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Search Results (185)

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Keywords = evolutionary metaheuristic algorithm

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16 pages, 1491 KiB  
Article
An Effective Hybrid Metaheuristic Approach Based on the Genetic Algorithm
by Olympia Roeva, Dafina Zoteva, Gergana Roeva, Maya Ignatova and Velislava Lyubenova
Mathematics 2024, 12(23), 3815; https://doi.org/10.3390/math12233815 - 2 Dec 2024
Viewed by 507
Abstract
This paper presents an effective hybrid metaheuristic algorithm combining the genetic algorithm (GA) and a simple algorithm based on evolutionary computation. The evolutionary approach (EA) is applied to form the initial population of the GA, thus improving the algorithm’s performance, especially its convergence [...] Read more.
This paper presents an effective hybrid metaheuristic algorithm combining the genetic algorithm (GA) and a simple algorithm based on evolutionary computation. The evolutionary approach (EA) is applied to form the initial population of the GA, thus improving the algorithm’s performance, especially its convergence speed. To assess its effectiveness, the proposed hybrid algorithm, the EAGA, is evaluated on selected benchmark functions, as well as on a real optimisation process. The EAGA is used to identify parameters in a nonlinear system of differential equations modelling an E. coli fed-batch fermentation process. The obtained results are compared against published results from hybrid metaheuristic algorithms applied to the selected optimisation problems. The EAGA hybrid outperforms the competing algorithms due to its effective initial population generation strategy. The risk of premature convergence is reduced. Better numerical outcomes are achieved. The investigations validate the potential of the proposed hybrid metaheuristic EAGA for solving real complex nonlinear optimisation tasks. Full article
(This article belongs to the Section Mathematical Biology)
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<p>Pseudo-code of the hybrid EAGA.</p>
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<p>Model predictions of the process variables (biomass and substrate)—time profiles.</p>
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<p>EAGA hybrid model results—scatter plot.</p>
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<p>EAGA hybrid—convergence curves.</p>
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<p>Comparison of hybrid algorithm performance—box plot of objective function evaluations over 30 runs.</p>
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<p>Comparison of hybrid algorithm performance—histograms of objective function evaluations over 30 runs.</p>
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23 pages, 10196 KiB  
Article
10 MW FOWT Semi-Submersible Multi-Objective Optimization: A Comparative Study of PSO, SA, and ACO
by Souleymane Drabo, Siqi Lai, Hongwei Liu and Xiangheng Feng
Energies 2024, 17(23), 5914; https://doi.org/10.3390/en17235914 - 25 Nov 2024
Viewed by 424
Abstract
The present study aims to carry out a comparative Multi-Objective Optimization (MOO) of a 10 MW FOWT semi-submersible using three different metaheuristic optimization techniques and a sophisticated approach for optimizing a floating platform. This novel framework enables highly efficient 3D plots, an optimization [...] Read more.
The present study aims to carry out a comparative Multi-Objective Optimization (MOO) of a 10 MW FOWT semi-submersible using three different metaheuristic optimization techniques and a sophisticated approach for optimizing a floating platform. This novel framework enables highly efficient 3D plots, an optimization loop, and the automatic and comparative output of solutions. Python, the main interface, integrated PyMAPDL and Pymoo for intricate modeling and simulation tasks. For this case study, the ZJUS10 Floating Offshore Wind Turbine (FOWT) platform, developed by the state key laboratory of mechatronics and fluid power at Zhejiang University, was employed as the basis. Key criteria such as platform stability, overall structural mass, and stress were pivotal in formulating the objective functions. Based on a preliminary study, the three metaheuristic optimization algorithms chosen for optimization were Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Ant Colony Optimization (ACO). Then, the solutions were evaluated based on Pareto dominance, leading to a Pareto front, a curve that represents the best possible trade-offs among the objectives. Each algorithm’s convergence was meticulously evaluated, leading to the selection of the optimal design solution. The results evaluated in simulations elucidate the strengths and limitations of each optimization method, providing valuable insights into their efficacy for complex engineering design challenges. In the post-processing phase, the performances of the optimized FOWT platforms were thoroughly compared both among themselves and with the original model, resulting in validation. Finally, the ACO algorithm delivered a highly effective solution within the framework, achieving reductions of 19.8% in weight, 40.1% in pitch, and 12.7% in stress relative to the original model. Full article
(This article belongs to the Section K: State-of-the-Art Energy Related Technologies)
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<p>ZJUS10 platform and coordinate system.</p>
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<p>The aerodynamic loads of a blade element.</p>
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<p>ZJUS10 FOWT system aerodynamic analysis.</p>
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<p>ZJUS10 catenary mooring system.</p>
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<p>Mooring load analysis from AQWA. (<b>a</b>) Mooring lines in CDM − wind force; (<b>b</b>) mooring lines in CDM + wind force.</p>
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<p>Hydrodynamic diffraction and response in AQWA. (<b>a</b>) AQWA hydrodynamic diffraction; (<b>b</b>) AQWA hydrodynamic response; (<b>c</b>) RAO-based rotation in hydrodynamic diffraction; (<b>d</b>) RAO-based translation in hydrodynamic diffraction; (<b>e</b>) radiation damping; (<b>f</b>) added mass; (<b>g</b>) ZJUS10 RAO-based CDM response under regular waves; (<b>h</b>) ZJUS10 actual CDM response under regular waves; (<b>i</b>) ZJUS10 RAO-based 6DOF CDM response under irregular waves; (<b>j</b>) ZJUS10 actual 6DOF CDM response under irregular waves.</p>
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<p>Hydrodynamic diffraction and response in AQWA. (<b>a</b>) AQWA hydrodynamic diffraction; (<b>b</b>) AQWA hydrodynamic response; (<b>c</b>) RAO-based rotation in hydrodynamic diffraction; (<b>d</b>) RAO-based translation in hydrodynamic diffraction; (<b>e</b>) radiation damping; (<b>f</b>) added mass; (<b>g</b>) ZJUS10 RAO-based CDM response under regular waves; (<b>h</b>) ZJUS10 actual CDM response under regular waves; (<b>i</b>) ZJUS10 RAO-based 6DOF CDM response under irregular waves; (<b>j</b>) ZJUS10 actual 6DOF CDM response under irregular waves.</p>
