Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (3,758)

Search Parameters:
Keywords = metaheuristic

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
33 pages, 4978 KB  
Article
Smart Enforcement of Disability Parking: A Drone-Based License Plate Recognition and Staged Optimization Framework
by Hanaa ZainEldin, Tamer Ahmed Farrag, Shymaa G. Eladl, Malik Almaliki, Mahmoud Badawy and Mostafa A. Elhosseini
Urban Sci. 2026, 10(4), 212; https://doi.org/10.3390/urbansci10040212 - 15 Apr 2026
Abstract
Unauthorized occupation of parking spaces designated for individuals with disabilities remains a persistent challenge in urban environments, limiting accessibility and inclusive mobility. This paper proposes an integrated UAV-assisted enforcement framework that combines drone-based imaging, onboard license plate recognition (LPR), IoT connectivity, and a [...] Read more.
Unauthorized occupation of parking spaces designated for individuals with disabilities remains a persistent challenge in urban environments, limiting accessibility and inclusive mobility. This paper proposes an integrated UAV-assisted enforcement framework that combines drone-based imaging, onboard license plate recognition (LPR), IoT connectivity, and a staged optimization strategy for energy-aware surveillance. The framework employs a two-phase approach: first, it derives energy-efficient UAV activation patterns via sleep–active scheduling, followed by coverage maximization under energy constraints. The inherently multi-objective problem—balancing energy consumption, coverage, and redundancy—is addressed via a weighted-aggregation formulation, enabling efficient optimization with classical metaheuristic algorithms. Seven algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), Differential Evolution (DE), Artificial Bee Colony (ABC), and a Greedy baseline—are implemented in both conventional and staged variants to enable comprehensive evaluation. Experimental results demonstrate 32–45% reductions in energy consumption, over 95% coverage effectiveness, and 50–60% faster convergence compared to single-phase approaches, with all improvements statistically significant (p < 0.001). The proposed framework provides a scalable, practically deployable solution for intelligent enforcement of disability parking regulations while also enabling energy-efficient UAV coordination in smart urban monitoring systems. Full article
28 pages, 26837 KB  
Article
KA-IHO: A Kinematic-Aware Improved Hippo Optimization Algorithm for Collision-Free Mobile Robot Path Planning in Complex Grid Environments
by Chunhong Yuan, Yule Cai, Haohua Que, Yuting Pei, Xiang Zhang, Jiayue Xie, Qian Zhang, Lei Mu and Fei Qiao
Sensors 2026, 26(8), 2416; https://doi.org/10.3390/s26082416 - 15 Apr 2026
Abstract
Autonomous path planning in obstacle-dense environments remains challenging for swarm intelligence methods due to infeasible initialization, insufficient exploration–exploitation balance, and poor trajectory smoothness for real-robot execution. To address these issues, this paper proposes a Kinematic-Aware Improved Hippo Optimization algorithm (KA-IHO) for mobile robot [...] Read more.
Autonomous path planning in obstacle-dense environments remains challenging for swarm intelligence methods due to infeasible initialization, insufficient exploration–exploitation balance, and poor trajectory smoothness for real-robot execution. To address these issues, this paper proposes a Kinematic-Aware Improved Hippo Optimization algorithm (KA-IHO) for mobile robot path planning. The proposed method integrates four components: an elite safety pool initialization strategy to improve feasible solution generation in dense maps, a hierarchical elite-scout update mechanism to better balance global exploration and local exploitation, anti-stagnation mechanisms including a Population Stagnation Restart strategy and a 10-Direction Radial Micro-Search to guarantee high feasibility rates across all map complexities, and a late-stage Laplacian Line-of-Sight Ironing Operator to reduce path redundancy and improve trajectory smoothness. Comparative experiments are conducted on five reproducible grid maps with different complexity levels (40×40 and 80×80), where KA-IHO is evaluated against six representative algorithms, including HO, SBOA, PSO, GWO, ARO, and INFO, over 20 independent runs. The results show that KA-IHO consistently achieves collision-free planning and obtains lower mean fitness values with smaller standard deviations than the compared methods, indicating improved robustness and solution quality. In addition, hardware closed-loop experiments on a differential-drive mobile robot demonstrate that the planned paths can be executed reliably in real environments, with trajectory tracking errors controlled within ±4 cm. Full article
42 pages, 8620 KB  
Article
Multi-Strategy Improved Stellar Oscillation Optimizer for Heterogeneous UAV Task Allocation in Post-Disaster Rescue
by Min Ding, Jing Du, Yijing Wang and Yue Lu
Drones 2026, 10(4), 288; https://doi.org/10.3390/drones10040288 - 15 Apr 2026
Abstract
To address load–energy dynamic coupling in heterogeneous unmanned aerial vehicle (UAV) emergency rescue, this paper proposes an energy-coupled heterogeneous UAV task allocation (EC-HUTA) model that explicitly characterizes nonlinear interdependencies among payload, velocity, and power consumption, minimizing aggregate mission costs subject to physical and [...] Read more.
To address load–energy dynamic coupling in heterogeneous unmanned aerial vehicle (UAV) emergency rescue, this paper proposes an energy-coupled heterogeneous UAV task allocation (EC-HUTA) model that explicitly characterizes nonlinear interdependencies among payload, velocity, and power consumption, minimizing aggregate mission costs subject to physical and temporal constraints. To tackle the resulting high-dimensional, nonconvex problem, we introduce a multi-strategy improved stellar oscillation optimizer (MISOO), establishing a closed-loop synergistic system through three coupled stages: (i) evolutionary game-theoretic strategy competition via replicator dynamics for adaptive exploration–exploitation balance; (ii) intuitionistic fuzzy entropy (IFE)-driven dimension-wise parameter control, where IFE calibrates global exploration intensity while dimension-specific crossover probabilities accommodate heterogeneous convergence; and (iii) memory-driven differential escape mechanisms modulated by historical memory parameters to evade local optima. Cross-stage coupling through IFE ensures state information flows across the “strategy selection-refined search-dynamic escape” pipeline. Coupled with a dual-layer encoding scheme, this framework ensures efficient feasible search. Ablation studies validate each mechanism’s contribution. Evaluations on CEC2017 benchmarks demonstrate MISOO’s superior convergence against six metaheuristics. Large-scale earthquake rescue simulations confirm that EC-HUTA/MISOO strictly adheres to nonlinear energy constraints while enhancing task completion and temporal compliance. These results validate the framework’s efficacy for time-critical emergency resource allocation. Full article
Show Figures

