Classical Algorithm Research Articles

OS-PSO: A Modified Ratio of Exponentially Weighted Averages-Based Optical and SAR Image Registration.

Optical and synthetic aperture radar (SAR) images exhibit non-negligible intensity differences due to their unique imaging mechanisms, which makes it difficult for classical SIFT-based algorithms to obtain sufficiently correct correspondences when processing the registration of these two types of images. To tackle this problem, an accurate optical and SAR image registration algorithm based on the SIFT algorithm (OS-PSO) is proposed. First, a modified ratio of exponentially weighted averages (MROEWA) operator is introduced to resolve the sudden dark patches in SAR images, thus generating more consistent gradients between optical and SAR images. Next, we innovatively construct the Harris scale space to replace the traditional difference in the Gaussian (DoG) scale space, identify repeatable key-points by searching for local maxima, and perform localization refinement on the identified key-points to improve their accuracy. Immediately after that, the gradient location orientation histogram (GLOH) method is adopted to construct the feature descriptors. Finally, we propose an enhanced matching method. The transformed relation is obtained in the initial matching stage using the nearest neighbor distance ratio (NNDR) and fast sample consensus (FSC) methods. And the re-matching takes into account the location, scale, and main direction of key-points to increase the number of correctly corresponding points. The proposed OS-PSO algorithm has been implemented on the Gaofen and Sentinel series with excellent results. The superior performance of the designed registration system can also be applied in complex scenarios, including urban, suburban, river, farmland, and lake areas, with more efficiency and accuracy than the state-of-the-art methods based on the WHU-OPT-SAR dataset and the BISTU-OPT-SAR dataset.

Leapfrogging Sycamore: Harnessing 1432 GPUs for 7× faster quantum random circuit sampling

Abstract Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical simulation time and challenged the claim of the first-generation quantum advantage experiments. However, in terms of generating uncorrelated samples, time-to-solution, and energy consumption, previous classical simulation experiments still underperform the Sycamore processor. Here we report an energy-efficient classical simulation algorithm, using 1432 GPUs to simulate quantum random circuit sampling which generates uncorrelated samples with higher linear cross entropy score and is 7 times faster than the Sycamore 53 qubits experiment. We propose a post-processing algorithm to reduce the overall complexity, and integrate state-of-the-art high-performance general-purpose GPU to achieve two orders of lower energy consumption compared to previous works. Our work provides the first unambiguous experimental evidence to refute Sycamore’s claim of quantum advantage, and redefines the boundary of quantum computational advantage using random circuit sampling.

Quantum computing and tensor networks for laminate design: A novel approach to stacking sequence retrieval

As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable task, due to an exponentially large configuration space and non-linear constraints. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems. However, before applying any quantum algorithm to a given problem, it must be translated into a form that is compatible with the underlying operations on a quantum computer. Our work specifically targets stacking sequence retrieval with lamination parameters, which is typically the second phase in a common bi-level optimization procedure for minimizing the weight of composite structures. To adapt stacking sequence retrieval for quantum computational methods, we map the possible stacking sequences onto a quantum state space. We further derive a linear operator, the Hamiltonian, within this state space that encapsulates the loss function inherent to the stacking sequence retrieval problem. Additionally, we demonstrate the incorporation of manufacturing constraints on stacking sequences as penalty terms in the Hamiltonian. This quantum representation is suitable for a variety of classical and quantum algorithms for finding the ground state of a quantum Hamiltonian. For a practical demonstration, we performed numerical state-vector simulations of two variational quantum algorithms and additionally chose a classical tensor network algorithm, the DMRG algorithm, to numerically validate our approach. For the DMRG algorithm, we derived a matrix product operator representation of the loss function Hamiltonian and the penalty terms. Although this work primarily concentrates on quantum computation, the application of tensor network algorithms presents a novel quantum-inspired approach for stacking sequence retrieval.

