[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
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

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

Search Results (2,296)

Search Parameters:
Keywords = meta-heuristic algorithm

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
23 pages, 2390 KiB  
Article
An Innovative NOx Emissions Prediction Model Based on Random Forest Feature Selection and Evolutionary Reformer
by Xianyu Meng, Xi Li, Jialei Chen, Yongyan Fu, Chu Zhang, Muhammad Shahzad Nazir and Tian Peng
Processes 2025, 13(1), 107; https://doi.org/10.3390/pr13010107 - 3 Jan 2025
Viewed by 258
Abstract
Developing more precise NOx emission prediction models is pivotal for effectively controlling NOx emissions from gas turbines. In this paper, a Reformer is combined with random forest (RF) feature selection and the chaos game optimization (CGO) algorithm to predict NOx in gas turbines. [...] Read more.
Developing more precise NOx emission prediction models is pivotal for effectively controlling NOx emissions from gas turbines. In this paper, a Reformer is combined with random forest (RF) feature selection and the chaos game optimization (CGO) algorithm to predict NOx in gas turbines. Firstly, RF evaluates the importance of data features and reduces the dimensionality of multidimensional data to improve the predictive performance of the model. Secondly, the Reformer model extracts the inherent pattern of different data and explores the intrinsic connection between gas turbine variables to establish a more accurate NOx emission prediction model. Thirdly, the CGO algorithm is a parameter-free meta-heuristic optimization algorithm used to find the best parameters for the prediction model. The CGO algorithm was improved using Chebyshev Chaos Mapping to improve the initial population quality of the CGO algorithm. To evaluate the efficiency of the proposed model, a dataset of gas turbines in north-western Turkey is studied, and the results obtained are compared with seven benchmark models. The final results of this paper show that RF can select appropriate input variables, and the Reformer can extract the intrinsic links of the data and build a more accurate NOx prediction model. At the same time, ICGO can optimize the parameters of the Reformer effectively. Full article
34 pages, 9850 KiB  
Article
Optimal Siting, Sizing, and Energy Management of Distributed Renewable Generation and Storage Under Atmospheric Conditions
by Mohammed Turki Fayyadh Al-Mahammedi and Mustafa Onat
Sustainability 2025, 17(1), 300; https://doi.org/10.3390/su17010300 - 3 Jan 2025
Viewed by 241
Abstract
Integrating new generation and storage resources within power systems is challenging because of the stochastic nature of renewable generation, voltage regulation, and the use of microgrids. Classical optimization methods struggle with these nonlinear, multifaceted issues. This paper presents a novel optimization framework for [...] Read more.
Integrating new generation and storage resources within power systems is challenging because of the stochastic nature of renewable generation, voltage regulation, and the use of microgrids. Classical optimization methods struggle with these nonlinear, multifaceted issues. This paper presents a novel optimization framework for integrating, sizing, and siting distributed renewable generation and energy storage systems in power distribution networks. To accurately reflect load variability, the framework considers four distinct load models—constant impedance, current, power, and ZIP (constant impedance, constant current, constant power). Our approach utilized three metaheuristic approaches to enhance the efficiency of power system management. The validation results on the IEEE 33 Bus System conclude that the Elephant Herding Optimization (EHO) emerged as the best performer regarding voltage stability and real power loss reduction with a voltage stability index of 0.0031346. Modified Ant Lion Optimization (ALO) achieved a best voltage stability index of 0.0024115 and power losses of 7.5092 MVA. The Red Colobus Monkey Optimization (RMO) algorithm realized a voltage stability index of 0.0052053 and real power losses of 20.7564 MVA. Overall, the results conclude that ALO is the most effective approach for optimizing distributed renewable energy systems under different climatic conditions. According to the analysis, the algorithm works best in ideal circumstances when the percentages of wind and irradiance are 60% or greater. Full article
Show Figures

Figure 1

Figure 1
<p>The flowchart of the proposed methodology.</p>
Full article ">Figure 2
<p>IEEE 33 Bus System.</p>
Full article ">Figure 3
<p>Simulation graph for IEEE 33 Bus System with four load models (before and after ALO).</p>
Full article ">Figure 4
<p>Convergence of ALO algorithm on IEEE 33 Bus System.</p>
Full article ">Figure 5
<p>Simulation graph for IEEE 33 Bus System with four load models (before and after EHO).</p>
Full article ">Figure 6
<p>Convergence of EHO algorithm on IEEE 33 Bus System.</p>
Full article ">Figure 7
<p>Simulation graph for IEEE 33 Bus System with four load models (before and after RCMO).</p>
Full article ">Figure 8
<p>Convergence of RCMO algorithm on IEEE 33 Bus System.</p>
Full article ">Figure 9
<p>Irradiance, power, cost due to underestimate, and cost due to overestimate scenario.</p>
Full article ">Figure 10
<p>Wind speed, power, cost due to underestimated, and cost due to overestimated scenarios.</p>
Full article ">Figure 11
<p>Voltage stability vs. irradiance and wind speeds for three optimization algorithms.</p>
Full article ">Figure 12
<p>Loss vs. irradiance and wind speed availability (in %) for loss estimation.</p>
Full article ">Figure 13
<p>Cost vs. irradiance and wind speed availability (in %) for three optimization algorithms.</p>
Full article ">Figure 14
<p>Graph representing the performance of the ALO algorithm (Voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">Figure 14 Cont.
<p>Graph representing the performance of the ALO algorithm (Voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">Figure 15
<p>Graph representing the performance of the EHO algorithm (Voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">Figure 15 Cont.
<p>Graph representing the performance of the EHO algorithm (Voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">Figure 16
<p>Graph representing the performance of the RCMO algorithm (voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">Figure 16 Cont.
<p>Graph representing the performance of the RCMO algorithm (voltage profile vs. wind speed and irradiance) under different load sheddings and all five scenarios represented as ((<b>A</b>) = 20%), ((<b>B</b>) = 40%), ((<b>C</b>) = 60%), ((<b>D</b>) = 80%), and ((<b>E</b>) = 100%).</p>
Full article ">
27 pages, 959 KiB  
Review
From Integer Programming to Machine Learning: A Technical Review on Solving University Timetabling Problems
by Xin Gu, Muralee Krish, Shaleeza Sohail, Sweta Thakur, Fariza Sabrina and Zongwen Fan
Computation 2025, 13(1), 10; https://doi.org/10.3390/computation13010010 - 3 Jan 2025
Viewed by 247
Abstract
Solving the university timetabling problem is crucial as it ensures efficient use of resources, minimises scheduling conflicts, and enhances overall productivity. This paper presents a comprehensive review of university timetabling problems using integer programming algorithms. This study explores various integer programming techniques and [...] Read more.
Solving the university timetabling problem is crucial as it ensures efficient use of resources, minimises scheduling conflicts, and enhances overall productivity. This paper presents a comprehensive review of university timetabling problems using integer programming algorithms. This study explores various integer programming techniques and their effectiveness in optimising complex scheduling requirements in higher education institutions. We analysed 95 integer programming-based models developed for solving university timetabling problems, covering relevant research from 1990 to 2023. The goal is to provide insights into the evolution of these algorithms and their impact on improving university scheduling. We identify that the implementation rate of models using integer programming is 98%, which is much higher than 34% implementation rates using meta-heuristics algorithms from the existing review. The integer programming models are analysed by the problem types, solutions, tools, and datasets. For three types of timetabling problems including course timetabling, class timetabling, and exam timetabling, we dive deeper into the commercial solvers CPLEX (47), Gurobi (11), Lingo (5), Open Solver (4), C++ GLPK (4), AIMMS (2), GAMS (2), XPRESS (2), CELCAT (1), AMPL (1), and Google OR-Tools CP-SAT (1) and identify that CPLEX is the most frequently used integer programming solver. We explored the uses of machine learning algorithms and the hybrid solutions of combining the integer programming and machine learning algorithms in higher education timetabling solutions. We also identify areas for future work, which includes an emphasis on using integer programming algorithms in other industrial areas, and using machine learning models for university timetabling to allow data-driven solutions. Full article
(This article belongs to the Section Computational Social Science)
Show Figures

