Global Optimization Method Research Articles

An Innovative Hybrid Approach Producing Trial Solutions for Global Optimization

Global optimization is critical in engineering, computer science, and various industrial applications as it aims to find optimal solutions for complex problems. The development of efficient algorithms has emerged from the need for optimization, with each algorithm offering specific advantages and disadvantages. An effective approach to solving complex problems is the hybrid method, which combines established global optimization algorithms. This paper presents a hybrid global optimization method, which produces trial solutions for an objective problem utilizing a genetic algorithm’s genetic operators and solutions obtained through a linear search process. Then, the generated solutions are used to form new test solutions, by applying differential evolution techniques. These operations are based on samples derived either from internal line searches or genetically modified samples in specific subsets of Euclidean space. Additionally, other relevant approaches are explored to enhance the method’s efficiency. The new method was applied on a wide series of benchmark problems from recent studies and comparison was made against other established methods of global optimization.

Mathematical modeling for the potential energy of the aminophenol derivative azomethine molecule via Bezier surfaces and fuzzy inference system

Abstract In this study, we have managed to model the energy surface of the aminophenol derivative azomethine molecule mathematically depending on two torsion angles SC1(C9C10C12N14) and SC2(C2C1C6C11). For this purpose, firstly, discrete data obtained from Density Functional Theory calculations have been converted into continuous data with the help of the Fuzzy Inference System. Thus, it is possible to calculate energy values for untested data, which are very costly in terms of time to obtain with other methods/experiments. Then, the continuous and non-smooth surface obtained from the fuzzy inference system and representing the energy values of the molecule has been transformed into a differentiable surface with the help of Bezier surfaces. Thus, an objective function has been obtained in which global optimization methods based on the derivative (or gradient) operator could be used.

Gravity data inversion for parameters assessment over geologically faulted structures—A hybrid particle swarm optimization and gravitational search algorithm technique

AbstractInterpreting gravity anomalies caused by fault formations is associated with hydrocarbon systems, mineralized areas and hazardous zones and is the main goal of this research. To achieve an effective and robust model over the geologically faulted structures from gravity anomalies, we present a nature‐inspired hybrid algorithm, which synergizes the physics of the particle swarm optimization and gravitational search algorithm with variable inertia weights. The basic principle of developed particle swarm optimization and gravitational search algorithm method is to synergistically use the exploratory strengths of gravitational search algorithm with the exploitation capacity of particle swarm optimization in order to optimize and enhance the effectiveness by both algorithms. The technique has been tested on synthetic gravity data with varying settings of noises over geologically faulted structure before being applied to field data taken from Ahiri‐Cherla and Aswaraopet master fault present in Pranhita–Godavari valley, India. The optimization process is further refined through normalized Gaussian probability density functions, confidence intervals, histograms and correlation matrices to quantify uncertainty, stability, sensitivity and resolution. When dealing with field data, the true model is never known; in these circumstances, the quality of the outcome can only be inferred from the uncertainty in the mean model. The research utilizes a 68.27% confidence intervals to identify a location where the probability density function is more dominant. This region is then used to evaluate the mean model, which is expected to be more appropriate and closer to the genuine model. Correlation matrices further provide a clear demonstration of the strong connection between layer parameters. The results suggest that particle swarm optimization and gravitational search algorithm is less affected by model parameters and yields geologically more consistent outcomes with little uncertainty in the model, aligning well with the available results. The analysed results show that the method we came up with works well and is stable when it comes to solving the two‐dimensional gravity inverse problem. Future research may involve extending the approach to three‐dimensional inversion problems, with potential improvements in computational efficiency and search accuracy for global optimization methods.

