Global Optimization Method Research Articles

A branch-and-bound algorithm with growing datasets for large-scale parameter estimation

The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.

A new method of smoothness‐constrained magnetotelluric modelling with the utility of Pareto‐optimal multi‐objective particle swarm optimization

AbstractParticle swarm optimization, one of the modern global optimization methods, is attracting widespread interest because it overcomes the difficulties of conventional inversion techniques, such as trapping at a local minimum and/or initial model dependence. The main characteristic of particle swarm optimization is the large search space of parameters, which in a sense allows the exploration of the entire objective function space if the input parameters are properly chosen. However, in the case of a high‐dimensional model space, the numerical instability of the solution may increase and lead to unrealistic models and misinterpretations due to the sampling problem of particle swarm optimization. Therefore, smoothness‐constrained regularization techniques used for the objective function or model reduction techniques are required to stabilize the solution. However, weighting and combining objective function terms is partly a subjective process, as the regularization parameter is generally chosen based on some kind of criteria of how the smoothing constraints affect the data misfits. This means that it cannot be completely predefined but needs to be adjusted during the inversion process, which begins with the response of an initial model. In this paper, a new modelling approach is proposed to obtain a smoothness‐constrained model from magnetotelluric data utilizing multi‐objective particle swarm optimization based on the Pareto optimality approach without using a regularization parameter and combining several objective function terms. The presented approach was verified on synthetic models and an application with field data set from the Çanakkale–Tuzla geothermal field in Turkey. Findings from these analyses confirm the usefulness of the method as a new approach for all constrained inversions of geophysical data without the need to combine the objective function terms weighted by a regularization parameter.

Robust individual pig tracking

The locations of pigs in the group housing enable activity monitoring and improve animal welfare. Vision-based methods for tracking individual pigs are noninvasive but have low tracking accuracy owing to long-term pig occlusion. In this study, we developed a vision-based method that accurately tracked individual pigs in group housing. We prepared and labeled datasets taken from an actual pig farm, trained a faster region-based convolutional neural network to recognize pigs’ bodies and heads, and tracked individual pigs across video frames. To quantify the tracking performance, we compared the proposed method with the global optimization (GO) method with the cost function and the simple online and real-time tracking (SORT) method on four additional test datasets that we prepared, labeled, and made publicly available. The predictive model detects pigs’ bodies accurately, with F1-scores of 0.75 to 1.00, on the four test datasets. The proposed method achieves the largest multi-object tracking accuracy (MOTA) values at 0.75, 0.98, and 1.00 for three test datasets. In the remaining dataset, the proposed method has the second-highest MOTA of 0.73. The proposed tracking method is robust to long-term occlusion, outperforms the competitive baselines in most datasets, and has practical utility in helping to track individual pigs accurately.

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

Optimizing implementations of linear layers using two and higher input XOR gates.

Maximum distance separable (MDS) matrices are often used in the linear layer of a block cipher due to their good diffusion property. A well-designed lightweight MDS matrix, especially an involutory one, can provide both security and performance benefits to the cipher. Finding the corresponding effective linear straight-line program (SLP) of the circuit of a linear layer is still a challenging problem. In this article, first, we propose a new heuristic algorithm called Superior Boyar-Peralta (SBP) in the computation of the minimum number of two-input Exclusive-OR (XOR) gates with the minimum circuit depth for the SLPs. Contrary to the existing global optimization methods supporting only two-input XOR gates, SBP heuristic algorithm provides the best global optimization solutions, especially for extracting low-latency circuits. Moreover, we give a new 4 × 4 involutory MDS matrix over F24, which requires only 41 XOR gates and depth 3 after applying SBP heuristic, whereas the previously best-known cost is 45 XOR gates with the same depth. In the second part of the article, for further optimization of the circuit area of linear layers with multiple-input XOR gates, we enhance the recently proposed BDKCI heuristic algorithm by incorporating circuit depth awareness, which limits the depth of the circuits created. By using the proposed circuit depth-bounded version of BDKCI, we present better circuit implementations of linear layers of block ciphers than those given in the literature. For instance, the given circuit for the AES MixColumn matrix only requires 44 XOR gates/depth 3/240.95 GE in the STM 130 nm (simply called ASIC4) library, while the previous best-known result is 55 XOR gates/depth 5/243.00 GE. Much better, our new 4 × 4 involutory MDS matrix requires only 19 XOR gates/depth3/79.75 GE in the STM 90 nm (simply called ASIC1) library, which is the lightest and superior to the state-of-the-art results.

