining the overtopping discharge. A total of 20 trials have been run to evaluate the performance of our methodology. Even the worst-performing Trial 7 among these 20 trials shows a satisfactory performance, with a reduction of 17.67% in overtopping discharge and a 12.1% decrease in cost compared to the original solution. Furthermore, compared to other optimization schemes using GAs (Genetic Algorithms) with the same decision vectors, constraints, and multi-objective functions, the methodology has been proven to be more effective and robust. Additionally, when facing different combinations of wave conditions and water levels, there was a 27.8% reduction in objective function value compared to the original solution. The optimal results indicate that this method can still be effectively applied for optimizing the seawall cross-section as it is a general method.

Surrogate and Autoencoder-Assisted Multitask Particle Swarm Optimization for High-Dimensional Expensive Multimodal Problems

In practice, some optimization problems require expensive calculation and exhibit multimodal characteristics simultaneously. These problems are called high-dimensional expensive multimodal optimization problems. When addressing such problems, existing surrogate-assisted evolutionary algorithms (SAEAs) encounter the “curse of dimensionality," which severely affects their capability to search optimal solutions. Therefore, this study proposed a surrogate and autoencoder-assisted multitask particle swarm optimization algorithm. First, an autoencoder-embedded multitask evolutionary framework was established to transform a high-dimensional multimodal optimization problem into multiple low-dimensional subproblems or subtasks. Further, a multi-level surrogate model management mechanism combining mirror learning was proposed. An appropriate local surrogate model can be rapidly generated for each modality of the problem. Moreover, a dual-mode local exploitation strategy was developed to improve the capability of swarm to exploit each subtask. The proposed algorithm was compared with seven existing SAEAs on 33 benchmark functions and the aeroengine aerodynamic design optimization problem. Experimental results revealed that the proposed algorithm can obtain multiple highly competitive optimal solutions, including global optimal solutions.

Theoretical and experimental investigations on a data-driven trajectory planning scheme for dynamic shape control of piezo-actuated compliant morphing structures

Piezo-actuated compliant morphing structures can transmit motion and force via elastic deformation with lower weight, simplified design, and higher accuracy, a typical example is the variable camber wing. However, the rapid shape change of compliant structures is a challenging control problem because it often results in a high level of vibration due to the structural flexibility necessary to achieve the morphing requirement. This study presents a model-free data-driven trajectory planning approach based on spline curves and surrogate-based optimization (SBO) to obtain smooth “rest-to-rest” morphing trajectories. The macro-fiber composite (MFC) patches are used for piezoelectric actuators to generate elastic deformation. The flexible beam and variable camber wing are used for both linear numerical simulation and experimental tests with various nonlinearities and uncertainties. An optimization criterion is proposed to minimize both transient and residual vibrations during the “rest-to-rest” motion. An extraordinarily terminal displacement error function is added to eliminate the effects of the hysteresis and creep of the actuator. The control inputs, i.e., voltage profiles for the MFCs, are defined using cubic spline curves via only a few control points. Then, the optimization problem is solved by employing a Kriging surrogate model-based algorithm integrated with the expected improvement (EI) infilling-sampling criterion, which constructs an efficient algorithm similar to reinforcement learning. The optimal morphing trajectories can be highly efficiently obtained by using only 4 control points and less than 150 samplings. The experimental results of both the plate model and the variable camber wing model show that the proposed method can not only achieve a smooth dynamic morphing trajectory with minimized vibration but also automatically compensate for hysteresis and creep. The proposed method provides an effective means for the rapid realization of an optimized morphing trajectory for compliant morphing structures.

