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Keywords = Differential Evolution Algorithm

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21 pages, 8146 KiB  
Article
Inverse Kinematics of Robotic Manipulators Based on Hybrid Differential Evolution and Jacobian Pseudoinverse Approach
by Jesus Hernandez-Barragan, Josue Plascencia-Lopez, Michel Lopez-Franco, Nancy Arana-Daniel and Carlos Lopez-Franco
Algorithms 2024, 17(10), 454; https://doi.org/10.3390/a17100454 (registering DOI) - 12 Oct 2024
Abstract
Robot manipulators play a critical role in several industrial applications by providing high precision and accuracy. To perform these tasks, manipulator robots require the effective computation of inverse kinematics. Conventional methods to solve IK often encounter significant challenges, such as singularities, non-linear equations, [...] Read more.
Robot manipulators play a critical role in several industrial applications by providing high precision and accuracy. To perform these tasks, manipulator robots require the effective computation of inverse kinematics. Conventional methods to solve IK often encounter significant challenges, such as singularities, non-linear equations, and poor generalization across different robotic configurations. In this work, we propose a novel approach to solve the inverse kinematics (IK) problem in robotic manipulators using a metaheuristic algorithm enhanced with a Jacobian step. Our method overcomes those limitations by selectively applying the Jacobian step to the differential evolution (DE) algorithm. The effectiveness and versatility of the proposed approach are demonstrated through simulations and real-world experimentation on a 5 DOF KUKA robotic arm. Full article
(This article belongs to the Special Issue Bio-Inspired Algorithms)
Show Figures

Figure 1

Figure 1
<p>Coordinate frames’ assignment for the Puma-560 manipulator.</p>
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<p>Coordinate frames’ assignment for the Baxter manipulator.</p>
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<p>Coordinate frames’ assignment for the KUKA iiwa manipulator.</p>
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<p>Randomly generated set of values.</p>
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<p>Comparison of standard and hybrid algorithms in solving inverse kinematics of the Puma-560 robot. (<b>a</b>) Standard algorithms. (<b>b</b>) Hybrid algorithms.</p>
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<p>Comparison of standard and hybrid algorithms in solving inverse kinematics of the Baxter robot. (<b>a</b>) Standard algorithms. (<b>b</b>) Hybrid algorithms.</p>
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<p>Comparison of standard and hybrid algorithms in solving inverse kinematics of the KUKA iiwa robot. (<b>a</b>) Standard algorithms. (<b>b</b>) Hybrid algorithms.</p>
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<p>Comparison of hybrid algorithms for solving the inverse kinematics of the Baxter robot in an orientation-unreachable end-effector pose.</p>
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<p>Unreachable pose experiment results. Coordinate frames in red represents the unreachable poses and coordinate frames in blue the achieved ones.</p>
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<p>KUKA YouBot manipulator with 5 DOF.</p>
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<p>Coordinate frames’ assignment for the KUKA YouBot manipulator.</p>
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<p>Time history with a cubic polynomial timing law for Experiment 1. (<b>a</b>) Joint positions. (<b>b</b>) Joint velocities.</p>
