Direct Search Algorithm Research Articles

A hybrid algorithm for the dimensional synthesis of parallel manipulators

Increasing the number of non-dominated solutions among multiple objectives is beneficial for determining the optimal comprehensive performance of parallel manipulators (PMs). In engineering, we often achieve this by increasing the population size of intelligent optimization algorithms, which leads to an exponential increase in computational costs, especially for high computationally intensive objective functions. How to increase the number of non-dominated solutions without significantly increasing computational costs is a challenge faced by the dimensional synthesis of PMs. A hybrid algorithm combing particle swarm optimization (PSO) and direct search algorithms was proposed in this work to fix this issue. And, a procedure for direct search algorithm to determine the Pareto optimal front is proposed. The proposed hybrid algorithm is implemented in three steps: (1) The design parameter space is coarsely meshed to determine the amplitude of objective functions to achieve its dimensionless purpose; (2) the PSO algorithm is adopted to obtain the approximate Pareto front, as well as the Pareto front hypersurface stretched by the optimal design parameter space; (3) the neighborhood of the approximate Pareto optimal set was finely meshed, and the direct search algorithm is proposed to update the non-dominated solutions that are closer to the real Pareto front. The proposed hybrid algorithm can obtain more non-dominated solutions while avoiding the significant increase in computational costs caused by increasing population size. The proposed algorithm was implemented using the dimensional synthesis of the 2UPR-RPU PM. Compared with the PSO algorithm, which produced 80 sets of non-dominated solutions, the proposed hybrid algorithm generated 242 sets of solutions with the computational costs only increased 32%.

Rapid acquisition and surface defects recognition based on panoramic image of small-section hydraulic tunnel

Small-section hydraulic tunnels are characterized by small spaces and various section forms, under complex environments, which makes it difficult to carry out an inspection by the mobile acquisition equipment. To resolve these problems, an arbitrarily adjustable camera module deployment method and the corresponding automatic image acquisition equipment with multi-area array cameras are proposed and developed. Such method enables the acquisition of full-length surface images of the hydraulic tunnels with different cross-section forms and diameters by a one-way travel, and the overlap rate and accuracy of the acquired image sets meet the requirements of three-dimensional reconstruction and panoramic image generation. In addition, to improve the speed and accuracy of traditional algorithms for tunnel surface defects detection, this paper proposes an improved YOLOv5s-DECA model. The algorithm introduces DenseNet to optimize the backbone feature extraction network and incorporates an efficient channel attention ECA module to make a better extraction of features of defects. The experimental results show that mAP, and F1-Score of YOLOv5-DECA are 73.4% and 74.6%, respectively, which are better than the common model in terms of accuracy and robustness. The proposed YOLOv5-DECA has great detection performance for targets with variable shapes and can solve the problem of classification imbalance in surface defects. Then, by combining YOLOv5-DECA with the direction search algorithm, a “point-ring-section” method is established to allow rapid identification of common surface defects by detecting them layer by layer with the bottom image of the stitched panorama as the seed. The presented method in this paper effectively solves the problem that a single image fails to show the overall distribution of the defects and their accurate positioning in a whole large tunnel section and the effective features of defects in an excessively large panoramic image size are difficult to be captured by the neural network. Field applications demonstrated that the presented method is adequate for high-precision and intelligent surface defect detection and positioning for different small-section hydraulic tunnels such as circular, arch-wall, and box-shaped hydraulic tunnels.

Euclidean direction search algorithm with maximum correntropy criterion for active noise control system

Based on the principle of superposition, the active noise control (ANC) technique can achieve satisfactory noise reduction. The filtered-x least mean square (FxLMS) algorithm has been extensively implemented in the ANC problem but it is easily plunged into instability in impulsive noise scenarios. To ameliorate this disadvantage, benefiting from the reduced computational load of the Euclidean direction search (EDS) algorithm and robustness of the maximum correntropy criterion (MCC), a novel filtered-x EDS-MCC (FxEDS-MCC) algorithm is proposed to attenuate the impulsive interference. The theoretical analysis of the FxEDS-MCC algorithm is based on the rotated method and the Taylor series expansion approximation. Simulations validate the accuracy of the theoretical performance and verify the improved performance of the FxEDS-MCC algorithm in comparison with the existing algorithms.

