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Search Results (1,513)

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Keywords = metaheuristics optimization methods

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24 pages, 1898 KB  
Article
Hyperchaotic Network Synchronization via Green-AI Metaheuristics: A Performance Comparison of Quantum and Bio-Inspired Solvers
by Leonardo Loza-Sandoval, Robin F. Conchas, Jesus G. Alvarez, Gabriel Martinez-Soltero and Alma Y. Alanis
Algorithms 2026, 19(6), 478; https://doi.org/10.3390/a19060478 (registering DOI) - 13 Jun 2026
Abstract
Complex networks have become a fundamental paradigm for modeling real-world systems. Synchronization of such networks, particularly under hyperchaotic dynamics, presents a significant control challenge due to the high-dimensional state space and multiple positive Lyapunov exponents. This paper addresses the driver node selection problem [...] Read more.
Complex networks have become a fundamental paradigm for modeling real-world systems. Synchronization of such networks, particularly under hyperchaotic dynamics, presents a significant control challenge due to the high-dimensional state space and multiple positive Lyapunov exponents. This paper addresses the driver node selection problem in a 4D Hyperchaotic Lorenz complex network, formulating it as a constrained binary optimization task. We evaluate a pool of advanced metaheuristics, including the quantum genetic algorithm (QGA), seahorse optimizer (SHO), and artificial bee colony (ABC), across multiple network experiments conducted over 30 independent runs to guarantee statistical validity. The performance of these solvers is rigorously benchmarked against traditional topological heuristics, a random selection baseline comprising 600 feasible configurations, and verified through Wilcoxon statistical testing. Furthermore, addressing computational sustainability, we introduce a “Green-Artificial Intelligence” architecture based on dual-tier structured query language memoization (SQL-memoization) and provide a detailed runtime comparison evaluating its efficiency. The empirical results indicate that swarm-intelligence methods such as ABC and SHO exhibit robust competitive performance in minimizing synchronization errors while the Green-AI framework consistently and drastically reduces the computation of the repetitive simulations. Full article
51 pages, 4229 KB  
Article
Blackcap Optimization Algorithm (BCOA): A Novel Metaheuristic Algorithm for Global and Engineering Optimization Problems
by Ali Asghari and Mohammadhossein Mohammadi
Biomimetics 2026, 11(6), 419; https://doi.org/10.3390/biomimetics11060419 (registering DOI) - 13 Jun 2026
Abstract
Metaheuristic algorithms are widely used to find optimal or near-optimal solutions for complex problems by taking inspiration from natural behaviors and processes. Although many different methods have been developed, a common problem in many of them is maintaining a good balance between exploration [...] Read more.
Metaheuristic algorithms are widely used to find optimal or near-optimal solutions for complex problems by taking inspiration from natural behaviors and processes. Although many different methods have been developed, a common problem in many of them is maintaining a good balance between exploration and exploitation and avoiding local optima. To deal with this issue, this paper proposes a new method called the Blackcap Optimization Algorithm (BCOA), which is inspired by the navigation and migration behavior of Blackcap birds. Instead of using complicated distance calculations, the proposed method is based on angular movement vectors. The movement of each search agent is controlled by an angle-based mathematical model that combines the global best angle, a successful neighboring angle, and an adaptive exponential disturbance factor. In addition, the algorithm uses a quasi-genetic path transition mechanism to combine successful parent paths together, along with a territorial competition stage. This structure helps reduce computational cost and improves the balance between exploration and exploitation. The performance of the proposed algorithm is tested on 32 benchmark functions and seven engineering and network optimization problems. The simulation results show that BCOA has a good ability to avoid local optima and can achieve acceptable convergence speed and cost reduction compared to several existing methods. Full article
(This article belongs to the Section Biological Optimisation and Management)
32 pages, 1039 KB  
Article
NSGA-II-Based Stochastic Multi-Objective Optimization for Demand Response–Enabled Smart Meter Placement in EVCS/PV-Integrated Distribution Networks
by Hossein Lotfi and Hossein Parsadust
World Electr. Veh. J. 2026, 17(6), 308; https://doi.org/10.3390/wevj17060308 (registering DOI) - 12 Jun 2026
Abstract
The growing penetration of electric vehicles (EVs) and distributed photovoltaic (PV) generation is increasing operational uncertainty in distribution networks and intensifying long-standing challenges such as higher power losses, rising peak demand, and voltage instability. To address these issues, this paper proposes a multi-objective [...] Read more.
