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Advances in Natural Computing: Methods and Application

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 18850

Special Issue Editor

Special Issue Information

Dear Colleagues,

One of the ever-present grand challenges and central goals of computer science is to understand the world around us in terms of information processing. Each time progress is made in achieving this goal, both the world around us and computer science benefit.

Nature is a dominating part of the world around us, and one way to understand it in terms of information processing is to study computing taking place in nature. Natural computing is concerned with this type of computing and with its main benefit for computer science, viz., human-designed computing inspired by nature.

By its very nature, the science of natural computing is genuinely interdisciplinary; therefore, natural computing forms a bridge between natural sciences and computer science. In this way, natural computing elevates computer science to an even more prominent role in the broad rainbow of scientific disciplines.

Human-designed computing inspired by nature is based on the use of paradigms, principles, and mechanisms underlying natural systems. Some disciplines of human-designed computing are relatively old and are well established by now. Well-known examples of such disciplines are evolutionary computing and neural computing. Evolutionary algorithms are based on the concepts of mutation, recombination, and natural selection from the theory of evolution, while neural networks are based on concepts originating in the study of the highly interconnected neural structures in the brain and nervous system. On the other hand, molecular computing and quantum computing are younger disciplines of natural computing: molecular computing is based on paradigms from molecular biology, while quantum computing is based on quantum physics and exploits quantum parallelism.

Natural computing refers to computational processes observed in nature, and human-designed computing inspired by nature. When complex natural phenomena are analyzed in terms of computational processes, our understanding of both the nature and essence of computation is enhanced. Characteristic for human-designed computing inspired by nature is the metaphorical use of concepts, principles, and mechanisms underlying natural systems. Natural computing includes evolutionary algorithms, neural networks, molecular computing, and quantum computing.

The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in different fields of evolutionary algorithms, neural networks, molecular computing, quantum computing and artificial immune systems, and others.

Prof. Dr. Gaige Wang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • natural computing
  • evolutionary algorithms
  • swarm intelligence
  • neural networks
  • molecular computing
  • quantum computing
  • artificial immune systems

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Published Papers (8 papers)