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<p>Hydrodynamic diffraction and response in AQWA. (<b>a</b>) AQWA hydrodynamic diffraction; (<b>b</b>) AQWA hydrodynamic response; (<b>c</b>) RAO-based rotation in hydrodynamic diffraction; (<b>d</b>) RAO-based translation in hydrodynamic diffraction; (<b>e</b>) radiation damping; (<b>f</b>) added mass; (<b>g</b>) ZJUS10 RAO-based CDM response under regular waves; (<b>h</b>) ZJUS10 actual CDM response under regular waves; (<b>i</b>) ZJUS10 RAO-based 6DOF CDM response under irregular waves; (<b>j</b>) ZJUS10 actual 6DOF CDM response under irregular waves.</p>
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<p>ZJUS10 stress analysis.</p>
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<p>Sensitivity analysis of ZJUS10.</p>
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<p>Manufactured platform and experiment setup.</p>
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<p>Optimization methodology.</p>
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<p>ZJUS10 stress FEA and stress computation in PyMAPDL.</p>
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<p>Flow charts of PSO (<b>a</b>), SA (<b>b</b>), and ACO (<b>c</b>) [<a href="#B53-energies-17-05914" class="html-bibr">53</a>,<a href="#B54-energies-17-05914" class="html-bibr">54</a>].</p>
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<p>3D Pareto fronts generated with PSO, SA, and ACO.</p>
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<p>Optimized models built on PyMAPDL.</p>
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<p>Mass evaluation.</p>
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<p>Von Mises stress results from PyMAPDL.</p>
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<p>Stability analysis. (<b>a</b>) PSOX CDM under regular waves; (<b>b</b>) PSOX CDM under irregular waves; (<b>c</b>) SAX CDM under regular waves; (<b>d</b>) SAX CDM under irregular waves; (<b>e</b>) ACOX CDM under regular waves; (<b>f</b>) ACOX CDM under irregular waves.</p>
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<p>Stability analysis. (<b>a</b>) PSOX CDM under regular waves; (<b>b</b>) PSOX CDM under irregular waves; (<b>c</b>) SAX CDM under regular waves; (<b>d</b>) SAX CDM under irregular waves; (<b>e</b>) ACOX CDM under regular waves; (<b>f</b>) ACOX CDM under irregular waves.</p>
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44 pages, 3247 KiB  
Article
Enhancing Metaheuristic Algorithm Performance Through Structured Population and Evolutionary Game Theory
by Héctor Escobar-Cuevas, Erik Cuevas, Alberto Luque-Chang, Oscar Barba-Toscano and Marco Pérez-Cisneros
Mathematics 2024, 12(23), 3676; https://doi.org/10.3390/math12233676 - 24 Nov 2024
Viewed by 487
Abstract
Diversity is crucial for metaheuristic algorithms. It prevents early convergence, balances exploration and exploitation, and helps to avoid local optima. Traditional metaheuristic algorithms tend to rely on a single strategy for generating new solutions, often resulting in a lack of diversity. In contrast, [...] Read more.
Diversity is crucial for metaheuristic algorithms. It prevents early convergence, balances exploration and exploitation, and helps to avoid local optima. Traditional metaheuristic algorithms tend to rely on a single strategy for generating new solutions, often resulting in a lack of diversity. In contrast, employing multiple strategies encourages a variety of search behaviors and a diverse pool of potential solutions, thereby improving the exploration of the search space. Evolutionary Game Theory (EGT) modifies agents’ strategies through competition, promoting successful strategies and eliminating weaker ones. Structured populations, as opposed to unstructured ones, preserve diverse strategies through localized competition, meaning that an individual’s strategy is influenced by only a subset or group of the population and not all elements. This paper presents a novel metaheuristic method based on EGT applied to structured populations. Initially, individuals are positioned near optimal regions using the Metropolis–Hastings algorithm. Subsequently, each individual is endowed with a unique search strategy. Considering a certain number of clusters, the complete population is segmented. Within these clusters, the method enhances search efficiency and solution quality by adapting all strategies through an intra-cluster competition. To assess the effectiveness of the proposed method, it has been compared against several well-known metaheuristic algorithms across a suite of 30 test functions. The results indicated that the new methodology outperformed the established techniques, delivering higher-quality solutions and faster convergence rates. Full article
(This article belongs to the Section Mathematics and Computer Science)
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<p>Visual representation of the population segmentation process. (<bold>a</bold>) Objective function’s shape along with a contour map, (<bold>b</bold>) distribution of 50 individuals, (<bold>c</bold>) results of the application of the K-means algorithm considering seven distinct groups <inline-formula><mml:math id="mm389"><mml:semantics><mml:mrow><mml:mfenced open="{" close="}" separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>, and (<bold>d</bold>) a magnified view of individuals associated with Cluster <inline-formula><mml:math id="mm390"><mml:semantics><mml:mrow><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>.</p>
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<p>Flow chart that illustrates the operations of our algorithm and the order in which they are executed.</p>
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<p>Performance of the proposed approach over a minimization objective function depending on the selected number of clusters.</p>
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<p>Description of the welded beam design problem.</p>
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<p>Description of the three-bar truss design problem.</p>
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<p>Description of the tension/compression spring design problem.</p>
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<p>Curve convergence graphs.</p>
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21 pages, 3324 KiB  
Article
A Web-Interface Based Decision Support System for Optimizing Home Healthcare Waste Collection Vehicle Routing
by Kubra Sar and Pezhman Ghadimi
Logistics 2024, 8(4), 119; https://doi.org/10.3390/logistics8040119 - 18 Nov 2024
Viewed by 651
Abstract
Background: The significant increase in home healthcare (HHC) driven by technological advancements, an ageing population, and heightened disease outbreaks—especially evident during the COVID-19 pandemic—has created an urgent need for improved medical waste management. Methods: This paper presents the development of a decision [...] Read more.