Figure 1

Figure 1
<p>Data Collection and Screening Process.</p>
Full article ">Figure 2
<p>Timetabling problems categories.</p>
Full article ">Figure 3
<p>Pie Chart of Linear Programming Models Used.</p>
Full article ">Figure 4
<p>Comparison of Linear Programming Models with Purpose of Timetabling.</p>
Full article ">Figure 5
<p>Flow Chart for Developing Integer Linear Programming Algorithm.</p>
Full article ">Figure 6
<p>All University Timetabling Integer Programming Solutions.</p>
Full article ">Figure 7
<p>Solvers Used in University Timetabling Implementations.</p>
Full article ">Figure 8
<p>CPLEX Used in University Timetabling Implementations.</p>
Full article ">Figure 9
<p>Types of Data Used for Evaluation, All Instances Considered.</p>
Full article ">Figure 10
<p>University Timetabling Implementations: Types of Data Used for Evaluation, Only Known Instances Considered.</p>
Full article ">
32 pages, 5618 KiB  
Article
Multi-Objective Optimization for Green BTS Site Selection in Telecommunication Networks Using NSGA-II and MOPSO
by Salar Babaei, Mehran Khalaj, Mehdi Keramatpour and Ramin Enayati
Algorithms 2025, 18(1), 9; https://doi.org/10.3390/a18010009 - 2 Jan 2025
Viewed by 281
Abstract
Today, facility location planning primarily pertains to the long-term strategic and operational decision-making of large public and private organizations, and the significant costs associated with facility location, construction, and operation have turned location research into long-term decision-making. Presenting a hub location model for [...] Read more.
Today, facility location planning primarily pertains to the long-term strategic and operational decision-making of large public and private organizations, and the significant costs associated with facility location, construction, and operation have turned location research into long-term decision-making. Presenting a hub location model for the green supply chain can address the current status of facilities and significantly improve demand coverage at an acceptable cost. Therefore, in this study, a network of facilities for hub location in the service site domain, considering existing and potential facilities under probable scenarios, has been proposed. After presenting the mathematical model, validation was performed on a small scale, followed by sensitivity analysis of the main parameters of the model. Furthermore, a metaheuristic algorithm was employed to analyze the NP-Hardness of the model. Additionally, two metaheuristic algorithms, NSGAII and MOPSO, were developed to demonstrate the efficiency of the model. Based on the conducted analysis, it can be observed that the computational time increases exponentially with the size of sample problems, indicating the NP-Hardness of the problem. However, the NSGAII algorithm performs better in terms of computational time for medium-sized problems compared to the MOPSO algorithm. These algorithms were chosen due to their proven efficiency in handling NP-hard optimization problems and their ability to balance exploration and exploitation in search spaces. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Different scenarios of demand point coverage.</p>
Full article ">Figure 2
<p>Average of averages plot for NSGA II algorithm [<a href="#B22-algorithms-18-00009" class="html-bibr">22</a>].</p>
Full article ">Figure 3
<p>Average S/N ratio plot for NSGA II algorithm [<a href="#B22-algorithms-18-00009" class="html-bibr">22</a>].</p>
Full article ">Figure 4
<p>Average means plot for the MOPSO algorithm [<a href="#B22-algorithms-18-00009" class="html-bibr">22</a>].</p>
Full article ">Figure 5
<p>Average S/N ratio plot for the MOPSO algorithm [<a href="#B22-algorithms-18-00009" class="html-bibr">22</a>].</p>
Full article ">Figure 6
<p>Pareto front obtained from solving the small-sized problem using NSGA II and MOPSO algorithms.</p>
Full article ">Figure 7
<p>Computational time required by the NSGAII and MOPSO algorithms for varying problem sizes.</p>
Full article ">Figure 8
<p>Depicts the Pareto front solutions generated by the NSGAII and MOPSO algorithms.</p>
Full article ">Figure 9
<p>Comparison of mean values of the first objective function in sample problems with metaheuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 10
<p>Box plot for confirming or rejecting the null hypothesis for the means of the first objective function [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 11
<p>Comparison of the mean values of the second objective function in sample problems using metaheuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 12
<p>Box plot for confirming or rejecting the null hypothesis for the means of the second objective function [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 13
<p>Comparison of average number of efficient solutions in sample problems using metaheuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 14
<p>Box plot to confirm or reject the null hypothesis for the averages of the number of efficient solutions [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 15
<p>Comparison of the means of the maximum spread indicator in sample problems with metaheuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 16
<p>Box plot to confirm or reject the null hypothesis for the means of the maximum spread indicator [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 17
<p>Comparison of average spacing index in example problems with meta-heuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 18
<p>Box plot to confirm or reject the null hypothesis for the averages of distance index [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 19
<p>Comparison of computing time averages in example problems with meta-heuristic algorithms [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">Figure 20
<p>Box plot for confirming or rejecting the null hypothesis for computing time averages [<a href="#B23-algorithms-18-00009" class="html-bibr">23</a>].</p>
Full article ">
19 pages, 8859 KiB  
Article
Nesting Process Automation in the Footwear Industry: A Hybrid Approach to Minimize Material Waste
by Eliseo Aguilar-Tortosa, Eduard-Andrei Duta-Costache, Elías Vera-Brazal, José-Luis Sánchez-Romero, José Francisco Gómez-Hernández, Antonio Jimeno-Morenilla and Antonio Maciá-Lillo
Appl. Sci. 2025, 15(1), 320; https://doi.org/10.3390/app15010320 - 31 Dec 2024
Viewed by 374
Abstract
In any industry, maximizing the use of raw materials is essential to reduce waste and costs, which also positively impacts the environment. In footwear production, components are typically derived from cutting processes, requiring optimized systems to maximize the use of different materials, minimize [...] Read more.
In any industry, maximizing the use of raw materials is essential to reduce waste and costs, which also positively impacts the environment. In footwear production, components are typically derived from cutting processes, requiring optimized systems to maximize the use of different materials, minimize waste, and accelerate production. In this context, nesting is a technique that arranges shapes within a confined space to maximize area utilization and reduce unused space. As this problem is classified as NP-Hard, only algorithmic approximations can be employed. This paper focuses on optimizing the cutting of leather parts for shoe manufacturing. Footwear parts are cut from cattle hides, which are not only irregular in shape but also vary in resistance and quality across different areas of the same piece of leather. This study proposes automated nesting methods that aim to compete with current manual approaches, which are conducted exclusively by experts with deep knowledge of the characteristics of both the pieces and the leather, making the manual process time-intensive. This research reviews current methods and introduces hybrid ones, achieving up to 38.4× acceleration and up to 10.18% increase in nested pieces over manual methods. Full article
(This article belongs to the Special Issue Digital Technologies Enabling Modern Industries)
Show Figures