Control of Aerodynamic Characteristics of Thick Airfoils at Low Reynolds Numbers Using Methods of Boundary Layer Control

The article explores flow behavior around thick airfoils at low Reynolds numbers and the potential application of energy methods to manipulate the flow field for increased lift and reduced drag. The study relies on a set of propulsion airfoils calculated using a combined approach of solving the inverse problem of aerodynamics and applying stochastic global optimization methods. The calculations consider the transition from laminar to turbulent flow regimes, which significantly affects lift and airfoil drag. The suitability of different turbulence models for airfoil modeling in low Reynolds numbers is discussed, and numerical simulation results determine the lift coefficient dependence on angle of attack and the optimal air flow rate taken from the airfoil surface for each angle of attack. The accuracy of different turbulence models is analyzed by comparing numerical simulation results to physical experiment data.

Optimization Design of Oil Groove Shape on the Surface of Friction Plate in High-Speed Wet Clutch Aimed at Minimizing Drag Torque

Abstract The wet clutch, a crucial component of the vehicle transmission system, experiences high-frequency impact and friction between the friction plate and the steel plate under high-speed separation conditions. This leads to a significant increase in drag torque, which is detrimental to the transmission efficiency and reliability of the high-speed wet clutch. This article aims to reduce the high-speed drag torque in a no-load wet clutch by optimizing the oil groove shape on the surface of the friction plate. Initially, a theoretical model of high-speed drag torque for the friction plate with arbitrary oil groove shape is established. Subsequently, a low-drag oil groove shape optimization model is proposed by establishing design parameters, constraint conditions, and an objective function, combined with an experiment design method, approximation modeling, and a global search optimization method. Finally, the stiffness and damping coefficients of the clearance flow field and the drag torque with the optimized oil groove shape are calculated. The simulation results and the proposed optimization method are validated through experiments. The experiment indicates that a friction plate with the optimized oil groove shape can significantly decrease high-speed drag torque, demonstrating strong practical engineering value.

Study on the Consumption Mechanism and Lubrication of Mold Powder Based on Non-Sinusoidal Oscillation Mode

A two-dimensional mold model coupled multiphase flow, heat transfer, solidification and mold oscillation was established based on the casting parameters of the mold of plant. The accuracy of the model was verified by comparing the measured by plant and calculated mold powder consumption under the same casting conditions. The mechanism of mold powder consumption and lubrication was analyzed based on the non-sinusoidal oscillation mode, and the effect of non-sinusoidal oscillation parameters on mold powder consumption was discussed. Mold powder consumption was determined by the downward flow velocity of liquid mold powder and the thickness of liquid mold powder film, the liquid mold powder consumption decreased with the decrease of those. When the mold moved downward, the mold powder thickness and downward flow velocity decreased, the minimum mold powder consumption reached at the middle of the negative strip time, and the variation was to opposite when the mold moved upward, the maximum mold powder consumption appeared during the positive strip time. With the decrease of casting speed and modification ratio, and increase of oscillation frequency and oscillation amplitude, the mold powder consumption had the tendency to increase. The nonlinear regression equation was fitted by the Levenberg–Marquardt method combined with the universal global optimization method to evaluate mold powder consumption.

Wind energy harvesting with building-integrated ducted openings: CFD simulation and neural network optimization

Building-integrated wind energy harvesting offers a promising local and decentralized energy generation solution, reducing transmission losses and infrastructure expenses. However, the complex urban wind patterns demand accurate aerodynamic optimization for optimal performance. This study seeks to optimize the geometric design of building-integrated ducted openings to maximize wind energy harvesting. The research aims to create a data-driven model predicting the openings' performance accurately, explore the interlinked impacts of different geometrical variables, find optimal configurations across different building heights, and understand underlying aerodynamic mechanisms. The proposed design comprises a nozzle, throat, and diffuser. To increase power density, a data-driven design optimization method is employed. The optimization process involves determining the optimum opening height from the ground, along with five geometrical variables: inlet diameter, throat diameter, outlet diameter, nozzle length, and diffuser length. A comprehensive test matrix is developed using design of experiments (DoE) to build an artificial neural network (ANN) model. This neural network is developed using computational fluid dynamics (CFD) simulations validated with experimental data. Subsequently, a gradient-based global optimization method fine-tunes the neural network and identifies optimal designs for various heights. The research concludes that nozzle and diffuser opening angles within the range of 19° ≤ ΦNoz ≤ 23°and 7.5° ≤ ΦDif ≤ 8.2°, respectively, result in the optimal converging-diverging ducted opening geometry. This optimal opening can yield a power density increase of 31.5 to 35.5 times when compared to freestream flow and 17.5 to 22.4 times in comparison to cylindrical openings, depending on the opening location along the building height.