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Research

Jump to: Review

12 pages, 2213 KiB  
Article
Short Text Event Coreference Resolution Based on Context Prediction
by Xinyou Yong, Chongqing Zeng, Lican Dai, Wanli Liu and Shimin Cai
Appl. Sci. 2024, 14(2), 527; https://doi.org/10.3390/app14020527 - 7 Jan 2024
Viewed by 1398
Abstract
Event coreference resolution is the task of clustering event mentions that refer to the same entity or situation in text and performing operations like linking, information completion, and validation. Existing methods model this task as a text similarity problem, focusing solely on semantic [...] Read more.
Event coreference resolution is the task of clustering event mentions that refer to the same entity or situation in text and performing operations like linking, information completion, and validation. Existing methods model this task as a text similarity problem, focusing solely on semantic information, neglecting key features like event trigger words and subject. In this paper, we introduce the event coreference resolution based on context prediction (ECR-CP) as an alternative to traditional methods. ECR-CP treats the task as sentence-level relationship prediction, examining if two event descriptions can create a continuous sentence-level connection to identify coreference. We enhance ECR-CP with a fusion coding model (ECR-CP+) to incorporate event-specific structure and semantics. The model identifies key text information such as trigger words, argument roles, event types, and tenses via an event extraction module, integrating them into the encoding process as auxiliary features. Extensive experiments on the benchmark CCKS 2021 dataset demonstrate that ECR-CP and ECR-CP+ outperform existing methods in terms of precision, recall, and F1 Score, indicating their superior performance. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>Example illustration of ECR task.</p>
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<p>Model architecture of ECR-CP with the fusion coding model (i.e., ECR-CP<sup>+</sup>).</p>
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18 pages, 3414 KiB  
Article
Distributed Genetic Algorithm for Community Detection in Large Graphs with a Parallel Fuzzy Cognitive Map for Focal Node Identification
by Haritha K., Judy M. V., Konstantinos Papageorgiou and Elpiniki Papageorgiou
Appl. Sci. 2023, 13(15), 8735; https://doi.org/10.3390/app13158735 - 28 Jul 2023
Cited by 1 | Viewed by 1476
Abstract
This study addresses the importance of focal nodes in understanding the structural composition of networks. To identify these crucial nodes, a novel technique based on parallel Fuzzy Cognitive Maps (FCMs) is proposed. By utilising the focal nodes produced by the parallel FCMs, the [...] Read more.
This study addresses the importance of focal nodes in understanding the structural composition of networks. To identify these crucial nodes, a novel technique based on parallel Fuzzy Cognitive Maps (FCMs) is proposed. By utilising the focal nodes produced by the parallel FCMs, the algorithm efficiently creates initial clusters within the population. The community discovery process is accelerated through a distributed genetic algorithm that leverages the focal nodes obtained from the parallel FCM. This approach mitigates the randomness of the algorithm, addressing the limitations of the random population selection commonly found in genetic algorithms. The proposed algorithm improves the performance of the genetic algorithm by enabling informed decision making and forming a better initial population. This enhancement leads to improved convergence and overall algorithm performance. Furthermore, as graph sizes grow, traditional algorithms struggle to handle the increased complexity. To address this challenge, distributed algorithms are necessary for effectively managing larger data sizes and complexity. The proposed method is evaluated on diverse benchmark networks, encompassing both weighted and unweighted networks. The results demonstrate the superior scalability and performance of the proposed approach compared to the existing state-of-the-art methods. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>The genetic algorithm framework for community detection.</p>
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<p>Constructing the FCM using the initial state vector and weight matrix.</p>
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<p>Parallel FCM learning [<a href="#B60-applsci-13-08735" class="html-bibr">60</a>].</p>
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<p>Parallelizing the population in the GA.</p>
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<p>One of the directed acyclic graphs of the parallel FCM processing.</p>
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<p>Comparison of the execution times of a distributed GA with a parallel FCM and other genetic algorithms for community detection.</p>
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<p>Derived time complexity.</p>
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<p>Actual running time.</p>
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14 pages, 3811 KiB  
Article
Short Words for Writer Identification Using Neural Networks
by Georgia Koukiou
Appl. Sci. 2023, 13(11), 6841; https://doi.org/10.3390/app13116841 - 5 Jun 2023
Cited by 2 | Viewed by 1607
Abstract
In biometrics, it is desirable to distinguish a person using only a short sample of his handwriting. This problem is treated in the present work using only a short word with three letters. It is shown that short words can contribute to high-performance [...] Read more.
In biometrics, it is desirable to distinguish a person using only a short sample of his handwriting. This problem is treated in the present work using only a short word with three letters. It is shown that short words can contribute to high-performance writer identification if line characteristics are extracted using morphological directional transformations. Thus, directional morphological structuring elements are used as a tool for extracting this kind of information with the morphological opening operation. The line characteristics are organized based on Markov chains so that the elements of the transition matrix are used as feature vectors for identification. The Markov chains describe the alternation in the directional line features along the word. The analysis of the feature space is carried out using the Fisher linear discriminant method. The identification performance is assessed using neural networks, where the simplest neural structures are sought. The capabilities of these simple neural structures are investigated theoretically concerning the achieved separability into the feature space. The identification capabilities of the neural networks are further assessed using the leave-one-out method. It is proved that the neural methods achieve identification performance that approaches 100%. The significance of the proposed method is that it is the only one in the literature that presents high identification performance using only one short word. Furthermore, the features used as well as the classifiers are simple and robust. The method is independent of the language used regardless of the direction of writing. The NIST database is used for extracting short-length words having only three letters each. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>Schematic representation showing the proposed writer identification procedure.</p>