Dynamic deformation and fracture of brass: Experiments and dislocation-based model

In this work, we perform a comprehensive study of the dynamic deformation and fracture of brass, including Taylor tests with classical and profiled cylinders and ball throwing experiments reaching the strain rates of about (0.1−1)/μs, as well as atomistic and continuum-level numerical modeling. Molecular dynamics (MD) simulations are used to construct the equation of state (EOS) of brass and to study its fracture characteristics at shear deformation under negative pressure. An original model of fracture under combined tensile-shear loading is formulated, which takes into account both the accumulation of empty volume in the process of lattice loosening due to the lattice defect production in the course of plastic deformation and further mechanical growth of voids controlled by the dislocation plasticity. This atomic-scale model is transmitted to the macroscopic experiment-scale level and embedded into 3D dislocation plasticity model to describe the dynamic deformation and fracture of brass using the numerical scheme of smoothed particle hydrodynamics (SPH). A part of experimental data is used to find the optimal parameters of the dislocation plasticity model by means of the Bayesian global optimization method accelerated with the help of artificial-neural-network (ANN)-based emulator of the 3D model. Another part of experimental data is used to fit the fracture model parameter. The remaining experimental data, which are not used in the parameterization, are applied to verify the parameterized model. The developed physical-based model provides correct and meaningful description of the dynamic deformation and fracture of brass, while the developed formalized approach to its parameterization opens a way to wider use of this type of models in the engineering applications, including studies on dynamic performance and high-speed processing technologies.

Mетод визначення зміни просторового положення об'єкта орбітального сервісу з невідомою формою

This paper presents a method for determining the pose of an on-orbit service object (target) with an unknown surface shape based on processing target surface point clouds. It is assumed that a point cloud is obtained using a sensor in the form of a lidar-based system onboard the service spacecraft. The algorithm of the method operates with a simplified description of the cloud; it uses only the coordinates of the cloud points without identifying any surface features. The idea of the method is as follows. From all cloud points obtained at a certain time instant, select points that are close to a certain degree to a given set of planes arranged in space in a certain way. From the point cloud corresponding to the next time instant, select points that are close to the same set of planes, but moved in space in a known way. By convention, let the arrangement of the projections of the selected cloud points onto the given planes be called a pattern of the intersection of the point clouds with the planes. By varying the displacement of the set of planes, maximize the coincidence of the intersection patterns of the first and second clouds of points. The degree of coincidence of the intersection patterns is characterized by a specified objective function whose arguments are target pose parameters. The target displacement parameters are found as the arguments of the objective function that maximize it. A variant of the objective function is proposed. A test example of the application of the proposed method is considered. A global optimization method known as the direct search method was used to find the arguments of the objective function. Test calculations were performed, and they confirmed the workability of the algorithm and determined its scope of applicability. The computational burden was not considered: the goal was to verify the workability of the method in principle. The advantage of the proposed method is its ability to determine a change in the pose of an object with an unknown surface shape. The proposed method may be considered as a source of observation data for a filtering procedure when estimating the parameters of the relative motion of a target with an unknown surface shape.

Adaptive metamodeling-based simulation optimisation

Simulation Optimisation is a powerful decision-making tool, but it can be challenging for complex, time-intensive models. This paper introduces Adaptive Metamodeling-based Simulation Optimisation (AMSO), a novel framework that enhances solution quality by integrating machine learning and metaheuristic techniques. AMSO combines Bagged-gradient Boosted Trees, Genetic Algorithms, Hyperparameter Optimisation, and Design of Experiments to efficiently explore promising solution areas. The study demonstrates AMSO’s application in two real-world scenarios: a resource allocation problem in a manufacturing digital twin model and a capacity expansion project at a mining plant. AMSO outperformed the Efficient Global Optimisation method, achieving solutions 8.1% and 9.7% better on average for the first and second case studies, respectively, with no significant increase in computational time. Additionally, AMSO matched the Genetic Algorithm method’s solution quality but reduced computational time by 83.6% and 90.6% in the first and second cases, respectively. AMSO is presented as a robust alternative for solving complex simulation models, complementing existing metamodeling-based methods and opening new research avenues with other machine learning models for faster, more accurate decision-making.