The growing penetration of electric vehicles (EVs) and distributed photovoltaic (PV) generation is increasing operational uncertainty in distribution networks and intensifying long-standing challenges such as higher power losses, rising peak demand, and voltage instability. To address these issues, this paper proposes a multi-objective optimization framework for the strategic placement of smart meters equipped with demand response (DR) capability in radial distribution systems. Unlike conventional placement approaches that mainly focus on monitoring or reducing non-technical losses, the proposed method integrates active load control into the planning stage and explicitly considers the stochastic behavior of loads, PV generation, and electric vehicle charging stations (EVCSs). The problem is formulated with four objectives: minimizing total power losses, substation peak demand, voltage deviation penalty, and installation cost. A scenario-based stochastic model is employed to represent operational variability across the network. The resulting nonlinear mixed discrete optimization problem is solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), an evolutionary multi-objective optimization technique that generates a set of Pareto-optimal solutions representing trade-offs among conflicting objectives. Smart meters are allowed to curtail a portion of controllable demand during critical loading conditions, which helps reduce feeder loading and improve voltage profiles. The proposed approach is evaluated on the IEEE 33-bus and IEEE 69-bus distribution systems. Simulation results demonstrate significant reductions in power losses and peak demand, with the IEEE 33-bus system achieving up to a 26.2% reduction in power losses and 52.5% reduction in substation peak demand compared with existing metaheuristic approaches. The results also indicate improved voltage stability and effective performance in the IEEE 69-bus system, confirming the importance of topology-aware DR-enabled planning. Overall, the findings show that embedding demand response capability within smart meter allocation can significantly enhance the resilience and operational efficiency of modern distribution networks with high EV and PV penetration. Full article
(This article belongs to the Section Charging Infrastructure and Grid Integration)
23 pages, 2475 KB  
Review
Optimization Techniques for Home Energy Management Systems: A Comprehensive Review, Critical Analysis, and Future Directions
by Md Mamun Ur Rashid, Jiefeng Hu, Md Alamgir Hossain, Nima Amjady and Syed Islam
Urban Sci. 2026, 10(6), 324; https://doi.org/10.3390/urbansci10060324 - 10 Jun 2026
Viewed by 156
Abstract
The increasing integration of renewable energy sources, smart appliances, and distributed energy technologies has significantly increased the complexity of residential energy systems, necessitating advanced Home Energy Management Systems (HEMS). Optimization techniques play a critical role in achieving key objectives, including energy cost reduction, [...] Read more.
The increasing integration of renewable energy sources, smart appliances, and distributed energy technologies has significantly increased the complexity of residential energy systems, necessitating advanced Home Energy Management Systems (HEMS). Optimization techniques play a critical role in achieving key objectives, including energy cost reduction, load balancing, minimizing the peak-to-average ratio, and enhancing user comfort. This paper presents a comprehensive review and critical analysis of optimization techniques employed in HEMS, including mathematical methods, metaheuristic algorithms, artificial intelligence (AI)-based approaches, and rule-based strategies. These techniques are systematically classified and compared based on scalability, computational complexity, uncertainty handling, and real-time applicability. The analysis reveals that while conventional methods provide reliable solutions for structured problems, AI-based techniques offer superior adaptability and performance in dynamic and data-driven environments. Furthermore, key research gaps are identified, including limited multi-objective optimization, inadequate consideration of uncertainty and electric vehicle integration, and the lack of real-world implementation. Finally, future research directions are outlined, emphasizing hybrid optimization frameworks and intelligent, IoT-enabled energy management systems. Full article
(This article belongs to the Special Issue Urban Smart Grids and Power Systems)
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16 pages, 1057 KB  
Article
A Hybrid Multi-Objective Lemurs Optimizer-Backtracking Search Algorithm for Engineering Optimization Problems
by Khadijetou Maaloum Din, Rabii El Maani, Ahmed Tchvagha Zeine and Rachid Ellaia
AppliedMath 2026, 6(6), 92; https://doi.org/10.3390/appliedmath6060092 - 10 Jun 2026
Viewed by 91
Abstract
Multi-objective optimization plays a fundamental role in solving complex engineering design problems characterized by conflicting objectives and nonlinear constraints. In this study, a novel hybrid optimization algorithm, named Multi-objective Lemurs Optimizer-Backtracking Search Algorithm (MOLOBSA), is proposed to improve the exploration and exploitation capabilities [...] Read more.