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<p>One of the full-page binary images of the 3669 HSFs from the original NIST Special Database 19 (f0000_14.png). Six replicas for the word “the” and three for the word “and” were extracted to uniquely represent the specific writer.</p>
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<p>A thresholded word image after negation and line-thinning using morphological transforms.</p>
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<p>Directional structuring elements with a length of 3 pixels.</p>
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<p>Processing of the letter ‘h’ in the word ‘the’ with morphological opening using a vertical directional structuring element of length 3. The vertical lines in the letter remain unchanged. The vertical line content of the letter is obvious from the strips that contain white information.</p>
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<p>The word ‘the’ in image f0000_1_1.tif from the NIST Special Database 19 and the corresponding sequence of the orientation SEs from <a href="#applsci-13-06841-f003" class="html-fig">Figure 3</a> that fit along the word. Each number corresponds to one of the SEs. Zero corresponds to blank space.</p>
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<p>Writer discrimination results. The clusters correspond to the same word “the”, written 6 times by 10 different writers. The FLD is used to project the clusters onto three dimensions with the maximum separability. The measurements were obtained using morphological structuring element of length 3 and 5; consequently, dimensionality reduction from 50 to 3 dimensions was performed. Two different aspects of the same 3-D feature space are given in (<b>a</b>,<b>b</b>).</p>
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<p>The maximum number of separable regions in a 2-D feature space. (<b>a</b>) Two regions are defined with one linear subspace. (<b>b</b>) Four regions are defined with two linear subspaces. (<b>c</b>) Seven regions are defined with three subspaces in general position.</p>
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<p>The 2-D space with maximum separability obtained using the FLD from the 50-D space. The writers are well separable.</p>
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<p>The separation of the feature space shown in <a href="#applsci-13-06841-f008" class="html-fig">Figure 8</a> using a neural structure of two layers with three and four perceptrons, respectively. Colored regions represent the decision regions belonging to each separate cluster.</p>
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<p>In the case of retraining the neural structure of two layers with three and four perceptrons, respectively, with the same clusters, the achieved separation of the feature space is almost the same as the one shown in <a href="#applsci-13-06841-f010" class="html-fig">Figure 10</a> (convergence stability). Colored regions represent the decision regions belonging to each separate cluster.</p>
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14 pages, 3274 KiB  
Article
Pharmacophore-Modeling-Based Optimal Placement and Sizing of Large-Scale Energy Storage Stations in a Power System including Wind Farms
by Hady H. Fayek, Fady H. Fayek and Eugen Rusu
Appl. Sci. 2023, 13(10), 6175; https://doi.org/10.3390/app13106175 - 18 May 2023
Cited by 2 | Viewed by 1506
Abstract
The world is targeting fully sustainable electricity by 2050. Energy storage systems have the biggest role to play in the 100% renewable energy scenario. This paper presents an optimal method for energy storage sizing and allocation in a power system including a share [...] Read more.
The world is targeting fully sustainable electricity by 2050. Energy storage systems have the biggest role to play in the 100% renewable energy scenario. This paper presents an optimal method for energy storage sizing and allocation in a power system including a share of wind farms. The power system, which is used as a test system, is a modified version of the IEEE 39 bus system. The optimization is applied using novel pharmacophore modeling (PM), which is compared to state-of-the-art techniques. The objective of the optimization is to minimize the costs of power losses, peak demand and voltage deviation. The PM optimization is applied using two methods, namely, weighting factor and normalization. The optimization and simulation are applied in the DIgSILENT power factory software application. The results show that normalization of PM optimization drives the power system to less cost in terms of total power losses by up to 29% and voltage deviation by up to 4% and better covers peak demand than state-of-the-art optimization techniques. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>Pharmacophore modeling optimization technique flowchart.</p>
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<p>Flowchart of PM application for optimal sizing and allocation of energy storage in a power system.</p>
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<p>Modified IEEE 39 bus system [<a href="#B22-applsci-13-06175" class="html-bibr">22</a>].</p>
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<p>Power losses at normal operation conditions after optimal allocation of energy storage stations considering the daily change in demand and wind speeds.</p>
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<p>Voltage deviation at normal operation conditions after optimal allocation of energy storage stations considering the daily change in demand and wind speeds.</p>
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<p>Power losses in the generator contingency case after optimal allocation of energy storage stations considering the daily change in demand and wind speeds.</p>
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<p>Voltage deviation in the generator contingency case after optimal allocation of energy storage stations considering the daily change in demand and wind speeds.</p>
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23 pages, 1682 KiB  
Article
Transfer Learning Based on Clustering Difference for Dynamic Multi-Objective Optimization
by Fangpei Yao and Gai-Ge Wang
Appl. Sci. 2023, 13(8), 4795; https://doi.org/10.3390/app13084795 - 11 Apr 2023
Cited by 6 | Viewed by 2126
Abstract