Background: The significant increase in home healthcare (HHC) driven by technological advancements, an ageing population, and heightened disease outbreaks—especially evident during the COVID-19 pandemic—has created an urgent need for improved medical waste management. Methods: This paper presents the development of a decision support system with a web-based interface designed for efficient medical waste collection in the HHC sector. Results: The system utilises Flask for backend operations, with HTML and CSS for the user interface, and manages data using JSON files. Its flexible design supports real-time adjustments for various vehicle types and changing waste production locations. It incorporates dynamic routing by employing two sophisticated metaheuristic algorithms: the Strength Pareto Evolutionary Algorithm (SPEA-2) and the Non-Dominated Sorting Genetic Algorithm (NSGA-II). This setup supports different dataset sizes and vehicle fleets, including Internal Combustion Engine (ICE) vehicles and Electric Vehicles (EVs). Conclusions: The automation reduces uncertainties in waste collection by minimising human intervention. The system is built to be easily adaptable for other sectors with minor modifications and can be expanded to test various scenarios with new selectable parameters. Full article
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<p>Smart Waste Collection Routing System Illustration.</p>
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<p>NSGA-II algorithm procedure.</p>
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<p>Random solution representation with ten nodes and three vehicles.</p>
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<p>OX Procedure Representation.</p>
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<p>Swap Mutation Procedure Representation.</p>
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<p>Web Application Layer.</p>
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<p>Overview of web application user interface.</p>
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<p>Vehicle Routing Map Visualisation.</p>
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26 pages, 2454 KiB  
Review
Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design
by Seda Göktepe Körpeoğlu and Süleyman Mesut Yılmaz
Appl. Sci. 2024, 14(21), 9951; https://doi.org/10.3390/app14219951 - 31 Oct 2024
Viewed by 899
Abstract
The seismic design of structures is an emerging practice in earthquake-resistant construction. Therefore, using energy-dissipation devices and optimizing these devices for various purposes are important. Evolutionary computation, nature-inspired, and meta-heuristic algorithms have been studied more in recent years for the optimization of these [...] Read more.
The seismic design of structures is an emerging practice in earthquake-resistant construction. Therefore, using energy-dissipation devices and optimizing these devices for various purposes are important. Evolutionary computation, nature-inspired, and meta-heuristic algorithms have been studied more in recent years for the optimization of these devices. In this study, the development of evolutionary algorithms for seismic design in the context of multi-objective optimization is examined through bibliometric analysis. In particular, evolutionary algorithms such as genetic algorithms and particle swarm optimization are used to optimize the performance of structures to meet seismic loads. While genetic algorithms are used to improve both the cost and seismic performance of the structure, particle swarm optimization is used to optimize the vibration and displacement performance of structures. In this study, a bibliometric analysis of 661 publications is performed on the Web of Science and Scopus databases and on how the research in this field has developed since 1986. The R-studio program with the biblioshiny package is used for the analyses. The increase in studies on the optimization of energy dissipation devices in recent years reveals the effectiveness of evolutionary algorithms in this field. Full article
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<p>Conceptual framework.</p>
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<p>Flowchart of the publication selection process.</p>
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<p>From 1986 to 2024, the number of published studies.</p>
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<p>Thirty-seven co-authors in a collaboration network with more than two publications.</p>
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<p>One hundred of the most popular author keywords as word clouds.</p>
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<p>Co-occurrence network for the top 100 author keywords in popularity.</p>
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<p>Network of 26 countries that are partners engaged in cross-border collaboration.</p>
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<p>A three-field diagram illustrating the network with institutions on the left, countries in the middle, and journals on the right.</p>
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24 pages, 988 KiB  
Article
Refining the Eel and Grouper Optimizer with Intelligent Modifications for Global Optimization
by Glykeria Kyrou, Vasileios Charilogis and Ioannis G. Tsoulos
Computation 2024, 12(10), 205; https://doi.org/10.3390/computation12100205 - 14 Oct 2024
Viewed by 733
Abstract
Global optimization is used in many practical and scientific problems. For this reason, various computational techniques have been developed. Particularly important are the evolutionary techniques, which simulate natural phenomena with the aim of detecting the global minimum in complex problems. A new evolutionary [...] Read more.