Research on optimization algorithms for localization and capacity determination of chargers considering the spatiotemporal distribution of electric vehicles

The optimized layout of electric vehicle (EV) chargers is not only crucial for users' convenience but also a key element in urban sustainable development, energy transition, and the promotion of new energy vehicles. In order to provide a basis for the problem of localization and capacity determination of chargers and compare the merits of several mainstream algorithms, this paper first establishes an optimization model with the objective of minimizing the total investment cost of all the chargers and the constraint of meeting the charging demands of all electric vehicles. Optimizations were performed using genetic algorithm (GA), surrogate optimization algorithm (SOA), and mixed integer linear programming (MILP) algorithm, respectively. In the case of using MILP, the original nonlinear optimization problem was transformed into a linear problem. In the planning of city-level EV chargers, MILP took 14182.57 s to calculate the minimum cost of 34.62 million yuan. After retaining only 10% of the original data amount, SOA took 87651.34 s to calculate the minimum cost of 3.01 million yuan. The results indicate that GA is prone to falling into local optima and is not suitable for large-scale optimization problems. SOA, on the other hand, requires significant memory consumption, so the issue of memory usage needs to be carefully considered when using it directly. Although MILP is only applicable to linear programming problems, it has the advantages of lower memory usage and higher reliability if the problem can be transformed into a linear one.

Does architectural design require single-objective or multi-objective optimisation? A critical choice with a comparative study between model-based algorithms and genetic algorithms

Efficiency and accuracy have been challenging in the design optimisation process driven by building simulation. The literature review identified the limitations of previous studies, prompting this study to explore the performance of single-objective versus multi-objective efficiency and accuracy on equivalent problems based on control variables and to consider more algorithmic options for a broader range of designs. This study constructed a comparative energy-related experiment whose results are in the same unit, either as a single-objective optimisation or split into two objectives. The project aims to reduce annual energy consumption and increase solar utilisation potential. Our approach focuses on the use of a surrogate modelling algorithm, Radial Basis Function Optimisation Algorithm (RBFOpt), with its multi-objective version RBFMOpt, to optimise the energy performance while quickly identifying new energy requirements for an iterative office building design logic, contrast to traditional genetic-algorithm-driven. In addition, the research also conducted a comparative study between RBFOpt and Covariance Matrix Adaptation Evolutionary Strategies (CMAES) in a single-objective comparison and between RBFMOpt and Nondominated Sorting Genetic Algorithm II (NSGA-II) in a multi-objective optimisation process. The comparison of these sets of Opt algorithms with evolutionary algorithms helps to provide data-driven evidence to support early design decisions.

Sequentially Quadratic Surrogate Algorithm for Time-dependent Reliability and Reliability Sensitivity Analysis

Time-dependent reliability and reliability sensitivity analysis in presence of random uncertainty is widespread in equipment structures. To this end, this paper establishes a sequentially quadratic surrogate method. Firstly, the global reliability sensitivity analysis (GRS) is transformed into the classification problem of the time-dependent performance function outputs by means of conditional probability formula. Secondly, referring to the strategy of the Meta-IS method, the Kriging model of time-dependent performance function is employed to construct the importance sampling function to generate the importance sampling (IS) samples of failure domain efficiently. Furthermore, the Kriging model is updated in the IS samples set through the single-loop adaptive Kriging method to realize the accurate identification of the failure indicator function of IS samples, as well as simulation of time-dependent failure probability. Finally, utilize the information of the failure samples obtained by the estimation of time-dependent reliability to evaluate GRS. The proposed algorithm has excellent computational efficiency and applicability due to the conversion of the conditional probability formula, which enables the computational consumption of the time-dependent reliability and GRS analysis independent of the dimensions of the inputs, as well as the Meta-IS method, which improves the sampling efficiency and is applicable to the case of complex implicit performance function. The given examples fully verify the conclusions.