Multi-objective optimization plays a fundamental role in solving complex engineering design problems characterized by conflicting objectives and nonlinear constraints. In this study, a novel hybrid optimization algorithm, named Multi-objective Lemurs Optimizer-Backtracking Search Algorithm (MOLOBSA), is proposed to improve the exploration and exploitation capabilities of existing metaheuristic methods. The proposed approach integrates the global exploration ability of the Lemurs Optimizer (LO) with the efficient mutation and crossover mechanisms of the Backtracking Search Algorithm (BSA) within a multi-objective optimization framework. The effectiveness of the proposed algorithm is evaluated using the CEC2020 multimodal multi-objective benchmark suite, where its performance is assessed using the PSP and IGDX performance indicators. In addition, the proposed method was successfully applied to the multi-objective design optimization of an I-beam structure, where the objectives were to minimize the structural weight and the maximum displacement under mechanical constraints. The obtained Pareto solutions exhibit better diversity and improved trade-off characteristics compared with those produced by the baseline algorithm. Full article
(This article belongs to the Section Computational and Numerical Mathematics)
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36 pages, 2728 KB  
Article
Self-Adaptive AdamW-Guided Optimization: A Learning-Driven Metaheuristic for Solving Complex Real-World Engineering Problems
by Yuhang Xie, Wei Li, Cheng Zhong, Shang Gao, Kai Xu, Juanjuan Tu and Bin Qin
Entropy 2026, 28(6), 660; https://doi.org/10.3390/e28060660 - 9 Jun 2026
Viewed by 96
Abstract
Given the growing complexity of continuous optimization problems in strongly coupled and black-box environments, this study proposes a novel adaptive gradient-guided metaheuristic, referred to as Self-Adaptive AdamW-Guided Optimization (SAWG). Without requiring explicit gradient information, SAWG constructs population-based pseudo-gradients and systematically integrates key AdamW [...] Read more.
Given the growing complexity of continuous optimization problems in strongly coupled and black-box environments, this study proposes a novel adaptive gradient-guided metaheuristic, referred to as Self-Adaptive AdamW-Guided Optimization (SAWG). Without requiring explicit gradient information, SAWG constructs population-based pseudo-gradients and systematically integrates key AdamW mechanisms, including adaptive moment estimation, step-size regulation, and weight decay, to guide efficient population updates. Furthermore, a stagnation-aware adaptive control strategy is introduced to alleviate premature convergence and dynamically balance exploration and exploitation. To evaluate the optimization performance of SAWG, experiments were conducted on the CEC2017 and CEC2020 benchmark suites and eight engineering optimization problems. SAWG was also compared with nine other typical and novel high-performance optimizers. Experimental results and statistical analysis show that SAWG achieved excellent optimization performance in most test tasks and maintained strong adaptability and competitiveness in various numerical optimization problems. Therefore, SAWG can be regarded as a high-performance optimizer, providing a novel and effective method for solving complex numerical optimization tasks. Full article
(This article belongs to the Section Multidisciplinary Applications)
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26 pages, 628 KB  
Article
A Two-Stage PPO–RLMPA Framework for Dynamic Economic Dispatch with Renewable Energy and Storage Integration
by Kemal Keskin
Biomimetics 2026, 11(6), 400; https://doi.org/10.3390/biomimetics11060400 - 6 Jun 2026
Viewed by 186
Abstract
The Dynamic Economic Dispatch (DED) problem underpins the cost-efficient and reliable operation of modern power systems, yet valve-point loading, ramp-rate coupling, and the growing share of intermittent wind, photovoltaic, and pumped-storage hydro (PSH) resources render it highly non-convex. Metaheuristic methods typically require large [...] Read more.
