Global Optimization Algorithm Research Articles

A dynamic aggregation strategy enhanced efficient global optimization algorithm for solving high-dimensional turbomachinery design problems

ABSTRACT To address challenges effectively in turbomachinery design optimization involving high-dimensional ( d ≥ 30 ) expensive black-box problems, a dedicated Efficient Global Optimization (EGO) algorithm is proposed with dynamic aggregation. This specialized approach efficiently navigates optimization tasks with limited sample evaluations. Specifically, the Dynamic Aggregate Efficient Global Optimization (DA-EGO) algorithm decomposes the original high-dimensional design space into low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite-point for the global search. Most importantly, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. After being validated on 21 benchmark functions ranging from 30 to 90 dimensions, the DA-EGO is used for the optimization of a transonic compressor rotor with 28 variables and a multi-stage compressor optimization with 60 variables. With the above, the effectiveness of the proposed algorithm is well demonstrated.

Global Opposition Learning and Diversity ENhancement based Differential Evolution with exponential crossover for numerical optimization

Since the inception of Differential Evolution (DE), the vast majority of studies on it indicate that exponential crossover does not solve the real-parameter optimization in continuous spaces very well. However, we find that once the appropriate crossover rate CR and its corresponding parameter control are found, the DE variants with exponential crossover can achieve comparable performance with the ones employing binomial crossover. In this paper, a new DE algorithm, called Global Opposition Learning and Diversity ENhancement based DE with exponential crossover (GOLDEN-DE), is proposed to fill the gap in this field. The GOLDEN-DE algorithm has the following highlights: First, a novel global opposition learning mechanism is proposed in our GOLDEN-DE algorithm; Second, a Novel Parameter Control, namely NPC technique, with fitness-independent characteristic is incorporated in the GOLDEN-DE algorithm. Third, a novel population Diversity ENhancement (DEN) mechanism is proposed, and individuals in the stagnation status can be re-calculated in order to enhance population diversity. Fourth, a time stamp mechanism for handling too old inferior solutions in the external archive is also put forward. We evaluate the GOLDEN-DE algorithm for real-parameter single-objective global optimization on 88 benchmarks from the three universal test sets, including CEC2013, CEC2014, and CEC2017 test suites, and experiment results show that our GOLDEN-DE algorithm is competitive with several state-of-the-art DE variants.

An improved cuckoo search algorithm for global optimization

An improved cuckoo search algorithm for global optimization

A Novel Hybrid Binary Bat Algorithm for Global Optimization

In this article, a novel hybrid binary bat algorithm named HBBA is proposed for global optimization problems. First, to avoid simultaneous updating of bat velocity's dimensional components, i.e., elements of velocity vector, a random black hole model is modified to adapt to binary algorithm for updating in unknown spaces for each dimensional component individually. Through this way, the search ability of bats around the current group best is increased greatly. Second, a time-varying v-shaped transfer function, rather than a time-invariant one as in closely related works, is proposed to map velocity in continuous search space to a binary one. This accelerates the speed to switch individuals' positions, i.e., solutions in binary space. Third, a chaotic map is utilized to replace monotonous parameters in original binary bat algorithm, which is beneficial for avoiding premature convergence. Simulation results demonstrate the effectiveness of the proposed algorithm by three types of benchmark functions and unit commitment problem.

A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

Hybrid algorithm for global optimization based on periodic selection scheme in engineering computation

PurposeMetaheuristic algorithms based on biology, evolutionary theory and physical principles, have been widely developed for complex global optimization. This paper aims to present a new hybrid optimization algorithm that combines the characteristics of biogeography-based optimization (BBO), invasive weed optimization (IWO) and genetic algorithms (GAs).Design/methodology/approachThe significant difference between the new algorithm and original optimizers is a periodic selection scheme for offspring. The selection criterion is a function of cyclic discharge and the fitness of populations. It differs from traditional optimization methods where the elite always gains advantages. With this method, fitter populations may still be rejected, while poorer ones might be likely retained. The selection scheme is applied to help escape from local optima and maintain solution diversity.FindingsThe efficiency of the proposed method is tested on 13 high-dimensional, nonlinear benchmark functions and a homogenous slope stability problem. The results of the benchmark function show that the new method performs well in terms of accuracy and solution diversity. The algorithm converges with a magnitude of 10-4, compared to 102 in BBO and 10-2 in IWO. In the slope stability problem, the safety factor acquired by the analogy of slope erosion (ASE) is closer to the recommended value.Originality/valueThis paper introduces a periodic selection strategy and constructs a hybrid optimizer, which enhances the global exploration capacity of metaheuristic algorithms.