Comparative analysis of direct search methods for material design optimization

This paper contributes to the field of optimization for periodic composite material design by systematically evaluating the performance of four direct search algorithms: greedy, simulated annealing (SA), genetic algorithms (GA), and particle swarm optimization (PSO). The central goal is to determine the optimal arrangement of two material domains inside a representative volume element (RVE) while respecting the constraint that half volume of the domains is composed of a specific material, with the effective shear modulus as the objective function. The main contribution of this work is the detailed comparison of these algorithms in terms of success rates and computational efficiency, providing critical insights into their suitability for different problem scales. For a small-scale problem (16 cells), PSO achieves a 100% success rate, while SA demonstrates over 90% success but at a higher computational cost. The greedy algorithm, despite its simplicity, achieves a 72% success rate with the lowest computational effort, requiring an average of 256 objective function evaluations. GA, however, exhibits the lowest success rate at 52% and requires the highest average number of evaluations (5003.2). Furthermore, the paper extends the analysis to a more complex problem (36 cells), where the adaptability and efficiency of the algorithms are tested. This investigation highlights the trade-offs between algorithmic complexity, success rate, and computational cost, offering practical guidelines for selecting suitable optimization methods based on problem size and characteristics.

Realizing linear-polarization-decoupled quasi-perfect absorption through mirror-symmetric QR-code metasurfaces.

Metamaterial absorbers (MAs) with irregular structures facilitate the attainment of unique absorption properties, leveraging the extensive geometric freedom. However, a challenge arises from the fact that polarization-dependent spectra do not coincide with cross-polarization. In this study, we introduce a MA featuring a mirror-symmetric quick response (QR)-code structure to achieve linear-polarization-decoupled absorption characteristics. We employ a direct binary search algorithm to reverse design the MA structure by specifying absorptivity for eigen-polarization states. Moreover, the absorptivity for arbitrary polarizations can be predicted through linear superposition of the two eigen-polarization states, opening up avenues for investigating polarization-controlled metasurfaces and metamaterials.

Integrating Deep Learning and Synthetic Biology: A Co-Design Approach for Enhancing Gene Expression via N-Terminal Coding Sequences.

N-terminal coding sequence (NCS) influences gene expression by impacting the translation initiation rate. The NCS optimization problem is to find an NCS that maximizes gene expression. The problem is important in genetic engineering. However, current methods for NCS optimization such as rational design and statistics-guided approaches are labor-intensive yield only relatively small improvements. This paper introduces a deep learning/synthetic biology codesigned few-shot training workflow for NCS optimization. Our method utilizes k-nearest encoding followed by word2vec to encode the NCS, then performs feature extraction using attention mechanisms, before constructing a time-series network for predicting gene expression intensity, and finally a direct search algorithm identifies the optimal NCS with limited training data. We took green fluorescent protein (GFP) expressed by Bacillus subtilis as a reporting protein of NCSs, and employed the fluorescence enhancement factor as the metric of NCS optimization. Within just six iterative experiments, our model generated an NCS (MLD62) that increased average GFP expression by 5.41-fold, outperforming the state-of-the-art NCS designs. Extending our findings beyond GFP, we showed that our engineered NCS (MLD62) can effectively boost the production of N-acetylneuraminic acid by enhancing the expression of the crucial rate-limiting GNA1 gene, demonstrating its practical utility. We have open-sourced our NCS expression database and experimental procedures for public use.

Hybrid differential evolution algorithm for Falkner-Skan flow with rotation

A hybrid differential evolution algorithm is used in this work to study the rotating transport of Falkner-Skan flow. The problem is modeled as an equivalent optimization problem by using Padé rational approximation functions. The primary model of the governing partial differential equations is imposed to subjugate the error between profiles. A hybrid evolutionary algorithm based on differential evolution and a convergent version of Nelder-Mead direct search algorithm is employed to perform global exploratory search along with an enhanced exploitation to improve the accuracy of the proposed solution scheme. The resulting scheme is named as evolutionary Padé approximation (EPA) scheme. The performance of the proposed EPA scheme on the Falkner-Skan boundary value problem is investigated by considering various values of the rotation parameters. The developed optimizer in EPA scheme was able to minimize the residuals up to10−10. Results are displayed graphically in order to study the effect of various types of parameters. EPA scheme determined that angular velocity increases or decreases accordingly as fluid parameter (β) and the rotation parameter (λ) but shows inverse behavior with respect to power law index(n). Similarly, the response of velocity profile along y−axis was decreasing function of β as well as n but increasing function of λ. The performance of the proposed EPA scheme has been demonstrated by comparing results with a hybrid neural network scheme and found in excellent agreement.