Figure 1

43 pages, 5163 KB  
Article
Research on Path Planning for Fire Evacuation Using the Enhanced Hiking Optimization Algorithm
by Faguo Zhou, Yi Wu, Zhe You, Shuyu Yao, Kaile Lyu, Menglin Chen and Jianshen Yang
Biomimetics 2026, 11(4), 272; https://doi.org/10.3390/biomimetics11040272 - 15 Apr 2026
Abstract
To address the key challenges in fire evacuation path planning, such as the tendency to converge to local optima, unbalanced computational efficiency, and suboptimal path quality, this study proposes the enhanced Hiking Optimization Algorithm of Differentiated Weighted Dynamic (WDHOA). The WDHOA integrates a [...] Read more.
To address the key challenges in fire evacuation path planning, such as the tendency to converge to local optima, unbalanced computational efficiency, and suboptimal path quality, this study proposes the enhanced Hiking Optimization Algorithm of Differentiated Weighted Dynamic (WDHOA). The WDHOA integrates a three-phase cooperative framework, incorporating dynamic grouping, hybrid search, and angle generation. Comprehensive evaluations on the CEC 2017 and CEC 2022 benchmark suites demonstrate that WDHOA significantly outperforms eight widely used algorithms, such as LSHADE, RIME, SCA in convergence accuracy, stability, and robustness, especially for high-dimensional and multimodal functions. Wilcoxon rank-sum tests and Friedman tests confirm statistical significance across most functions. Ablation experiment further verifies the effectiveness of the three enhanced strategies. When applied to fire evacuation path planning, WDHOA achieves the best solutions while satisfying all nonlinear constraints. These experiments confirm that WDHOA effectively balance optimization accuracy and practical applicability in fire evacuation path planning problems. Full article
(This article belongs to the Special Issue Advances in Biological and Bio-Inspired Algorithms: 2nd Edition)
Show Figures