Figure 1

Figure 1
<p>Leather skin on a digitizing table. In the background, its digitization and the definition of its different quality zones can be seen.</p>
Full article ">Figure 2
<p>Example of nesting on a piece of leather with quality areas.</p>
Full article ">Figure 3
<p>On the (<b>left</b>), a scheme of the “glued” or “conventional” type of assembly seen in cross-section. On the (<b>right</b>), shoes mounted with this type of construction.</p>
Full article ">Figure 4
<p>On the (<b>left</b>), a scheme of the Strobel construction. On the (<b>right</b>), a representation of a sneaker assembled with this type of construction.</p>
Full article ">Figure 5
<p>On the (<b>left</b>), a scheme of the moccasin construction. On the (<b>right</b>), a moccasin.</p>
Full article ">Figure 6
<p>Close-up view of a moccasin made of leather.</p>
Full article ">Figure 7
<p>Example of partes in traditionally constructed of glue shoes.</p>
Full article ">Figure 8
<p>On the (<b>left</b>), is an example of the parts of a half moccasin. On the (<b>right</b>), is an example of the Strobel cut in a single piece.</p>
Full article ">Figure 9
<p>Example of nesting carried out manually by a professional.</p>
Full article ">Figure 10
<p>Pieces of leather used in this study and its references.</p>
Full article ">Figure 11
<p>On the (<b>left</b>), automatic nesting on two parts of the full moccasin. On the (<b>right</b>), automatic nesting on four parts (two moccasins).</p>
Full article ">Figure 12
<p>On the (<b>left</b>), automatic nesting on three full moccasins. On the (<b>right</b>) automatic nesting on four full moccasins.</p>
Full article ">Figure 13
<p>On the (<b>left</b>), the initial placement of ten sets of full moccasins. On the (<b>right</b>), the result of the automatic nesting.</p>
Full article ">Figure 14
<p>On the (<b>left</b>), manual nesting (18 complete sets + 4 pieces). On the (<b>right</b>), automatic nesting Jaya + NFP (18 complete sets). Leather model 9460.</p>
Full article ">Figure 15
<p>On the (<b>left</b>), manual nesting (14 sets + 3 pieces). On the (<b>right</b>), automatic nesting Jaya + NFP (14 sets + 1 piece). Leather model 9464.</p>
Full article ">Figure 16
<p>Automatic nesting on a set of parts from a moccasin without wrinkles.</p>
Full article ">Figure 17
<p>Automatic nesting Jaya + NFP (15 sets + 36 pieces). Leather 9460.</p>
Full article ">Figure 18
<p>Automatic nesting on a set of half moccasin parts.</p>
Full article ">Figure 19
<p>Automatic nesting on two parts of half moccasin.</p>
Full article ">Figure 20
<p>On the (<b>left</b>), manual nesting (14 sets + 5 pieces). On the (<b>right</b>), automatic nesting Jaya + NFP (13 sets + 16 pieces). Leather 9464.</p>
Full article ">Figure 21
<p>Automatic nesting using only NFP algorithm (11 sets + 9 pieces). Leather 9464.</p>
Full article ">
42 pages, 26326 KiB  
Article
A Novel Hybrid Improved RIME Algorithm for Global Optimization Problems
by Wuke Li, Xiong Yang, Yuchen Yin and Qian Wang
Biomimetics 2025, 10(1), 14; https://doi.org/10.3390/biomimetics10010014 - 31 Dec 2024
Viewed by 332
Abstract
The RIME algorithm is a novel physical-based meta-heuristic algorithm with a strong ability to solve global optimization problems and address challenges in engineering applications. It implements exploration and exploitation behaviors by constructing a rime-ice growth process. However, RIME comes with a couple of [...] Read more.
The RIME algorithm is a novel physical-based meta-heuristic algorithm with a strong ability to solve global optimization problems and address challenges in engineering applications. It implements exploration and exploitation behaviors by constructing a rime-ice growth process. However, RIME comes with a couple of disadvantages: a limited exploratory capability, slow convergence, and inherent asymmetry between exploration and exploitation. An improved version with more efficiency and adaptability to solve these issues now comes in the form of Hybrid Estimation Rime-ice Optimization, in short, HERIME. A probabilistic model-based sampling approach of the estimated distribution algorithm is utilized to enhance the quality of the RIME population and boost its global exploration capability. A roulette-based fitness distance balanced selection strategy is used to strengthen the hard-rime phase of RIME to effectively enhance the balance between the exploitation and exploration phases of the optimization process. We validate HERIME using 41 functions from the IEEE CEC2017 and IEEE CEC2022 test suites and compare its optimization accuracy, convergence, and stability with four classical and recent metaheuristic algorithms as well as five advanced algorithms to reveal the fact that the proposed algorithm outperforms all of them. Statistical research using the Friedman test and Wilcoxon rank sum test also confirms its excellent performance. Moreover, ablation experiments validate the effectiveness of each strategy individually. Thus, the experimental results show that HERIME has better search efficiency and optimization accuracy and is effective in dealing with global optimization problems. Full article
(This article belongs to the Special Issue Nature-Inspired Metaheuristic Optimization Algorithms 2025)
Show Figures

Figure 1

Figure 1
<p>Classification of meta-heuristic optimization algorithms.</p>
Full article ">Figure 2
<p>Sketch for procedure of the synergistic fusion framework.</p>
Full article ">Figure 3
<p>The flowchart of proposed HERIME algorithm.</p>
Full article ">Figure 4
<p>The visualization of Wilcoxon rank sum test results for RIME, CRIME, RRIME, and HERIME based on CEC 2017 and CEC 2022.</p>
Full article ">Figure 5
<p>The ranking heatmap of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure 6
<p>The visualization of Friedman test results of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure 7
<p>The visualization of Wilcoxon rank sum test results of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure 8
<p>The convergence curves of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure 9
<p>The boxplots of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure 9 Cont.
<p>The boxplots of HERIME and competitors in solving CEC2017/CEC2022.</p>
Full article ">Figure A1
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (10D).</p>
Full article ">Figure A1 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (10D).</p>
Full article ">Figure A1 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (10D).</p>
Full article ">Figure A2
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (30D).</p>
Full article ">Figure A2 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (30D).</p>
Full article ">Figure A2 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (30D).</p>
Full article ">Figure A3
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (50D).</p>
Full article ">Figure A3 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (50D).</p>
Full article ">Figure A3 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (50D).</p>
Full article ">Figure A4
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (100D).</p>
Full article ">Figure A4 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (100D).</p>
Full article ">Figure A4 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2017 (100D).</p>
Full article ">Figure A5
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2022 (10D).</p>
Full article ">Figure A5 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2022 (10D).</p>
Full article ">Figure A6
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2022 (20D).</p>
Full article ">Figure A6 Cont.
<p>The convergence curves and boxplots of HERIME and other competitors based on CEC2022 (20D).</p>
Full article ">
53 pages, 21334 KiB  
Article
An Improved Grey Wolf Optimizer Based on Attention Mechanism for Solving Engineering Design Problems
by Yuming Zhang, Yuelin Gao, Liming Huang and Xiaofeng Xie
Symmetry 2025, 17(1), 50; https://doi.org/10.3390/sym17010050 - 30 Dec 2024
Viewed by 253
Abstract
The grey wolf optimization (GWO) algorithm is a simple and effective meta-heuristic algorithm that mimics the leadership of grey wolves and the social behavior of wolves in nature. However, the updating of GWO population positions only relies on the guidance of α-wolf, [...] Read more.
The grey wolf optimization (GWO) algorithm is a simple and effective meta-heuristic algorithm that mimics the leadership of grey wolves and the social behavior of wolves in nature. However, the updating of GWO population positions only relies on the guidance of α-wolf, β-wolf, and δ-wolf, and individuals are updated with equal weights. This results in the GWO search process being unable to utilize the knowledge of superior wolves better. Therefore, in this study, we propose for the first time an attention mechanism-based GWO (AtGWO). Firstly, when each position is updated, the attention strategy can adaptively assign the weight of the corresponding leader wolf to improve the global exploration ability. Second, with the introduction of omega-wolves, each position update is not only guided by the three leader wolves but also learns from their current optimal values. Finally, a hyperbolic tangent nonlinear function is used to control the convergence factor to better balance exploration and exploitation. To validate its effectiveness, AtGWO is compared with the latest GWO variant with other popular algorithms on the CEC-2014 (dim 30, 50) and CEC-2017 (dim 30, 50, 100) benchmark function sets. The experimental results indicate that AtGWO outperforms the GWO-related variants almost all the time in terms of mean, variance, and best value, which indicates its superior ability and robustness to find optimal solutions. And it is also competitive when compared to other algorithms in multimodal functions. AtGWO outperforms the comparison algorithms in terms of the mean and best value in six real-world engineering optimization problems. Full article
(This article belongs to the Section Engineering and Materials)
Show Figures

