Intelligent Optimization Algorithm: Theory and Applications

Topic Information

Dear Colleagues,

Intelligent optimization algorithms (IOAs) belong to a branch of artificial intelligence that emphasizes developing and using information learned from data to solve complex searching, learning, and simulation problems. Many real-world applications for complex industrial engineering or design problems could be modeled as searching, learning, and simulation problems. With the learning ability, IOAs are emerging approaches that utilize advanced computation power with meta-heuristics algorithms and massive data processing techniques. These approaches have been actively investigated and applied to many real-world applications, such as scheduling and logistics operations.

Intelligent optimization algorithms, learned from biological or social phenomena, involve the collection of search and optimization techniques. IOAs include bio-inspired intelligent algorithms, evolutionary computation methods, swarm intelligence, etc. With these methods, the optimization problems, which can be represented in any form, do not need to be mathematically represented as continuous and differentiable functions. The only requirement for representing optimization problems is to evaluate each individual as the termed fitness value. Therefore, IOAs could be utilized to solve more general optimization problems, especially for issues that are difficult to solve with traditional hill-climbing algorithms.

Real-world applications have complex properties. Massive data are collected and used in scheduling tasks to optimize route selection, taxi dispatching, dynamic transit bus scheduling, and other mobility services to improve operational efficiency. Another example is logistics, where material movements within and between supply chain entities, including warehouses, factories, distribution centers, and retail shops, are improved and optimized with advanced data-oriented techniques. Many applications of IOAs have been reported. However, more research should be conducted on the theory of IOAs. More efficient algorithms could be designed with the understanding of the search process on IOAs.

Due to the complexity of real-world applications, no one panacea can solve all troubles. IOAs are practical approaches to handling such complexity, utilizing evolutionary computation, swarm intelligence, and other meta-heuristic methods based on domain expert knowledge and experience.

Scope of the topic:

Submissions involving real-world case studies are encouraged in the following topics (but not limited to):

• Artificial intelligence;
• Deep learning;
• Data mining;
• Data-driven optimization methods;
• Time-series forecasting;
• Time-series anomaly detection;
• Swarm intelligence;
• Intelligent computing;
• Bio-inspired algorithms, nature-inspired computing;
• Computational intelligence and evolutionary algorithms;
• Meta-heuristic algorithms;
• Intelligent optimization algorithms;
• Other related topics. 

Dr. Shi Cheng
Dr. Chaomin Luo
Prof. Dr. Shangce Gao
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Algorithms algorithms	2.1	4.5	2008	17.8 Days	CHF 1800	Submit
AppliedMath appliedmath	0.7	1.1	2021	23.5 Days	CHF 1200	Submit
Computation computation	1.9	4.1	2013	16.7 Days	CHF 1800	Submit
Mathematics mathematics	2.2	4.6	2013	18.4 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.3	2009	17.1 Days	CHF 2400	Submit

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Published Papers (7 papers)

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28 pages, 16312 KB  

Open AccessArticle

PS-InSAR Monitoring Integrated with a Bayesian-Optimized CNN–LSTM for Predicting Surface Subsidence in Complex Mining Goafs Under a Symmetry Perspective

by Tianlong Su, Linxin Zhang, Xuzhao Yuan, Xiaoquan Li, Xuefeng Li, Xuxing Huang, Zheng Huang and Danhua Zhu

Symmetry 2025, 17(12), 2152; https://doi.org/10.3390/sym17122152 (registering DOI) - 14 Dec 2025

Abstract

Mine-induced surface subsidence threatens infrastructure and can trigger cascading geohazards, so accurate and computationally efficient monitoring and forecasting are essential for early warning. We integrate Persistent Scatterer InSAR (PS-InSAR) time series with a Bayesian-optimized CNN–LSTM designed for spatiotemporal prediction. The CNN extracts spatial [...] Read more.