Figure 1

45 pages, 7429 KB  
Article
An Improved Genghis Khan Shark Optimization Algorithm for Solving Optimization Problems
by Yanjiao Wang and Jiaqi Wang
Biomimetics 2026, 11(4), 270; https://doi.org/10.3390/biomimetics11040270 - 14 Apr 2026
Abstract
As an innovative metaheuristic algorithm, Genghis Khan Shark Optimization (GKSO) faces challenges, including a tendency towards local optima and poor convergence speed and accuracy. To mitigate these limitations, an improved Genghis Khan shark optimizer (IGKSO) is proposed in this paper. A population partitioning [...] Read more.
As an innovative metaheuristic algorithm, Genghis Khan Shark Optimization (GKSO) faces challenges, including a tendency towards local optima and poor convergence speed and accuracy. To mitigate these limitations, an improved Genghis Khan shark optimizer (IGKSO) is proposed in this paper. A population partitioning method based on cosine similarity and fitness is introduced, where individuals are strategically assigned to different evolutionary phases: Disadvantaged populations are responsible for the foraging stage. By contrast, advantaged populations dominate the moving stage. In the moving stage, the base vector is randomly selected from multiple candidates, which ensures the evolutionary direction of the population while maintaining its diversity. An adaptive step-size mechanism is introduced to avoid boundary overflow problems. A subspace method is employed to prevent diversity loss during foraging. Additionally, in the hunting stage, a novel opposition-based learning strategy is proposed to moderate the tendency of converging to suboptimal solutions. Furthermore, during the self-protection phase, a criterion for assessing the diversity of the whole population is employed to monitor and supplement diversity in real time. The results of the CEC2017 and CEC2019 benchmark test sets reveal that IGKSO exhibits substantial advantages over the GKSO algorithm and eight other high-performance algorithms in terms of convergence speed and accuracy. Full article
(This article belongs to the Special Issue Bio-Inspired Optimization Algorithms)
56 pages, 1525 KB  
Systematic Review
A Systematic Review of Electric Vehicle Optimization Problems: Taxonomy, Methods, and Research Challenges
by Lucero Ortiz-Aguilar, Marcela Palacios-Ortega, Martin Carpio and Julio Funes-Tapia
Automation 2026, 7(2), 61; https://doi.org/10.3390/automation7020061 - 14 Apr 2026
Abstract
The rapid integration of electric vehicles (EVs) into transportation systems and power grids has significantly increased the complexity of optimization challenges related to routing, charging coordination, scheduling, and energy management. Despite significant research growth, the field remains conceptually fragmented, lacking a unified framework [...] Read more.
The rapid integration of electric vehicles (EVs) into transportation systems and power grids has significantly increased the complexity of optimization challenges related to routing, charging coordination, scheduling, and energy management. Despite significant research growth, the field remains conceptually fragmented, lacking a unified framework to systematically organize Electric Vehicle Optimization Problems (EVOPs). To address this gap, this study presents a systematic review of 144 peer-reviewed articles published between 2011 and January 2025 and proposes a structured EVOP taxonomy based on problem characteristics and dominant decision variables. The analysis examines mathematical formulations, solution methodologies, and emerging research trends. The results indicate the predominance of metaheuristic methods, while exact techniques are mainly limited to small-scale problems. Additionally, there is a growing trend toward multi-objective and stochastic models that incorporate uncertainty and dynamic decision-making environments. However, challenges remain regarding large-scale validation, standardized benchmarking, and integrated multi-domain modeling. The proposed taxonomy provides a coherent framework that facilitates comparison across optimization domains and supports the development of scalable and intelligent EV management systems. Full article
(This article belongs to the Section Smart Transportation and Autonomous Vehicles)
48 pages, 9238 KB  
Article
Spherical Coordinate System-Based Fusion Path Planning Algorithm for UAVs in Complex Emergency Rescue and Civil Environments
by Xingyi Pan, Xingyu He, Xiaoyue Ren and Duo Qi
Drones 2026, 10(4), 285; https://doi.org/10.3390/drones10040285 - 14 Apr 2026
Abstract
This study proposes a heterogeneous fusion path planning framework for unmanned aerial vehicles (UAVs) operating in complex emergency rescue and civil environments. Existing single-mechanism metaheuristics—including Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithms (GAs)—suffer from fundamental limitations in three-dimensional kinematic [...] Read more.