Broadband super-resolution wavelength-controlled zoom metalens

A design method is proposed for a broadband super-resolution wavelength-controlled zoom metalens with simultaneous modulation of phase, dispersion, and amplitude, and on the basis of enhancing the axial zoom capability of the metalens, the point spread function of the metalens is continuously compressed using the hierarchical direct binary search algorithm, so that the full width at half maximum of the metalens is continuously close to or even less than the diffraction limit of 0.5λ/NA (NA is the numerical aperture). As a theoretical verification, a super-resolution wavelength-controlled zoom metalens was designed operating in the wavelength range of 68–80 μm. The simulation results show that its axial zoom capability is about 1.65 times that of the conventional diffractive metalens, and the lateral resolution in the wavelength range of 68–80 μm is less than the diffraction limit.

Calibration Optimization of Kinematics and Dynamics for Delta Robot Driven by Integrated Joints in Machining Task

For the application of Delta robots with a 3-R(RPaR) configuration in machining tasks, this paper constructed a 54-parameter kinematic error model and a simplified dynamic model incorporating an integrated joint’s position error and friction, respectively. Utilizing Singular Value Decomposition (SVD) of the Linear Model Coefficient Matrix (LMCM) and the coefficient chart, a criterion for identifiability of error components is established. For good identification results, the optimal measurement surface with Fourier series form is obtained using a combination of the Hook–Jeeves Direct Search Algorithm (DSA) and Inner Point Method (IPM). The friction coefficients and other dynamic parameters are obtained through fitting the integrated joint torque-angle pairs measured along specific trajectories using nonlinear least squares regression. The validation of the calibration process is conducted through simulations and experiments. The calibration results provide a foundation for the precise control of integrated joints and the high-precision motion of robots.

A generation-storage coordination dispatch strategy for power system based on causal reinforcement learning

In the backdrop of global energy transformation, power systems integrating high proportions of renewable energy sources are facing unprecedented challenges in operational stability and dispatch efficiency. To address these challenges, this study introduces a generation-storage coordination real-time dispatch strategy based on Causal Power System Dynamic Reinforcement Learning (CPSDRL). Diverging from traditional reinforcement learning approaches, CPSDRL innovatively incorporates causal inference within the state prediction model – the crux of model-based reinforcement learning – thereby establishing the Power Causal Dynamic Model (PCDM). Assisted by the prior knowledge of power systems, the model significantly enhances prediction accuracy and reliability through a two-stage training process. Utilizing PCDM, this study further applies a direct policy search algorithm to optimize the real-time dispatch strategy. Experimental results indicate that the proposed method improves the stability of generation-storage coordination real-time dispatch and exhibits competitive advantages in sample efficiency and computational speed, compared to traditional model-based and model-free reinforcement learning algorithms. This method is expected to enhance the practicality and adaptability of causal reinforcement learning techniques in power system scheduling and control.

Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

We investigate the feasibility of gradient-free aeroacoustic shape optimization using the flux reconstruction (FR) approach to study two-dimensional flow at low Reynolds numbers. The overall sound pressure level (OASPL) is computed via the direct acoustic approach, and optimization is performed using the gradient-free mesh adaptive direct search (MADS) algorithm. The proposed framework is assessed across three problems. First, flow over an open cavity is investigated at a Reynolds number of Re=1500 and freestream Mach number of M∞=0.15, resulting in a 7.9 dB noise reduction. The second case considers tandem cylinders at Re=200 and M∞=0.2, achieving a 16.5 dB noise reduction by optimizing the distance between the cylinders and their diameter ratio. Finally, a NACA0012 airfoil is optimized at Re=10,000 and M∞=0.2 to reduce trailing edge noise. The airfoil’s shape is optimized to generate a new four-digit NACA airfoil at an appropriate angle of attack to reduce OASPL while maintaining the baseline time-averaged lift coefficient and preventing an increase in the baseline time-averaged drag coefficient. The optimized airfoil is silent at 0 dB and the drag coefficient is decreased by 24.95%. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.