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<p>KUKA YouBot final joint configuration for Experiment 1. (<b>a</b>) Real-world final joint configuration. (<b>b</b>) Joint motion results measured by encoders.</p>
Full article ">Figure 14
<p>Time history with a cubic polynomial timing law for Experiment 2. (<b>a</b>) Joint positions. (<b>b</b>) Joint velocities.</p>
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<p>KUKA YouBot final joint configuration for Experiment 2. (<b>a</b>) Real-world final joint configuration. (<b>b</b>) Joint motion results measured by encoders.</p>
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<p>Time history with a cubic polynomial timing law for Experiment 3. (<b>a</b>) Joint positions. (<b>b</b>) Joint velocities.</p>
Full article ">Figure 17
<p>KUKA YouBot final joint configuration for Experiment 3. (<b>a</b>) Real-world final joint configuration. (<b>b</b>) Joint motion results measured by encoders.</p>
Full article ">
27 pages, 9621 KiB  
Article
Estimating and Modeling Pinus contorta Transpiration in a Montane Meadow Using Sap-Flow Measurements
by Simon Marks, Christopher Surfleet and Bwalya Malama
Forests 2024, 15(10), 1786; https://doi.org/10.3390/f15101786 - 11 Oct 2024
Viewed by 200
Abstract
This study quantifies the transpiration of encroached lodgepole pine (Pinus contorta var. murryana (Grev. & Balf.) Engelm.) in a montane meadow using pre-restoration sap-flow measurements. Lodgepole pine transpiration and its response to environmental variables were examined in Rock Creek Meadow (RCM), Southern [...] Read more.
This study quantifies the transpiration of encroached lodgepole pine (Pinus contorta var. murryana (Grev. & Balf.) Engelm.) in a montane meadow using pre-restoration sap-flow measurements. Lodgepole pine transpiration and its response to environmental variables were examined in Rock Creek Meadow (RCM), Southern Cascade Range, CA, USA. Sap-flow data from lodgepole pines were scaled to the meadow using tree survey data and then validated with MODIS evapotranspiration estimates for the 2019 and 2020 growing seasons. A modified Jarvis–Stewart model calibrated to 2020 sap-flow data analyzed lodgepole pine transpiration’s correlation with solar radiation, air temperature, vapor pressure deficit, and soil volumetric water content. Model validation utilized 2021 growing season sap-flow data. Calibration and validation employed a Markov Chain Monte Carlo (MCMC) approach through the DREAM(ZS) algorithm with a generalized likelihood (GL) function, enabling parameter and total uncertainty assessment. The model’s scaling was compared with simple scaling estimates. Average lodgepole pine transpiration at RCM ranged between 220.6 ± 25.3 and 393.4 ± 45.7 mm for the campaign (mid-July 2019 to mid-August 2020) and 100.2 ± 11.5 to 178.8 ± 20.7 mm for the 2020 partial growing season (April to mid-August), akin to MODIS ET. The model aligned well with observed normalized sap-velocity during the 2020 growing season (RMSE = 0.087). However, sap-velocity, on average, was underpredicted by the model (PBIAS = −6.579%). Model validation mirrored calibration in performance metrics (RMSE = 0.1233; PBIAS = −2.873%). The 95% total predictive uncertainty confidence intervals generated by GL-DREAM(ZS) enveloped close to the theoretically expected 95% of total observations for the calibration (94.5%) and validation (81.8%) periods. The performance of the GL-DREAM(ZS) approach and uncertainty assessment in this study shows promise for future MJS model applications, and the model-derived 2020 transpiration estimates highlight the MJS model utility for scaling sap-flow measurements from individual trees to stands of trees. Full article
(This article belongs to the Section Forest Ecophysiology and Biology)
Show Figures