Figure 1

Figure 1
<p>The most popular meta-heuristic classifications and the year they were proposed; all meta-heuristic variants are excluded from this figure for the sake of brevity.</p>
Full article ">Figure 2
<p>(<bold>a</bold>,<bold>b</bold>) Denote the social structure of the grey wolf and <inline-formula><mml:math id="mm281"><mml:semantics><mml:mover accent="true"><mml:mi>A</mml:mi><mml:mo>→</mml:mo></mml:mover></mml:semantics></mml:math></inline-formula> control population searching for prey, respectively.</p>
Full article ">Figure 3
<p>Flowchart of the GWO.</p>
Full article ">Figure 4
<p>The embedding function curves (<bold>a</bold>) and control factor function curves (<bold>b</bold>), respectively.</p>
Full article ">Figure 5
<p>The computational process of the attention mechanism.</p>
Full article ">Figure 6
<p>The social hierarchy and characteristics of wolves.</p>
Full article ">Figure 7
<p>(<bold>a</bold>,<bold>b</bold>) comparisons of images with different convergence factors and different values of <inline-formula><mml:math id="mm282"><mml:semantics><mml:mi>γ</mml:mi></mml:semantics></mml:math></inline-formula>, respectively.</p>
Full article ">Figure 8
<p>Flowchart of the AtGWO.</p>
Full article ">Figure 9
<p>Subfigures (<bold>a</bold>–<bold>c</bold>) represent the average convergence plots for unimodal, hybrid, and composition functions in CEC-2014 (50-D), respectively.</p>
Full article ">Figure 10
<p>Average convergence curves of multimodal functions for CEC-2014 (50-D).</p>
Full article ">Figure 11
<p>Radar chart of the results of CEC-2014 (50-D).</p>
Full article ">Figure 12
<p>Box plots of multimodal functions for CEC-2014 (50-D).</p>
Full article ">Figure 13
<p>Subfigures (<bold>a</bold>–<bold>c</bold>) show boxplots of unimodal, hybrid, and composite functions in CEC-2014 (50-D), respectively.</p>
Full article ">Figure 13 Cont.
<p>Subfigures (<bold>a</bold>–<bold>c</bold>) show boxplots of unimodal, hybrid, and composite functions in CEC-2014 (50-D), respectively.</p>
Full article ">Figure 14
<p>Radar chart of the results of CEC-2017 (30-D).</p>
Full article ">Figure 15
<p>Average convergence curves of unimodal/multimodal functions for CEC-2017 (100-D).</p>
Full article ">Figure 16
<p>Average convergence curves of hybrid functions for CEC-2017 (100-D).</p>
Full article ">Figure 17
<p>Average convergence curves of composition functions for CEC-2017 (100-D).</p>
Full article ">Figure 18
<p>Box plots of hybrid/composition functions for CEC-2017 (100-D).</p>
Full article ">Figure 19
<p>Box plots of unimodal/multimodal functions for CEC-2017 (100-D).</p>
Full article ">Figure 20
<p>Box plots of CEC-2014(30-D) functions.</p>
Full article ">Figure 21
<p>Average convergence curves of CEC-2014 (30-D) functions.</p>
Full article ">Figure 22
<p>Average convergence curves of unimodal/multimodal functions for CEC-2017 (50-D).</p>
Full article ">Figure 23
<p>Average convergence curves of hybrid functions for CEC-2017 (50-D).</p>
Full article ">Figure 24
<p>Average convergence curves of composite functions for CEC-2017 (50-D).</p>
Full article ">Figure 25
<p>Box plots of CEC-2017 (50-D) functions.</p>
Full article ">Figure 26
<p>Box plots of CEC-2017 (50-D) functions.</p>
Full article ">Figure 27
<p>Box plots of CEC-2017 (50-D) functions.</p>
Full article ">Figure 28
<p>Radar charts of the results of CEC-2017 (50-D).</p>
Full article ">Figure 29
<p>Schematic representation of problem T/CSD.</p>
Full article ">Figure 30
<p>Schematic diagram of the problem PVD.</p>
Full article ">Figure 31
<p>Schematic representation of problem 3-BTD.</p>
Full article ">Figure 32
<p>Schematic illustration of the WBD problem.</p>
Full article ">Figure 33
<p>Schematic representation of problem SRD.</p>
Full article ">Figure 34
<p>Schematic of the problem GTD.</p>
Full article ">
20 pages, 901 KiB  
Article
Nature–Inspired Metaheuristic Optimization for Control Tuning of Complex Systems
by Jesús Garicano-Mena and Matilde Santos
Biomimetics 2025, 10(1), 13; https://doi.org/10.3390/biomimetics10010013 - 30 Dec 2024
Viewed by 285
Abstract
In this contribution, a methodology for the optimal tuning of controllers of complex systems based on meta–heuristic techniques is proposed. Two bio-inspired meta-heuristic optimization algorithms –the Antlion Optimizer (ALO) and the Whale Optimization Algorithm (WOA)– have been applied to two different dynamic systems: [...] Read more.
In this contribution, a methodology for the optimal tuning of controllers of complex systems based on meta–heuristic techniques is proposed. Two bio-inspired meta-heuristic optimization algorithms –the Antlion Optimizer (ALO) and the Whale Optimization Algorithm (WOA)– have been applied to two different dynamic systems: the Hoop & Ball electromechanical system, a system where a linearized description is adequate; and to a Wind Turbine–Generator–Rectifier, as an example of a complex non-linear dynamic system. The performance of the ALO and WOA techniques for the tuning of conventional PID controllers is evaluated in relation to the number of agents nS and the maximum number of iterations nMaxIter; given the stochastic nature of both methods, repeatability is also addressed. Finally, the computational effort required for their implementation is considered. By analyzing the obtained metrics, it is observed that both methods provide comparable results for the two systems considered and, therefore, the ALO and WOA techniques can complement each other by exploiting the advantages of each of them in controller tuning. Full article
Show Figures