Dynamic multi-objective optimization problems (DMOPs) have become a research hotspot in engineering optimization, because their objective functions, constraints, or parameters may change over time, while quickly and accurately tracking the changing Pareto optimal set (POS) during the optimization process. Therefore, solving dynamic multi-objective [...] Read more.
Dynamic multi-objective optimization problems (DMOPs) have become a research hotspot in engineering optimization, because their objective functions, constraints, or parameters may change over time, while quickly and accurately tracking the changing Pareto optimal set (POS) during the optimization process. Therefore, solving dynamic multi-objective optimization problems presents great challenges. In recent years, transfer learning has been proved to be one of the effective means to solve dynamic multi-objective optimization problems. However, this paper proposes a new transfer learning method based on clustering difference to solve DMOPs (TCD-DMOEA). Different from the existing methods, it uses the clustering difference strategy to optimize the population quality and reduce the data difference between the target domain and the source domain. On this basis, transfer learning technology is used to accelerate the construction of initialization population. The advantage of the TCD-DMOEA method is that it reduces the possibility of negative transfer and improves the performance of the algorithm by improving the similarity between the source domain and the target domain. Experimental results show that compared with several advanced dynamic multi-objective optimization algorithms based on different benchmark problems, the proposed TCD-DMOEA method can significantly improve the quality of the solution and the convergence speed. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>Description of environmental response strategies and methods. (<b>a</b>) diversity maintenance. (<b>b</b>) Memory based approach. (<b>c</b>) Prediction based approach (<b>d</b>) Manifold transfer learning method.</p>
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<p>Procedure of TCD-DMOEA.</p>
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<p>Classification of clustering dynamics.</p>
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<p>Schematic of procedure case transfer.</p>
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<p>IGD values of six algorithms under S2 configuration.</p>
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<p>Average running time (s) obtained by comparing algorithms under the configuration of <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>t</mi> </msub> </mrow> </semantics></math> = 5, <math display="inline"><semantics> <mrow> <msub> <mi>τ</mi> <mi>t</mi> </msub> </mrow> </semantics></math> = 10.</p>
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26 pages, 9152 KiB  
Article
A Comparative Study in Forming Behavior of Different Grades of Steel in Cold Forging Backward Extrusion by Integrating Artificial Neural Network (ANN) with Differential Evolution (DE) Algorithm
by Praveenkumar M. Petkar, Vinayak N. Gaitonde, Vinayak N. Kulkarni, Ramesh S. Karnik and João Paulo Davim
Appl. Sci. 2023, 13(3), 1276; https://doi.org/10.3390/app13031276 - 18 Jan 2023
Cited by 5 | Viewed by 1634
Abstract
The cold forging backward extrusion is employed to produce parts that are characterized by better mechanical strength. However, in this process, punches are often prone to breakages because of the large forces encountered in deforming the steel billets. The service life of the [...] Read more.
The cold forging backward extrusion is employed to produce parts that are characterized by better mechanical strength. However, in this process, punches are often prone to breakages because of the large forces encountered in deforming the steel billets. The service life of the punches is affected majorly by the geometrical attributes, the type of steel undergoing deformation, and hence the present investigation focuses on the applications of natural computing algorithms such as artificial neural network (ANN) and differential evolution (DE) optimization algorithm to study the differential influence on the forming behavior of different grades steel and enhance the punch service life. The AISI steel grades, such as AISI 1010, 1018, and 1045, employed extensively in the production of automotive components, have been compared in terms of forming behavior, such as effective stress, strain, strain rate, and punch force. The multi-layer feed-forward ANN architecture was utilized for process modeling with forming responses of finite element (FE) simulations that are strategically planned through the design of experiments (DoE) approach. Considerable variations were found for the effective stress and punch force amongst the steels, while marginal deviations were observed for effective strain and strain rates. Confirmatory experiments were conducted to validate the results of optimal combinations obtained through the DE optimization technique, and the deviations were observed to be in the acceptable range. The cold forging backward extruded components have also been examined for better mechanical soundness through microstructure and micro-hardness analysis that clearly revealed the mechanical integrity and strength enhancement within the forged components. The proposed study would assist the industries engaged in the production of cold-forged steel components in determining the appropriate values of variables to minimize the forming responses and, thus, help in enhancing the life of the tooling. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>The research approach for the current investigation.</p>
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<p>(<b>a</b>) FE Simulation; (<b>b</b>) load versus stroke curve to capture maximum punch force.</p>
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<p>ANN Architecture of current investigation.</p>
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<p>Variation between MSE and the number of epochs of ANN training for AISI 1010, 1018, and 1045 steel.</p>
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<p>Punches and billets preparation (Courtesy: KLE Technological University, Hubballi, India).</p>
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<p>(<b>a</b>) Close frame 600 Ton hydraulic press; (<b>b</b>) the master gauge and experimental set-up (Courtesy: S. S. Industries, Bangalore, India).</p>
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<p>Billet as machined, annealed, MoS₂ coated forged, and sectioned part.</p>
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<p>Comparison of forming response: effective stress.</p>
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<p>Comparison of forming response: effective strain.</p>
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<p>Comparison of forming response: effective strain rate.</p>
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<p>Comparison of forming response: punch force.</p>