The Dynamic Economic Dispatch (DED) problem underpins the cost-efficient and reliable operation of modern power systems, yet valve-point loading, ramp-rate coupling, and the growing share of intermittent wind, photovoltaic, and pumped-storage hydro (PSH) resources render it highly non-convex. Metaheuristic methods typically require large computational budgets and hand-crafted constraint-handling rules, whereas deep reinforcement learning agents rarely guarantee the feasibility of the schedules they produce. To address both limitations, this paper proposes a Two-Stage PPO–RLMPA framework that couples data-driven policy learning with a biomimetic metaheuristic search inspired by marine predator–prey dynamics. In the first stage, a Proximal Policy Optimization (PPO) agent is trained on a Markov Decision Process reformulation of DED in which a deterministic Safety Layer projects every raw action onto the feasible set defined by capacity, ramp-rate, and power-balance constraints, so the policy only observes physically viable transitions. In the second stage, the PPO dispatch is refined by the RLMPA module, a Marine Predators Algorithm (MPA) whose exploration–exploitation balance, Lévy-flight foraging, and Fish Aggregating Devices (FADs) attraction mechanisms emulate strategies documented in marine ecosystems; its step-size factor and FADs probability are further adapted online by a Deep Q-Network. This biomimetics-informed refinement translates predator–prey foraging intelligence into economically efficient thermal dispatch under valve-point non-convexity. Across 30 independent runs on ten- and twenty-unit benchmark systems with wind, PV, and PSH integration, the framework attains best costs of USD 368,763 and USD 737,348 on Test Systems 1 and 2, corresponding to reductions of approximately 1.1% and 4.4% over the CFCEP baseline, with zero post-repair constraint violations in every run. Full article
(This article belongs to the Special Issue Nature-Inspired Sustainable Engineering)
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19 pages, 15393 KB  
Article
A Robotic Disassembly Planning Method for Retired Batteries Based on a Long Short-Term Memory Collaborative Framework
by Jie Li, Shuo Zhang, Jiahui Si and Jinsong Bao
Symmetry 2026, 18(6), 981; https://doi.org/10.3390/sym18060981 - 5 Jun 2026
Viewed by 204
Abstract
This paper addresses non-steady-state scenarios in the human–robot collaborative disassembly process of retired power batteries, including component aging, ambiguous instructions, and sensor drift. In such scenarios, the robot exhibits execution robustness problems. This paper proposes a Planning Domain Definition Language (PDDL) generation framework [...] Read more.