Bi-Level Operation Optimization and Performance Analysis for a Distributed Energy System with Energy Network

The increasing energy crisis and environmental problems promote the development of distributed energy systems (DESs) that utilize combined heat and power technology, renewable energy technology, and waste heat recovery technology to meet various load requirements. Although there is existing work and research on a variety of DESs, most previous studies tend to focus on energy production with little consideration of a distributed energy network and its energy loss, which results in large errors in energy-efficiency calculations and performance analyses. In this paper, a new DES model is proposed with full consideration of an energy network and the full use of solar energy, terrestrial heat, and exhaust gases. At the same time, an effective bi-level optimization method is also proposed for the daily operation of the DES in order to improve the system performance and benefits in the energy, the economy, and the environment. Specifically, the co-generation energy station and water heating network in the DES are optimized separately with two different optimization models. The first-level optimization model is used to seek the optimal values of water mass flow rate and water temperature of the water heating network, and the second-level optimization model is built to determine the optimal energy purchasing strategy and the optimal energy outputs of the co-generation energy station. In order to verify the advantages and effectiveness of the proposed system and method, a contrastive simulation study is undertaken to provide a comparison of the global optimization method. Simulation results show that energy loss, energy cost, and energy consumption of the DES using the bi-level optimization operation strategy only account for 22.51%, 33.42%, and 51.31% of the quantities of the global optimization method, respectively. The hourly curves of the optimal operating variables also demonstrate that the proposed bi-level optimization method can improve the operating stability of the DES better than the global optimization method.

Supervised kernel principal component analysis-polynomial chaos-Kriging for high-dimensional surrogate modelling and optimization

Surrogate-based optimization (SBO) approach is becoming more and more popular in the expensive aerodynamic design of aircraft. However, with increasing number of design variables required for parameterizing a complex shape, SBO is suffering from the serious difficulty of the curse of dimensionality. To ameliorate this issue, a supervised nonlinear dimensionality-reduction surrogate modelling method was proposed. Such a method combines the supervised kernel principal component analysis (SKPCA) and polynomial chaos-Kriging (PCK) techniques into the jointly surrogate modelling process and adaptively establishes the accurate mapping from the high-dimensional inputs to the output of the system. This SKPCA-PCK method, which fully considers the effect of inputs on outputs and adaptively trains these hyper-parameters in the surrogate modelling process, escapes from the low prediction accuracy and instability of the surrogate model in conjunction with current linear or unsupervised dimensionality-reduction methods. Further, an efficient SKPCA-PCK-based global optimization method for high-dimensional aerodynamic design was developed. The performance of the proposed method is examined by investigating two numerical examples, the transonic RAE2822 airfoil and the wing of the NASA Common Research Model. Results demonstrate that the proposed SKPCA-PCK method significantly improves the modelling efficiency and accuracy compared to the unsupervised linear PCA-Kriging method. More importantly, the proposed SKPCA-PCK-based optimization method provides better performance and an appreciably higher optimization efficiency for expensive single-point and robust aerodynamic design involving high-dimensional design variables compared to the Kriging-based optimization method. These results provide further evidence that the proposed method provides a promising approach for mitigating the curse of dimensionality in SBO.

Multiobjective optimization by using cutting angle methods and hypervolume criterion

We translate a multiobjective optimization problem into a single objective Lipschitz problem by using the hypervolume criterion of the Pareto set. Deterministic global optimization methods allow one to track the whole Pareto front rather than converging to a single non-dominated solution. We augmented an efficient hypervolume computation technique with hypervolume increment strategy, and established Lipschitzianity of the resulting objective function. We used two deterministic Lipschitz optimization methods together with the hypervolume objective and benchmarked them against some state-of-the-art alternative multiobjective optimization methods, establishing the competitiveness of the proposed approach.

Revisiting the fitting of the Nelson–Siegel and Svensson models

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis.

Analysis and evaluation of the effectiveness of program codes for particle swarm and ant colony methods for lower semi-continuous functions

In this paper, a comparative analysis of two stochastic methods of global optimization is carried out: the Particle Swarm Optimization method and the Ant Colony Optimization method. The analysis and evaluation of efficiency were carried out using parameters such as the number of calls to the objective function, the rate of convergence, resources, computational efficiency, sensitivity to parameters, and resistance to initial conditions. The article presents the program codes of these methods in the Python environment, designed to calculate the global extremum of semi-continuous functions from below. Well- known test functions were used to construct (by gluing) semi-continuous functions at different values of input parameters.