Figure 1

Figure 1
<p><tt>HB</tt> system: sketch, reproduced from [<a href="#B17-biomimetics-10-00013" class="html-bibr">17</a>].</p>
Full article ">Figure 2
<p><tt>HB</tt> system: in (<b>a</b>), evolution of the cost function; in (<b>b</b>), different solutions found by the optimization algorithms <tt>ALO</tt> (∘) and <tt>WOA</tt> (<span style="color: #FF0000"><b>*</b></span>); in (<b>c</b>,<b>d</b>), variability of the system solutions identified by <tt>ALO</tt>; in (<b>e</b>,<b>f</b>) the same for <tt>WOA</tt>.</p>
Full article ">Figure 3
<p><tt>WTGRL</tt> system: wind gusts affecting the wind turbine subsystem.</p>
Full article ">Figure 4
<p><tt>WTGRL</tt> system: simulink model of the wind turbine—generator—load with <span class="html-italic">PI</span> control for the angle of attack <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <tt>MPPT</tt> control for the rectifier subsystem. The wind turbine, the generator and the rectifier subsystems are shown in (<b>a</b>); the rectifier and the DC-DC boost converter are shown in (<b>b</b>).</p>
Full article ">Figure 4 Cont.
<p><tt>WTGRL</tt> system: simulink model of the wind turbine—generator—load with <span class="html-italic">PI</span> control for the angle of attack <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <tt>MPPT</tt> control for the rectifier subsystem. The wind turbine, the generator and the rectifier subsystems are shown in (<b>a</b>); the rectifier and the DC-DC boost converter are shown in (<b>b</b>).</p>
Full article ">Figure 5
<p>Flowchart of the methodology of PID tuning with ALO/WOA.</p>
Full article ">Figure 6
<p><tt>HB</tt> system: sensitivity analysis of convergence for different combinations of number of agents <math display="inline"><semantics> <msub> <mi>n</mi> <mi>S</mi> </msub> </semantics></math> and number of iterations <math display="inline"><semantics> <msub> <mi>n</mi> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mi>t</mi> <mi>I</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </semantics></math>: <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> runs for <tt>ALO</tt> (<span style="color: #000000">—∘—</span>) and <tt>WOA</tt> (<span style="color: #FF0000">—□—</span>), respectively.</p>
Full article ">Figure 7
<p><tt>HB</tt> system: comparison of the optimal solutions identified by <tt>ALO</tt> (<span style="color: #000000">—∘—</span>) and <tt>WOA</tt> (<span style="color: #FF0000">—□—</span>).</p>
Full article ">Figure 8
<p><tt>HB</tt> system: unit step response of the controlled system found by <tt>ALO</tt> (<span style="color: #000000">—∘—</span>) and <tt>WOA</tt> (<span style="color: #FF0000">—□—</span>).</p>
Full article ">Figure 9
<p><tt>WTGRL</tt> system: in (<b>a</b>), evolution of the cost function; in (<b>b</b>), different solutions identified by <tt>ALO</tt> (∘) and <tt>WOA</tt> (<span style="color: #FF0000"><b>*</b></span>); in (<b>c</b>,<b>d</b>), comparison of the optimal solutions found by <tt>ALO</tt> and <tt>WOA</tt>  algorithms.</p>
Full article ">
28 pages, 12012 KiB  
Article
Integrated Scheduling of Multi-Objective Job Shops and Material Handling Robots with Reinforcement Learning Guided Meta-Heuristics
by Zhangying Xu, Qi Jia, Kaizhou Gao, Yaping Fu, Li Yin and Qiangqiang Sun
Mathematics 2025, 13(1), 102; https://doi.org/10.3390/math13010102 - 30 Dec 2024
Viewed by 291
Abstract
This study investigates the integrated multi-objective scheduling problems of job shops and material handling robots (MHR) with minimising the maximum completion time (makespan), earliness or tardiness, and total energy consumption. The collaborative scheduling of MHR and machines can enhance efficiency and reduce costs. [...] Read more.
This study investigates the integrated multi-objective scheduling problems of job shops and material handling robots (MHR) with minimising the maximum completion time (makespan), earliness or tardiness, and total energy consumption. The collaborative scheduling of MHR and machines can enhance efficiency and reduce costs. First, a mathematical model is constructed to articulate the concerned problems. Second, three meta-heuristics, i.e., genetic algorithm (GA), differential evolution, and harmony search, are employed, and their variants with seven local search operators are devised to enhance solution quality. Then, reinforcement learning algorithms, i.e., Q-learning and state–action–reward–state–action (SARSA), are utilised to select suitable local search operators during iterations. Three reward setting strategies are designed for reinforcement learning algorithms. Finally, the proposed algorithms are examined by solving 82 benchmark instances. Based on the solutions and their analysis, we conclude that the proposed GA integrating SARSA with the first reward setting strategy is the most competitive one among 27 compared algorithms. Full article
Show Figures