The analysis of Hermite factor of BKZ algorithm on small lattices

Lattice cryptography is one of the promising directions in modern cryptography research. Digital signatures and key encapsulation mechanisms on lattices have already been used in practice. In the future, such quantum-resistant transformations on lattices replace all standards that are not resistant to attacks on quantum computers. This makes the analysis of their security extremely relevant. Analysis of the security of cryptographic transformations on lattices is often reduced to the estimation of the minimum block size in the lattice reduction algorithm. For the expansion of small vectors, a reduction algorithm can be obtained for a given block size, the GSA model is often used, which uses the so-called Hermitian factor to predict the size of the vectors that the lattice reduction algorithm can obtain given the parameters. Asymptotic formulas have been developed to evaluate it in practice, but the question of their accuracy on cryptographic lattices has not been fully investigated. The work obtained estimates of the accuracy of the existing asymptotic estimates of the Hermite factor for lattices of sizes 120, 145, 170 for the classical BKZ algorithm. Research was conducted using the fpylll library. It was shown that the existing estimators are equivalent from a practical point of view and have a sufficiently small root mean square deviation from the true values. A formula was obtained that binds the root-mean-square error of approximation of the Hermit factor to the cryptographic parameters of lattices. The obtained results are useful for refining the security assessments of existing cryptographic transformations.

Solving Boolean Satisfiability Problems With The Quantum Approximate Optimization Algorithm

One of the most prominent application areas for quantum computers is solving hard constraint satisfaction and optimization problems. However, detailed analyses of the complexity of standard quantum algorithms have suggested that outperforming classical methods for these problems would require extremely large and powerful quantum computers. The quantum approximate optimization algorithm (QAOA) is designed for near-term quantum computers, yet previous work has shown strong limitations on the ability of QAOA to outperform classical algorithms for optimization problems. Here we instead apply QAOA to hard constraint satisfaction problems, where both classical and quantum algorithms are expected to require exponential time. We analytically characterize the average success probability of QAOA on a constraint satisfaction problem commonly studied using statistical physics methods: random k-SAT at the threshold for satisfiability, as the number of variables n goes to infinity. We complement these theoretical results with numerical experiments on the performance of QAOA for small n, which match the limiting theoretical bounds closely. We then compare QAOA with leading classical solvers. For random 8-SAT, we find that for more than 14 quantum circuit layers, QAOA achieves more efficient scaling than the highest-performance classical solver we tested, WalkSATlm. Our results suggest that near-term quantum algorithms for solving constraint satisfaction problems may outperform their classical counterparts. Published by the American Physical Society 2024

An automated convergence diagnostic for phylogenetic MCMC analyses.

Assessing convergence of Markov chain Monte Carlo (MCMC) based analyses is crucial but challenging, especially so in high dimensional and complex spaces such as the space of phylogenetic trees (treespace). In practice, it is assumed that the target distribution is the unique stationary distribution of the MCMC and convergence is achieved when samples appear to be stationary. Here we leverage recent advances in computational geometry of the treespace and introduce a method that combines classical statistical techniques and algorithms with geometric properties of the treespace to automatically evaluate and assess practical convergence of phylogenetic MCMC analyses. Our method monitors convergence across multiple MCMC chains and achieves high accuracy in detecting both practical convergence and convergence issues within treespace. Furthermore, our approach is developed to allow for real-time evaluation during the MCMC algorithm run, eliminating any of the chain post-processing steps that are currently required. Our tool therefore improves reliability and efficiency of MCMC based phylogenetic inference methods and makes analyses easier to reproduce and compare. We demonstrate the efficacy of our diagnostic via a well-calibrated simulation study and provide examples of its performance on real data sets. Although our method performs well in practice, a significant part of the underlying treespace probability theory is still missing, which creates an excellent opportunity for future mathematical research in this area. The open source package for the phylogenetic inference framework BEAST2, called ASM, that implements these methods, making them accessible through a user-friendly GUI, is available from https://github.com/rbouckaert/asm/. The open source Python package, called tetres, that provides an interface for these methods enabling their applications beyond BEAST2 can be accessed at https://github.com/bioDS/tetres/.