This study proposes a heterogeneous fusion path planning framework for unmanned aerial vehicles (UAVs) operating in complex emergency rescue and civil environments. Existing single-mechanism metaheuristics—including Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Genetic Algorithms (GAs)—suffer from fundamental limitations in three-dimensional kinematic path planning: PSO converges rapidly but stagnates at local optima due to population variance collapse; ACO offers robust local exploitation but incurs prohibitive cold-start overhead; GAs maintain diversity at the cost of expensive crossover operations. To address these complementary deficiencies simultaneously, the proposed framework introduces a spherical coordinate representation that reduces computational complexity and naturally enforces UAV kinematic constraints, combined with adaptive weight factors and a serial PSO-ACO fusion strategy, and subsequently incorporates adaptive weight factors. A serial fusion strategy is then introduced, wherein the sub-optimal trajectory generated by the Spherical PSO phase is mapped into the ACO pheromone field via a Gaussian Kernel Density Mapping (GKDM) mechanism, enabling the ACO phase to perform fine-grained local exploitation within a kinematically feasible corridor. Various constraints along the flight path are formulated into distinct cost functions, which cover aircraft track length, pitch angle variation, altitude difference variation, obstacle avoidance, and smoothness; the core task of the algorithm is to find the flight path with the minimum total cost. The proposed algorithm is dedicated to UAV path planning in complex emergency rescue environments (disaster-stricken areas, hazardous zones) and is further applicable to civil low-altitude logistics delivery, industrial facility inspection, ecological environment monitoring and urban air mobility (UAM) scenarios with complex obstacle constraints. It can effectively improve the safety and efficiency of UAVs in reaching rescue points, delivering emergency supplies, conducting disaster surveys, and completing various civil low-altitude operation tasks. Full article
(This article belongs to the Section Innovative Urban Mobility)
23 pages, 3264 KB  
Article
Design and Optimization of a Two-Tier Supply Chain Network Under Demand Uncertainty Using a Genetic Algorithm and Particle Swarm Optimization
by Sena Nur Durgunlu, Aytun Onay, Durdu Hakan Utku and Fatih Kasimoglu
Appl. Sci. 2026, 16(8), 3817; https://doi.org/10.3390/app16083817 - 14 Apr 2026
Abstract
Supply chain management (SCM) involves complex coordination among multiple actors under demand uncertainty. However, most existing studies focus on simplified network structures that fail to capture all relevant dimensions of real-world supply chains or assume deterministic demand. This study proposes a comprehensive stochastic [...] Read more.
Supply chain management (SCM) involves complex coordination among multiple actors under demand uncertainty. However, most existing studies focus on simplified network structures that fail to capture all relevant dimensions of real-world supply chains or assume deterministic demand. This study proposes a comprehensive stochastic bi-level optimization framework for a multi-factory, multi-retailer, multi-customer, and multi-product supply chain network. The model captures the hierarchical interaction between decision-makers, where the production facility owner acts as the leader and the retailer as the follower, and jointly optimizes profit across both levels. To efficiently solve the resulting bi-level problem, two tailored metaheuristic solution approaches—a two-tier genetic algorithm (TT-GA) and a two-tier particle swarm optimization (TT-PSO)—are developed. Computational experiments across multiple scenarios demonstrate that TT-PSO outperforms TT-GA in Scenarios 1 and 2, achieving overall profit improvements of 6.46% and 0.76%, respectively, while TT-GA yields superior performance in Scenario 3 with a 2.80% profit improvement. The proposed framework provides decision-makers with a robust and practical tool for improving profitability and operational efficiency in complex, uncertain supply chain environments. Full article
19 pages, 3225 KB  
Article
Metaheuristic Optimized Random Forest Regression with Streamlit Web Application for Predicting Jute Yarn Tenacity
by Nageshkumar T, Avijit Das, Sanjoy Debnath and D. B. Shakyawar
Textiles 2026, 6(2), 46; https://doi.org/10.3390/textiles6020046 - 14 Apr 2026
Abstract
Yarn tenacity is one of the vital quality parameters that determine the performance, fabric durability and end use suitability. The tenacity of yarn is largely influenced by the fibre characteristics used. The physical properties of jute fibres, including root content, defect, bundle strength, [...] Read more.
Yarn tenacity is one of the vital quality parameters that determine the performance, fabric durability and end use suitability. The tenacity of yarn is largely influenced by the fibre characteristics used. The physical properties of jute fibres, including root content, defect, bundle strength, and fineness, exert a significant influence on yarn tenacity. This study utilized metaheuristic optimized random forest regression (RFR) to predict jute yarn tenacity from fibre parameters. The hyperparameters of the RFR models were optimized using four metaheuristic algorithms: whale optimization algorithm (WOA), grey wolf optimization (GWO), beetle antennae search (BAS) and ant colony optimization (ACO). The model utilized a dataset comprising 414 experimental data with 70% data for training and 30% for testing the model, using input variables such as bundle strength (g/tex), defects (%), root content (%) and fineness (tex) to predict yarn tenacity (cN/tex). The developed models effectively predicted yarn tenacity. However, RFR–GWO achieved slightly better performance with R2 of 1.0 for training set and 0.96 for test set. Regarding execution time, RFR–GWO is the fastest requiring only 14.25 s. SHAP analysis revealed that bundle strength and root content of jute fibre are the most influential factors, whereas defect and fineness exert the least influence on model’s prediction. The best model RFR–GWO was deployed into an interactive Streamlit web application, offering an intuitive and user-friendly platform for the real-time estimation of yarn tenacity. Full article
Show Figures