Figure 1

Figure 1
<p>An example of a scheduling solution for multi-objective JSP with MHR.</p>
Full article ">Figure 2
<p>Multi-objective JSP with MHR coding method.</p>
Full article ">Figure 3
<p>Neighbourhood structures.</p>
Full article ">Figure 4
<p>Framework of RL.</p>
Full article ">Figure 5
<p>The framework of the proposed algorithms.</p>
Full article ">Figure 6
<p>Parameter level trend of GA.</p>
Full article ">Figure 7
<p>Parameter level trend of DE.</p>
Full article ">Figure 8
<p>Parameter level trend of HS.</p>
Full article ">Figure 9
<p>Parameter level trend of Q-learning.</p>
Full article ">Figure 10
<p>Parameter level trend of SARSA.</p>
Full article ">Figure 11
<p>Nemenyi post hoc analysis of algorithms on benchmark instances. (<b>a</b>) Nemenyi post hoc analysis of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Nemenyi post hoc analysis of algorithms IGD values.</p>
Full article ">Figure 12
<p>Distribution of ranks for algorithms across benchmark instances. (<b>a</b>) Ranked distribution of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Ranked distribution of algorithms IGD values.</p>
Full article ">Figure 13
<p>Nemenyi post hoc analysis of algorithms on benchmark instances. (<b>a</b>) Nemenyi post hoc analysis of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Nemenyi post hoc analysis of algorithms IGD values.</p>
Full article ">Figure 14
<p>Distribution of ranks for algorithms across benchmark instances. (<b>a</b>) Ranked distribution of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Ranked distribution of algorithms IGD values.</p>
Full article ">Figure 15
<p>Nemenyi post hoc analysis of algorithms on benchmark instances. (<b>a</b>) Nemenyi post hoc analysis of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Nemenyi post hoc analysis of algorithms IGD values.</p>
Full article ">Figure 16
<p>Distribution of ranks for algorithms across benchmark instances. (<b>a</b>) Ranked distribution of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Ranked distribution of algorithms IGD values.</p>
Full article ">Figure 17
<p>Nemenyi post hoc analysis of seven algorithms on benchmark instances. (<b>a</b>) Nemenyi post hoc analysis of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Nemenyi post hoc analysis of algorithms IGD values.</p>
Full article ">Figure 18
<p>Distribution of ranks for algorithms across benchmark instances. (<b>a</b>) Ranked distribution of algorithms <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> values. (<b>b</b>) Ranked distribution of algorithms IGD values.</p>
Full article ">
36 pages, 6141 KiB  
Article
Unveiling the Potential of Metaheuristics in Transportation: A Path Towards Efficiency, Optimization, and Intelligent Management
by Álvaro Bueno-Ferrer, Jaime De Pablo Valenciano and Jerónimo De Burgos Jiménez
Infrastructures 2025, 10(1), 4; https://doi.org/10.3390/infrastructures10010004 - 28 Dec 2024
Viewed by 792
Abstract
Importance: This bibliometric analysis of the application of metaheuristics in transportation and logistics examines over two decades of research (1999–present), aiming to uncover global trends, anticipate future directions, and highlight how interconnections between key factors facilitate the development of practical and sustainable solutions [...] Read more.
Importance: This bibliometric analysis of the application of metaheuristics in transportation and logistics examines over two decades of research (1999–present), aiming to uncover global trends, anticipate future directions, and highlight how interconnections between key factors facilitate the development of practical and sustainable solutions for the industry. Methodology: A quantitative approach is employed to analyze the evolution of the discipline by reviewing an extensive database of relevant research and key authors and utilizing advanced data processing tools. This analysis enables the assessment of advances in the optimization of metaheuristic models, with an impact on time and cost savings from an economically sustainable perspective. Results: The use of metaheuristics optimizes the efficiency and competitiveness of the transportation sector while promoting a positive economic impact on companies. The main areas of application are optimization and metaheuristic methods, cost and operational efficiency, planning and scheduling, logistics and transportation, supply chain and logistics networks, energy and sustainability, and demand and users. Additionally, genetic algorithms stand out as particularly important. Conclusions: This research provides a comprehensive and detailed view of the impact of metaheuristics on the transportation sector, highlighting their current and future trends (such as artificial intelligence) and their economic relevance. Full article
Show Figures

Figure 1

Figure 1
<p>The stages of bibliometric analysis.</p>
Full article ">Figure 2
<p>Annual scientific production. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 3
<p>Most relevant sources. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 4
<p>Source’s cumulative dynamic. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 5
<p>Most relevant authors. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 6
<p>Authors’ production over time. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 7
<p>Most relevant affiliations. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 8
<p>Most cited countries. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 9
<p>Collaboration between countries. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 10
<p>Keyword cloud. Generated with Bibliometrix (2024 version).</p>
Full article ">Figure 11
<p>Co-occurrence keywords. Generated with VOSviewer 1.6.18.0 version.</p>
Full article ">Figure 12
<p>Co-occurrence of metaheuristics keywords: a direct relationship. Generated with VOSviewer 1.6.18.0 version.</p>
Full article ">Figure 13
<p>Co-occurrence of metaheuristics keywords: main relationships between key terms. Generated with VOSviewer 1.6.18.0 version.</p>
Full article ">
25 pages, 1471 KiB  
Article
Optimal Placement and Sizing of Modular Series Static Synchronous Compensators (M-SSSCs) for Enhanced Transmission Line Loadability, Loss Reduction, and Stability Improvement
by Cristian Urrea-Aguirre, Sergio D. Saldarriaga-Zuluaga, Santiago Bustamante-Mesa, Jesús M. López-Lezama and Nicolás Muñoz-Galeano
Processes 2025, 13(1), 34; https://doi.org/10.3390/pr13010034 - 27 Dec 2024
Viewed by 392
Abstract
This paper addresses the optimal placement and sizing of Modular Static Synchronous Series Compensators (M-SSSCs) to enhance power system performance. The proposed methodology optimizes four key objectives: reducing transmission line loadability, minimizing power losses, mitigating voltage deviations, and enhancing voltage stability using the [...] Read more.
This paper addresses the optimal placement and sizing of Modular Static Synchronous Series Compensators (M-SSSCs) to enhance power system performance. The proposed methodology optimizes four key objectives: reducing transmission line loadability, minimizing power losses, mitigating voltage deviations, and enhancing voltage stability using the L-index. The methodology is validated on two systems: the IEEE 14-bus test network and a sub-area of the Colombian power grid, characterized by aging infrastructure and operational challenges. The optimization process employs three metaheuristic algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Teaching–Learning-Based Optimization (TLBO)—to identify optimal configurations. System performance is analyzed under both normal operating conditions and contingency scenarios (N − 1). The results demonstrate that M-SSSC deployment significantly reduces congestion, enhances voltage stability, and improves overall system efficiency. Furthermore, this work highlights the practical application of M-SSSC in modernizing real-world grids, aligning with sustainable energy transition goals. This study identifies the optimal M-SSSC configurations and placement alternatives for the analyzed systems. Specifically, for the Colombian sub-area, the most suitable solutions involve installing M-SSSC devices in capacitive mode on the Termocol–Guajira and Santa Marta–Guajira 220 kV transmission lines. Full article
Show Figures

Figure 1

Figure 1
<p>Basic operating diagram of the M-SSSC.</p>
Full article ">Figure 2
<p>I-V and I-X characteristic of the M-SSSC device.</p>
Full article ">Figure 3
<p>Flowchart of the implemented GA.</p>
Full article ">Figure 4
<p>Flowchart of the implemented PSO.</p>
Full article ">Figure 5
<p>Flowchart of the implemented TLBO algorithm.</p>
Full article ">Figure 6
<p>IEEE 14-bus test system.</p>
Full article ">Figure 7
<p>Results for different metaheuristics (IEEE 14-bus test system).</p>
Full article ">Figure 8
<p>Computation time vs. value of the OF.</p>
Full article ">Figure 9
<p>Sub-area GCM in 2024.</p>
Full article ">Figure 10
<p>Sub-area GCM in 2026.</p>
Full article ">
15 pages, 2237 KiB  
Article
Wireless Sensor Network Coverage Optimization Using a Modified Marine Predator Algorithm
by Guohao Wang and Xun Li
Sensors 2025, 25(1), 69; https://doi.org/10.3390/s25010069 - 26 Dec 2024
Viewed by 299
Abstract
To solve the coverage problem caused by the random deployment of wireless sensor network nodes in the forest fire-monitoring system, a modified marine predator algorithm (MMPA) is proposed. Four modifications have been made based on the standard marine predator algorithm (MPA). Firstly, tent [...] Read more.
To solve the coverage problem caused by the random deployment of wireless sensor network nodes in the forest fire-monitoring system, a modified marine predator algorithm (MMPA) is proposed. Four modifications have been made based on the standard marine predator algorithm (MPA). Firstly, tent mapping is integrated into the initialization step to improve the searching ability of the early stage. Secondly, a hybrid search strategy is used to enhance the ability to search and jump out of local optimum. Thirdly, the golden sine guiding mechanism is applied to accelerate the convergence of the algorithm. Finally, a stage-adjustment strategy is proposed to make the transition of stages more smoothly. Six specific test functions chosen from the CEC2017 function and the benchmark function are used to evaluate the performance of MMPA. It shows that this modified algorithm has good optimization capability and stability compared to MPA, grey wolf optimizer, sine cosine algorithm, and sea horse optimizer. The results of coverage tests show that MMPA has a better uniformity of node distribution compared to MPA. The average coverage rates of MMPA are the highest compared to the commonly used metaheuristic-based algorithms, which are 91.8% in scenario 1, 95.98% in scenario 2, and 93.88% in scenario 3, respectively. This demonstrates the superiority of this proposed algorithm in coverage optimization of the wireless sensor network. Full article
(This article belongs to the Section Sensor Networks)
Show Figures