Global optimization is used in many practical and scientific problems. For this reason, various computational techniques have been developed. Particularly important are the evolutionary techniques, which simulate natural phenomena with the aim of detecting the global minimum in complex problems. A new evolutionary method is the Eel and Grouper Optimization (EGO) algorithm, inspired by the symbiotic relationship and foraging strategy of eels and groupers in marine ecosystems. In the present work, a series of improvements are proposed that aim both at the efficiency of the algorithm to discover the total minimum of multidimensional functions and at the reduction in the required execution time through the effective reduction in the number of functional evaluations. These modifications include the incorporation of a stochastic termination technique as well as an improvement sampling technique. The proposed modifications are tested on multidimensional functions available from the relevant literature and compared with other evolutionary methods. Full article
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Graphical abstract

Graphical abstract
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<p>Flowchart of the suggested global optimization procedure.</p>
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<p>The flowchart of the K-means procedure.</p>
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<p>Total function calls for the considered optimization methods. The numbers represent the sum of function calls for each mentioned method.</p>
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<p>Box plot used to compare the EGO method and the modified version as suggested in the current work.</p>
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<p>Comparison of average function calls for the incorporated optimization methods, using the proposed initial distribution.</p>
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<p>Statistical comparison of all used methods.</p>
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<p>Scatter plot for different initial distributions.</p>
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<p>Time comparison for the ELP function and the proposed optimization method using the four sampling techniques mentioned before. The time depicted in the figure is the sum of the execution times for 30 independent runs.</p>
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47 pages, 2834 KiB  
Review
Advancements in Optimization: Critical Analysis of Evolutionary, Swarm, and Behavior-Based Algorithms
by Noor A. Rashed, Yossra H. Ali and Tarik A. Rashid
Algorithms 2024, 17(9), 416; https://doi.org/10.3390/a17090416 - 19 Sep 2024
Cited by 1 | Viewed by 1292
Abstract
The research work on optimization has witnessed significant growth in the past few years, particularly within multi- and single-objective optimization algorithm areas. This study provides a comprehensive overview and critical evaluation of a wide range of optimization algorithms from conventional methods to innovative [...] Read more.
The research work on optimization has witnessed significant growth in the past few years, particularly within multi- and single-objective optimization algorithm areas. This study provides a comprehensive overview and critical evaluation of a wide range of optimization algorithms from conventional methods to innovative metaheuristic techniques. The methods used for analysis include bibliometric analysis, keyword analysis, and content analysis, focusing on studies from the period 2000–2023. Databases such as IEEE Xplore, SpringerLink, and ScienceDirect were extensively utilized. Our analysis reveals that while traditional algorithms like evolutionary optimization (EO) and particle swarm optimization (PSO) remain popular, newer methods like the fitness-dependent optimizer (FDO) and learner performance-based behavior (LPBB) are gaining attraction due to their adaptability and efficiency. The main conclusion emphasizes the importance of algorithmic diversity, benchmarking standards, and performance evaluation metrics, highlighting future research paths including the exploration of hybrid algorithms, use of domain-specific knowledge, and addressing scalability issues in multi-objective optimization. Full article
(This article belongs to the Special Issue Scheduling: Algorithms and Real-World Applications)
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<p>Development process of common intelligent optimization algorithms in publication journals.</p>
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<p>Study selection and screening process for literature review of optimization algorithms.</p>
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<p>Temporal trends in both multi- and single optimization algorithms.</p>
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<p>Analysis of publication trends: authors and chronological distribution in the field of single and MOO algorithm research.</p>
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<p>An analysis of academic publications across multiple journals and conferences spanning from 2019 to 2024.</p>
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<p>The type of optimization algorithm.</p>
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<p>Diagram illustrating a two-step MOO process.</p>
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32 pages, 5897 KiB  
Article
A Self-Adaptive Neighborhood Search Differential Evolution Algorithm for Planning Sustainable Sequential Cyber–Physical Production Systems
by Fu-Shiung Hsieh
Appl. Sci. 2024, 14(17), 8044; https://doi.org/10.3390/app14178044 - 8 Sep 2024
Viewed by 871
Abstract
Although Cyber–Physical Systems (CPSs) provide a flexible architecture for enterprises to deal with changing demand, an effective method to organize and allocate resources while considering sustainability factors is required to meet customers’ order requirements and mitigate negative impacts on the environment. The planning [...] Read more.
Although Cyber–Physical Systems (CPSs) provide a flexible architecture for enterprises to deal with changing demand, an effective method to organize and allocate resources while considering sustainability factors is required to meet customers’ order requirements and mitigate negative impacts on the environment. The planning of processes to achieve sustainable CPSs becomes an important issue to meet demand timely in a dynamic environment. The problem with planning processes in sustainable CPSs is the determination of the configuration of workflows/resources to compose processes with desirable properties, taking into account time and energy consumption factors. The planning problem in sustainable CPSs can be formulated as an integer programming problem with constraints, and this poses a challenge due to computational complexity. Furthermore, the ever-shrinking life cycle of technologies leads to frequent changes in processes and makes the planning of processes a challenging task. To plan processes in a changing environment, an effective planning method must be developed to automate the planning task. To tackle computational complexity, evolutionary computation approaches such as bio-inspired computing and metaheuristics have been adopted extensively in solving complex optimization problems. This paper aims to propose a solution methodology and an effective evolutionary algorithm with a local search mechanism to support the planning of processes in sustainable CPSs based on an auction mechanism. To achieve this goal, we focus on developing a self-adaptive neighborhood search-based Differential Evolution method. An effective planning method should be robust in terms of performance with respect to algorithmic parameters. We assess the performance and robustness of this approach by performing experiments for several cases. By comparing the results of these experiments, it shows that the proposed method outperforms several other algorithms in the literature. To illustrate the robustness of the proposed self-adaptive algorithm, experiments with different settings of algorithmic parameters were conducted. The results show that the proposed self-adaptive algorithm is robust with respect to algorithmic parameters. Full article