Modularity based community detection in hypergraphs

Abstract In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h–Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.

The static voltage stability analysis of photovoltaic energy storage systems based on NPU algorithm

Although the data-driven static voltage stability problems have been widely studied, most of the classical algorithms focus more on improving the accuracy of the system prediction, ignoring the error classification errors generated during the prediction process. Furthermore, current research ignores the utilization of data-driven voltage stability assessment of energy storage systems. Therefore, this paper proposes a static voltage stability assessment method for photovoltaic energy storage systems based on considering the error classification constraint algorithm using Neyman-Pearson umbrella algorithms. Firstly, the Spearman Correlation Coefficient is employed in the feature selection phase. Secondly, an updated voltage stability assessment (VSA) model is proposed. Compared with the existing data-driven prediction of system static voltage stability in the literature, it can realize voltage stability assessment more quickly. Furthermore, on the basis of rapid voltage stability assessment, the umbrella NP classifier can also effectively limit the first-class error and attenuate the effect of error classification by mirroring the control of the number of cycle splits and the type I classification error threshold. Finally, the simulation and experimental results show that the effectiveness and robustness of the scheme proposed in this paper in grid-connected photovoltaic energy farms.

Fitting x-ray diffraction peaks by a genetic algorithm and Monte Carlo Markov Chain procedure

A fitting procedure based on the use of the Genetic algorithms (GA) and the Markov Chain Monte Carlo (MCMC) bayesian technique is proposed for the modelization of the x-ray diffraction peaks by using the usual standard bell-type functions (pseudo-Voigt, Voigt, etc). The method has been tested with simulated Voigt-shaped profiles at different overlapping degrees and the results have been compared with those obtained by means of the classical Levenberg-Marquardt algorithm, showing its reliability.

Dynamic Niches-Based Hybrid Breeding Optimization Algorithm for Solving Multi-Modal Optimization Problem

Some problems exist in classical optimization algorithms to solve multi-modal optimization problems and other complex systems. A Dynamic Niches-based Improved Hybrid Breeding Optimization (DNIHBO) algorithm is proposed to address the multi-modal optimization problem in the paper. By dynamically adjusting the niche scale, it effectively addresses the issue of niche parameter sensitivity. The structure of the algorithm includes three distinct groups: maintainer, restorer, and sterile lines for updating operations. However, the maintainer individuals often stagnate, leading to the risk of the local optima. To overcome this, neighborhood search and elite mutation strategies are incorporated, enhancing the balance between exploration and exploitation. To further improve individual utilization within niches, a niche restart strategy is introduced, ensuring sustained population diversity. The efficacy of DNIHBO is validated through simulations on 16 multi-modal test functions, followed by comparative analyses with various multi-modal optimization algorithms. The results convincingly demonstrate that DNIHBO not only effectively locates multiple global optima but also consistently outperforms other algorithms on test functions. These findings underscore the superiority of DNIHBO as a high-performing solution for multi-modal optimization.

The Effect of Linear Discriminant Analysis and Quantum Feature Maps on QSVM Performance for Obesity Diagnosis

Obesity, characterized by an excessive increase in body fat, is not only a significant disease but also a condition that serves as the basis for many other illnesses. Therefore, early intervention and necessary precautions for diagnosing and treating obesity are of paramount importance. Classical machine learning algorithms are actively utilized in medical fields to expedite prediction processes. However, the increasing volume of data renders even effective classification algorithms inadequate for experts to diagnose diseases. Quantum computing-based algorithms come into play at this point, offering a new perspective in machine learning by utilizing quantum physics, which is contrary to the rules of classical physics. Dimensionality reduction techniques required for the use of quantum-based algorithms play an essential role in both classical and quantum applications. In this study, Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA), classical dimensionality reduction methods, were applied to the obesity dataset and analyzed with Quantum Support Vector Machine (QSVM) and Support Vector Machine (SVM) algorithms. To conduct QSVM studies, the comparison of three different quantum feature maps providing the qubit transformation of classical bit data is also included in this study. As a result of the analysis, it was determined that the proposed method as LDA-QSVM achieved 100% success when used with Z and Pauli X feature maps. This success, which is rare in literature studies on obesity data, emphasizes the future potential of quantum-based algorithms in obesity diagnosis and treatment.