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<p>Comparison of optimal values of punch face angle (<span class="html-italic">a</span>) for different steels.</p>
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<p>Comparison of optimal values of land height (<span class="html-italic">h</span>) of different steels.</p>
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<p>Comparison of optimal values of effective stress of different steels.</p>
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<p>Comparison of optimal values of the effective strain of different steels.</p>
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<p>Comparison of optimal values of effective strain rate of different steels.</p>
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<p>Comparison of optimal values of punch force of different steels.</p>
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<p>Comparison of DE optimal and experimental values for punch force.</p>
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<p>Variation between optimal and experimental values of punch force at different reduction ratios.</p>
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<p>(<b>a</b>) Three-zone representation of the cold forging backward extrusion process. (<b>b</b>) Strain distribution areas for the three-zone representation.</p>
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<p>Comparison of DE optimal and experimental values for effective strain.</p>
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<p>Comparison of DE optimal and experimental values for effective stress.</p>
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<p>Comparison of DE optimal and experimental values for effective strain rate.</p>
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<p>Microstructure of AISI steels. (<b>a1</b>,<b>a2</b>) AISI 1010; (<b>b1</b>,<b>b2</b>) AISI 1018; (<b>c1</b>,<b>c2</b>) AISI 1045.</p>
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<p>Microstructure of AISI steels. (<b>a1</b>,<b>a2</b>) AISI 1010; (<b>b1</b>,<b>b2</b>) AISI 1018; (<b>c1</b>,<b>c2</b>) AISI 1045.</p>
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<p>Comparison of micro-hardness values for AISI steels.</p>
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21 pages, 4226 KiB  
Article
Natural Computing-Based Designing of Hybrid UHMWPE Composites for Orthopedic Implants
by Vinoth Arulraj, Shubhabrata Datta and João Paulo Davim
Appl. Sci. 2022, 12(20), 10408; https://doi.org/10.3390/app122010408 - 15 Oct 2022
Viewed by 1564
Abstract
The current study deals with the design of ultra-high molecular weight polyethylene (UHMWPE) composites by integrating various micro and nanoparticles as reinforcements for enhanced performance of acetabular cups in hip prostheses. For the design, a data-driven design approach was implemented, exploiting natural computing [...] Read more.
The current study deals with the design of ultra-high molecular weight polyethylene (UHMWPE) composites by integrating various micro and nanoparticles as reinforcements for enhanced performance of acetabular cups in hip prostheses. For the design, a data-driven design approach was implemented, exploiting natural computing techniques such as Artificial Neural Network (ANN) and Genetic Algorithm (GA). Experimental data related to UHMWPE reinforced with carbon nanotube, graphene, carbon fiber, and hydroxyapatite were gathered from the published works of previous researchers. To study the relationship between the volume fraction and the morphology of the particles with the tribological and mechanical properties of the composites, ANN modeling and sensitivity analyses were used. Optimization of the properties was done with the developed ANN models as objective functions in order to find the optimal combinations of reinforcements, which helps to achieve enhanced tribo-mechanical properties of the composites. This natural computing approach of designing the UHMWPE composites paved a way for experimentation. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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<p>Configuration of ANN.</p>
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<p>Process flowchart of the computational arrangement.</p>
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<p>Predictability of the ANN models for (<b>a</b>) UTS, (<b>b</b>) H, (<b>c</b>) E, (<b>d</b>) SWR, and (<b>e</b>) CoF.</p>
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<p>Predictability of the ANN models for (<b>a</b>) UTS, (<b>b</b>) H, (<b>c</b>) E, (<b>d</b>) SWR, and (<b>e</b>) CoF.</p>
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<p>Sensitivity analysis for UTS, H, and E.</p>
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<p>Sensitivity analysis for CoF and SWR.</p>
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<p>Surface plots showing the variation in (<b>a</b>) E with CNT–HA wt%, (<b>b</b>) E with graphene–HA wt%, (<b>c</b>) E with CF–HA%, (<b>d</b>) UTS with CNT–HA wt%, (<b>e</b>) UTS with graphene–HA wt%, (<b>f</b>) UTS with CF–HA%, (<b>g</b>) CoF with graphene–HA wt%, (<b>h</b>) CoF with CNT–HA wt%, (<b>i</b>) CoF with CF–HA%, (<b>j</b>) SWR with CNT–HA wt%, (<b>k</b>) SWR with graphene–HA wt%, and (<b>l</b>) SWR with CF–HA%.</p>
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<p>Surface plots showing the variation in (<b>a</b>) E with CNT–HA wt%, (<b>b</b>) E with graphene–HA wt%, (<b>c</b>) E with CF–HA%, (<b>d</b>) UTS with CNT–HA wt%, (<b>e</b>) UTS with graphene–HA wt%, (<b>f</b>) UTS with CF–HA%, (<b>g</b>) CoF with graphene–HA wt%, (<b>h</b>) CoF with CNT–HA wt%, (<b>i</b>) CoF with CF–HA%, (<b>j</b>) SWR with CNT–HA wt%, (<b>k</b>) SWR with graphene–HA wt%, and (<b>l</b>) SWR with CF–HA%.</p>
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<p>Surface plots showing the variation in (<b>a</b>) E with CNT–HA wt%, (<b>b</b>) E with graphene–HA wt%, (<b>c</b>) E with CF–HA%, (<b>d</b>) UTS with CNT–HA wt%, (<b>e</b>) UTS with graphene–HA wt%, (<b>f</b>) UTS with CF–HA%, (<b>g</b>) CoF with graphene–HA wt%, (<b>h</b>) CoF with CNT–HA wt%, (<b>i</b>) CoF with CF–HA%, (<b>j</b>) SWR with CNT–HA wt%, (<b>k</b>) SWR with graphene–HA wt%, and (<b>l</b>) SWR with CF–HA%.</p>
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<p>3D Pareto front of E, CoF, and SWR without constraints on varying the molecular weight of UHMWPE (<b>a</b>) 3, (<b>b</b>) 4, (<b>c</b>) 5, and (<b>d</b>) 6.</p>
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<p>Deviation of the particles in the Pareto solutions for E, CoF, and SWR.</p>
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<p>3D Pareto front of H, CoF, and SWR without constraints on varying the molecular weight of UHMWPE (<b>a</b>) 3, (<b>b</b>) 4, (<b>c</b>) 5, and (<b>d</b>) 6.</p>
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<p>Deviation in the reinforcements in the Pareto solutions for H, CoF, and SWR.</p>
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Review