(This article belongs to the Special Issue Bio-Inspired Collective Intelligence in Multi-Agent Systems)
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<p>The Cyber World models for the five operations of process agent <math display="inline"><semantics> <mi>n</mi> </semantics></math>: (<b>a</b>) the DTPN model <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>1</mn> </msubsup> </mrow> </semantics></math> for the first operation; (<b>b</b>) the DTPN model <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> for the second operation; (<b>c</b>) the DTPN model <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>3</mn> </msubsup> </mrow> </semantics></math> for the third operation; (<b>d</b>) the DTPN model <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </semantics></math> for the fourth operation; (<b>e</b>) the DTPN model <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>5</mn> </msubsup> </mrow> </semantics></math> for the fifth operation.</p>
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<p>The DTPN model <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> </msub> </mrow> </semantics></math> of a process agent, where <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> </msub> </mrow> </semantics></math> = <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>2</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>3</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>4</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </mrow> </mrow> </semantics></math>.</p>
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<p>Examples of resource activity models for resource agents. (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> <mn>1</mn> </msubsup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>3</mn> </msub> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>3</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>4</mn> </msub> </mrow> <mn>1</mn> </msubsup> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>5</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>6</mn> </msub> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>6</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </semantics></math>; (<b>g</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>7</mn> </msub> </mrow> <mn>3</mn> </msubsup> </mrow> </semantics></math>; (<b>h</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>8</mn> </msub> </mrow> <mn>2</mn> </msubsup> </mrow> </semantics></math>; (<b>i</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>a</mi> <mn>9</mn> </msub> </mrow> <mn>4</mn> </msubsup> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) The Cyber World model for the configuration <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> </msub> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>1</mn> </msub> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>8</mn> </msub> </mrow> <mn>2</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>7</mn> </msub> </mrow> <mn>3</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>9</mn> </msub> </mrow> <mn>4</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>2</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </semantics></math>; (<b>b</b>) the Cyber World model for the configuration <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> </msub> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>8</mn> </msub> </mrow> <mn>2</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>7</mn> </msub> </mrow> <mn>3</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>9</mn> </msub> </mrow> <mn>4</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>3</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </semantics></math>; (<b>c</b>) the Cyber World model for the configuration <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>n</mi> </msub> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>6</mn> </msub> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>8</mn> </msub> </mrow> <mn>2</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>7</mn> </msub> </mrow> <mn>3</mn> </msubsup> </mrow> </mrow> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>9</mn> </msub> </mrow> <mn>4</mn> </msubsup> <mrow> <mo>‖</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mi>n</mi> <msub> <mi>r</mi> <mn>6</mn> </msub> </mrow> <mn>5</mn> </msubsup> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </semantics></math>.</p>
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<p>Average fitness function values for discrete SaNSDE (<span class="html-italic">LP</span> = 1000), NSDE and PSO with <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </semantics></math> = 10.</p>
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<p>Average fitness function values for discrete SaNSDE (<span class="html-italic">LP</span> = 1000), DE1, DE2, DE3, DE4, DE5 and DE6 with <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </semantics></math> = 10.</p>
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<p>Average fitness function values for discrete SaNSDE (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi>P</mi> </mrow> </semantics></math> = 1000), NSDE and PSO with <span class="html-italic">NP</span> = 30.</p>
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<p>Average fitness function values for SaNSDE (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi>P</mi> </mrow> </semantics></math> = 1000), DE1, DE2, DE3, DE4, DE5 and DE6 with <span class="html-italic">NP</span> = 30.</p>
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<p>Average fitness function values for discrete SaNSDE (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi>P</mi> </mrow> </semantics></math> = 1000), NSDE and PSO with <span class="html-italic">NP</span> = 50.</p>
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<p>Average fitness function values for SaNSDE (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi>P</mi> </mrow> </semantics></math> = 1000), DE1, DE2, DE3, DE4, DE5 and DE6 with <span class="html-italic">NP</span> = 50.</p>
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<p>The average fitness function values obtained by SaNSDE with <math display="inline"><semantics> <mrow> <mi>L</mi> <mi>P</mi> </mrow> </semantics></math> = 10, 1000 and 2000 for Case 1, Case 2, Case 3, Case 4 and Case 5.</p>
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<p>The average fitness function values obtained by SaNSDE with <span class="html-italic">LP</span> = 10, 1000 and 2000 for Case 6, Case 7, Case 8, Case 9 and Case 10.</p>
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<p>The average fitness function values obtained by SaNSDE with <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </semantics></math> = 10, 30 and 50 for Case 1, Case 2, Case 3, Case 4 and Case 5.</p>
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<p>The average fitness function values obtained by SaNSDE with <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>P</mi> </mrow> </semantics></math> = 10, 30 and 50 for Case 6, Case 7, Case 8, Case 9 and Case 10.</p>
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45 pages, 3228 KiB  
Review
Holistic Review of UAV-Centric Situational Awareness: Applications, Limitations, and Algorithmic Challenges
by Somaiyeh MahmoudZadeh, Amirmehdi Yazdani, Yashar Kalantari, Bekir Ciftler, Fathi Aidarus and Mhd Omar Al Kadri
Robotics 2024, 13(8), 117; https://doi.org/10.3390/robotics13080117 - 29 Jul 2024
Cited by 2 | Viewed by 2620
Abstract
This paper presents a comprehensive survey of UAV-centric situational awareness (SA), delineating its applications, limitations, and underlying algorithmic challenges. It highlights the pivotal role of advanced algorithmic and strategic insights, including sensor integration, robust communication frameworks, and sophisticated data processing methodologies. The paper [...] Read more.