Opposition-based manta ray foraging algorithm for global optimization and its application to optimize nonlinear type-2 fuzzy logic control

Interval Type-2 Fuzzy Logic Control (IT2FLC) possesses a high control ability in a way that it can optimally handle the presence of uncertainty in a system dynamic. However, the design of such a control scheme is a challenging task due to its complex structure and nonlinear behavior. A Manta Ray Foraging Optimization (MRFO) is a promising algorithm that can be applied to optimize the control design. However, MRFO still suffers the local optima problem due to unbalance exploration-exploitation of the MRFO agents and hence limiting the performance of the desired control. In this paper, Standard, Quasi, Super, and Quasi-Reflected opposition strategies are integrated into the MRFO structure. Each strategy enhances the exploration-exploitation capability and offers different approaches of varying agent’s step size relative to the algorithm’s iteration. The proposed opposition-based MRFO (OMRFO) algorithms are applied to optimize the IT2FLC control design for a laboratory-scaled inverted pendulum system. Moreover, as the algorithms are also promising strategies to other problems, they are applied to solve 50D of 30 IEEE CEC14 benchmark functions representing problems with different features. Performance analysis of the algorithms is statistically conducted using Wilcoxon sign rank and Friedman tests. The result shows that the performance of MRFO and Quasi-Reflected-OMRFO are equal, while all other OMRFO variants show a significant improvement and better rank over the MRFO. The Super and Quasi OMRFO-IT2FLC schemes acquired the best responses for the cart and pendulum, respectively.

An impedance matching section based on composite right/left‐handed transmission line model in viewpoint of phase shift and noise figure

AbstractIn this paper, a genetic‐based synthesis approach for an impedance matching section based on a composite right‐/left‐handed (CRLH) transmission line model called CRLH transmission line impedance matching section (CRLHTLIMS) in viewpoint of transmission phase shift and noise figure is newly presented. To find the unknown values of right‐/left‐handed inductances and capacitances of a CRLHTLIMS, a type of global optimization algorithm called continuous parameter genetic algorithm is used. The length, transmission phase shift, and noise figure of the CRLHTLIMS are computed by using simple equations. Different examples for a uniform CRLHTLIMS are given. According to the results, this approach is an easy and effective way for the synthesis of transmission line impedance matching sections in viewpoint of transmission phase shift and noise figure.

HPB3C-3PG algorithm: A new hybrid global optimization algorithm and its application to plant classification

This paper proposes a hybrid bio-inspired search and optimization algorithm that combines the strengths of the PB3C (Parallel Big Bang Big Crunch) and 3PGA (3 Parent Genetic Algorithm) algorithms. The hybrid algorithm employs a single population-based evolutionary search coupled with multi-population parallel processing techniques to address optimization problems. The proposed algorithm is implemented in MATLAB software. We evaluate the performance of the proposed algorithm on the CEC2021 standard test bench suite. The performance of the proposed approach is compared with that of the other nine algorithms. The comparative analysis shows that the proposed hybrid PB3C and 3PGA algorithms performed better than the other nine optimization algorithms. Furthermore, this chapter proposes an HPB3C-3PGA-based approach to evolve the near-optimal architecture of CNN. The proposed plant image classification approach is implemented in Python and compared with 12 other approaches. The proposed approach achieved an accuracy of 98.96% on the Mendeley dataset and 98.97% on the CVIP100 dataset. The proposed approach outperforms all other approaches for the plant leaf classification problem. This research significantly contributes to overcoming limitations in existing approaches, providing a robust solution for optimization problems and image classification tasks.

Determining blood platelet morphology modelled by a superellipsoid from the solution of the inverse light-scattering problem

In this work, we propose a new optical model to describe the morphology of a platelet in the form of a special axisymmetric superellipsoid. This model is more general than the widely used classical oblate spheroid model of the platelet and includes the oblate spheroid as a special case. The inverse light scattering (ILS) problem within the developed optical model was solved using the light scattering profile (LSP) of individual platelets obtained by the scanning flow cytometer. Solving the ILS problem we used a hybrid method that combines the DIRECT algorithm of global optimization with the linear interpolation between the nodes of the pre-calculated regular database of superellipsoid LSPs. The statistical F-test shows that the new optical model is better than the conventional oblate spheroid model in more than 60 percent of cases. This made it possible to obtain the refined shape index distributions for platelets consisting of three fractions, namely resting, partially and fully activated platelets.

Метод эффективных вычитаний: работа с данными Иркутского радара некогерентного рассеяния

For incoherent scatter measurements, the effective subtraction technique is to alternate the duration of amplitude-modulated signals between a pair of consequently radiated pulses. The resulting gain of spatial resolution enables us to steadily assess the electron density profile by the Faraday rotation method. The paper describes the electron density measurement technique, which involves analyzing narrow-band signals from Irkutsk Incoherent Scatter Radar, and proposes an automated method of determining the electron density for the problem in which the convolution of the radiated signal waveform with backscatter signal cannot be neglected. The inverse problem of electron density recovery is considered as a standard nonlinear optimization problem, which is solved using the algorithms for global and local optimization applied consequently. We compare the electron density profiles obtained by analyzing different pulse waveforms and from Irkutsk ionosonde data.