Figure 1

24 pages, 2758 KB  
Review
Optimization in Chemical Engineering: A Systematic Review of Its Evolution, State of the Art, and Emerging Trends
by Carlos Antonio Padilla-Esquivel, Gema Báez-Barrón, Carlos Daniel Gil-Cisneros, Diana Karen Zavala-Vega, Eduardo García-García, Vanessa Villazón-León, Heriberto Alcocer-García, Fabricio Nápoles-Rivera, César Ramírez-Márquez and José María Ponce-Ortega
Processes 2026, 14(8), 1247; https://doi.org/10.3390/pr14081247 - 14 Apr 2026
Abstract
Optimization has played a fundamental role in the evolution of chemical engineering, enabling systematic decision-making under technical, economic, and environmental constraints. This review presents a structured and comparative analysis of the historical development and current state of optimization methodologies applied to chemical engineering, [...] Read more.
Optimization has played a fundamental role in the evolution of chemical engineering, enabling systematic decision-making under technical, economic, and environmental constraints. This review presents a structured and comparative analysis of the historical development and current state of optimization methodologies applied to chemical engineering, covering the transition from early linear and nonlinear programming approaches to advanced data-driven and artificial intelligence-based frameworks. A systematic literature review was conducted following the PRISMA guidelines, through which a total of 101 articles were retained for analysis. The results indicate that mixed-integer programming and decomposition-based methods remain widely adopted for structured industrial problems, while metaheuristic and hybrid data-driven approaches have experienced significant growth in recent years. In particular, a clear trend toward the integration of machine learning and surrogate modeling techniques is observed, driven by the need to address large-scale, non-convex, and highly nonlinear systems. The analysis reveals a clear methodological shift from classical linear optimization frameworks toward hybrid optimization strategies capable of addressing large-scale, non-convex, and highly nonlinear problems. Finally, current challenges and future research directions are identified, emphasizing the need for robust hybrid approaches that combine mathematical programming and intelligent algorithms to effectively manage complexity in next-generation chemical systems. Full article
Show Figures