Comparative analysis of the application of direct search algorithms for estimating values of parameters in ecosystems models for the Neva Bay and Vistula Lagoon of the Baltic Sea

Comparative analysis of the application of direct search algorithms for estimating values of parameters in ecosystems models for the Neva Bay and Vistula Lagoon of the Baltic Sea

Optimized wideband and compact multifunctional photonic device based on Sb2S3 phase change material.

In this paper, a 1 × 2 photonic switch is designed based on a silicon-on-insulator (SOI) platform combined with the phase change material (PCM), Sb2S3, assisted by the direct binary search (DBS) algorithm. The designed photonic switch exhibits an impressive operating bandwidth ranging from 1450 to 1650 nm. The device has an insertion loss (IL) from 0.44 dB to 0.70 dB (of less than 0.7 dB) and cross talk (CT) from -26 dB to -20 dB (of less than -20 dB) over an operating bandwidth of 200 nm, especially an IL of 0.52 dB and CT of -24 dB at 1550 nm. Notably, the device is highly compact, with footprints of merely 3 × 4 µm2. Furthermore, we have extended the device's functionality for multifunctional operation in the C-band that can serve as both a 1 × 2 photonic switch and a 3 dB photonic power splitter. In the photonic switch mode, the device demonstrates an IL of 0.7 dB and a CT of -13.5 dB. In addition, when operating as a 3 dB photonic power splitter, the IL is less than 0.5 dB.

Reverse design of multifunctional demultiplexing devices

A novel direct binary search algorithm based on rotation (RDBS) is proposed in this paper. A 1*2 ultra-compact 2.4*3.6µm2 multimode wavelength demultiplexer (DEMUX) is designed in reverse, which is roughly two orders of magnitude smaller than the size of a conventional waveguide device. It can simultaneously perform wavelength demultiplexing and mode conversion. This DEMUX separates the 1310 and 1550 nm wavelengths while converting the input light from the fundamental transverse electric mode (TE0) to the first-order transverse electric mode (TE1). The simulation results using RDBS show that the insertion loss(IL) of the upper channel (wavelength 1310 nm) is −0.9644 dB, the IL of the lower channel (wavelength 1550 nm) is −0.9752 dB, and the crosstalk values(CT) are −10.079 dB and −9.261 dB, respectively.

Reverse design and optimization of digital terahertz bandpass filters

In this paper, an ingenious reverse design method is applied to the design and optimization of terahertz bandpass filters in order to achieve standardized design of high-performance terahertz functional devices. An equivalent model of subwavelength metasurface mapped to digital space is established. Based on ideal objective functions and constraints, intelligent algorithms begin a bold journey to explore the vast potential structure in the solution space. Through iterative refinement, the algorithm reveals optimal structural patterns, unlocking areas of unparalleled performance. The direct binary search (DBS) algorithm and the binary particle swarm optimization (BPSO) algorithm are compared in optimization process. When using the DBS algorithm to optimize the design area, it takes a long time to poll the logic states of all pixel units point by point, and it is easy to get stuck in the local optimal value. However, BPSO algorithm has stronger global search capabilities, faster convergence speed, and higher accuracy. Through a comprehensive comparison of the device performance optimized by the two algorithms, the solution optimized by BPSO algorithm has better out-of-band suppression performance and a narrower full width at half peak, but slightly lower transmittance at the center frequency. The bandpass filter has a center frequency of 0.51 THz, a bandwidth of 41.5 GHz, and an insertion loss of -0.1071 dB. When considering computational efficiency, DBS algorithm lags behind, the simulation time is 11550 s, while BPSO algorithm only needs 9750 s. Compared with the traditional forward design, the reverse design method can achieve the narrower band, lower insertion loss, better out-of-band suppression and polarization stability. The fine structural changes of the optimal results have a significant influence on spectral performance, demonstrating the superiority and uniqueness of reverse design. This technology contributes to the design and optimization of high-performance and novel functional devices.