Effective subtraction technique: implementation for Irkutsk Incoherent Scatter Radar

For incoherent scatter measurements, the effective subtraction technique is to alternate the duration of amplitude-modulated signals between a pair of consequently radiated pulses. The resulting gain of spatial resolution enables us to steadily assess the electron density profile by the Faraday rotation method. The paper describes the electron density measurement technique, which involves analyzing narrow-band signals from Irkutsk Incoherent Scatter Radar, and proposes an automated method of determining the electron density for the problem in which the convolution of the radiated signal waveform with backscatter signal cannot be neglected. The inverse problem of electron density recovery is considered as a standard nonlinear optimization problem, which is solved using the algorithms for global and local optimization applied consequently. We compare the electron density profiles obtained by analyzing different pulse waveforms and from Irkutsk ionosonde data.

FRF-based model updating of liquid-filled pipeline system considering tolerance intervals of test errors in the antiresonant frequencies

The frequency response function (FRF)-based model updating technique is an effective method to calibrate system parameters of the dynamic simulation model of pipeline systems. However, the existing FRF-based model updating methods is difficult to solve the problem of the test errors in the antiresonant frequencies, which significantly affects the accuracy of the updated results. Hence, this paper proposes a new FRF-based model updating method of the liquid-filled pipeline considering the tolerance intervals of test errors in the antiresonant frequencies. In this method, the effect of test errors on FRFs is quantified by employing the interval method, and then the tolerance intervals of test errors in the antiresonant frequencies can be identified from the interval FRFs. The obtained tolerance intervals are integrated into the objective function of the FRF-based model updating through the penalty function method, and the optimal system parameters can be obtained by using a global optimization algorithm. Compared with the existing FRF-based model updating methods, the proposed method can not only effectively reduce the effect of test errors in the measured FRFs on the updated results but also alleviate the ill-condition of model updating calculations, so that the accuracy and convergence of model updating calculations are improved simultaneously. Numerical and experimental validations of the proposed method are carried out by using an L-shaped water-filled pipeline system. The performances of the proposed method are compared with the typical FRF-based model updating method. The results demonstrate that the proposed method can obtain the updated results with higher accuracy and reliability than the typical method.

An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems

This paper investigates a class of linear fractional programs (LFP) with linear constraints, which are widely applied in transportation, economic investment and so on. We start with transforming LFP into its equivalent two-layer problem. Subsequently, we introduce a novel linear relaxation approach and integrate it within the branch and bound framework, and a new global optimization algorithm is presented in cooperation with a region deleting rule. Additionally, we discuss the convergence and complexity of this algorithm. Preliminary numerical results validate the practicality and effectiveness of our proposed method.

An enhanced Coati Optimization Algorithm for global optimization and feature selection in EEG emotion recognition

Emotion recognition based on Electroencephalography (EEG) signals has garnered significant attention across diverse domains including healthcare, education, information sharing, and gaming, among others. Despite its potential, the absence of a standardized feature set poses a challenge in efficiently classifying various emotions. Addressing the issue of high dimensionality, this paper introduces an advanced variant of the Coati Optimization Algorithm (COA), called eCOA for global optimization and selecting the best subset of EEG features for emotion recognition. Specifically, COA suffers from local optima and imbalanced exploitation abilities as other metaheuristic methods. The proposed eCOA incorporates the COA and RUNge Kutta Optimizer (RUN) algorithms. The Scale Factor (SF) and Enhanced Solution Quality (ESQ) mechanism from RUN are applied to resolve the raised shortcomings of COA. The proposed eCOA algorithm has been extensively evaluated using the CEC’22 test suite and two EEG emotion recognition datasets, DEAP and DREAMER. Furthermore, the eCOA is applied for binary and multi-class classification of emotions in the dimensions of valence, arousal, and dominance using a multi-layer perceptron neural network (MLPNN). The experimental results revealed that the eCOA algorithm has more powerful search capabilities than the original COA and seven well-known counterpart methods related to statistical, convergence, and diversity measures. Furthermore, eCOA can efficiently support feature selection to find the best EEG features to maximize performance on four quadratic emotion classification problems compared to the methods of its counterparts. The suggested method obtains a classification accuracy of 85.17% and 95.21% in the binary classification of low and high arousal emotions in two public datasets: DEAP and DREAMER, respectively, which are 5.58% and 8.98% superior to existing approaches working on the same datasets for different subjects, respectively.