A genetic algorithm-based optimal selection and blending ratio of plastic waste for maximizing economic potential

Pyrolysis of plastic waste presents an innovative solution to convert plastics into valuable fuels like oil and gas, thereby contributing to circular economy and sustainability. The efficiency of this process highly depends on the types and compositions of plastics utilized, as each type reacts uniquely during pyrolysis, affecting fuel yield and quality. However, previous studies have not thoroughly examined the impact of plastic selection and blending ratios on the pyrolysis outcome, as this requires extensive experimentation due to the numerous possible combinations. Optimizing these factors, along with operational conditions, is essential for enhancing the economic viability of plastic recycling via pyrolysis. This study introduces an optimal selection and blending ratio for plastic waste in pyrolysis fuel production to enhance economic viability using the surrogate model-based genetic algorithm (GA). The optimization process involves (1) generating data via a process model of the plastic waste pyrolysis reactor, (2) preprocessing data, (3) developing a surrogate model based on deep neural networks (DNNs), and (4) deriving the optimal solution using GA. The results reveal an optimal blending ratio: 4 wt% LDPE, 30 wt% HDPE, 43 wt% PP, and 24 wt% PS. Additionally, the optimal pyrolysis temperature is 607 ℃. By adopting this optimal solution, the net profit could increase by 20% compared to the conventional scenario, resulting in an additional annual net profit of US$ 407,811, thus highlighting the potential this approach offers to attain maximum economic feasibility in industrial applications.

A lightweight optimal design method for magnetic adhesion module of wall-climbing robot based on surrogate model and DBO algorithm

A lightweight optimal design method for magnetic adhesion module of wall-climbing robot based on surrogate model and DBO algorithm

On-chip spiking neural networks based on add-drop ring microresonators and electrically reconfigurable phase-change material photonic switches

We propose and numerically demonstrate a photonic computing primitive designed for integrated spiking neural networks (SNNs) based on add-drop ring microresonators (ADRMRs) and electrically reconfigurable phase-change material (PCM) photonic switches. In this neuromorphic system, the passive silicon-based ADRMR, equipped with a power-tunable auxiliary light, effectively demonstrates nonlinearity-induced dual neural dynamics encompassing spiking response and synaptic plasticity that can generate single-wavelength optical neural spikes with synaptic weight. By cascading these ADRMRs with different resonant wavelengths, weighted multiple-wavelength spikes can be feasibly output from the ADRMR-based hardware arrays when external wavelength-addressable optical pulses are injected; subsequently, the cumulative power of these weighted output spikes is utilized to ascertain the activation status of the reconfigurable PCM photonic switches. Moreover, the reconfigurable mechanism driving the interconversion of the PCMs between the resonant-bonded crystalline states and the covalent-bonded amorphous states is achieved through precise thermal modulation. Drawing from the thermal properties, an innovative thermodynamic leaky integrate-and-firing (TLIF) neuron system is proposed. With the TLIF neuron system as the fundamental unit, a fully connected SNN is constructed to complete a classic deep learning task: the recognition of handwritten digit patterns. The simulation results reveal that the exemplary SNN can effectively recognize 10 numbers directly in the optical domain by employing the surrogate gradient algorithm. The theoretical verification of our architecture paves a whole new path for integrated photonic SNNs, with the potential to advance the field of neuromorphic photonic systems and enable more efficient spiking information processing.

Multi-objective optimization integrating weighted average surrogate model and NSGA-II intelligent algorithm applied to a self-excited oscillation mixer used in mixed flow descaling

This study proposes a multi-objective optimization method based on a hybrid of computational fluid dynamics (CFD) and experimental techniques, which integrates a weighted average surrogate model and the NSGA-II intelligent algorithm. To validate the feasibility of this method, structural optimization for the self-excited oscillation mixer (SEOM) was conducted. The optimization objectives aimed to reduce potential abrasives accumulation in the mixed-flow cavity and minimize erosion on the elbow of the slurry outlet caused by mixed slurry, thereby enhancing the service life and rust removal efficiency of the mixed flow rotary jet descaling (MFD). A comparison between the optimized model and original model revealed a 2.51% increase in negative pressure within the cavity of the optimized model, as well as a 10.36% decrease in velocity at the outlet of mixed slurry based on simulation results. Experimental methods measured both mass flow rate of inhaled abrasive particles and impact force of mixed slurry outlet. The experimental results demonstrated that compared to its original counterpart, the optimized model exhibited superior performance with a 22.81% increase in abrasive particle flow rate and an 11.34% reduction in mixed slurry impact force indirectly, verifying better simulation effectiveness for SEOM with optimized structure. This approach also enhanced efficiency and surface quality of MFD processing strip steel, providing guidance for structural optimization of similar SEOMs used in mixed flow descaling.