This paper addresses non-steady-state scenarios in the human–robot collaborative disassembly process of retired power batteries, including component aging, ambiguous instructions, and sensor drift. In such scenarios, the robot exhibits execution robustness problems. This paper proposes a Planning Domain Definition Language (PDDL) generation framework that integrates long-term and short-term memory. The framework combines large language models with knowledge graphs as a long-term memory module for symbolic task decomposition and domain semantic rule generalization, while using meta-heuristic optimization algorithms as a short-term memory module to adapt and optimize action parameters based on real-time sensor feedback. Through this closed-loop mechanism that combines long-term memory guidance with short-term memory adaptation, the system addresses the limitation of traditional PDDL, which, when facing open, time-varying, and heterogeneous industrial disassembly scenarios, has symbolic action models that have difficulty capturing the uncertainty and unpredictable disturbances in real physical systems, limiting its practicality in complex non-steady-state scenarios. Furthermore, the system establishes a feedback mechanism from short-term memory to long-term memory, enhancing disassembly capabilities in non-steady-state environments by transforming scenario information into supplementary understanding. The research validates this method on a real disassembly platform. Compared with baselines of traditional PDDL, a planning method using only large language models (LLMs), and heuristic algorithms, this method achieved an 88.0% task success rate (significantly superior to the 38.0% of traditional PDDL). Full article
(This article belongs to the Special Issue Symmetry-Aware Embodied Intelligence: Foundations and Applications)
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21 pages, 2399 KB  
Article
Comparative Robustness Analysis of Frequency-Constrained Metaheuristic PID Tuning for Zero-Overshoot Polymerase Chain Reaction Thermal Control
by Mehmet Ekici
Electronics 2026, 15(11), 2480; https://doi.org/10.3390/electronics15112480 - 5 Jun 2026
Viewed by 168
Abstract
The success of DNA amplification in Polymerase Chain Reaction (PCR) devices inherently depends on the rapid and absolute zero-overshoot temperature control of thermoelectric cooler (TEC) systems. In the literature, metaheuristic algorithms employed for proportional–integral–derivative (PID) tuning typically operate within unconstrained search spaces, relying [...] Read more.
The success of DNA amplification in Polymerase Chain Reaction (PCR) devices inherently depends on the rapid and absolute zero-overshoot temperature control of thermoelectric cooler (TEC) systems. In the literature, metaheuristic algorithms employed for proportional–integral–derivative (PID) tuning typically operate within unconstrained search spaces, relying exclusively on time-domain error metrics like ITAE. This conventional approach causes ‘gradient blindness’ and neglects frequency-domain robustness, resulting in excessive temperature overshoots that violate biological safety limits and lead to enzyme denaturation. To solve this problem, we propose a hybrid frequency-time domain optimization framework. Utilizing a first order plus dead-time (FOPDT) model for TEC dynamics, the PID search space is analytically restricted via Ziegler–Nichol’s stability boundaries. Furthermore, Phase Margin (PM ≥ 45°) and absolute zero-overshoot conditions are integrated into the objective function as a strict penalty mechanism. Evaluations conducted with five distinct metaheuristic algorithms (PSO, GWO, WOA, ABC, and ACO) prove that while traditional unconstrained methods yield overshoots up to 19.04%, the proposed architecture successfully confines all optimization agents to a globally stable region, enabling specific algorithms like ABC, PSO, and WOA to achieve exactly 0.00% overshoot. Validated across a realistic multi-step PCR cycle (95–55–75 °C), the developed robust controller settles into the denaturation phase with a 0.00 °C peak error, guaranteeing biological sample safety and delivering a reliable control framework for rapid-cycle PCR platforms. Full article
(This article belongs to the Special Issue Energy Saving Management Systems: Challenges and Applications)
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41 pages, 18361 KB  
Article
Improved Educational Competition Optimizer for Prediction of Grades in Tourism Service Communication Courses
by Zhu Song, Yang Lv, Yutong Duan and Liehao Yang
Symmetry 2026, 18(6), 970; https://doi.org/10.3390/sym18060970 - 4 Jun 2026
Viewed by 227
Abstract
Accurate prediction of student performance and identification of key influencing factors are essential for improving teaching quality and enabling data-driven educational decision-making. However, conventional metaheuristic optimization algorithms often suffer from premature convergence, insufficient population diversity, and an inadequate balance between exploration and exploitation [...] Read more.