Stable and efficient seismic impedance inversion using quantum annealing with L1 norm regularization

Abstract Seismic impedance inversion makes a significant contribution to locating hydrocarbons and interpreting seismic data. However, it suffers from non-unique solutions, and a direct linear inversion produces large errors. Global optimization methods, such as simulated annealing, have been applied in seismic impedance inversion and achieved promising inversion results. Over the last decades, there has been an increasing interest in quantum computing. Owing to its natural parallelism, quantum computing has a powerful computational capability and certain advantages in solving complex inverse problems. In this article, we present a stable and efficient impedance inversion using quantum annealing with L1 norm regularization, which significantly improves the inversion accuracy compared to the traditional simulated annealing method. Tests on a one-dimensional 10-layer model with noisy data demonstrate that the new method exhibits significantly improved accuracy and stability. Additionally, we perform seismic impedance inversion for synthetic data from the overthrust model and field data using two methods. These results demonstrate that the quantum annealing impedance inversion with L1 norm regularization dramatically enhances the accuracy and anti-noise ability.

A Survey On Non – linear Optimization And Global Optimization Methods

Non-linear optimization and global optimization methods are crucial in solving complex real-world problems where the objective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

A Survey On Non – linear Optimization And Global Optimization Methods

bjective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

Method for determining estimates of random variable models for describing phase equilibrium in rectification processes

The phase equilibrium modeling for multi-component systems is essential in process systems engineering. In particular, phase stability analysis, Gibbs free energy minimization and estimation of parameters in thermodynamic models are challenging global optimization problems involved in phase equilibrium calculations and modeling for both reactive and non-reactive systems. To date, many significant works have been performed in the area of global optimization, and several algorithms and computational contributions of global optimization have been used for solving these problems; global optimization methods used include both deterministic and stochastic algorithms. To the best of our knowledge, there is no review in the literature that focuses on the global optimization methods and their applications to phase equilibrium modeling and calculations. In this paper, we briefly describe the deterministic and stochastic optimization algorithms selected for our rectification process, and then consider their use for phase stability analysis, Gibbs free energy minimization, and parameter estimation in phase equilibrium models. In short, we present an overview of global optimization for modeling and computing the phase behavior of systems with and without chemical reactions, including the prediction of azeotropes and critical points.

Radio sources location determination by the difference-range measuring method based on swarm intelligence

The solution of the location determining problem by the difference-range measuring method in most cases boils down to finding the extremums of functions using various modifications of the gradient optimization method, which has a number of disadvantages, including the need to specify the first approximation of the coordinates of the source, the dependence of the solution of the system of equations on this approximation, as well as the potential possibility of finding a local extremum, instead of a global one. Because of this, there is a need to use global optimization methods that do not have these disadvantages. One of such methods is a heuristic method based on the intelligence of a swarm of particles. The article presents the results of research on the possibility of using swarm intelligence to solve the problem of determining the location of radio sources by the difference-rangefinder method. An analytical description of the method of global optimization of functions based on the intelligence of a "swarm" of particles is presented. The objective function of coordinates of radio emission sources is formed in relation to the difference-rangefinder method of location determination using the Mahalanobis metric. The results of solving the problem of determining the coordinates of radio emission sources based on the search for the minimum of the formed objective function by the "swarm" of particles are presented. The obtained results can be used in the development of mathematical models and software and hardware complexes for determining the location of radio sources by the difference-rangefinder method.

Flow and heat transfer characteristics of high-pressure natural gas in the gaps of high-speed motors with a high radius ratio

A motor stator-gap-rotor model is established based on the numerical heat transfer theory by using the finite volume method. The flow evolution of high-pressure natural gas in the gap with a radius ratio of 0.971 is investigated. The results demonstrate that the flow patterns of high-pressure natural gas in the motor gap can be categorized into turbulent, spiral Taylor-Couette, and turbulent Taylor-Couette flow; the flow ranges are determined based on the Ta/Re2. Then, the flow and heat transfer characteristics of the cooling medium in the gap under different flow regimes as well as the mechanism of locally enhanced heat transfer in the gap by the Taylor-Couette flow are explored. Finally, the mathematical expressions for the Nusselt number of motor gap are determined in terms of the Reynolds number, Taylor number, and Prandtl number by fitting using the Levenberg-Marquardt and global optimization methods. Using these expressions, the flow and heat transfer characteristics in the motor gap can be predicted. Overall, this study provides useful and novel insights on the design of cooling systems for high-speed motors.

Structurally Constrained Fuzzy Selective LQ WADC Based on the Spectral Decomposition of Gramians

We propose a number of improvements for a previously presented method of selective wide-area damping control (WADC) using spectral decomposition of Lyapunov equation solutions. Namely, accounting for structural constraints, fuzzy selectivity, and compatibility with global optimization methods. We demonstrate that the improved method is capable of providing useful WADC strategies when the availability of measurement data is severely limited.