Mine-induced surface subsidence threatens infrastructure and can trigger cascading geohazards, so accurate and computationally efficient monitoring and forecasting are essential for early warning. We integrate Persistent Scatterer InSAR (PS-InSAR) time series with a Bayesian-optimized CNN–LSTM designed for spatiotemporal prediction. The CNN extracts spatial deformation patterns, the LSTM models temporal dependence, and Bayesian optimization selects the architecture, training hyperparameters, and the most informative exogenous drivers. Groundwater level and backfilling intensity are encoded as multichannel inputs. Endpoint anchoring with affine calibration aligns the historical series and the forward projections. PS-InSAR indicates a maximum subsidence rate of 85.6 mm yr⁻¹, and the estimates are corroborated against nearby leveling benchmarks and FLAC^3D simulations. Cross-site comparisons show acceleration followed by deceleration after backfilling and groundwater recovery, which is consistent with geological engineering conditions. A symmetry-aware preprocessing step exploits axial regularities of the deformation field through mirroring augmentation and documents symmetry-breaking hotspots linked to geological heterogeneity. These choices improve generalization to shifted and oscillatory patterns in both the spatial CNN and the temporal LSTM branches. Short-term forecasts from the BO–CNN–LSTM indicate subsequent stabilization with localized rebound, highlighting its practical value for operational planning and risk mitigation. The framework combines automated hyperparameter search with physically consistent objectives, reduces manual tuning, enhances reproducibility and generalizability, and provides a transferable quantitative workflow for forecasting mine-induced deformation in complex goaf systems. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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21 pages, 610 KB  

Open AccessArticle

mDA: Evolutionary Machine Learning Algorithm for Feature Selection in Medical Domain

by Ibrahim Aljarah, Abdullah Alzaqebah, Nailah Al-Madi, Ala’ M. Al-Zoubi and Amro Saleh

Computation 2025, 13(12), 292; https://doi.org/10.3390/computation13120292 (registering DOI) - 13 Dec 2025

Abstract

The rapid expansion of medical data, characterized by its complex high-dimensional attributes, presents numerous promising opportunities and substantial challenges in healthcare analytics. Adopting effective feature selection techniques is essential to take advantage of the potential of such data. This research presents a modified [...] Read more.

The rapid expansion of medical data, characterized by its complex high-dimensional attributes, presents numerous promising opportunities and substantial challenges in healthcare analytics. Adopting effective feature selection techniques is essential to take advantage of the potential of such data. This research presents a modified algorithm called (mDA), which is the hybrid algorithm between the Evolutionary Population Dynamics and the Dragonfly Algorithm. This method combines Evolutionary Population Dynamics’s strength with the Dragonfly Algorithm’s flexible capabilities, offering a robust evolutionary machine learning approach specifically designed for medical data analysis. By integrating the dynamic population modeling of Evolutionary Population Dynamics with the adaptive search techniques of Dragonfly Algorithm, the proposed mDA significantly improves accuracy, reduces the number of features, and obtains the minimum average of the fitness scores. Comparative experiments conducted on seven diverse medical datasets against other established algorithms confirm the superior performance of the proposed mDA, establishing it as a valuable approach in examining complex medical data. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

26 pages, 3560 KB  

Open AccessArticle

Intelligent Identification Method of Valve Internal Leakage in Thermal Power Station Based on Improved Kepler Optimization Algorithm-Support Vector Regression (IKOA-SVR)

by Fengsheng Jia, Tao Jin, Ruizhou Guo, Xinghua Yuan, Zihao Guo and Chengbing He

Computation 2025, 13(11), 251; https://doi.org/10.3390/computation13110251 - 2 Nov 2025

Cited by 1 | Viewed by 356

Abstract

Valve internal leakage in thermal power stations exhibits a strong concealed nature. If it cannot be discovered and predicted of development trend in time, it will affect the safe and economical operation of plant equipment. This paper proposed an intelligent identification method for [...] Read more.

Valve internal leakage in thermal power stations exhibits a strong concealed nature. If it cannot be discovered and predicted of development trend in time, it will affect the safe and economical operation of plant equipment. This paper proposed an intelligent identification method for valve internal leakage that integrated an Improved Kepler Optimization Algorithm (IKOA) with Support Vector Regression (SVR). The Kepler Optimization Algorithm (KOA) was improved using the Sobol sequence and an adaptive Gaussian mutation strategy to achieve self-optimization of the key parameters in the SVR model. A multi-step sliding cross-validation method was employed to train the model, ultimately yielding the IKOA-SVR intelligent identification model for valve internal leakage quantification. Taking the main steam drain pipe valve as an example, a simulation case validation was carried out. The calculation example used Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and determination coefficient (R²) as performance evaluation metrics, and compared and analyzed the training and testing dataset using IKOA-SVR, KOA-SVR, Particle Swarm Optimization (PSO)-SVR, Random Search (RS)-SVR, Grid Search (GS)-SVR, and Bayesian Optimization (BO)-SVR methods, respectively. For the testing dataset, the MSE of IKOA-SVR is 0.65, RMSE is 0.81, MAE is 0.49, and MAPE is 0.0043, with the smallest values among the six methods. The R² of IKOA-SVR is 0.9998, with the largest value among the six methods. It indicated that IKOA-SVR can effectively solve problems such as getting stuck in local optima and overfitting during the optimization process. An Out-Of-Distribution (OOD) test was conducted for two scenarios: noise injection and Region-Holdout. The identification performance of all six methods decreased, with IKOA-SVR showing the smallest performance decline. The results show that IKOA-SVR has the strongest generalization ability and robustness, the best effect in improving fitting ability, the smallest identification error, the highest identification accuracy, and results closer to the actual value. The method presented in this paper provides an effective approach to solve the problem of intelligent identification of valve internal leakage in thermal power station. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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27 pages, 5819 KB  