Layered target design method for global spectrum optimization of radioisotope production

Targets are irradiated in high-flux reactors to produce transplutonium isotopes. Neutron environment of the target is crucial for the production efficiency of transplutonium isotopes. To improve the production efficiency of transplutonium isotopes, it is necessary to research the optimization design of target. Taking the production of Californium-252 as an example, this study analyzed the impact of self-shielding effect in targets on the yield of transplutonium isotope based on the High Flux Isotope Reactor (HFIR) and High-Flux Fast Reactor (HFFR). The self-shielding effect leads to the hardening of the neutron spectrum inside the target and significantly reduces the conversion rate of nuclides. After conducting a refined energy spectrum analysis, we proposed a layered target design method based on the Genetic Algorithm (GA). To reduce computational costs, we propose a fixed source-burnup coupling approximate calculation method, which can avoid tedious burnup calculation and provide optimization direction. Using this method, we designed an optimal layered target scheme. Compared with non-layered target, the production efficiency of Cf-252 was increased by approximately 4.1 times. This study provides technical support for energy spectrum analysis and target design in producing transplutonium isotopes.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Set Packing Optimization by Evolutionary Algorithms with Theoretical Guarantees.

The set packing problem is a core NP-complete combinatorial optimization problem which aims to find the maximum collection of disjoint sets from a given collection of sets, S, over a ground set, U. Evolutionary algorithms (EAs) have been widely used as general-purpose global optimization methods and have shown promising performance for the set packing problem. While most previous studies are mainly based on experimentation, there is little theoretical investigation available in this area. In this study, we analyze the approximation performance of simplified versions of EAs, specifically the (1+1) EA, for the set packing problem from a theoretical perspective. Our analysis demonstrates that the (1+1) EA can provide an approximation guarantee in solving the k-set packing problem. Additionally, we construct a problem instance and prove that the (1+1) EA beats the local search algorithm on this specific instance. This proof reveals that evolutionary algorithms can have theoretical guarantees for solving NP-hard optimization problems.

Robust estimation of hydrogeological parameters from wireline logs usingsemi-supervised deep neural networks assisted with global optimization-based regression methods

Understanding the distribution of hydrogeological properties of the aquifers is crucial for sustainable groundwater resource development. This research explores the application of deep autoencoder neural networks (AE-NN), assisted with global optimization methods for estimating hydrogeological parameters in the Quaternary aquifer system in the Debrecen area, Hungary. Traditional methods for estimating aquifer parameters typically depend on field experiments and laboratory analyses, which are both costly and time-consuming, and often fail to account for the heterogeneity of groundwater formations. In this study, deep AE-NN models are trained to extract latent space (LS) representations that capture key features from the available well logs, including spontaneous potential (SP), natural gamma ray (NGR), shallow resistivity (RS), and deep resistivity (RD). The LS log is then correlated with shale volume and hydraulic conductivity, as determined by the Larionov and Csókás methods, respectively. Regression analysis revealed a Gaussian relationship between the LS log and shale volume and a negative nonlinear relationship with hydraulic conductivity. Global optimization methods, including simulated annealing (SA) and particle swarm optimization (PSO), were used to refine the regression parameters, enhancing the predictive capabilities of the models. The results demonstrated that AE-NN assisted with global optimization methods can be effectively used to estimate shale volume and hydraulic conductivity, proposing a novel and independent approach for estimating hydrogeological parameters critical to groundwater flow and contaminant transport modeling.

Lithium-Ion Battery Health Assessment Method Based on Double Optimization Belief Rule Base with Interpretability

Health assessment is necessary to ensure that lithium-ion batteries operate safely and dependably. Nonetheless, there are the following two common problems with the health assessment models for lithium-ion batteries that are currently in use: inability to comprehend the assessment results and the uncertainty around the chemical reactions occurring inside the battery. A rule-based modeling strategy that can handle ambiguous data in health state evaluation is the belief rule base (BRB). In existing BRB studies, experts often provide parameters such as the initial belief degree, but the parameters may not match the current data. In addition, random global optimization methods may undermine the interpretability of expert knowledge. Therefore, this paper proposes a lithium-ion battery health assessment method based on the double optimization belief rule base with interpretability (DO-BRB-I). First, the belief degree is optimized according to the data distribution. Then, to increase accuracy, belief degrees and other parameters are further optimized using the projection covariance matrix adaptive evolution strategy (P-CMA-ES). At the same time, four interpretability constraint strategies are suggested based on the features of lithium-ion batteries to preserve interpretability throughout the optimization process. Finally, to confirm the efficacy of the suggested approach, a sample of the health status assessment of the B0006 lithium-ion battery is provided.