Figure 1

33 pages, 970 KB  
Article
A Modular Adaptive Hybrid Metaheuristic Based on Distributed Population Evolution for 2D Irregular Packing Problems
by Shuo Liu, Fu Zhao and Yanjue Gong
Mathematics 2026, 14(8), 1301; https://doi.org/10.3390/math14081301 - 13 Apr 2026
Abstract
This paper addresses the NP-hard 2D irregular packing problem with non-convex geometric constraints. We propose a distributed hybrid metaheuristic based on an island population structure, integrating a genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and a grey wolf optimizer (GWO), [...] Read more.
This paper addresses the NP-hard 2D irregular packing problem with non-convex geometric constraints. We propose a distributed hybrid metaheuristic based on an island population structure, integrating a genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and a grey wolf optimizer (GWO), with a novel Modular Adaptive Optimization Module (MAOM). The passivity and stability of the MAOM are rigorously proven via a Lyapunov energy function. The convergence rate of the island model is proven to be O(Tmax/K), demonstrating linear speedup. Extensive experiments on 11 benchmark datasets show that the proposed algorithm achieves material utilization ranging from 61.73% to 79.42% with excellent stability (CV<0.03). Statistical tests confirm significant improvements over traditional metaheuristics (p<0.05). This work provides a theoretically grounded and practically effective approach for 2D irregular nesting. Full article
26 pages, 1640 KB  
Article
Integrated Optimization Framework for AS/RS: Coupling Storage Allocation, Collaborative Scheduling, and Path Planning via Hybrid Meta-Heuristics
by Dingnan Zhang, Boyang Liu, Enqi Yue and Dongsheng Wu
Appl. Sci. 2026, 16(8), 3757; https://doi.org/10.3390/app16083757 - 11 Apr 2026
Viewed by 208
Abstract
Automated Storage and Retrieval Systems (AS/RSs) are pivotal hubs in modern intelligent logistics, yet their operational efficiency is often constrained by the complex coupling of storage allocation, equipment scheduling, and path planning. This study proposes a systematic optimization framework to address these three [...] Read more.
Automated Storage and Retrieval Systems (AS/RSs) are pivotal hubs in modern intelligent logistics, yet their operational efficiency is often constrained by the complex coupling of storage allocation, equipment scheduling, and path planning. This study proposes a systematic optimization framework to address these three critical control challenges. First, a multi-objective mathematical model for storage location allocation is established, considering efficiency, stability, and correlation. To solve this high-dimensional discrete problem, a Tabu Variable Neighborhood Search (TVNS) algorithm is proposed, integrating short-term memory mechanisms with multi-structure exploration to prevent premature convergence. Second, regarding stacker crane and forklift collaborative scheduling, a Pheromone-guided Artificial Hummingbird Algorithm (PT-AHA) is introduced. By incorporating pheromone feedback into foraging behavior, the algorithm significantly enhances global search capability to minimize total task completion time. Third, stacker crane path planning is modeled as a constrained Traveling Salesman Problem (TSP) and solved using a hybrid Simulated Annealing-Whale Optimization Algorithm (SA-WOA). Quantitative simulation results demonstrate that the TVNS algorithm improves storage allocation fitness by 1.1% over standard Genetic Algorithms, while the PT-AHA reduces task completion time (Makespan) by 21.9% for small-scale batches and consistently outperforms ACO by up to 3.6% in large-scale operations. Validation through an Intelligent Warehouse Management System (WMS) confirms that the integrated framework maintains high industrial resilience by triggering fault alarms and initiating recovery within 3.2 s during simulated equipment failures, providing a robust solution for enterprise-level deployments. Full article
(This article belongs to the Section Applied Industrial Technologies)
Show Figures