Open AccessArticle

Dynamic Error Correction for Fine-Wire Thermocouples Based on CRBM-DBN with PINN Constraint

by Chenyang Zhao, Guangyu Zhou, Junsheng Zhang, Zhijie Zhang, Gang Huang and Qianfang Xie

Symmetry 2025, 17(11), 1831; https://doi.org/10.3390/sym17111831 - 1 Nov 2025

Viewed by 458

Abstract

In high-temperature testing scenarios that rely on contact, fine-wire thermocouples demonstrate commendable dynamic performance. Nonetheless, their thermal inertia leads to notable dynamic nonlinear inaccuracies, including response delays and amplitude reduction. To mitigate these challenges, a novel dynamic error correction approach is introduced, which [...] Read more.

In high-temperature testing scenarios that rely on contact, fine-wire thermocouples demonstrate commendable dynamic performance. Nonetheless, their thermal inertia leads to notable dynamic nonlinear inaccuracies, including response delays and amplitude reduction. To mitigate these challenges, a novel dynamic error correction approach is introduced, which combines a Continuous Restricted Boltzmann Machine, Deep Belief Network, and Physics-Informed Neural Network (CDBN-PINN). The unique heat transfer properties of the thermocouple’s bimetallic structure are represented through an Inverse Heat Conduction Equation (IHCP). An analysis is conducted to explore the connection between the analytical solution’s ill-posed nature and the thermocouple’s dynamic errors. The transient temperature response’s nonlinear characteristics are captured using CRBM-DBN. To maintain physical validity and minimize noise amplification, filtered kernel regularization is applied as a constraint within the PINN framework. This approach was tested and confirmed through laser pulse calibration on thermocouples with butt-welded and ball-welded configurations of 0.25 mm and 0.38 mm. Findings reveal that the proposed method achieved a peak relative error of merely 0.83%, superior to Tikhonov regularization by −2.2%, Wiener deconvolution by 20.40%, FBPINNs by 1.40%, and the ablation technique by 2.05%. In detonation tests, the corrected temperature peak reached 1045.7 °C, with the relative error decreasing from 77.7% to 5.1%. Additionally, this method improves response times, with the rise time in laser calibration enhanced by up to 31 ms and in explosion testing by 26 ms. By merging physical constraints with data-driven methodologies, this technique successfully corrected dynamic errors even with limited sample sizes. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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19 pages, 4719 KB  

Open AccessArticle

Laser Stripe Segmentation Network Based on Evidential Uncertainty Theory Modeling Fine-Tuning Optimization Symmetric Algorithm

by Chenbo Shi, Delin Wang, Xiangyu Zhang, Chun Zhang, Jia Yan, Changsheng Zhu and Xiaobing Feng

Symmetry 2025, 17(8), 1280; https://doi.org/10.3390/sym17081280 - 9 Aug 2025

Viewed by 805

Abstract

In welding applications, line-structured-light vision is widely used for seam tracking, but intense noise from arc glow, spatter, smoke, and reflections makes reliable laser-stripe segmentation difficult. To address these challenges, we propose EUFNet, an uncertainty-driven symmetrical two-stage segmentation network for precise stripe extraction [...] Read more.

In welding applications, line-structured-light vision is widely used for seam tracking, but intense noise from arc glow, spatter, smoke, and reflections makes reliable laser-stripe segmentation difficult. To address these challenges, we propose EUFNet, an uncertainty-driven symmetrical two-stage segmentation network for precise stripe extraction under real-world welding conditions. In the first stage, a lightweight backbone generates a coarse stripe mask and a pixel-wise uncertainty map; in the second stage, a functionally mirrored refinement network uses this uncertainty map to symmetrically guide fine-tuning of the same image regions, thereby preserving stripe continuity. We further employ an uncertainty-weighted loss that treats ambiguous pixels and their corresponding evidence in a one-to-one, symmetric manner. Evaluated on a large-scale dataset of 3100 annotated welding images, EUFNet achieves a mean IoU of 89.3% and a mean accuracy of 95.9% at 236.7 FPS (compared to U-Net’s 82.5% mean IoU and 90.2% mean accuracy), significantly outperforming existing approaches in both accuracy and real-time performance. Moreover, EUFNet generalizes effectively to the public WLSD benchmark, surpassing state-of-the-art baselines in both accuracy and speed. These results confirm that a structurally and functionally symmetric, uncertainty-driven two-stage refinement strategy—combined with targeted loss design and efficient feature integration—yields high-precision, real-time performance for automated welding vision. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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30 pages, 7785 KB  