A fixed point evolution algorithm based on expanded Aitken rapid iteration method for global numeric optimization

Evolution algorithms based on mathematical models whose reproduction operators are derived from mathematical models are a promising branch of metaheuristic algorithms. Aitken rapid iteration method, as a fixed point iteration technique for solving nonlinear equations, performs a procedure of progressive display of a root and generates an iterative sequence that exhibits a convergent trend. Inspired by the idea that an iterative sequence gradually converges to the optimal point during the progressive display procedure of a fixed point of an equation, a fixed point evolution algorithm based on the expanded Aitken rapid iteration method (FPEea) is proposed. To develop FPEea, an expanded Aitken rapid model is first constructed. Then, three polynomials which are derived from the expanded Aitken rapid model are used as the reproduction operator of FPEea to produce offspring. The performance of FPEea is investigated on CEC2019 and CEC2020 benchmark function sets, as well as four engineering design problems. Experimental results show that FPEea is an effective and competitive algorithm compared with several classical evolution algorithms and state-of-the-art algorithms.

Research on bond-slip behavior of corroded square rebar-concrete in historical reinforced concrete buildings

Corrosion of rebar often leads to the degradation of the bond-slip performance of reinforced concrete members, which is a serious issue in historical buildings. The bond-slip behavior of square rebar, which is widely used in historical reinforced concrete buildings, is significantly different from that of round rebar. In this paper, a bond-slip model of corroded square rebar reinforced concrete was developed. First, 18 square rebar reinforced concrete cube pull-out specimens are made, and the corrosion of rebars is accelerated by electrochemical corrosion experiments. Second, a universal global optimization method was used to construct the bond slip expression and the four-fold line bond-slip model with different corrosion rates was obtained by using the minimum Euclidean distance point. Third, the calculation formulas for the bond strength reduction coefficient and slip ratio of corroded square rebar-concrete in historical reinforced concrete buildings are derived. Finally, the bond-slip constitutive model of corroded square rebar-concrete in historical reinforced concrete buildings is established. The results show that the model is more accurate, simple, effective, and easy to use in practical engineering. The research results provide an important theoretical basis for the structural evaluation and conservation of historical reinforced concrete buildings.

Inverse design of bistable composite laminates with switching tunneling method for global optimization

Bistability enables adaptive designs with tunable deflections for applications including morphing wings, robotic grippers, and consumer products. Composite laminates may be designed to exhibit bistability due to pre-strains that develop during the processing of the polymer matrix, enabling fast reconfiguration between two stable shapes. Unfortunately, designing bistable laminates is challenging because of their highly nonlinear behavior. Here, we propose the Switching Tunneling Method to address this challenge by alternating between gradient-based local minimization and tunneling search phases, with the enhancement of objective expression switching to improve numerical conditioning. Results demonstrate high effectiveness compared to existing optimizers; the Switching Tunneling Method achieves a 99% success rate in finding all energy minima across general composite layups. Additionally, our method facilitates the inverse design of variable pre-strain fields, enabling bioinspired, positive Gaussian curvatures, which are not possible with conventional pre-strain laminates. Validations through both finite element analysis and 3D printed samples confirm the optimal designs.

A class of one-parameter filled functions with the same local minima as the objective function for global optimization problems

As an effective global optimization method, the filled function algorithm obtains the optimal solution of optimization problems by alternately minimizing the objective function and filled function. One development direction of the filled function method is to construct the filled function with good properties, which directly affects the efficiency of the algorithm and has attracted the attention of scholars. This paper presents a class of one-parameter filled function that is easy to adjust. It is proved theoretically that the filled function is continuously differentiable and has the same local minimizers as the objective function, and these minimizers are all better than the current local minimizer of the objective function. Meanwhile, some natures of the constructed filled function are conducted as followed by a new algorithm is presented. The new filled function algorithm optimizes the iterative framework of the conventional filled function method, improving the efficiency and decreasing the computational cost. The numerical experiments of the new algorithm on several optimization issues are reported with satisfactory computational results, verifying the feasibility and efficiency of the algorithm.