Global Optimization Algorithm Research Articles

Improved artificial rabbits algorithm for global optimization and multi-level thresholding color image segmentation

The Artificial Rabbits Optimization Algorithm is a metaheuristic optimization algorithm proposed in 2022. This algorithm has weak local search ability, which can easily lead to the algorithm falling into local optimal solutions. To overcome these limitations, this paper introduces an Improved Artificial Rabbits Optimization Algorithm (IARO) and demonstrates its effectiveness in multi-level threshold color image segmentation using the Otsu method. Initially, we apply a center-driven strategy to enhance exploration by updating the rabbit’s position during the random hiding phase. Additionally, when the algorithm stalls, a Gaussian Randomized Wandering (GRW) strategy is utilized to enable the algorithm to escape local optima and improve convergence accuracy. The performance of the IARO algorithm is evaluated using 23 standard benchmark functions and CEC2020 benchmark functions, and compared with nine other algorithms. Experimental results indicate that IARO excels in global optimization and demonstrates notable robustness. To assess its effectiveness in multi-threshold color image segmentation, the algorithm is tested on classical Berkeley images. Evaluation metrics including execution time, Peak Signal-to-Noise Ratio (PSNR), Feature Similarity (FSIM), Structural Similarity (SSIM), Boundary Displacement Error (BDE), The Probabilistic Rand Index (PRI), Variation of Information (VOI) and average fitness value are used to measure segmentation quality. The results reveal that IARO achieves high accuracy and fast segmentation speed, validating its efficiency and practical utility in real-world applications.

A Novel Slime Mould Multiverse Algorithm for Global Optimization and Mechanical Engineering Design Problems

The slime mould optimization algorithm (SMA) is one of the well-established optimization algorithms with a superior performance in a variety of real-life optimization problems. The SMA has certain limitations that reduce the diversity and accuracy of solutions, raising the risk of premature convergence with an inadequate balance between its exploitation and exploration phases. In this study, a novel hybrid slime mould multi-verse algorithm (SMMVA) is proposed to improve the performance of SMA algorithm. The SMA and multi-verse optimization (MVO) algorithm hybrid is introduced while updating variation parameter through novel nonlinear convergence factor. The proposed algorithm balances the ability of the SMA algorithm to explore and exploit, boosts the global exploration capability and improves the accuracy, stability, and convergence speed. The performance of SMMVA algorithm is compared with 16 well-established and recently-published metaheuristic algorithms on 23 standard benchmark functions, CEC2017, CEC2022 test functions, five engineering design problems, and five UCI repository datasets. The statistical tests such as Friedman’s test, box plot comparison and Wilcoxon rank sum test are employed to verify the SMMVA’s stability and statistical superiority. The algorithm was tested on total 64 benchmark functions, achieving an overall success rate of 68.75% across 30 runs compared to the other counterparts. The results for the feature selection problem show that the proposed algorithm with k-nearest neighbour (KNN) classifier obtained more informative features with higher accuracy values. Thus, the proposed SMMVA algorithm is proven to perform excellent performance in solving optimization problems with better solution accuracy and promising prospect.

CSearch: chemical space search via virtual synthesis and global optimization

The two key components of computational molecular design are virtually generating molecules and predicting the properties of these generated molecules. This study focuses on an effective method for molecular generation through virtual synthesis and global optimization of a given objective function. Using a pre-trained graph neural network (GNN) objective function to approximate the docking energies of compounds for four target receptors, we generated highly optimized compounds with 300–400 times less computational effort compared to virtual compound library screening. These optimized compounds exhibit similar synthesizability and diversity to known binders with high potency and are notably novel compared to library chemicals or known ligands. This method, called CSearch, can be effectively utilized to generate chemicals optimized for a given objective function. With the GNN function approximating docking energies, CSearch generated molecules with predicted binding poses to the target receptors similar to known inhibitors, demonstrating its effectiveness in producing drug-like binders.Scientific Contribution We have developed a method for effectively exploring the chemical space of drug-like molecules using a global optimization algorithm with fragment-based virtual synthesis. The compounds generated using this method optimize the given objective function efficiently and are synthesizable like commercial library compounds. Furthermore, they are diverse, novel drug-like molecules with properties similar to known inhibitors for target receptors.