Jump to: Research

25 pages, 631 KiB  
Review
A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
by Zitong Wang, Yan Pei and Jianqiang Li
Appl. Sci. 2023, 13(7), 4643; https://doi.org/10.3390/app13074643 - 6 Apr 2023
Cited by 32 | Viewed by 5460
Abstract
The multi-objective optimization problem is difficult to solve with conventional optimization methods and algorithms because there are conflicts among several optimization objectives and functions. Through the efforts of researchers and experts from different fields for the last 30 years, the research and application [...] Read more.
The multi-objective optimization problem is difficult to solve with conventional optimization methods and algorithms because there are conflicts among several optimization objectives and functions. Through the efforts of researchers and experts from different fields for the last 30 years, the research and application of multi-objective evolutionary algorithms (MOEA) have made excellent progress in solving such problems. MOEA has become one of the primary used methods and technologies in the realm of multi-objective optimization. It is also a hotspot in the evolutionary computation research community. This survey provides a comprehensive investigation of MOEA algorithms that have emerged in recent decades and summarizes and classifies the classical MOEAs by evolutionary mechanism from the viewpoint of the search strategy. This paper divides them into three categories considering the search strategy of MOEA, i.e., decomposition-based MOEA algorithms, dominant relation-based MOEA algorithms, and evaluation index-based MOEA algorithms. This paper selects the relevant representative algorithms for a detailed summary and analysis. As a prospective research direction, we propose to combine the chaotic evolution algorithm with these representative search strategies for improving the search capability of multi-objective optimization algorithms. The capability of the new multi-objective evolutionary algorithm has been discussed, which further proposes the future research direction of MOEA. It also lays a foundation for the application and development of MOEA with these prospective works in the future. Full article
(This article belongs to the Special Issue Advances in Natural Computing: Methods and Application)
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Figure 1

