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Similar to other swarm-based algorithms, the recently developed whale optimization algorithm (WOA) has the problems of low accuracy and slow convergence. It is also easy to fall into local optimum. Moreover, WOA and its variants cannot perform well enough in solving high-dimensional optimization problems. This paper puts forward a new improved WOA with joint search mechanisms called JSWOA for solving the above disadvantages. First, the improved algorithm uses tent chaotic map to maintain the diversity of the initial population for global search. Second, a new adaptive inertia weight is given to improve the convergence accuracy and speed, together with jump out from local optimum. Finally, to enhance the quality and diversity of the whale population, as well as increase the probability of obtaining global optimal solution, opposition-based learning mechanism is used to update the individuals of the whale population continuously during each iteration process. The performance of the proposed JSWOA is tested by twenty-three benchmark functions of various types and dimensions. Then, the results are compared with the basic WOA, several variants of WOA and other swarm-based intelligent algorithms. The experimental results show that the proposed JSWOA algorithm with multi-mechanisms is superior to WOA and the other state-of-the-art algorithms in the competition, exhibiting remarkable advantages in the solution accuracy and convergence speed. It is also suitable for dealing with high-dimensional global optimization problems.

Surrogate-based optimization is criticized in high-dimensional cases because it cannot scale well with the input dimension. In order to overcome this issue, we adopt a snapshot active subspace method to reduce the input dimension. A smoothing operation of samples is used to reduce the demand for snapshots in the construction of active subspaces. This operation significantly reduces the computational cost on the one hand, and on the other hand, it leads to more feasible subspaces. We use a 90∼95% energy coverage criterion to define the dimension of the subspace. With this criterion, the surrogate-based airfoil optimization in the active subspace is both efficient and effective. We also validate this optimization approach in an ONERA M6 wing optimization case with 220 shape variables. Compared with original surrogate-based optimization, the new approach reduces the computational time by 70% and obtains a more practical design with a smaller drag.

To address the limitations of traditional optimization methods in achieving high accuracy in high-dimensional problems, this paper introduces the snow leopard optimization (SLO) algorithm. SLO is a novel meta-heuristic approach inspired by the territorial behaviors of snow leopards. By emulating strategies such as territory delineation, neighborhood relocation, and dispute mechanisms, SLO achieves a balance between exploration and exploitation, to navigate vast and complex search spaces. The algorithm’s performance was evaluated using the CEC2017 benchmark and high-dimensional genetic data feature selection tasks, demonstrating SLO’s competitive advantage in solving high-dimensional optimization problems. In the CEC2017 experiments, SLO ranked first in the Friedman test, outperforming several well-known algorithms, including ETBBPSO, ARBBPSO, HCOA, AVOA, WOA, SSA, and HHO. The effective application of SLO in high-dimensional genetic data feature selection further highlights its adaptability and practical utility, marking significant progress in the field of high-dimensional optimization and feature selection.

Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability ( RMOP ) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.

Surrogate-based Bayesian optimization is efficient and useful for global optimization when objective functions are expensive to evaluate. Yet, the commonly used surrogate model, the Gaussian process, faces the scalability challenge for high-dimensional problems due to the high computational cost associated with the inversion of covariance matrices. In this paper, a new exploitation-enhanced sparse Gaussian process (EE-SGP) modeling method is proposed for scalable Bayesian optimization. The proposed EE-SGP strategically selects optimal samples to maximize the likelihood of identifying the global optimum, guided by the Gumbel distribution. This new sampling strategy, coupled with a sparse Gaussian process, significantly reduces the computational burden associated with high-dimensional problems. The optimization process leverages the biogeography-based optimization metaheuristic algorithm, further enhancing the efficiency and effectiveness of the proposed approach. EE-SGP's performance is assessed with analytical benchmark problems and constrained engineering optimization examples. The evaluation criteria include convergence speed and robustness. The studies demonstrate that EE-SGP is a robust, efficient, and scalable algorithm for searching for optimum solutions in high-dimensional spaces.