A multi-strategy enhanced reptile search algorithm for global optimization and engineering optimization design problems

The reptile search algorithm (RSA) is a well-known swarm-based metaheuristic algorithm inspired by the hunting behaviors of crocodiles. To overcome the problems of falling into local optima and premature convergence, this paper proposes a multi-strategy enhanced reptile search algorithm (MRSA), which integrates a novel dynamic evolutionary sense, prey approaching strategy and Cauchy mutation strategy. The prey approaching strategy comes from the secretary bird optimization algorithm and is applied to strengthen the exploration capability of RSA. A comparative performance analysis is conducted using the CEC2005, CEC2017 and CEC2022 benchmark functions. And fifteen algorithms are employed for the performance comparison. The results of numerical, convergence curves, boxplots, Wilcoxon rank-sum test and Friedman ranking confirm the efficacy and stability of proposed MRSA, indicating its superior performance compared to other algorithms. Moreover, seven practical engineering design tasks are used to test the performance of MRSA in real-world optimization problems. The results also show that MRSA can efficiently obtain better optimal solution compared to existing methods.

A merging approach for hole identification with the NMM and WOA-BP cooperative neural network in heat conduction problem

Defect identification is an important issue in structural health monitoring. Herein, originated from inverse techniques, a merging approach is established by the numerical manifold method (NMM) and whale optimization algorithm-back propagation (WOA-BP) cooperative neural network to identify hole defects in heat conduction problems. On the one hand, the NMM can simulate varying hole configurations on a fixed mathematical cover, which eases the generation of “big data” for the training of neural network to a large extent. On the other hand, the WOA, a global optimization algorithm, is adopted to optimize the initial weights and thresholds of the BP neural network to alleviate its frequently encountered local optimum phenomenon. The boundary temperatures of sampling points by the NMM and the associated hole geometries are used for the learning of WOA-BP neural network, which is then applied to predict the hole defects. Numerical examples concerning the detection of circular/ elliptical holes demonstrate that the proposed method possesses higher accuracy and satisfying robustness in holes prediction compared with standard BP network under the same condition. The present work provides a convenient pathway and great potential in application of structural health monitoring.

A Single-Stage SOC Reference Trajectory Prediction Method for Series PHEV Based on GRNN

In this paper, a single-stage SOC reference trajectory (SOC-RT) prediction method is proposed. Different from the two-stage prediction method mostly used in previous studies, the proposed strategy predicts the SOC-RT slope directly based on the operating condition, instead of predicting the vehicle speed first and then solving it based on a global optimization algorithm. Therefore, the proposed method can significantly reduce the computational load and has high application value. A generalized regression neural network (GRNN) is employed as the prediction model for its strong nonlinear fitting ability. Meanwhile, to solve the problem of error accumulation due to the slope prediction, the prediction trajectory is corrected by the linear trajectory, and the correction factor is determined based on particle swarm optimization algorithm (PSO). Finally, the trajectory is followed by equivalent consumption minimization strategy (ECMS) and the performance of the proposed strategy is verified. The results show that the prediction accuracy is improved by 52.10% and 3.73% compared to the linear trajectory under the two tested cycles, respectively. Meanwhile, the proposed strategy achieves the best fuel economy, with fuel consumption decreasing by 2.61% and 6.40%, respectively, compared to the rule-based control strategy. Finally, its real-time control performance in a real hardware environment is verified through the hardware-in-the-loop test.

Rabbit algorithm for global optimization

In this paper, a novel bio-inspired meta-heuristic algorithm, namely Rabbit Optimizer, is proposed. It draws inspiration from how rabbits survive in nature through foraging tactics, random hiding and rapid growth. The foraging strategy involves rabbits avoiding grazing near their dens, thus preventing their dens from being discovered. Random hiding refers to cunning rabbits maintaining three dens to reduce the chance of being eliminated. Additionally, rapid growth and strong reproductive abilities enable rabbits to thrive as the fittest species. Rabbit Optimizer employs three subgroups of male, female and child rabbits to conduct an efficient collaborative search under an elite learning strategy, achieving a good balance of exploration and exploitation. Key parameters like distance factor, balance factor and learning factor strike a balance between depth search and width searches, making Rabbit Optimizer versatile and flexible. The performance of Rabbit Optimizer was evaluated by handling the CEC2022 and various dimensions of the CEC05 test suites up to 5000. Using Friedman analysis, Rabbit Optimizer ranked first and was proven to be significantly superior to 13 well-known metaheuristic algorithms. Finally, it addressed ten problems from the CEC2020 to demonstrate its ability to solve real-world engineering optimization problems. Experimental results show that Rabbit Optimizer is effective and efficient for solving complex large-scale optimization problems.