Energy-oriented optimization of the task allocation for mobile robots

Production systems need to be flexible in order to handle increasingly complex operational requirements. In many cases, mobile robots are used to flexibly connect production facilities. In this case, task allocation is a challenging procedure and should be optimized to ensure that processing deadlines are met and processing times are minimized. For this purpose, it is essential to be able to accurately predict the energy and time requirement of each action that the mobile robots could execute. This paper investigates how detailed modelling of mobile robots can reduce energy requirements and optimize planning of the logistics. Two concepts for task allocation are examined and one is presented in detail due to its applicability: global optimization by use of an open source software library and local optimization by use of an auction procedure. The global optimization method is suitable for small problems of low complexity, while the auction procedure can handle scenarios that are more complex. In this case, a central entity selects the mobile robot with the lowest bid to complete the task based on a developed prediction model for time and energy requirements.

Optical color routing enabled by deep learning.

Nano-color routing has emerged as an immensely popular and widely discussed subject in the realms of light field manipulation, image sensing, and the integration of deep learning. The conventional dye filters employed in commercial applications have long been hampered by several limitations, including subpar signal-to-noise ratio, restricted upper bounds on optical efficiency, and challenges associated with miniaturization. Nonetheless, the advent of bandpass-free color routing has opened up unprecedented avenues for achieving remarkable optical spectral efficiency and operation at sub-wavelength scales within the area of image sensing applications. This has brought about a paradigm shift, fundamentally transforming the field by offering a promising solution to surmount the constraints encountered with traditional dye filters. This review presents a comprehensive exploration of representative deep learning-driven nano-color routing structure designs, encompassing forward simulation algorithms, photonic neural networks, and various global and local topology optimization methods. A thorough comparison is drawn between the exceptional light-splitting capabilities exhibited by these methods and those of traditional design approaches. Additionally, the existing research on color routing is summarized, highlighting a promising direction for forthcoming development, delivering valuable insights to advance the field of color routing and serving as a powerful reference for future endeavors.

Software Testing Using Cuckoo Search Algorithm with Machine Learning Techniques

Software testing are any errors, flaws, bugs, mistakes, failures in a piece of software that might cause the programme to produce incorrect or unexpected results. Testing in software almost always increase both the time and money needed to finish a project. And finding bugs and fixing them is a laborious and expensive software process in and of itself. While it's unrealistic to expect to completely eradicate all testing from a project, their severity may be mitigated. It is possible to predict where bugs may appear in software using a method known as software defect prediction (SDP). The goal of each software development project should be to provide a bug-free product. Predicting where bugs may appear in code, often known as software defect prediction (SDP), is an important part of fixing software. Software of a high calibre should have few bugs. A software metric is a quantitative or qualitative evaluation of some aspect of the programme or its requirements. One of the more recent population-based algorithms, Cuckoo Search (CS) was inspired by the flight patterns of some cuckoo species as well as the Lévy flying patterns of other birds and fruit flies. The needs for international convergence are met by CS. KNN is a significant non-parameter supervised learning technique. This paper presents an overview of Stochastic Diffusion Search (SDS) in the form of a social metaphor to illustrate the processes by which SDS allots resources. The best-fit pattern identification and matching difficulties were addressed by SDS using a novel probabilistic method. As a multiagent population-based global search and optimization method, SDS is a distributed model of computing that makes use of interaction amongst basic agents. The behaviour of SDS is described by studying its resource allocation, convergence to global optimum, resilience, minimum convergence criterion, and linear time complexity within a rigorous mathematical framework, setting it apart from many nature-inspired search algorithms. This paper proposes a hybrid optimization strategy based on CS-SDS techniques. By using the global search strategy solution of the SDS algorithm, this hybridization idea aims to enhance the cuckoo bird's search strategy for the optimum host nest. To that end, the SDS method would be used to place the cuckoo egg in the most advantageous location. When compared to other classifiers, PC2's improved performance may be attributed to its higher recall values. When compared to the Naive Bayes and Radial Bias Neural Network classifiers, the KNN performs 7.64% and 2.20% better, respectively.

Lipschitz global optimization and machine learning: helping each other to solve complex problems

In this paper we consider global optimization problems and methods for solving them. The numerical solution of this class of problems is computationally challenging. The most complex problems are multicriteria problems in which the objective functions are multiextremal and non-differentiable, and, moreover, given in the form of a “black box”, i.e. calculating the objective function at a point is a time-consuming operation. Particularly, we consider an approach to acceleration of the global search using machine learning methods. At the same time, the problem of tuning the hyperparameters of the machine learning methods themselves is very important. The quality of machine learning methods is substantially affected by their hyperparameters, while the evaluation of the quality metrics is a time-consuming operation. We also consider an approach to hyperparameter tuning based on the Lipschitz global optimization. These approaches are implemented in the iOpt open-source framework of intelligent optimization methods.