SPADA: A Toolbox of Designing Soft Pneumatic Actuators for Shape Matching Based on Surrogate Modeling.

Soft pneumatic actuators (SPAs) produce motions for soft robots with simple pressure input, however, they require to be appropriately designed to fit the target application. Available design methods employ kinematic models and optimization to estimate the actuator response and the optimal design parameters to achieve a target actuator's shape. Within SPAs, bellow SPAs excel in rapid prototyping and large deformation, yet their kinematic models often lack accuracy due to the geometry complexity and the material nonlinearity. Furthermore, existing shape-matching algorithms are not providing an end-to-end solution from the desired shape to the actuator. In addition, despite the availability of computational design pipelines, an accessible and user-friendly toolbox for direct application remains elusive. This article addresses these challenges, offering an end-to-end shape-matching design framework for bellow SPAs to streamline the design process, and the open-source toolbox SPADA (Soft Pneumatic Actuator Design frAmework) implementing the framework with a graphic user interface for easy access. It provides a kinematic model grounded on a modular design to improve accuracy, finite element method (FEM) simulations, and piecewise constant curvature (PCC) approximation. An artificial neural network-trained surrogate model, based on FEM simulation data, is trained for fast computation in optimization. A shape-matching algorithm, merging three-dimensional (3D) PCC segmentation and a surrogate model-based genetic algorithm, identifies optimal actuator design parameters for desired shapes. The toolbox, implementing the proposed design framework, has proven its end-to-end capability in designing actuators to precisely match two-dimensional shapes with root-mean-squared-errors of 4.16, 2.70, and 2.51 mm, and demonstrating its potential by designing a 3D deformable actuator.

Analysis of the Identifying Regulation With Adversarial Surrogates Algorithm

Analysis of the Identifying Regulation With Adversarial Surrogates Algorithm

A hierarchical surrogate assisted optimization algorithm using teaching-learning-based optimization and differential evolution for high-dimensional expensive problems

Surrogate-assisted evolutionary algorithms (SAEAs) are increasingly used in solving computationally expensive optimization problems. However, when tackling high-dimensional expensive problems, a large number of exact function evaluations (FEs) need to be consumed for existing SAEAs to achieve an acceptable solution. In this paper, a hierarchical surrogate assisted optimization algorithm (HSAOA) using teaching-learning-based optimization and differential evolution is proposed for solving high-dimensional expensive problems with a relatively small number of exact FEs. To keep a balance between global exploration and local exploitation, a hierarchical surrogate framework with hybrid evolutionary algorithms is devised. In the global search phase, a radial basis function surrogate is utilized to assist the teaching-learning-based optimization in locating the promising sub-regions. In the local search phase, a novel dynamic ensemble of surrogates is proposed to assist the differential evolution in speeding up the convergence process. Eight test functions with 10 to 100 dimensions and a spatial truss design problem are employed to compare the proposed method with several state-of-the-art SAEAs. The results show that the proposed HSAOA is superior to the comparison algorithms for solving expensive optimization problems, and needs a much smaller number of exact FEs than other competing SAEAs to produce competitive or even better results for high-dimensional expensive problems.

Inverse distance weighting and radial basis function based surrogate model for high-dimensional expensive multi-objective optimization

Radial basis function (RBF) models have attracted a lot of attention in assisting evolutionary algorithms for solving computationally expensive optimization problems. However, most RBFs cannot directly provide the uncertainty information of their predictions, making it difficult to adopt principled infill sampling criteria for model management. To overcome this limitation, an inverse distance weighting (IDW) and RBF based surrogate assisted evolutionary algorithm, named IR-SAEA, is proposed to address high-dimensional expensive multi-objective optimization problems. First, an RBF-IDW model is developed, which can provide both the predicted objective values and the uncertainty of the predictions. Moreover, a modified lower confidence bound infill criterion is proposed based on the RBF-IDW for the balance of exploration and exploitation. Extensive experiments have been conducted on widely used benchmark problems with up to 100 dimensions. The empirical results have validated that the proposed algorithm is able to achieve a competitive performance compared with state-of-the-art SAEAs.