Nature-Inspired Approach: A Novel Rat Optimization Algorithm for Global Optimization

This work presents a rat optimization algorithm (ROA), which simulates the social behavior of rats and is a new nature-inspired optimization technique. The ROA consists of three operators that simulate rats searching for prey, chasing and fighting prey, and jumping and hunting prey to deal with optimization issues. The Levy flight strategy is introduced into the ROA to keep the algorithm from running into issues with slow convergence and local optimums. The ROA is tested with four real-world engineering optimization issues and twenty-two benchmark functions. Experiments show that the ROA is particularly effective at solving real-world optimization problems compared to other well-known optimization techniques.

Adaptive Partition Linearization Global Optimization Algorithm and Its Application on the Simultaneous Heat Exchanger Network and Organic Rankine Cycle Optimization

Adaptive Partition Linearization Global Optimization Algorithm and Its Application on the Simultaneous Heat Exchanger Network and Organic Rankine Cycle Optimization

Leveraging Machine Learning Potentials for In-Situ Searching of Active sites in Heterogeneous Catalysis.

This Perspective explores the integration of machine learning potentials (MLPs) in the research of heterogeneous catalysis, focusing on their role in identifying in situ active sites and enhancing the understanding of catalytic processes. MLPs utilize extensive databases from high-throughput density functional theory (DFT) calculations to train models that predict atomic configurations, energies, and forces with near-DFT accuracy. These capabilities allow MLPs to handle significantly larger systems and extend simulation times beyond the limitations of traditional ab initio methods. Coupled with global optimization algorithms, MLPs enable systematic investigations across vast structural spaces, making substantial contributions to the modeling of catalyst surface structures under reactive conditions. The review aims to provide a broad introduction to recent advancements and practical guidance on employing MLPs and also showcases several exemplary cases of MLP-driven discoveries related to surface structure changes under reactive conditions and the nature of active sites in heterogeneous catalysis. The prevailing challenges faced by this approach are also discussed.

Pairing a Global Optimization Algorithm with EXAFS to Characterize Lanthanide Structure in Solution.

Ensemble-average sampling of structures from ab initio molecular dynamics (AIMD) simulations can be used to predict theoretical extended X-ray absorption fine structure (EXAFS) signals that closely match experimental spectra. However, AIMD simulations are time-consuming and resource-intensive, particularly for solvated lanthanide ions, which often form multiple nonrigid geometries with high coordination numbers. To accelerate the characterization of lanthanide structures in solution, we employed the Northwest Potential Energy Surface Search Engine (NWPEsSe), an adaptive-learning global optimization algorithm, to efficiently screen first-shell structures. As case studies, we examine two systems: Eu(NO3)3 dissolved in acetonitrile with a terpyridine ligand (terpyNO2), and Nd(NO3)3 dissolved in acetonitrile. The theoretical spectra for structures identified by NWPEsSe were compared to both experimental and AIMD-derived EXAFS spectra. The NWPEsSe algorithm successfully identified the proper solvation structure for both Eu(NO3)3(terpyNO2) and Nd(NO3)(acetonitrile)3, with the calculated EXAFS signals closely matching the experimental spectra for the Eu-ligand complex and showing good similarity for the Nd salt; the better agreement with the ligand-containing structure is attributed to a less dynamic coordination environment due to the rigid ligand. The key advantage of the global optimization algorithm lies in its ability to sample the coordination environment across the potential energy surface and reduce the time required to identify structures from generally a month to within a week. Additionally, this approach is versatile and can be adapted to characterize main-group metal complexes.

Cooperative metaheuristic algorithm for global optimization and engineering problems inspired by heterosis theory

Swarm Intelligence-based metaheuristic algorithms are widely applied to global optimization and engineering design problems. However, these algorithms often suffer from two main drawbacks: susceptibility to the local optima in large search space and slow convergence rate. To address these issues, this paper develops a novel cooperative metaheuristic algorithm (CMA), which is inspired by heterosis theory. Firstly, simulating hybrid rice optimization algorithm (HRO) constucted based on heterosis theory, the population is sorted by fitness and divided into three subpopulations, corresponding to the maintainer, restorer, and sterile line in HRO, respectively, which engage in cooperative evolution. Subsequently, in each subpopulation, a novel three-phase local optima avoidance technique-Search-Escape-Synchronize (SES) is introduced. In the search phase, the well-established Particle Swarm Optimization algorithm (PSO) is used for global exploration. During the escape phase, escape energy is dynamically calculated for each agent. If it exceeds a threshold, a large-scale Lévy flight jump is performed; otherwise, PSO continues to conduct the local search. In the synchronize phase, the best solutions from subpopulations are shared through an elite-based strategy, while the classical Ant Colony Optimization algorithm is employed to perform fine-tuned local optimization near the shared optimal solutions. This process accelerates convergence, maintains population diversity, and ensures a balanced transition between global exploration and local exploitation. To validate the effectiveness of CMA, this study evaluates the algorithm using 26 well-known benchmark functions and 5 real-world engineering problems. Experimental results demonstrate that CMA outperforms the 10 state-of-the-art algorithms evaluated in the study, which is a very promising for engineering optimization problem solving.