Accurate prediction of student performance and identification of key influencing factors are essential for improving teaching quality and enabling data-driven educational decision-making. However, conventional metaheuristic optimization algorithms often suffer from premature convergence, insufficient population diversity, and an inadequate balance between exploration and exploitation when solving complex optimization problems. To address these limitations, this study proposes an Improved Educational Competition Optimizer (IECO), which integrates three complementary strategies: an elite exemplar-guided cooperative learning mechanism to preserve population diversity, a rank-adaptive stage-wise search control strategy to dynamically regulate search intensity, and an elite-mean opposition-based refinement strategy to strengthen global exploration capability and local exploitation performance. To evaluate the effectiveness of the proposed method, IECO is applied to optimize the hyperparameters of the K-nearest neighbors (KNN) classifier, leading to the construction of an IECO-KNN grade prediction model. Extensive experiments conducted on the CEC2017 and CEC2022 benchmark suites demonstrate that IECO achieves superior optimization accuracy, faster convergence speed, and stronger robustness compared with several classical and advanced metaheuristic algorithms. Statistical analyses based on the Wilcoxon rank-sum test and Friedman ranking test further confirm the significance and stability of the proposed algorithm. Furthermore, experiments on a real-world educational dataset show that the proposed IECO-KNN model consistently outperforms the other optimization-based KNN models in terms of accuracy, Cohen’s Kappa coefficient, macro-precision, and macro-recall. In particular, the proposed model achieves the highest classification performance and demonstrates more stable prediction capability across independent runs. Correlation analysis further reveals that learning interest, classroom interaction frequency, and extracurricular information acquisition are the most influential factors affecting students’ academic performance. Overall, the proposed IECO and IECO-KNN framework provide an effective and reliable solution for complex optimization and intelligent educational prediction tasks, offering both theoretical contributions to swarm intelligence optimization and practical value for intelligent teaching evaluation systems. Full article
(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)
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31 pages, 1249 KB  
Review
Multi-Objective Harris Hawks Optimization: Principles, Variants, Applications, and Future Directions
by Sharif Naser Makhadmeh, Yousef Sanjalawe, Mohammed Azmi Al-Betar, Ahmad H. Sawalmeh and Mohammad Aladaileh
Algorithms 2026, 19(6), 453; https://doi.org/10.3390/a19060453 - 3 Jun 2026
Viewed by 271
Abstract
Multi-objective optimization problems (MOPs) are common in practical scenarios where decision-makers need to accomplish several competing goals. Single-objective optimization techniques do not guarantee applicability in these scenarios. As such, there has been a need for the development of metaheuristics capable of generating multiple [...] Read more.
Multi-objective optimization problems (MOPs) are common in practical scenarios where decision-makers need to accomplish several competing goals. Single-objective optimization techniques do not guarantee applicability in these scenarios. As such, there has been a need for the development of metaheuristics capable of generating multiple trade-off solutions. Harris Hawks Optimization (HHO) has been shown to possess strong exploration and exploitation capabilities for the solution of optimization problems, owing to the collaborative hunting tactics of Harris’s hawks. Therefore, the Multi-objective Harris Hawks Optimization (MHHO) algorithm was suggested to generalize HHO to handle MOPs. By combining the mechanisms of Pareto dominance, diversity preservation, elitism, adaptiveness, and others, MHHO approaches the Pareto-optimal front and provides decision-makers with several high-quality nondominated solutions. This study comprehensively examines MHHO, elaborating on its theoretical background, algorithmic variants, and fields of application. MHHO has been implemented in different disciplines. Using the Scopus database to conduct a bibliometric study, the publication growth, research development, and the application of MHHO in various fields of study were analyzed. By classifying the extant contributions into original, modified, and hybrid versions, the study provides a detailed outline of the algorithm’s progression. Applications spanning engineering, cloud computing, scheduling, networking, bioinformatics, and energy systems are analyzed, illustrating the broad adaptability of MHHO. A constructive critique has been conducted to evaluate some limitations including premature convergence, scalability issues, and difficulty in addressing disconnected Pareto regions. This review shows the versatility and potential of MHHO in tackling different optimization problems. In addition, further research is needed on the development of more sophisticated hybrid methods, tailored improvements, and more refined techniques for the preservation of diversity. Full article
(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)
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19 pages, 2734 KB  
Article
Predicting Shield Machine Penetration Rate Using the CTCM-DELM Algorithm
by Da Yuan, Dong Huang, Yu Lei, Minhao Wang, Ji Lu, Xude Li, Xuedong Luo and Yong Liu
Appl. Sci. 2026, 16(11), 5549; https://doi.org/10.3390/app16115549 - 2 Jun 2026
Viewed by 113
Abstract
The penetration rate (PR) is a critical indicator affecting the safety and cost of shield tunnel construction. However, due to the complexity of geological conditions and the nonlinear nature of tunneling parameters, traditional prediction methods struggle to achieve high-accuracy predictions. To address this [...] Read more.