Finding reasonably good solutions using a fewer number of objective function evaluations has long been recognized as a good attribute of an optimization algorithm. This becomes more important, especially when dealing with very high-dimensional optimization problems, since contemporary algorithms often need a high number of iterations to converge. Furthermore, the excessive computational effort required to handle the large number of design variables involved in the optimization of large-scale steel double-layer grids with complex configurations is perceived as the main challenge for contemporary structural optimization techniques. This paper aims to enhance the convergence properties of the standard guided stochastic search (GSS) algorithm to handle computationally expensive and very high-dimensional optimization problems of steel double-layer grids. To this end, a repair deceleration mechanism (RDM) is proposed, and its efficiency is evaluated through challenging test examples of steel double-layer grids. First, parameter tuning based on rigorous analyses of two preliminary test instances is performed. Next, the usefulness of the proposed RDM is further investigated through two very high-dimensional instances of steel double-layer grids, namely a 21,212-member free-form double-layer grid, and a 25,514-member double-layer multi-dome, with 21,212 and 25,514 design variables, respectively. The obtained numerical results indicate that the proposed RDM can significantly enhance the convergence rate of the GSS algorithm, rendering it an efficient tool to handle very high-dimensional sizing optimization problems.

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction techniques is proposed to reduce such computational burden. Proper orthogonal decomposition (POD) and active subspace genetic algorithm (ASGA) are applied for a dimensional reduction of the original (high fidelity) model and for an efficient genetic optimization based on active subspace property. The parameterization of the shape is applied directly to the computational mesh, propagating the generic deformation map applied to the surface (of the object to optimize) to the mesh nodes using a radial basis function (RBF) interpolation. Thus, topology and quality of the original mesh are preserved, enabling application of POD-based reduced order modeling techniques, and avoiding the necessity of additional meshing steps. Model order reduction is performed coupling POD and Gaussian process regression (GPR) in a data-driven fashion. The framework is validated on a benchmark ship.

The efficient global optimization (EGO) algorithm is widely used for solving expensive optimization problems, but it has been frequently criticized for its incapability of solving high-dimensional problems, i.e., problems with 100 or more variables. Extending the EGO algorithm to high dimensions encounters two major challenges: the training time of the Kriging model goes up rapidly and the difficulty of solving the infill optimization problem increases exponentially as the dimension of the problem increases. In this work, we propose a simple and efficient cooperative framework to tackle these two problems simultaneously. In the proposed framework, we first randomly decompose the original high-dimensional problem into several sub-problems, and then train the Kriging model and solve the infill optimization problem for each sub-problem. Context vectors are used to link the sub-problems such that the Kriging models are trained and the infill optimization problems are solved in a cooperative way. Once all the sub-problems have been solved, we start another random decomposition again and repeat the divide-and-conquer process until the computational budget is reached. Experiment results show that the proposed cooperative approach can bring nearly linear speedup with respect to the number of sub-problems. The proposed approach also shows competitive optimization performance when compared with the standard EGO and six high-dimensional versions of EGO. This work provides an efficient and effective approach for high-dimensional expensive optimization.

In recent years, swarm intelligence metaheuristic algorithms have emerged as powerful tools for solving real-world engineering optimization problems. However, their performance often degrades when applied to complex, high-dimensional problems. To address this limitation, we propose an Adaptive Fuzzy Swarm-based Search Algorithm (AFSSA), which incorporates a Fuzzy Dynamic Control Mechanism to dynamically adjust the optimization coefficients of swarm intelligence algorithms. AFSSA employs a Mamdani fuzzy inference system to enable smooth phase transitions during optimization, ensuring adaptability to the problem's unique characteristics. In this study, AFSSA is applied to enhance the acceleration coefficients of Particle Swarm Optimization (PSO) and Golden Search Optimization (GSO), resulting in AFSSA-PSO and AFSSA-GSO. The performance of these modified algorithms is evaluated on 23 standard benchmark functions (with dimensions of 30, 100, and 500) and the CEC2019 test suite, showing competitive results compared to other well-known optimization methods. Additionally, AFSSA is tested on data clustering problems, further demonstrating its versatility in handling complex real-world applications.

In surrogate-based optimization (SBO), the recognized issues associated with the high-dimensional surrogate models focus on the prohibitive computational costs and the low model accuracy. However, there is a lack of effective solutions in the face of the ‘curse of dimensionality’. In this paper, we propose a novel Kriging metamodel to remedy this deficiency. The Kriging model based on projection correlation (KPC) introduces the projection correlation into the Kriging modeling process as prior information, taking into account the nature of hyperparameters. The effectiveness and accuracy of the KPC are illustrated through 10–70-dimensional numerical examples. Furthermore, a parallel computing strategy that combines the multi-peak characteristics of expected improvement and minimizing prediction (MEI&MP) is proposed to further improve high-dimensional optimization efficiency and potential. The global performance and optimization efficiency of our method are validated via typical test functions and structural optimization problems.