Fractional-order equivalent circuit model for commercial sodium-ion batteries in a wide temperature range considering aging

With the development of electric vehicles and microgrids, the demand for energy storage is growing rapidly. Sodium-ion batteries, due to their abundant reserves, high energy density, and good safety, are beginning to be used in electric vehicles and energy storage power stations. High-precision modeling is the basis for state estimation and energy management of sodium-ion batteries. Fractional-order equivalent circuit model is favored for its balance between computational complexity and accuracy. In this study, electrochemical impedance spectroscopy tests were conducted on sodium-ion batteries, and a fractional-order equivalent circuit model in a wide temperature range considering aging, was established. The model parameters can be identified online using the global optimization algorithm based on dynamic cycling condition. The model’s accuracy was verified under different temperatures and dynamic working conditions. The results show that, compared to the Thevenin model and second-order equivalent circuit model, the fractional-order equivalent circuit model can better fit the terminal voltage of sodium-ion batteries, with a mean relative error of less than 4%.

Subsurface S-wave velocity structure inversion using particle swarm optimization based on horizontal site response extracted using generalized inversion technique

A new methodology, including a mature algorithm with adjustments and a new target for the subsurface sedimentary inversion problem was introduced. This study adopted the particle swarm optimization (PSO) algorithm as a global optimization algorithm. PSO incorporates the patterns embedded in natural bird foraging behaviors to invert the subsurface S-wave velocity structure. Using the concept of particle velocity, PSO involves particle individual inertia, individual experience, and social experience of the swarm, pursuing the global optimum solution in a multidimensional abstract space. The inversion target was the horizontal site amplification factor (HSAF), which was extracted using the generalized inversion technique for the observed strong ground motions. HSAF is an appropriate target in the S-wave velocity structure inversion problem as it directly represents the site response to the incident S-wave at the seismological bedrock. We validated the convergence ability of the PSO and applied it to three field earthquake observation stations. From the perspective of the misfit between the target and estimation velocity profile, improvements exceeding 95 % and 70 % can be confirmed in the validation case and practical applications, respectively. The use of HSAF as the target and PSO as the algorithm is currently limited but is demonstrably effective. This study introduces a methodology that has significant potential for solving velocity structure inversion problems at subsurface levels.

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.

A Novel Adaptive Sand Cat Swarm Optimization Algorithm for Feature Selection and Global Optimization.

Feature selection (FS) constitutes a critical stage within the realms of machine learning and data mining, with the objective of eliminating irrelevant features while guaranteeing model accuracy. Nevertheless, in datasets featuring a multitude of features, choosing the optimal feature poses a significant challenge. This study presents an enhanced Sand Cat Swarm Optimization algorithm (MSCSO) to improve the feature selection process, augmenting the algorithm's global search capacity and convergence rate via multiple innovative strategies. Specifically, this study devised logistic chaotic mapping and lens imaging reverse learning approaches for population initialization to enhance population diversity; balanced global exploration and local development capabilities through nonlinear parameter processing; and introduced a Weibull flight strategy and triangular parade strategy to optimize individual position updates. Additionally, the Gaussian-Cauchy mutation strategy was employed to improve the algorithm's ability to overcome local optima. The experimental results demonstrate that MSCSO performs well on 65.2% of the test functions in the CEC2005 benchmark test; on the 15 datasets of UCI, MSCSO achieved the best average fitness in 93.3% of the datasets and achieved the fewest feature selections in 86.7% of the datasets while attaining the best average accuracy across 100% of the datasets, significantly outperforming other comparative algorithms.