Regression-classification ensemble machine learning model for loading capacity and bucking mode prediction of cold-formed steel built-up I-section columns

This paper presents a regression-classification ensemble machine learning (ML) model for loading capacity and, in particular, buckling mode prediction with respect to cold-formed steel (CFS) I-section columns. The ML model comprises two sub-models, including the regression sub-model for load capacity prediction and the classification sub-model for buckling mode prediction. A total of 541 experimental and numerical data for CFS built-up I-section columns with varies geometric dimensions, material properties and buckling modes were collected from the literature to construct a dataset. To improve the accuracy and the explainability of the ML model on relative small-scale dataset, physical information-enhanced features based on the knowledge of the direct strength method were adopted as the input features of the ML model, including the yield strength, the elastic local buckling load, the elastic distortional buckling load and the elastic global buckling load, instead of directly using the parameters of geometric dimensions and material properties as the input features. The appropriateness of seven classical machine learning algorithms was compared, namely Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVM), K-Nearest Neighbour (KNN), Adaptive Boosting (ADA), Extreme Gradient Boosting (XG), and Categorical Boosting (CB). The statistical analysis showed that the XG algorithm had the highest level of accuracy for both loading capacity and buckling mode prediction. In addition, the explainability analysis indicated that the developed ML model successfully learned the mechanical characteristic of CFS built-up I-section columns. Finally, the developed ML model was further compared with the existing codified method in the literature. The comparison results indicated that the developed ML model can significantly improve the level of accuracy for loading capacity and buckling mode prediction, which provides a promising alternative choice for the design of CFS built-up I-section columns

Solving the homogeneous Bethe-Salpeter equation with a quantum annealer

The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the GEVP by means of a quantum annealer, i.e., to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the simulated-annealing package and the D-Wave . The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. Published by the American Physical Society 2024

Function-Genes and Disease-Genes Prediction Based on Network Embedding and One-Class Classification.

Using genes which have been experimentally-validated for diseases (functions) can develop machine learning methods to predict new disease/function-genes. However, the prediction of both function-genes and disease-genes faces the same problem: there are only certain positive examples, but no negative examples. To solve this problem, we proposed a function/disease-genes prediction algorithm based on network embedding (Variational Graph Auto-Encoders, VGAE) and one-class classification (Fast Minimum Covariance Determinant, Fast-MCD): VGAEMCD. Firstly, we constructed a protein-protein interaction (PPI) network centered on experimentally-validated genes; then VGAE was used to get the embeddings of nodes (genes) in the network; finally, the embeddings were input into the improved deep learning one-class classifier based on Fast-MCD to predict function/disease-genes. VGAEMCD can predict function-gene and disease-gene in a unified way, and only the experimentally-verified genes are needed to provide (no need for expression profile). VGAEMCD outperforms classical one-class classification algorithms in Recall, Precision, F-measure, Specificity, and Accuracy. Further experiments show that seven metrics of VGAEMCD are higher than those of state-of-art function/disease-genes prediction algorithms. The above results indicate that VGAEMCD can well learn the distribution characteristics of positive examples and accurately identify function/disease-genes.

Target Fitting Method for Spherical Point Clouds Based on Projection Filtering and K-Means Clustered Voxelization.