Figure 1

Figure 1
<p>Flow chart of MMPA.</p>
Full article ">Figure 2
<p>Convergence plot comparison between the proposed MMPA and the other four algorithms on the test functions of (<b>a</b>) F1, (<b>b</b>) F2, (<b>c</b>) F3, (<b>d</b>) F4, (<b>e</b>) F5, and (<b>f</b>) F6.</p>
Full article ">Figure 3
<p>Distribution maps of sensor nodes at (<b>a</b>) scenario 1 using MPA, (<b>b</b>) scenario 1 using MMPA, (<b>c</b>) scenario 2 using MPA, (<b>d</b>) scenario 2 using MMPA, (<b>e</b>) scenario 3 using MPA, and (<b>f</b>) scenario 3 using MMPA, respectively.</p>
Full article ">Figure 3 Cont.
<p>Distribution maps of sensor nodes at (<b>a</b>) scenario 1 using MPA, (<b>b</b>) scenario 1 using MMPA, (<b>c</b>) scenario 2 using MPA, (<b>d</b>) scenario 2 using MMPA, (<b>e</b>) scenario 3 using MPA, and (<b>f</b>) scenario 3 using MMPA, respectively.</p>
Full article ">
26 pages, 5504 KiB  
Article
Advanced Hybrid Brain Tumor Segmentation in MRI: Elephant Herding Optimization Combined with Entropy-Guided Fuzzy Clustering
by Baiju Karun, Arunprasath Thiyagarajan, Pallikonda Rajasekaran Murugan, Natarajan Jeyaprakash, Kottaimalai Ramaraj and Rakhee Makreri
Math. Comput. Appl. 2025, 30(1), 1; https://doi.org/10.3390/mca30010001 - 25 Dec 2024
Viewed by 252
Abstract
Accurate and early detection of brain tumors is essential for improving clinical outcomes and guiding effective treatment planning. Traditional segmentation techniques in MRI often struggle with challenges such as noise, intensity variations, and complex tumor morphologies, which can hinder their effectiveness in critical [...] Read more.
Accurate and early detection of brain tumors is essential for improving clinical outcomes and guiding effective treatment planning. Traditional segmentation techniques in MRI often struggle with challenges such as noise, intensity variations, and complex tumor morphologies, which can hinder their effectiveness in critical healthcare scenarios. This study proposes an innovative hybrid methodology that integrates advanced metaheuristic optimization and entropy-based fuzzy clustering to enhance segmentation precision in brain tumor detection. This method combines the nature-inspired Elephant Herding Optimization (EHO) algorithm with Entropy-Driven Fuzzy C-Means (EnFCM) clustering, offering significant improvements over conventional methods. EHO is utilized to optimize the clustering process, enhancing the algorithm’s ability to delineate tumor boundaries, while entropy-based fuzzy clustering accounts for intensity inhomogeneity and diverse tumor characteristics, promoting more consistent and reliable segmentation results. This approach was evaluated using the BraTS challenge dataset, a benchmark in the field of brain tumor segmentation. The results demonstrate marked improvements across several performance metrics, including Dice similarity, mean squared error (MSE), peak signal-to-noise ratio (PSNR), and the Tanimoto coefficient (TC), underscoring this method’s robustness and segmentation accuracy. By managing image noise and reducing computational demands, the EHO-EnFCM approach not only captures intricate tumor structures but also facilitates efficient image processing, making it suitable for real-time clinical applications. Overall, the findings reveal the potential of this hybrid approach to advance MRI-based tumor detection, offering a promising tool that enhances both accuracy and computational efficiency for medical imaging and diagnosis. Full article
Show Figures

Figure 1

Figure 1
<p>Schematic of elephant life cycle.</p>
Full article ">Figure 2
<p>Illustration of EHO algorithms.</p>
Full article ">Figure 3
<p>Entropy-Driven Fuzzy C-Means (EnFCM) clustering.</p>
Full article ">Figure 4
<p>Workflow for EHO-EnFCM technique.</p>
Full article ">Figure 5
<p>Segmentation results obtained by applying the proposed EHO-EnFCM algorithm to the BraTS 2013 dataset.</p>
Full article ">Figure 6
<p>Segmentation results obtained by applying the proposed EHO-EnFCM algorithm to the BraTS 2015 dataset.</p>
Full article ">Figure 7
<p>Bar chart comparing Dice Score (DS) values achieved by various brain tumor segmentation methods evaluated on BraTS Challenge datasets (2013–2021). The methods include Lyksborg et al. [<a href="#B46-mca-30-00001" class="html-bibr">46</a>], Zikic et al. [<a href="#B47-mca-30-00001" class="html-bibr">47</a>], Havaei et al. [<a href="#B48-mca-30-00001" class="html-bibr">48</a>], Kamnitsas et al. [<a href="#B49-mca-30-00001" class="html-bibr">49</a>], Isensee et al. [<a href="#B50-mca-30-00001" class="html-bibr">50</a>], Wang et al. [<a href="#B51-mca-30-00001" class="html-bibr">51</a>], Jiang et al. [<a href="#B52-mca-30-00001" class="html-bibr">52</a>], Mushtaq et al. [<a href="#B53-mca-30-00001" class="html-bibr">53</a>], Ramaraj et al. [<a href="#B3-mca-30-00001" class="html-bibr">3</a>], Kronberg et al. [<a href="#B54-mca-30-00001" class="html-bibr">54</a>], Guan et al. [<a href="#B55-mca-30-00001" class="html-bibr">55</a>], Wang et al. [<a href="#B56-mca-30-00001" class="html-bibr">56</a>], Zhang et al. [<a href="#B57-mca-30-00001" class="html-bibr">57</a>], Peiris et al. [<a href="#B58-mca-30-00001" class="html-bibr">58</a>], and Jia &amp; Shu [<a href="#B59-mca-30-00001" class="html-bibr">59</a>]. The proposed method, EHO-ENFCM, is benchmarked across multiple datasets for comparison. (Note: The years shown along the <span class="html-italic">x</span>-axis represent the BraTS dataset years used for evaluation, not the publication years of the cited studies.).</p>
Full article ">Figure A1
<p>Example of FCM based segmentation.</p>
Full article ">
39 pages, 3488 KiB  
Article
Parameter Extraction for Photovoltaic Models with Flood-Algorithm-Based Optimization
by Yacine Bouali and Basem Alamri
Mathematics 2025, 13(1), 19; https://doi.org/10.3390/math13010019 - 25 Dec 2024
Viewed by 444
Abstract
Accurately modeling photovoltaic (PV) cells is crucial for optimizing PV systems. Researchers have proposed numerous mathematical models of PV cells to facilitate the design and simulation of PV systems. Usually, a PV cell is modeled by equivalent electrical circuit models with specific parameters, [...] Read more.
Accurately modeling photovoltaic (PV) cells is crucial for optimizing PV systems. Researchers have proposed numerous mathematical models of PV cells to facilitate the design and simulation of PV systems. Usually, a PV cell is modeled by equivalent electrical circuit models with specific parameters, which are often unknown; this leads to formulating an optimization problem that is addressed through metaheuristic algorithms to identify the PV cell/module parameters accurately. This paper introduces the flood algorithm (FLA), a novel and efficient optimization approach, to extract parameters for various PV models, including single-diode, double-diode, and three-diode models and PV module configurations. The FLA’s performance is systematically evaluated against nine recently developed optimization algorithms through comprehensive comparative and statistical analyses. The results highlight the FLA’s superior convergence speed, global search capability, and robustness. This study explores two distinct objective functions to enhance accuracy: one based on experimental current–voltage data and another integrating the Newton–Raphson method. Applying metaheuristic algorithms with the Newton–Raphson-based objective function reduced the root-mean-square error (RMSE) more effectively than traditional methods. These findings establish the FLA as a computationally efficient and reliable approach to PV parameter extraction, with promising implications for advancing PV system design and simulation. Full article
(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)
Show Figures