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<p>The basic flow of Pareto-based MOEA. The optimal set of solutions from the previous generation is retained and added to the new generation so that it continues to converge to the true Pareto front. This figure is adopted from [<a href="#B6-applsci-13-04643" class="html-bibr">6</a>].</p>
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<p>The contour of weighted sum approach. Concerning convex problems, several isometries can be drawn to discover the shortest distance points that together produce a different set of Pareto optimal vectors. For non-convex problems, the vertical line of each reference vector cannot be tangent to its leading edge. This figure is adopted from [<a href="#B20-applsci-13-04643" class="html-bibr">20</a>].</p>
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<p>The operation mechanism of VEGA. The MOP is divided into groups, each sub-objective function is evaluated and selected independently, then a new group is formed, crossover and variation operations are performed, and this proceeds cyclically, resulting in non-inferior solutions to the problem. This figure is adopted from [<a href="#B5-applsci-13-04643" class="html-bibr">5</a>].</p>
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<p>An example of the lexicographic optimization process for a bi-objective minimum optimization problem. Firstly, <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is minimized, while the optimal value obtained is used as a constraint. Secondly, after <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> has been minimized, its optimal value is used as a constraint for cyclic optimization. Finally, Pareto optimal solutions are found. This figure is adopted from [<a href="#B80-applsci-13-04643" class="html-bibr">80</a>].</p>
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<p>The niche sharing. Neither candidate <span class="html-italic">A</span> nor <span class="html-italic">B</span> is dominant, but <span class="html-italic">A</span> is more aggregated than <span class="html-italic">B</span>, so <span class="html-italic">A</span> has less shared fitness than <span class="html-italic">B</span> and chooses <span class="html-italic">B</span> to participate in the next generation of evolution. This figure is adopted from [<a href="#B7-applsci-13-04643" class="html-bibr">7</a>].</p>
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<p>The fundamental concept of the NSGA-II algorithm. A random initial population, using selection, crossover, and variation to produce a first generation of offspring populations. Parent and offspring populations are mixed and individuals are selected for new parent populations based on their non-dominance relationships and crowding levels, which in turn produce new offspring populations. This figure is adopted from [<a href="#B16-applsci-13-04643" class="html-bibr">16</a>].</p>
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<p>The crowding distance about the i-th solution. The average distance between the two points on either side of point <span class="html-italic">i</span> is calculated; based on each objective function, the vertices of the rectangle are determined by their nearest neighbors, i.e., <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math>, and the length of the cube is equal to the congestion factor of the solution in the graph. This figure is adopted from [<a href="#B16-applsci-13-04643" class="html-bibr">16</a>].</p>
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<p>The implementation steps for NSGA-II’s elite strategy. The new population is ranked non-dominantly; in this example, the population is divided into six Pareto ranks, and non-dominant individuals with Pareto rank 1 and 2 are placed in a new set of parents, after which their crowding is determined before ranking those with Pareto rank 3 and excluding all those with ranks 4 to 6. This figure is adopted from [<a href="#B16-applsci-13-04643" class="html-bibr">16</a>].</p>
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<p>The operation mechanism of the SMS-EMOA algorithm. An offspring is produced in each iteration and evaluated immediately before integration into the next generation of evolution, with poor individuals being eliminated as a new subpopulation. This figure is adopted from [<a href="#B90-applsci-13-04643" class="html-bibr">90</a>].</p>
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<p>The illustrations of <math display="inline"><semantics> <msub> <mi>I</mi> <mrow> <mi>H</mi> <mi>D</mi> </mrow> </msub> </semantics></math> indicator. In (<b>a</b>), when the individuals in the set <math display="inline"><semantics> <mi mathvariant="normal">A</mi> </semantics></math> and the individuals in the set <math display="inline"><semantics> <mi mathvariant="normal">B</mi> </semantics></math> are not dominated by each other, the yellow and red parts on the left indicate the areas of the independently dominated regions of <math display="inline"><semantics> <mi mathvariant="normal">A</mi> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="normal">B</mi> </semantics></math>, respectively. In (<b>b</b>), when <math display="inline"><semantics> <mi mathvariant="normal">A</mi> </semantics></math> is dominated by <math display="inline"><semantics> <mi mathvariant="normal">B</mi> </semantics></math>, the gray part of the figure indicates the area of the independently dominated region of <math display="inline"><semantics> <mi mathvariant="normal">B</mi> </semantics></math>. This figure is adopted from [<a href="#B91-applsci-13-04643" class="html-bibr">91</a>].</p>
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