Industrial computed tomography (CT) is widely used in the measurement field owing to its advantages such as non-contact and high precision. To obtain accurate size parameters, fitting parameters can be obtained rapidly by processing volume data in the form of point clouds. However, due to factors such as artifacts in the CT reconstruction process, many abnormal interference points exist in the point clouds obtained after segmentation. The classic least squares algorithm is easily affected by these points, resulting in significant deviation of the solution of linear equations from the normal value and poor robustness, while the random sample consensus (RANSAC) approach has insufficient fitting accuracy within a limited timeframe and the number of iterations. To address these shortcomings, we propose a spherical point cloud fitting algorithm based on projection filtering and K-Means clustering (PK-RANSAC), which strategically integrates and enhances these two methods to achieve excellent accuracy and robustness. The proposed method first uses RANSAC for rough parameter estimation, then corrects the deviation of the spherical center coordinates through two-dimensional projection, and finally obtains the spherical center point set by sampling and performing K-Means clustering. The largest cluster is weighted to obtain accurate fitting parameters. We conducted a comparative experiment using a three-dimensional ball-plate standard. The sphere center fitting deviation of PK-RANSAC was 1.91 μm, which is significantly better than RANSAC's value of 25.41 μm. The experimental results demonstrate that PK-RANSAC has higher accuracy and stronger robustness for fitting geometric parameters.

An agent-based cooperative co-evolutionary framework for optimizing the production planning of energy supply chains under uncertainty scenarios

Nowadays, energy and power companies compete to get the raw materials and equipment they need on time, as project times lengthen, costs spiral, stock-out continues to plague plans to a decarbonized energy future. The risks reflect the impact of uncertainty and volatility on the resilience of the supply chains. Therefore, there is a need for the enhancement of the production planning in Energy Supply Chains (ESCs), as it enables affordable energy supplies and supports the companies transition to a clean, secure and sustainable energy mix. This study aims to understand the interactive behavior among individuals and optimize their production planning under uncertainty scenarios. In particular, we propose a novel framework to couple an Agent-based Modelling (ABM) and a Co-evolutionary Algorithm (CEA), to realize its capacity to solve a Many-objective Optimization Problem (MaOP) where the profits of multiple agents are concurrently maximized in their interactive transaction processes under normal conditions and uncertain disruption events.For demonstration, we illustrate the proposed approach by considering a five-layer oil and gas ESC model, where uncertainties from multiple sources and the structural dynamics challenge the balance between supply and demand. The results obtained by an integration of a Cooperative Co-evolutionary Particle Swarm Optimizer (CCPSO) algorithm into ABM show the pricing and orders of the target agents are optimized while the loss of ESC resilience is minimized under uncertainty scenarios, proving its capacity of improving the diversity and the convergence, compared to the classic evolutionary algorithms.

Tiny-Object Detection Based on Optimized YOLO-CSQ for Accurate Drone Detection in Wildfire Scenarios

Wildfires, which are distinguished by their destructive nature and challenging suppression, present a significant threat to ecological environments and socioeconomic systems. In order to address this issue, the development of efficient and accurate fire detection technologies for early warning and timely response is essential. This paper addresses the complexity of forest and mountain fire detection by proposing YOLO-CSQ, a drone-based fire detection method built upon an improved YOLOv8 algorithm. Firstly, we introduce the CBAM attention mechanism, which enhances the model’s multi-scale fire feature extraction capabilities by adaptively adjusting weights in both the channel and spatial dimensions of feature maps, thereby improving detection accuracy. Secondly, we propose an improved ShuffleNetV2 backbone network structure, which significantly reduces the model’s parameter count and computational complexity while maintaining feature extraction capabilities. This results in a more lightweight and efficient model. Thirdly, to address the challenges of varying fire scales and numerous weak emission targets in mountain fires, we propose a Quadrupled-ASFF detection head for weighted feature fusion. This enhances the model’s robustness in detecting targets of different scales. Finally, we introduce the WIoU loss function to replace the traditional CIoU object detection loss function, thereby enhancing the model’s localization accuracy. The experimental results demonstrate that the improved model achieves an mAP@50 of 96.87%, which is superior to the original YOLOV8, YOLOV9, and YOLOV10 by 10.9, 11.66, and 13.33 percentage points, respectively. Moreover, it exhibits significant advantages over other classic algorithms in key evaluation metrics such as precision, recall, and F1 score. These findings validate the effectiveness of the improved model in mountain fire detection scenarios, offering a novel solution for early warning and intelligent monitoring of mountain wildfires.