Figure 1

Figure 1
<p>Equivalent circuit of single-diode model.</p>
Full article ">Figure 2
<p>Equivalent circuit of double-diode model.</p>
Full article ">Figure 3
<p>Equivalent circuit of three-diode model.</p>
Full article ">Figure 4
<p>Equivalent circuit of PV module model.</p>
Full article ">Figure 5
<p>Concept of objective function <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> calculation.</p>
Full article ">Figure 6
<p>Concept of objective function <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math> calculation.</p>
Full article ">Figure 7
<p>The flowchart of FLA.</p>
Full article ">Figure 8
<p>RMSE evolution of different algorithms for the SDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>RMSE evolution of different algorithms for the SDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Average CPU times of different algorithms for the SDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>RMSE evolution of the FLA for the SDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>RMSE evolution of different algorithms for the DDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>RMSE evolution of different algorithms for the DDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 14
<p>Average CPU times of different algorithms for the DDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 15
<p>RMSE evolution of the FLA for the DDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 16
<p>RMSE evolution of different algorithms for the TDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 17
<p>RMSE evolution of different algorithms for the TDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 18
<p>Average CPU times of different algorithms for the TDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 19
<p>RMSE evolution of the FLA for the TDM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 20
<p>The I-V curves of the FLA for the (<b>a</b>) SDM, (<b>b</b>) DDM, and (<b>c</b>) TDM of RTC France, using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 21
<p>The P-V curves of the FLA for the (<b>a</b>) SDM, (<b>b</b>) DDM, and (<b>c</b>) TDM of RTC France, using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 22
<p>RMSE evolution of different algorithms for the PVM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 23
<p>RMSE evolution of different algorithms for the PVM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 24
<p>RMSE evolution of the FLA for the PVM using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 25
<p>The relative error values of the simulated current data and the experimental current data using the FLA for Photowatt-PWP201.</p>
Full article ">Figure 26
<p>The (<b>a</b>) I-V and (<b>b</b>) P-V curves of the FLA for Photowatt-PWP201, using <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>O</mi> <mi>b</mi> <msub> <mi>j</mi> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">
25 pages, 4843 KiB  
Article
Ameliorated Chameleon Algorithm-Based Shape Optimization of Disk Wang–Ball Curves
by Yan Liang, Rui Yang, Xianzhi Hu and Gang Hu
Biomimetics 2025, 10(1), 3; https://doi.org/10.3390/biomimetics10010003 - 24 Dec 2024
Viewed by 319
Abstract
The shape design and optimization of complex disk curves is a crucial and intractable technique in computer-aided design and manufacturing (CAD/CAM). Based on disk Wang–Ball (DWB) curves, this paper defines a novel combined disk Wang–Ball (CDWB) curve with constrained parameters and investigates the [...] Read more.
The shape design and optimization of complex disk curves is a crucial and intractable technique in computer-aided design and manufacturing (CAD/CAM). Based on disk Wang–Ball (DWB) curves, this paper defines a novel combined disk Wang–Ball (CDWB) curve with constrained parameters and investigates the shape optimization of CDWB curves by using the multi-strategy ameliorated chameleon swarm algorithm (MCSA). Firstly, in order to meet the various shape design requirements, the CDWB curves consisting of n DWB curves are defined, and the G1 and G2 geometric continuity conditions for the curves are derived. Secondly, the shape optimization of CDWB curves is considered as a minimization problem with curve energy as the objective, and an optimization model is developed under the constraints of the splicing conditions. Finally, the meta-heuristic algorithm MCSA is introduced to solve the established optimization model to obtain the minimum energy value, and its performance is verified by comparison with other algorithms. The results of representative numerical examples confirm the effectiveness and competitiveness of the MCSA for the CDWB curve shape optimization problems. Full article
Show Figures

Figure 1

Figure 1
<p>Main problems and methods.</p>
Full article ">Figure 2
<p>CDWB curve with overall G<sup>1</sup> continuity (<math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>). (<b>a</b>) The center curve; (<b>b</b>) the control disks; (<b>c</b>) the CDWB curve.</p>
Full article ">Figure 3
<p>CDWB curve with overall G<sup>1</sup> continuity (<math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>). (<b>a</b>) The center curve; (<b>b</b>) the control disks; (<b>c</b>) the CDWB curve.</p>
Full article ">Figure 4
<p>CDWB curve with overall G<sup>2</sup> continuity (<math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>). (<b>a</b>) The center curve; (<b>b</b>) the control disks; (<b>c</b>) the CDWB curve.</p>
Full article ">Figure 5
<p>The CDWB curve with overall G<sup>2</sup> continuity (<math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.3</mn> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>). (<b>a</b>) The center curve; (<b>b</b>) the control disks; (<b>c</b>) the CDWB curve.</p>
Full article ">Figure 6
<p>Modeling based on CDWB curves. (<b>a</b>) Windmill; (<b>b</b>) spring; (<b>c</b>) Chinese character “乐”.</p>
Full article ">Figure 7
<p>Flow chart for solving the energy minimum model based on MCSA.</p>
Full article ">Figure 8
<p>Chinese character “弓” based on CDWB curve with thickness. (<b>a</b>) GWO, (<b>b</b>) STOA, (<b>c</b>) MVO. (<b>d</b>) AOA, (<b>e</b>) SCA, (<b>f</b>) DE. (<b>g</b>) WSO, (<b>h</b>) MCSA, (<b>i</b>) convergence curves.</p>
Full article ">Figure 9
<p>“Snake” pattern based on CDWB curve. (<b>a</b>) MVO, (<b>b</b>) AOA, (<b>c</b>) GJO. (<b>d</b>) STOA, (<b>e</b>) SCA, (<b>f</b>) DE. (<b>g</b>) WSO, (<b>h</b>) MCSA, (<b>i</b>) convergence curves.</p>
Full article ">Figure 10
<p>“Chinese knot” pattern based on CDWB curve. (<b>a</b>) SCA, (<b>b</b>) DE, (<b>c</b>) GJO. (<b>d</b>) MVO, (<b>e</b>) AOA, (<b>f</b>) STOA. (<b>g</b>) WSO, (<b>h</b>) MCSA, (<b>i</b>) convergence curves.</p>
Full article ">
Back to TopTop