The penetration rate (PR) is a critical indicator affecting the safety and cost of shield tunnel construction. However, due to the complexity of geological conditions and the nonlinear nature of tunneling parameters, traditional prediction methods struggle to achieve high-accuracy predictions. To address this issue, six hybrid deep extreme learning machine models were developed for PR prediction. Normalized mutual information (NMI) was employed to select key features, and an isolation forest (IForest) algorithm was employed to remove outliers and construct a valid dataset. Subsequently, deep extreme learning machines optimized using six metaheuristic algorithms were applied to predict the penetration rate. Finally, the key factors influencing tunneling rate prediction were identified based on SHAP analysis. The experimental results demonstrate that among the six optimized algorithm models, along with the BP neural network, uniaxial compressive strength (UCS), rock quality designation (RQD), and cutterhead torque were identified as key factors influencing PR. For the first time, the CTCM-DELM model is applied to predict the advance rate of shield tunneling. Combined with SHAP analysis, it is quantitatively revealed that the contribution of geological parameters is greater than that of equipment parameters, which provides novel insight for engineering practice. Full article
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47 pages, 14821 KB  
Article
Multi-Strategy Improved Love Evolutionary Algorithm for Global Optimization and Art Image Segmentation
by Zhengxing Yang, Liwei Liu and Junjun Li
Symmetry 2026, 18(6), 961; https://doi.org/10.3390/sym18060961 - 2 Jun 2026
Viewed by 124
Abstract
Although the Love Evolution Algorithm (LEA) has achieved encouraging results in optimization tasks, several shortcomings still limit its effectiveness when solving high-dimensional multimodal problems. In particular, the fixed interaction threshold, stochastic reflection mechanism, and convergence-biased role evolution process may weaken population diversity and [...] Read more.
Although the Love Evolution Algorithm (LEA) has achieved encouraging results in optimization tasks, several shortcomings still limit its effectiveness when solving high-dimensional multimodal problems. In particular, the fixed interaction threshold, stochastic reflection mechanism, and convergence-biased role evolution process may weaken population diversity and reduce the coordination between exploration and exploitation during evolution. To overcome these issues, this paper develops a Multi-Strategy Improved Love Evolution Algorithm (MILEA) under a phase-oriented cooperative evolutionary framework. First, a diversity-enhanced reflection mechanism is incorporated to enlarge the search region and dynamically regulate evolutionary dispersion during the early search stage. Second, an adaptive acceptance threshold strategy is introduced to adjust pairwise interaction behaviors according to the evolutionary state, thereby improving search flexibility and adaptability. Third, an elite-guided role evolution mechanism is designed to strengthen local exploitation and guide the population toward promising regions more efficiently. Furthermore, a probability-based collaborative update scheme is employed to coordinate multiple search behaviors adaptively while preserving the same computational complexity order as the original LEA framework. To evaluate the effectiveness of the proposed algorithm, extensive experiments are conducted on the CEC2017 and CEC2022 benchmark suites. The experimental results indicate that MILEA exhibits competitive optimization performance with respect to convergence behavior, solution accuracy, and optimization stability when compared with several advanced metaheuristic algorithms. Relative to the original LEA, the proposed method obtains improved average fitness values on most benchmark functions and significantly suppresses result fluctuations on several multimodal and hybrid optimization problems, indicating enhanced robustness during repeated independent runs. In addition, statistical evaluations based on the Wilcoxon signed-rank test and Friedman ranking analysis further support the reliability of the proposed optimization framework. To verify its practical applicability, MILEA is also applied to Otsu-based multi-threshold image segmentation tasks. Experimental results evaluated by PSNR, SSIM, and FSIM demonstrate that the proposed algorithm can generate high-quality segmentation results and preserve important structural image information. Overall, the proposed MILEA provides an effective optimization framework for both benchmark optimization and practical image segmentation applications. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
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43 pages, 20683 KB  
Article
A Human Behavior Optimization Algorithm Based on Legal and Ethical Constraints for Numerical Optimization and Practical Applications
by Changheng Li and Chengpeng Li
Symmetry 2026, 18(6), 958; https://doi.org/10.3390/sym18060958 - 2 Jun 2026
Viewed by 127
Abstract
This paper proposes an improved metaheuristic algorithm named LHBBO, which incorporates legal and moral constraints into a human behavior-based optimization framework to tackle the limitations of conventional methods in high-dimensional and multimodal problem spaces. Three key innovations are introduced: a dual-layer normative audit [...] Read more.