Open AccessArticle

Data Value Assessment in Digital Economy Based on Backpropagation Neural Network Optimized by Genetic Algorithm

by Xujiang Qin, Qi He, Xin Zhang and Xiang Yang

Symmetry 2025, 17(5), 761; https://doi.org/10.3390/sym17050761 - 14 May 2025

Viewed by 945

Abstract

As a new form of economic activity driven by data resources and digital technologies, the digital economy underscores the strategic significance of data as a core production factor. This growing importance necessitates accurate and robust valuation methods. Data valuation poses core modeling challenges [...] Read more.

As a new form of economic activity driven by data resources and digital technologies, the digital economy underscores the strategic significance of data as a core production factor. This growing importance necessitates accurate and robust valuation methods. Data valuation poses core modeling challenges due to its nonlinear nature and the instability of neural networks, including gradient vanishing, parameter sensitivity, and slow convergence. To overcome these challenges, this study proposes a genetic algorithm-optimized BP (GA-BP) model, enhancing the efficiency and accuracy of data valuation. The BP neural network employs a symmetrical architecture, with neurons organized in layers and information transmitted symmetrically during both forward and backward propagation. Similarly, the genetic algorithm maintains a symmetric evolutionary process, featuring symmetric operations in both crossover and mutation. The empirical data used in this study are sourced from the Shanghai Data Exchange, comprising 519 data samples. Based on this dataset, the model incorporates 9 primary indicators and 21 secondary indicators to comprehensively assess data value, optimizing network weights and thresholds through the genetic algorithm. Experimental results show that the GA-BP model outperforms the traditional BP network in terms of mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R²), achieving a 47.6% improvement in prediction accuracy. Furthermore, GA-BP exhibits faster convergence and greater stability. When compared to other models such as long short-term memory (LSTM), convolutional neural networks (CNNs), and optimization-based BP variants like particle swarm optimization BP (PSO-BP) and whale optimization algorithm BP (WOA-BP), GA-BP demonstrates superior generalization and robustness. This approach provides valuable insights into the commercialization of data assets. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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21 pages, 1103 KB  

Open AccessArticle

Multi-Objective Cauchy Particle Swarm Optimization for Energy-Aware Virtual Machine Placement in Cloud Datacenters

by Xuan Liu, Chenyan Wang, Shan Jiang, Yutong Gao, Chaomurilige and Bo Cheng

Symmetry 2025, 17(5), 742; https://doi.org/10.3390/sym17050742 - 13 May 2025

Viewed by 907

Abstract

With the continuous expansion of application scenarios for cloud computing, large-scale service deployments in cloud data centers are accompanied by a significant increase in resource consumption. Virtual machines (VMs) in data centers are allocated to physical machines (PMs) and require the resources provided [...] Read more.

With the continuous expansion of application scenarios for cloud computing, large-scale service deployments in cloud data centers are accompanied by a significant increase in resource consumption. Virtual machines (VMs) in data centers are allocated to physical machines (PMs) and require the resources provided by PMs to run various services. Apparently, a simple solution to minimize energy consumption is to allocate VMs as compactly as possible. However, the above virtual machine placement (VMP) strategy may lead to system performance degradation and service failures due to imbalanced resource load, thereby reducing the robustness of the cloud data center. Therefore, an effective VMP solution that comprehensively considers both energy consumption and other performance metrics in data centers is urgently needed. In this paper, we first construct a multi-objective VMP model aiming to simultaneously optimize energy consumption, resource utilization, load balancing, and system robustness, and we then build a joint optimization function with resource constraints. Subsequently, a novel energy-aware Cauchy particle swarm optimization (EA-CPSO) algorithm is proposed, which implements particle asymmetric disturbances and an energy-efficient population iteration strategy, aiming to minimize the value of the joint optimization function. Finally, our extensive experiments demonstrated that EA-CPSO outperforms existing methods. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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