A multi-strategy boosted bald eagle search algorithm for global optimization and constrained engineering problems: case study on MLP classification problems

The Bald Eagle Search (BES) algorithm is an innovative population-based method inspired by the intelligent hunting behavior of bald eagles. While BES shows promise, it faces challenges such as susceptibility to local optima and imbalances between exploration and exploitation phases. To address these limitations, this paper introduces the Multi-Strategy Boosted Bald Eagle Search (MBBES) algorithm. MBBES enhances the original BES by incorporating an adaptive parameter, two distinct mutation strategies, and replacing the swoop stage with a fall stage. We rigorously evaluate MBBES against classic and improved algorithms using the CEC2014 and CEC2017 test sets. The experimental results demonstrate that MBBES significantly improves the ability to escape local optima and achieves superior convergence accuracy. Moreover, MBBES ranks first according to the Friedman test, outperforming its counterparts in solving five practical engineering problems and three MLP classification problems, underscoring its effectiveness in real-world optimization scenarios. These findings indicate that MBBES not only surpasses BES but also sets a new benchmark in optimization performance.

Fault detection of RV reducer cycloidal gear under robot working conditions based on optimization improved envelope spectrum sideband energy ratio

Abstract Under industrial robot operating conditions, the cycloidal gear in the rotary vector(RV) reducer in the robot joint runs in a compound rotation motion with a low-speed and incomplete cycle, which complicates the fault detection for the cycloidal gear. Until now, no effective detection method for the cycloidal gear tooth fault under industrial robot operating conditions has been reported. Consequently, a method based on optimization improved envelope spectrum sideband energy ratio is proposed in this paper. Firstly, encoder signals are acquired and used to estimate the instantaneous angular speed (IAS) signals, which are then separated into two sets of data based on rotational directions. Then, the data corresponding to the approximately stable speed is truncated and connected to form a constructed signal. Next, the coherence of the constructed signal is calculated using the fast spectral coherence algorithm. Subsequently, the improved envelope spectrum sideband energy ratio is used as the objective value, and a global optimization algorithm is employed to determine the integration frequency band of the improved envelope spectrum (IES). Finally, the IES of this frequency band is calculated to obtain the fault-relatedorder characteristics. An RV reducer test rig was used for the experiment, and the analysis results from the proposed approach, cyclic spectral coherence (CSCoh), and improved envelope spectrum via feature optimization-gram (IESFOgram) were contrasted. Experiment results show that the proposed method is valid for the detection of tooth faults in the cycloidal gear of the RV reducer in robot operating conditions.

Self-learning salp swarm algorithm for global optimization and its application in multi-layer perceptron model training

Optimization problems are common across various fields, and one effective solution is the swarm intelligence algorithm.It is essential for the algorithm to deliver high-quality solutions for problems with varying characteristics. However, most existing swarm intelligence rely on fixed and monotonic search strategies, which limits their ability to handle the diverse and complex situations encountered when solving real-world optimization problems with unknown fitness landscapes. To extend the applicability of swarm intelligence and thus offer users an efficient black-box optimizer for various applications, a novel self-learning mechanism is proposed and applied to the Salp Swarm Algorithm (SSA) to develop the self-learning salp swarm algorithm (SLSSA) in this paper. In SLSSA, four distinct search strategies, including a novel multiple food sources search strategy, are adopted to strengthen the search agents’ abilities to conquer various difficulties in the search space. To improve the efficiency of the search process, the self-learning strategy dynamically determines the execution probability of each search strategy according to the quality of solutions it produced previously. Moreover, a parameter setting method is proposed in this paper, which eliminates the need for a trial-and-error approach and allows for straightforward configuration of the parameters that optimize the performance of SLSSA. In comparison with several highly regarded state-of-the-art peer algorithms, the performance of SLSSA in solving the CEC2014 benchmark functions was thoroughly examined. Subsequently, SLSSA was applied to train multi-layer perceptron classifiers and test on the UCI machine-learning datasets. The experimental results and analysis on benchmark functions and multi-layer perceptron classifier training problems demonstrate that SLSSA outperforms the competing algorithms in terms of solution accuracy, stability, and overall convergence speed. Moreover, computational time comparisons reveal that SLSSA achieves significant performance improvement with only a marginal increase in time cost compared to the original SSA.

Optimization of expensive black-box problems with penalized expected improvement

This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate set. Specifically, the acquisition function is formulated by penalizing the expected improvement with the variation of improvement, and the infill candidate set is composed of some global and local maxima of the expected improvement function which are identified to be “mutually non-dominated”. Some conditions necessary for setting the penalty coefficient of the acquisition function are investigated, and the definition of “mutually non-dominated infill candidates” is presented. The proposed method is demonstrated with a 1-D analytical function and benchmarked using six 10-D analytical functions and an underwater vehicle structural optimization problem. The results show that the proposed method is efficient for the optimization of expensive black-box design problems.