This paper proposes an improved metaheuristic algorithm named LHBBO, which incorporates legal and moral constraints into a human behavior-based optimization framework to tackle the limitations of conventional methods in high-dimensional and multimodal problem spaces. Three key innovations are introduced: a dual-layer normative audit mechanism that enforces hard legal and soft moral constraints during candidate evaluation; a jury-guided collaborative consultation strategy that diversifies search direction references; and a directional migration mechanism triggered by population diversity and stagnation metrics. The proposed LHBBO is evaluated on the CEC2017 and CEC2022 benchmark suites, where it demonstrates significantly better convergence behavior and solution quality compared to several state-of-the-art algorithms. Notably, in 100-dimensional tests, LHBBO improves optimization precision by over 97% relative to the standard HBBO. When applied to unsupervised visual anomaly detection in industrial settings using the M2AD dataset, LHBBO effectively optimizes key parameters of a collaborative discrepancy-based model. The resulting system achieves a 9.05% increase in pixel-level localization accuracy (AUPRO) compared to the baseline CDO model, confirming its practical utility in complex, non-convex industrial optimization tasks. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Optimization Algorithms)
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21 pages, 998 KB  
Article
Edge Server Placement by a Novel Hybrid Meta-Heuristic Algorithm with Alternating Iteration
by Weili Si, Zhifeng Zhang and Bo Wang
Digital 2026, 6(2), 44; https://doi.org/10.3390/digital6020044 - 2 Jun 2026
Viewed by 212
Abstract
With the rapid growth of edge computing applications, optimizing both edge server placement and task offloading decisions is critical for minimizing system latency in edge–cloud environments. However, these two problems are tightly coupled and jointly form a binary non-linear programming (BNLP) problem that [...] Read more.
With the rapid growth of edge computing applications, optimizing both edge server placement and task offloading decisions is critical for minimizing system latency in edge–cloud environments. However, these two problems are tightly coupled and jointly form a binary non-linear programming (BNLP) problem that is NP-hard. To address this challenge, this paper proposes a novel hybrid meta-heuristic algorithm with alternating iteration, which decouples the joint optimization into two interdependent subproblems: edge server placement and task offloading. These subproblems are solved alternately using particle swarm optimization (PSO) for placement and a genetic algorithm (GA) for offloading, respectively. PSO efficiently explores the discrete placement space under bound constraints, while GA effectively navigates the high-dimensional binary offloading space. Compact encoding schemes are designed to inherently satisfy problem constraints, reducing search overhead and improving convergence. The overall algorithm exhibits polynomial-time complexity, making it scalable for practical deployments. Extensive experiments comparing the proposed method against ten baseline algorithms demonstrate that it achieves the best latency with the smallest standard deviation. The results validate the effectiveness, robustness, and scalability of the proposed alternating iterative hybrid meta-heuristic approach for joint edge server placement and task offloading optimization. Full article
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