This paper presents a comprehensive survey of UAV-centric situational awareness (SA), delineating its applications, limitations, and underlying algorithmic challenges. It highlights the pivotal role of advanced algorithmic and strategic insights, including sensor integration, robust communication frameworks, and sophisticated data processing methodologies. The paper critically analyzes multifaceted challenges such as real-time data processing demands, adaptability in dynamic environments, and complexities introduced by advanced AI and machine learning techniques. Key contributions include a detailed exploration of UAV-centric SA’s transformative potential in industries such as precision agriculture, disaster management, and urban infrastructure monitoring, supported by case studies. In addition, the paper delves into algorithmic approaches for path planning and control, as well as strategies for multi-agent cooperative SA, addressing their respective challenges and future directions. Moreover, this paper discusses forthcoming technological advancements, such as energy-efficient AI solutions, aimed at overcoming current limitations. This holistic review provides valuable insights into the UAV-centric SA, establishing a foundation for future research and practical applications in this domain. Full article
(This article belongs to the Special Issue UAV Systems and Swarm Robotics)
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<p>Endsley’s model of SA in the context of robotics.</p>
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<p>UAV for capturing SA and EA.</p>
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<p>Components of SA within UAV operations.</p>
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<p>Example of the classified UAVs [<a href="#B4-robotics-13-00117" class="html-bibr">4</a>,<a href="#B6-robotics-13-00117" class="html-bibr">6</a>,<a href="#B33-robotics-13-00117" class="html-bibr">33</a>,<a href="#B34-robotics-13-00117" class="html-bibr">34</a>,<a href="#B35-robotics-13-00117" class="html-bibr">35</a>,<a href="#B36-robotics-13-00117" class="html-bibr">36</a>,<a href="#B37-robotics-13-00117" class="html-bibr">37</a>].</p>
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<p>Popular multirotor UAVs for SA [<a href="#B44-robotics-13-00117" class="html-bibr">44</a>].</p>
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<p>Popular multirotor UAVs for SA [<a href="#B44-robotics-13-00117" class="html-bibr">44</a>].</p>
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<p>Conceptual example of capturing SA using distributed sensors, on-board camera, and LiDAR.</p>
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21 pages, 4127 KiB  
Article
Seismic Response Prediction of Porcelain Transformer Bushing Using Hybrid Metaheuristic and Machine Learning Techniques: A Comparative Study
by Quan Zhou, Yongheng Mao, Fengqi Guo and Yuxuan Liu
Mathematics 2024, 12(13), 2084; https://doi.org/10.3390/math12132084 - 3 Jul 2024
Cited by 1 | Viewed by 830
Abstract
Although seismic response predictions are widely used for engineering structures, their applications in electrical equipment are rare. Overstressing at the bottom of the porcelain insulators during seismic events has made power transformer bushings in substations prone to failure. Thus, this paper proposed and [...] Read more.
Although seismic response predictions are widely used for engineering structures, their applications in electrical equipment are rare. Overstressing at the bottom of the porcelain insulators during seismic events has made power transformer bushings in substations prone to failure. Thus, this paper proposed and compared six integrated machine learning (ML) models for seismic stress response predictions for porcelain transformer bushings using easily monitored acceleration responses. Metaheuristic algorithms such as particle swarm optimization were employed for architecture tuning. Prediction accuracies for stress response values and classifications were evaluated. Finally, shaking table tests and simulation analyses for a 1100 kV bushing were implemented to validate the accuracy of the six ML models. The results indicated that the proposed ML models can quickly forecast the maximum stress experienced by a porcelain bushing during earthquakes. Swarm intelligence evolutionary technologies could quickly and automatically aid in the retrofitting of architecture for the ML models. The K-nearest neighbor regression model had the best level of prediction accuracy among the six selected ML models for experimental and simulation validations. ML prediction models have clear benefits over frequently used seismic analytical techniques in terms of speed and accuracy for post-earthquake emergency relief in substations. Full article
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<p>Typical electrical equipment found in substations.</p>
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<p>MLP with two hidden layers [<a href="#B38-mathematics-12-02084" class="html-bibr">38</a>].</p>
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<p>K-nearest neighbor regression with K = 4.</p>
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<p>Typical decision tree analysis model.</p>
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<p>Structures and FE model of the bushing (unit: mm).</p>
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<p>Overall application framework for predicting peak stress responses of substation equipment.</p>
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<p>Sample partition and application.</p>
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<p>Approach employing PSO to tune the model structures.</p>
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<p>Spectral information for the selected ground motions and distributions of the variables.</p>
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<p>Testing results of the ML models and comparison with actual results.</p>
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<p>Prediction errors and distributions of the six ML models.</p>
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<p>Test model and strain gauge arrangement of the transformer bushing [<a href="#B27-mathematics-12-02084" class="html-bibr">27</a>].</p>
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<p>Comparison of the experimental and simulation results obtained using ML models.</p>
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<p>Artificial ground motion for exciting the simulation model.</p>
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21 pages, 2780 KiB  
Article
Improving Water and Energy Resource Management: A Comparative Study of Solution Representations for the Pump Scheduling Optimization Problem
by Sergio A. Silva-Rubio, Yamisleydi Salgueiro, Daniel Mora-Meliá and Jimmy H. Gutiérrez-Bahamondes
Mathematics 2024, 12(13), 1994; https://doi.org/10.3390/math12131994 - 27 Jun 2024
Viewed by 1474
Abstract
Water distribution networks (WDNs) are vital for communities, facing threats like climate change and aging infrastructure. Optimizing WDNs for energy and water savings is challenging due to their complexity. In particular, pump scheduling stands out as a fundamental tool for optimizing both resources. [...] Read more.