Accelerated formulation of optimal control law for adaptive cycle engines: A novel design methodology

Adaptive cycle engines (ACEs) represent a sophisticated class of power units, embodying numerous variable geometry components, marking them as pivotal for the advancement of next-generation high-speed civil and military engines. Nonetheless, this variability introduces substantial complexity into the engineering of control laws. Contemporary research predominantly relies on either manual methodologies or global optimization algorithms. The former rarely achieves peak performance, while the latter incurs substantial computational expenses. This research introduces an accelerated methodology by using variable-step gradient with boundary constraints (VGB) algorithm tailored for the nuanced optimization challenges posed by multi-variable, multi-constraint nonlinearities inherent in ACEs. Recognizing that ACE's peak performance is typically boundary-constrained, the algorithm strategically manipulates variable geometries to widen the operational gap from the most disadvantageous boundary (MDB), thereby inching closer to the engine's ideal operational nexus. This strategy culminates in a decease in computational overhead, diverging significantly from conventional global optimization approaches. Empirical findings represent the method's efficacy, with a maximal performance deviation of just 3.78 % across three steady-state missions. Post transient control law refinement, engine's starting time contracted by 5.93 s via VGB algorithm, opposed to baseline design point configurations. Collectively, this approach serves as a versatile and efficient blueprint for designing control laws.

Development of Novel Hybrid Multi-Verse Optimizer with Sine Cosine Algorithm for Better Global Optimization

The sine cosine algorithm (SCA) and multi-verse optimizer (MVO) are the recognized optimization strategies frequently employed in numerous scientific areas. However, both SCA and MVO grapple with optimizing the transition between the exploitation and exploration mechanisms. Furthermore, MVO exhibits constraints in its exploitation capabilities. To tackle these limitations, this paper introduces a hybrid model termed SMVO, combining the advantages of both SCA and MVO. This hybrid approach seeks to harmonize exploitation and exploration stages by leveraging the unique advantages of each parent algorithm. The efficacy of SMVO was assessed using 23 benchmark test functions, revealing its competitive performance against not only SCA and MVO but also the ant lion optimization (ALO) and the dragonfly algorithm (DA). Additionally, SMVO’s applicability was further validated by successfully addressing three distinct engineering optimization challenges, underscoring its stability and promise as a global optimization tool.

Correction to: Love evolution algorithm: a stimulus–value–role theory-inspired evolutionary algorithm for global optimization

Correction to: Love evolution algorithm: a stimulus–value–role theory-inspired evolutionary algorithm for global optimization

L1-norm optimisation of rank deficient GNSS networks by an improved Grey Wolf method

An improved grey wolf optimization (GWO) is proposed for direct L1-norm optimization in rank deficient GNSS networks to detect outliers since the standard GWO and the global optimization (GO) algorithms cannot deal with such problems. In contrast to the traditional method for L1-norm minimization which is solved by a cumbersome search of linear programming (LP) problem, in this algorithm, one only requires to input the target function. Furthermore, it has a greater ability to detect gross errors of observables with low reliability compared to traditional methods such as LP. Moreover, it does not consider the correct observables as blunders in contrast to some algorithms such as the iteratively reweighted least-squares (IRLS) method, which may consider them as outliers. The numerical results of real and simulated GNSS networks approve the efficiency of the new algorithm.

Improving multilayer perceptron neural network using two enhanced moth-flame optimizers to forecast iron ore prices

Abstract The quality of the output produced by the multi-layer perceptron neural network depends on the careful selection of its weights and biases. The gradient descent technique is commonly used for choosing MLP’s optimal configuration, but it can suffer from being stuck in local optima and slow convergence toward promising regions in the search space. In this article, we propose two new optimization algorithms based on the moth-flame optimization algorithm (MFO), which mimics moths’ special navigation methods at night. We use these algorithms to enhance the performance of the training process of the MLP neural network. To demonstrate the effectiveness of our approach, we apply it to the problem of predicting iron ore prices, which plays an important role in the continuous development of the steel industry. We use a large number of features to predict the iron ore price, and we select a promising set of features using two feature reduction methods: Pearson’s correlation and a newly proposed categorized correlation. Surprisingly, new features not mentioned in the literature are discovered, and some are discarded. The time series dataset used has been extracted from several sources and pre-processed to fit the proposed model. We compare our two proposed MFO algorithms, the roulette wheel moth-flame optimization algorithm and the global best moth-flame optimization algorithm, against four swarm intelligence algorithms and five classical machine learning techniques when predicting the iron ore price. The results acquired indicate the superior performance of the suggested algorithms concerning prediction accuracy, root-mean-square error, mean-square error, average absolute relative deviation, and mean absolute error. Overall, our work presents a promising approach for improving the performance of MLP neural networks, and it demonstrates its effectiveness in the challenging problem of predicting iron ore prices.