Particle swarm optimization for hybrid mutant slime mold: An efficient algorithm for solving the hyperparameters of adaptive Grey-Markov modified model

Thegrey prediction model is a scientific and effective prediction method for small amounts of incomplete data. In this paper, we proposed a particle swarm optimization for mixed mutant slime mold (namely SCPSO) combined with an extended adaptive Grey-Markov modified model called AOPGM(1,1,λ,µ), which constructs an AOPGM(1,1,λ,µ) based hyperparameters optimization for SCPSO. Firstly, the values of the exponential cumulative generation operator coefficient λ and the background value µ of the adaptive Grey-Markov modified model are refined, and λ and µ are also calculated using SCPSO. Secondly, a competitive SCPSO is formed by introducing a good point set, identifying attack strategy, mutation slime mold algorithm, and Sigmoid function into particle swarm optimization. It was also compared with the improved optimization algorithms on the CEC2020 test set and with classical and newer intelligent algorithms on the CEC2022 test set. The results of numerical experiments show that SCPSO can be considered a competitive and promising global optimization algorithm. Finally, SCPSO is used to optimize the hyperparameters of the AOPGM(1,1,λ,µ) and applied to the prediction of oil production and proven reserves in China. In terms of optimizing the hyperparameters of the AOPGM(1,1,λ,µ), the numerical experimental results of this method were better than the prediction results of 7 intelligent algorithms and the results of 4 prediction models. The validity of the proposed methodology was verified through five evaluation indicators.

UAV trajectory planning in NOMA-aided UAV-mounted RIS networks: A budgeted Multi-armed bandit approach

Abstract Reconfigurable Intelligent Surface (RIS) and Non-Orthogonal Multiple Access (NOMA) can be used as supporting technologies for driving the effective development of Unmanned Aerial Vehicles (UAV) communication systems. Herein, both technologies are combined to widen the millimeter-wave Base Stations (mmWave-BS) coverage range. In this work, we consider UAV Trajectory Planning (UTP) problem to enhance the performance of a NOMA-based UAV-mounted RIS communication network. The problem is formulated using two Budgeted Multi-Armed Bandits (BMAB) schemes. BMAB is a variant of the classical MAB algorithm that considers the random cost of selecting an arm. The UAV performs as a bandit player attempting to maximize its achievable rate (i.e., reward) via accessing different grids in its trajectory. This reward is accomplished simultaneously while minimizing the energy/cost of flying the UAV from one grid to another to preserve its battery lifetime. Hence, two variants of the Budgeted upper confidence bound (BUCB), namely the BUCB1 and BUCB2, are investigated, where the simulations show that both algorithms outperform other benchmarks.

Hybrid of non-dominated sorting genetic algorithm II and invasive weed optimization for fan duct surface heat exchanger configuration optimization design

In this research, configuration optimization was conducted for FDSHX (fan duct surface heat exchanger) that is a new type of heat exchanger adopted in aero-engine heat management in recent years. Firstly, a method of Taguchi-ANFIS (Taguchi-Adaptive Neuro-Fuzzy Inference System), which can reduce training data volume utilizing orthogonal experimental matrix, was proposed to construct a rapid response mathematical model between three configuration parameters, including fin pitch, fin thickness, and oil passages number, and two design indicators, including heat transfer capacity and operating weight, based on the data prepared by an experimental validated FDSHX heat transfer capacity calculation method using heat transfer unit simulation. Secondly, a hybrid method of NSGA II-IWO (Non-dominated Sorting Genetic Algorithm II-Invasive Weed Optimization), which can simultaneously obtain the strong abilities of exploration and escaping from trap into local optima, was proposed to drive the constructed response mathematical model to enhance heat transfer through adjusting the three configuration parameters. Optimization comparison was performed between NSGA II-IWO and four classic optimization algorithms including GA (Genetic Algorithm), IWO (Invasive Weed Optimization), CA (Cultural Algorithm), and HS (Harmony Search). This research provides an integrated solution to help mechanical engineers improve the applicability and reasonableness of FDSHX design.