Water distribution networks (WDNs) are vital for communities, facing threats like climate change and aging infrastructure. Optimizing WDNs for energy and water savings is challenging due to their complexity. In particular, pump scheduling stands out as a fundamental tool for optimizing both resources. Metaheuristics such as evolutionary algorithms (EAs) offer promising solutions, yet encounter limitations in robustness, parameterization, and applicability to real-sized networks. The encoding of decision variables significantly influences algorithm efficiency, an aspect frequently overlooked in the literature. This study addresses this gap by comparing solution representations for a multiobjective pump scheduling problem. By assessing metrics such as execution time, convergence, and diversity, it identifies effective representations. Embracing a multiobjective approach enhances comprehension and solution robustness. Through empirical validation across case studies, this research contributes insights for the more efficient optimization of WDNs, tackling critical challenges in water and energy management. The results demonstrate significant variations in the performance of different solution representations used in the literature. In conclusion, this study not only provides perspectives on effective pump scheduling strategies but also aims to guide future researchers in selecting the most suitable representation for optimization problems. Full article
(This article belongs to the Section Engineering Mathematics)
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<p>Construction of an approximate Pareto front.</p>
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<p>Anytown network.</p>
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<p>Anytown modified network.</p>
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<p>Curico network.</p>
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<p>Pareto front for the Anytown network.</p>
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<p>Pareto front for the Anytown Modified network.</p>
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<p>Pareto front for the Curicó network.</p>
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19 pages, 4600 KiB  
Article
An Enhanced Tree-Seed Algorithm for Function Optimization and Production Optimization
by Qingan Zhou, Rong Dai, Guoxiao Zhou, Shenghui Ma and Shunshe Luo
Biomimetics 2024, 9(6), 334; https://doi.org/10.3390/biomimetics9060334 - 31 May 2024
Viewed by 1062
Abstract
As the fields of engineering, energy, and geology become increasingly complex, decision makers face escalating challenges that require skilled solutions to meet practical production needs. Evolutionary algorithms, inspired by biological evolution, have emerged as powerful methods for tackling intricate optimization problems without relying [...] Read more.
As the fields of engineering, energy, and geology become increasingly complex, decision makers face escalating challenges that require skilled solutions to meet practical production needs. Evolutionary algorithms, inspired by biological evolution, have emerged as powerful methods for tackling intricate optimization problems without relying on gradient data. Among these, the tree-seed algorithm (TSA) distinguishes itself due to its unique mechanism and efficient searching capabilities. However, an imbalance between its exploitation and exploration phases can lead it to be stuck in local optima, impeding the discovery of globally optimal solutions. This study introduces an improved TSA that incorporates water-cycling and quantum rotation-gate mechanisms. These enhancements assist the algorithm in escaping local peaks and achieving a more harmonious balance between its exploitation and exploration phases. Comparative experimental evaluations, using the CEC 2017 benchmarks and a well-known metaheuristic algorithm, demonstrate the upgraded algorithm’s faster convergence rate and enhanced ability to locate global optima. Additionally, its application in optimizing reservoir production models underscores its superior performance compared to competing methods, further validating its real-world optimization capabilities. Full article
(This article belongs to the Special Issue Computer-Aided Biomimetics: 2nd Edition)
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<p>The flowchart of TSA.</p>
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<p>Flowchart of WQTSA.</p>
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<p>Comparison of convergence curves between WQTSA and other well-known optimization methods on IEEE CEC 2017 test functions.</p>
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<p>Log-permeability distribution of three-channel model.</p>
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<p>NPV obtained by the algorithms with iteration.</p>
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<p>The optimal water injection rate obtained by each algorithm for the three-channel model.</p>
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<p>The optimal liquid production rate obtained by each algorithm for the three-channel model.</p>
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49 pages, 9004 KiB  
Article
Improved Snake Optimizer Using Sobol Sequential Nonlinear Factors and Different Learning Strategies and Its Applications
by Wenda Zheng, Yibo Ai and Weidong Zhang
Mathematics 2024, 12(11), 1708; https://doi.org/10.3390/math12111708 - 30 May 2024
Viewed by 1087
Abstract
The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To [...] Read more.
The Snake Optimizer (SO) is an advanced metaheuristic algorithm for solving complicated real-world optimization problems. However, despite its advantages, the SO faces certain challenges, such as susceptibility to local optima and suboptimal convergence performance in cases involving discretized, high-dimensional, and multi-constraint problems. To address these problems, this paper presents an improved version of the SO, known as the Snake Optimizer using Sobol sequential nonlinear factors and different learning strategies (SNDSO). Firstly, using Sobol sequences to generate better distributed initial populations helps to locate the global optimum solution faster. Secondly, the use of nonlinear factors based on the inverse tangent function to control the exploration and exploitation phases effectively improves the exploitation capability of the algorithm. Finally, introducing learning strategies improves the population diversity and reduces the probability of the algorithm falling into the local optimum trap. The effectiveness of the proposed SNDSO in solving discretized, high-dimensional, and multi-constraint problems is validated through a series of experiments. The performance of the SNDSO in tackling high-dimensional numerical optimization problems is first confirmed by using the Congress on Evolutionary Computation (CEC) 2015 and CEC2017 test sets. Then, twelve feature selection problems are used to evaluate the effectiveness of the SNDSO in discretized scenarios. Finally, five real-world technical multi-constraint optimization problems are employed to evaluate the performance of the SNDSO in high-dimensional and multi-constraint domains. The experiments show that the SNDSO effectively overcomes the challenges of discretization, high dimensionality, and multi-constraint problems and outperforms superior algorithms. Full article
(This article belongs to the Special Issue Intelligence Optimization Algorithms and Applications)
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<p>Ref. [<a href="#B30-mathematics-12-01708" class="html-bibr">30</a>] (<b>a</b>). Sobol sequential random number distribution. (<b>b</b>). Pseudo-random number sequence distribution.</p>
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<p>Comparison between the original Q and the improved Q.</p>
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<p>Learning strategy simulation.</p>
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<p>The flowchart of the SNDSO.</p>
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<p>The mean value-based rank-filled of different parameter combinations.</p>
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<p>Convergence plot of the different population size on the CEC2015.</p>
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<p>The population diversity of SO and the SNDSO.</p>
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<p>The exploration and exploitation of the SNDSO.</p>
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<p>Mean ranking of algorithms on different test dimensions.</p>
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<p>Convergence plot of different algorithms on the CEC2017 test function set (<span class="html-italic">Dim</span> = 30).</p>
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<p>Boxplot of different algorithms on the CEC2017 test function set (<span class="html-italic">Dim</span> = 30).</p>
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<p>Box plots of algorithms dealing with FS problems.</p>
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<p>Convergence plot of the algorithm dealing with the FS problems.</p>
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<p>Ranking of all metrics for algorithms dealing with FS problems.</p>
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<p>3-bar truss design problem.</p>
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<p>10-bar truss design problem.</p>
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<p>Tension/compression spring design problem.</p>
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<p>Construction of speed reducer.</p>
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<p>Welded beam design problem.</p>
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39 pages, 5553 KiB  
Article
Weight Vector Definition for MOEA/D-Based Algorithms Using Augmented Covering Arrays for Many-Objective Optimization
by Carlos Cobos, Cristian Ordoñez, Jose Torres-Jimenez, Hugo Ordoñez and Martha Mendoza
Mathematics 2024, 12(11), 1680; https://doi.org/10.3390/math12111680 - 28 May 2024
Viewed by 1888
Abstract
Many-objective optimization problems are today ever more common. The decomposition-based approach stands out among the evolutionary algorithms used for their solution, with MOEA/D and its variations playing significant roles. MOEA/D variations seek to improve weight vector definition, improve the dynamic adjustment of weight [...] Read more.