Enhanced Global Optimization With Parallel Global and Local Structures for Real-Time Control Systems

In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop a parallel global optimization framework that combines direct search methods with parallel Bayesian optimization. It consists of an iterative global and local search that searches broadly through the entire global space for promising regions and then efficiently exploits each local promising region. We prove the asymptotic convergence properties of the proposed framework and conduct several numerical experiments to illustrate its empirical performance. We also provide a real-time control problem to illustrate the efficiency of our proposed algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by a collision avoidance problem of vessels aided with onboard agent-based simulations. The simulation on one vessel can predict potential conflicts with other vessels on a pre-defined trajectory. In heavy congestion regions, the environment is highly dynamic and thus it is difficult to find a much safer alternative trajectory if collision is predicted on the current one. Moreover, for such real-time decisions, the control system should be quick in response to improve safety. The proposed metamodel based algorithm is designed for quick decision in such highly dynamic systems. The algorithm employs a decomposition of the response surface to better handle the multi-modal surface resulting from the highly dynamic environment. Specifically, it first looks at the large-scale trend globally (filter out the many local fluctuations that may otherwise trap the algorithm) to locate potential promising regions and then proceeds to this local regions for more detailed local search. To make quick decisions, it uses fast direct search algorithms in the local search phase and applies a parallel search scheme to enjoy the abundant computing power. Both the theoretical analysis and the simulation studies demonstrate that the proposed algorithm can provide better decisions quickly. We also note that this algorithm is not limited to real-time control or simulation-based system. In the case where each run of the experiment is expensive and the budget is limited for the final decision and when the response function is multi-modal, this algorithm can hopefully become a quite efficient and competitive approach. The multi-modal responses have broad applications in the area of control, planning and operations research, such as robot navigating and reinforcement learning.

Optimized design of nano-photonic devices for temperature self-regulating on vanadium dioxide thin films

Phase change materials can enable temperature self-regulation due to their drastic changes in optical properties accompanying the phase transition. Significant reduction of the optical absorption after the transition is the key ingredient for an enhanced regulating performance. However, the absorptivity of unpatterned vanadium dioxide (VO2) thin films can hardly be reduced after phase transition at visual-to-infrared band. In this work, we combine the direct binary search (DBS) and particle swarm optimization (PSO) algorithms for an optimized design of temperature self-regulating nano-photonic devices on VO2 thin films. For a given incident wavelength, a pixelated structure is firstly inverse-designed by the DBS algorithm which maximizes the absorption contrast before and after the transition. To overcome fabrication challenges as pixel size is at deep sub-wavelength scale, the pixelated structure can then be replaced by geometric shapes which are more tractable in manufacturing processes. The geometrical parameters are optimized by the PSO algorithm where our optimized device brings the absorptivity down to 33% after the transition. These results provide an effective way for the inverse design of optimized nano-photonic structures based on phase change materials.

Long-distance high-fidelity continuous-variable quantum key distribution with non-Gaussian operations: An exact closed form solution

In this paper, we derive a closed-form expression for the output state of a CV-QKD protocol in the presence of zero-photon catalysis (ZPC) and a quantum scissor (QS). Then, based on this closed-form solution, we use a direct search algorithm to find the appropriate values of input state and QS parameters, which considerably enhance the range and the fidelity of a CV-QKD protocol. In the special case of pure loss channel, the largest range of the protocol is only 6.5% less than the fundamental limit of repeaterless quantum communication. In addition, examination of the protocol for different values of excess noise, reveals that there is a trade-off between range and fidelity, and a high value of fidelity can be obtained at the cost of a slight reduction in protocol range.

Stabilized videos source identification method based on undecimated dual-tree complex wavelet transform and Bayesian adaptive direct search algorithm

Stabilized videos source identification method based on undecimated dual-tree complex wavelet transform and Bayesian adaptive direct search algorithm

Four Directed Search Algorithm: A New Optimization Method and Its Hyper Strategy Investigation

Four Directed Search Algorithm: A New Optimization Method and Its Hyper Strategy Investigation