Figure 1

44 pages, 2847 KB  
Article
Advances in Optimal Reactive Power Dispatch: Formulations, Solution Approaches, and Future Directions
by Edgar E. Tibaduiza-Rincón, Walter M. Villa-Acevedo and Jesús M. López-Lezama
Processes 2026, 14(8), 1229; https://doi.org/10.3390/pr14081229 - 11 Apr 2026
Viewed by 120
Abstract
This paper provides a comprehensive analysis of the Optimal Reactive Power Dispatch (ORPD) problem, focusing on its mathematical formulations and the methodologies employed to solve it. This paper systematically categorizes the problem into single-objective and multi-objective formulations, as well as single-period and multi-period [...] Read more.
This paper provides a comprehensive analysis of the Optimal Reactive Power Dispatch (ORPD) problem, focusing on its mathematical formulations and the methodologies employed to solve it. This paper systematically categorizes the problem into single-objective and multi-objective formulations, as well as single-period and multi-period models, and addresses both single-area and multi-area operational frameworks. It explores a broad range of optimization techniques used to tackle the ORPD problem, including classical optimization methods, metaheuristic algorithms, and hybrid approaches. Additionally, this paper discusses the incorporation of uncertainty in ORPD models, highlighting methods to account for the stochastic nature of power systems. A critical assessment of the current literature identifies existing knowledge gaps and outlines promising future research directions. This paper aims to provide researchers with a thorough understanding of the ORPD problem, offering insights into emerging trends and areas for further exploration. Full article
(This article belongs to the Special Issue Optimization and Analysis of Energy System)
40 pages, 3974 KB  
Article
Particle Swarm Optimization Based on Cubic Chaotic Mapping and Random Differential Mutation
by Xingrui Li and Ying Guo
Algorithms 2026, 19(4), 297; https://doi.org/10.3390/a19040297 - 10 Apr 2026
Viewed by 183
Abstract
Particle swarm optimization is a metaheuristic optimization algorithm that boasts advantages such as fast convergence speed, fewer tunable parameters, and a simple search mechanism. However, it suffers from premature convergence and insufficient later-stage exploitation, limiting its performance on multimodal and high-dimensional problems. In [...] Read more.
Particle swarm optimization is a metaheuristic optimization algorithm that boasts advantages such as fast convergence speed, fewer tunable parameters, and a simple search mechanism. However, it suffers from premature convergence and insufficient later-stage exploitation, limiting its performance on multimodal and high-dimensional problems. In light of this, this paper proposes a Chaos-based Differential Mutation Particle Swarm Optimization (CDMPSO) algorithm to address these limitations. The algorithm employs four synergistic strategies: cubic chaotic mapping with inverse learning for population initialization; adaptive inertia weight to balance exploration and exploitation; convex lens imaging inverse learning to escape local optima; and random differential mutation to maintain population diversity. Ablation experiments validate the contribution of each strategy, with adaptive weight being the most significant. Comparative experiments demonstrate that CDMPSO achieves an average ranking of 1.00, outperforming standard PSO, CPSO (Constriction Particle Swarm Optimization), ACPSO (Adaptive Chaotic Particle Swarm Optimization), and HPSOALS (Hybrid Particle Swarm Optimization with Adaptive Learning Strategy). On the unimodal function f1, it attains ultra-high precision of 7.07 × 10−248, and on the multimodal function f9, it uniquely converges to the theoretical optimum of zero. The results demonstrate that CDMPSO possesses excellent convergence precision, global search capability, and robustness, providing an effective solution for complex engineering optimization problems. Full article
(This article belongs to the Section Evolutionary Algorithms and Machine Learning)
Show Figures

Figure 1

37 pages, 1073 KB  
Article
Optimizing the Classic and the Energy-Efficient Permutation Flowshop Scheduling Problem with a Hybrid Tyrannosaurus Rex Optimization Algorithm
by Maria Tsiftsoglou, Yannis Marinakis and Magdalene Marinaki
Biomimetics 2026, 11(4), 262; https://doi.org/10.3390/biomimetics11040262 - 10 Apr 2026
Viewed by 129
Abstract
This paper introduces a Hybrid Tyrannosaurus Rex Optimization Algorithm (Hybrid TROA) combined with Variable Neighborhood Search (VNS), two variations of the Path Relinking strategy, and a randomized Nawaz–Enscore–Ham (NEH) heuristic to address the Permutation Flowshop Scheduling Problem (PFSP). The TROA is a novel [...] Read more.
This paper introduces a Hybrid Tyrannosaurus Rex Optimization Algorithm (Hybrid TROA) combined with Variable Neighborhood Search (VNS), two variations of the Path Relinking strategy, and a randomized Nawaz–Enscore–Ham (NEH) heuristic to address the Permutation Flowshop Scheduling Problem (PFSP). The TROA is a novel bio-inspired meta-heuristic algorithm modeled on the hunting behavior of the prehistoric Tyrannosaurus Rex. Leveraging the potential of this newly developed and efficient algorithm, we propose a framework in which an initial population of solutions is generated using the randomized NEH heuristic. These solutions are then further optimized through VNS and Path Relinking, yielding highly satisfactory results for the PFSP. First, we consider two optimization criteria separately: the makespan and the total flow time. Next, we conduct a comparative study of the Hybrid TROA against other prominent meta-heuristics, along with a statistical analysis using non-parametric tests, to determine the best-performing method for each objective. According to our findings, the Hybrid TROA proves to be the most suitable method in this study for minimizing both targets. Finally, recognizing that contemporary industry demands both high productivity and energy efficiency, we propose an energy-efficient version of the classic PFSP, simultaneously considering two criteria for optimization: the makespan and total energy consumption. Our study introduces a novel objective function that achieves balanced optimization by integrating both criteria. Full article
Back to TopTop