Many-objective optimization problems are today ever more common. The decomposition-based approach stands out among the evolutionary algorithms used for their solution, with MOEA/D and its variations playing significant roles. MOEA/D variations seek to improve weight vector definition, improve the dynamic adjustment of weight vectors during the evolution process, improve the evolutionary operators, use alternative decomposition methods, and hybridize with other metaheuristics, among others. Although an essential topic for the success of MOEA/D depends on how well the weight vectors are defined when decomposing the problem, not as much research has been performed on this topic as on the others. This paper proposes using a new mathematical object called augmented covering arrays (ACAs) that enable a better sampling of interactions of M objectives using the least number of weight vectors based on an interaction level (strength), defined a priori by the user. The proposed method obtains better results, measured in inverted generational distance, using small to medium populations (up to 850 solutions) of 30 to 100 objectives over DTLZ and WFG problems against the traditional weight vector definition used by MOEA/D-DE and results obtained by NSGA-III. Other MOEA/D variations can include the proposed approach and thus improve their results. Full article
(This article belongs to the Special Issue Optimization Algorithms: Theory and Applications)
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Graphical abstract

Graphical abstract
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<p>Visual comparison of an OA, CA, and ACA in 3D objectives with v = 7 and t = 2.</p>
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<p>Visual comparison of an OA, CA, and ACA in 3D objectives with v = 7 and t = 2.</p>
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<p>Average execution time in seconds for all algorithms in the experiments with strength 2 and alphabet 9.</p>
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<p>IGD values obtained for all algorithms in the evaluation of strength 2 and alphabet 9 from 10 to 100 objectives. A: MOEA/D-DE-ACA, B: MOEA/D-DE, and C: NSGA-III.</p>
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<p>IGD values obtained for all algorithms in the evaluation of strength 2 and alphabet 9 from 10 to 100 objectives. A: MOEA/D-DE-ACA, B: MOEA/D-DE, and C: NSGA-III.</p>
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<p>Histograms for comparison of separation angles with different numbers of objectives and population sizes.</p>
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<p>Non-dominated solutions for MOEA/D-DE (goldenrod color) and MOEA/D-DE-ACA (green color) for problems DTLZ6, DTLZ7, WFG1, and WFG2 with 30 objectives.</p>
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<p>Non-dominated solutions for MOEA/D-DE (goldenrod color) and MOEA/D-DE-ACA (green color) for problems DTLZ6, DTLZ7, WFG1, and WFG2 with 30 objectives.</p>
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15 pages, 950 KiB  
Article
MOBCA: Multi-Objective Besiege and Conquer Algorithm
by Jianhua Jiang, Jiaqi Wu, Jinmeng Luo, Xi Yang and Zulu Huang
Biomimetics 2024, 9(6), 316; https://doi.org/10.3390/biomimetics9060316 - 24 May 2024
Cited by 2 | Viewed by 1500
Abstract
The besiege and conquer algorithm has shown excellent performance in single-objective optimization problems. However, there is no literature on the research of the BCA algorithm on multi-objective optimization problems. Therefore, this paper proposes a new multi-objective besiege and conquer algorithm to solve multi-objective [...] Read more.
The besiege and conquer algorithm has shown excellent performance in single-objective optimization problems. However, there is no literature on the research of the BCA algorithm on multi-objective optimization problems. Therefore, this paper proposes a new multi-objective besiege and conquer algorithm to solve multi-objective optimization problems. The grid mechanism, archiving mechanism, and leader selection mechanism are integrated into the BCA to estimate the Pareto optimal solution and approach the Pareto optimal frontier. The proposed algorithm is tested with MOPSO, MOEA/D, and NSGAIII on the benchmark function IMOP and ZDT. The experiment results show that the proposed algorithm can obtain competitive results in terms of the accuracy of the Pareto optimal solution. Full article
(This article belongs to the Special Issue Biomimicry for Optimization, Control, and Automation: 2nd Edition)
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<p>Single-objective optimization problem.</p>
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<p>Different situations in a multi-objective problem (for example: two objectives). (<b>a</b>) Situation 1: solution <span class="html-italic">x</span> dominates <span class="html-italic">y</span>. (<b>b</b>) Situation 2: <span class="html-italic">x</span> and <span class="html-italic">y</span> do not dominate each other.</p>
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<p>Pareto fronts for different optimization directions.</p>
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<p>The workflow of the BCA algrotihm.</p>
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<p>Obtained Pareto fronts by MOBCA, MOPSO, MOEA/D, and NSGAIII.</p>
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<p>The convergence of hypervolume with the number of function evaluations.</p>
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<p>The convergence of invert generation distance with the number of function evaluations.</p>
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