Surrogates for Liquid-Liquid Extraction.

Fuel surrogates are mixtures that mimic the properties of real fuels with only a small number of components, simplifying the calculation and simulation of fuel-related processes. This work extends a previously published surrogate optimization algorithm toward the generation of fuel surrogates with a focus on liquid-liquid extraction characteristics. For this purpose, experimental liquid-liquid equilibrium data from batch extraction experiments are incorporated into the calculation procedure as an additional constraint. The use of the method is demonstrated by optimizing a surrogate for the catalytic reformate. Application of the surrogate to an extraction process and comparison with experimental data demonstrate that the resulting surrogate accurately depicts the properties of the real mixture with regard to liquid-liquid extraction performance. This demonstrates that the use of such surrogates is of particular interest for mixtures used as extracting agents for biofuels.

Optimal configuration of dynamic wireless charging facilities considering electric vehicle battery capacity

Dynamic wireless charging facilities deployed on the road network offer an effective charging method to alleviate the electric vehicle users’ range anxiety and thus facilitate the promotion of electric vehicles. The main benefit of wireless charging is that it extends EV’s driving range by enabling EV en-route recharging, which consequently reduces the required battery size for EVs. Basically, given densely distributed wireless charging lanes on the road network, smaller and less expensive batteries would be able to meet the travel demand. From the societal point of view, the reduction of battery size/capacity is capable of justifying more construction of wireless charging lanes. While previous research works on optimal deployment of wireless charging facilities ignored this benefit, this study aims to explicitly consider the tradeoff between the costs of building recharging infrastructure and manufacturing batteries from the societal point of view in the optimal configuration of dynamic wireless charging facilities. The problem is formulated into a bi-level programming model, wherein the upper-level model seeks to minimize the total social cost, and the lower-level model captures EV drivers’ choices in terms of battery size, travel route, and driving and charging behavior. To handle the problem, we first relax the path cost constraint and apply the linearization techniques to reformulate the problem into a mixed-integer linear programming, from which a lower bound of the problem can be obtained. An efficient surrogate optimization algorithm is then developed to solve the problem.

Numerical investigation for subsonic performance of the high-pressure capturing wing configuration with wing dihedral

High-pressure capturing wing (HCW) aerodynamic configuration demonstrates favorable aerodynamic performance under hypersonic conditions, and its novel additional lifting wing (also known as HCW) has the potential to enhance lift characteristics under subsonic conditions. Therefore, this configuration presents a promising option for wide-speed-range vehicles. However, the stability characteristics of this novel configuration under subsonic conditions have not yet been investigated. In this paper, the effects of wing dihedral angles on the subsonic aerodynamic characteristics of a parametric conceptual HCW configuration with two lifting wings were investigated. Specifically, the design variables for this study were the dihedral angles of the upper HCW and the lower delta wing. To obtain the distributions of various aerodynamic parameters over the design space, a combination of the uniform experimental design method, computational fluid dynamics numerical simulation techniques, and kriging surrogate model algorithm was employed. The findings suggest that wing dihedral angles have a greater impact on the lift-drag ratio (L/D) at low angles of attack compared to high angles of attack. L/D can be enhanced by incorporating a positive dihedral angle in HCW, and as the delta wing's negative dihedral angle rises, L/D tends to increase earlier and decrease later at low angles of attack. Furthermore, for the longitudinal, lateral, and directional stability characteristics of this configuration, the positive dihedral angles of the delta wing offer greater overall advantages than negative ones in improving them, and the positive dihedral angles of HCW yield more significant enhancements in stability compared to negative ones.