Figure 1

Figure 1
<p>RCM near Chester, CA, including measurement locations. The sap-flow plot insert, displayed at a larger scale, shows the locations for the eight lodgepole pine (<span class="html-italic">Pinus contorta var. murryana</span> (Grev. &amp; Balf.) Engelm.) (LP) instrumented for sap-flow measurement.</p>
Full article ">Figure 2
<p>(<b>a</b>) Bark depth (D<sub>b</sub>) versus diameter at breast height (DBH) and (<b>b</b>) sapwood depth (D<sub>s</sub>) versus DBH in log–log space, both including simple linear regressions equation, R2, and line of best fit. Data (<span class="html-italic">n</span> = 47) in (<b>a</b>,<b>b</b>) are from cored trees sampled in the 10 random sample plots.</p>
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<p>(<b>a</b>) 30 min average sap-velocity and daily average daytime and nighttime sap-velocity; (<b>b</b>) daily total precipitation; (<b>c</b>) average daily VPD; and (<b>d</b>) average daily incoming solar radiation and air temperature.</p>
Full article ">Figure 4
<p>Hourly <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> response to environmental drivers for the calibration period: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. solar radiation with different values of VPD; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. VPD with different values of VWC; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. air temperature with different values of VWC; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. VWC with different values of air temperature.</p>
Full article ">Figure 5
<p>Hourly <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> response to environmental drivers for the validation period: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. solar radiation with different values of VPD; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. VPD with different values of VWC; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. air temperature with different values of VWC; and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>v</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> vs. VWC with different values of air temperature.</p>
Full article ">Figure 6
<p>MJS predicted vs. observed normalized average sap-velocity for the (<b>a</b>) calibration period (y = 0.022 + 0.88x, R<sup>2</sup> = 0.89) and (<b>b</b>) validation period (y = 0.033 + 0.9x, R<sup>2</sup> = 0.89), including 1:1 line (dashed green) and SLR line (blue).</p>
Full article ">Figure 7
<p>Ninety-five percent parameter uncertainty confidence interval and normalized average sap-velocity observations (red points) for (<b>a</b>) calibration and (<b>b</b>) validation periods. Gaps in the time series represent observation data that were removed from the analysis due to precipitation or it being nighttime. Insets show 10 days of sap-velocity observations, corresponding to 95% confidence parameter uncertainty interval for each period.</p>
Full article ">Figure 8
<p>Ninety-five percent total predictive uncertainty confidence interval and normalized average sap-velocity observations (blue and red points) for (<b>a</b>) calibration and (<b>b</b>) periods. Insets show 10 days of sap-velocity observations, corresponding to 95% confidence parameter uncertainty interval for each period.</p>
Full article ">Figure 9
<p>Daily average transpiration (T) estimated for the random plots in the (<b>a</b>) east stratum and (<b>b</b>) west stratum by sap-velocity radial profile. Ribbons represent ± 1 standard error of the daily mean.</p>
Full article ">Figure 10
<p>Time series of 8-day composite MODIS ET estimates compared with 8-day composite lodgepole pine transpiration (T) estimates by sap-velocity radial profile for (<b>a</b>) RCM, (<b>b</b>) east stratum, and (<b>c</b>) west stratum. Ribbons represent ±1 standard deviation of the MODIS ET 8-day composite, weighted mean.</p>
Full article ">Figure 11
<p>Time series of residuals between 8-day composite MODIS ET estimates and 8-day composite lodgepole pine transpiration (T) estimates by sap-velocity radial profile for (<b>a</b>) RCM, (<b>b</b>) east stratum, and (<b>c</b>) west stratum.</p>
Full article ">Figure 12
<p>Comparison of daily transpiration (T) estimates informed by calibrated MJS model and simple scaling for soil moisture set-up containing plots: (<b>a</b>) SFP (RCSM2b), (<b>b</b>) RCSM1, (<b>c</b>) RCSM3, and (<b>d</b>) RCSM5. The vertical dashed lines mark when VWC dropped below 0.184 during the period shown. Note the differences in vertical scale used for (<b>a</b>–<b>d</b>).</p>
Full article ">
34 pages, 3148 KiB  
Article
Historical Elite Differential Evolution Based on Particle Swarm Optimization Algorithm for Texture Optimization with Application in Particle Physics
by Emmanuel Martínez-Guerrero, Pedro Lagos-Eulogio, Pedro Miranda-Romagnoli, Roberto Noriega-Papaqui and Juan Carlos Seck-Tuoh-Mora
Appl. Sci. 2024, 14(19), 9110; https://doi.org/10.3390/app14199110 - 9 Oct 2024
Viewed by 444
Abstract
Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used [...] Read more.
Within the phenomenology of particle physics, the theoretical model of 4-zero textures is validated using a chi-square criterion that compares experimental data with the computational results of the model. Traditionally, analytical methods that often imply simplifications, combined with computational analysis, have been used to validate texture models. In this paper, we propose a new meta-heuristic variant of the differential evolution algorithm that incorporates aspects of the particle swarm optimization algorithm called “HE-DEPSO” to obtain chi-squared values that are less than a bound value, which exhaustive and traditional algorithms cannot obtain. The results show that the proposed algorithm can optimize the chi-square function according to the required criteria. We compare simulated data with experimental data in the allowed search region, thereby validating the 4-zero texture model. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
Show Figures

Figure 1

Figure 1
<p><math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> function projections over variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>u</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>A</mi> <mi>d</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math>. (<b>a</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> on the variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>u</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>A</mi> <mi>d</mi> </msub> </semantics></math> (right graph). From the contour lines (left-hand graph), we note that the region that minimizes <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> lies around a straight line at <math display="inline"><semantics> <msup> <mn>45</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>b</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>u</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> (right-hand graph) and corresponding contour lines (left-hand graph). We note a periodicity of the maxima of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variable <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math>. (<b>c</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>u</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> (right-hand graph) and corresponding contour lines (left-hand graph). We note a periodicity of the maxima and the minima of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variable <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math>. (<b>d</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> (right-hand graph) and corresponding contour lines (left-hand graph). We note a periodicity of the maxima of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variable <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math>. (<b>e</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variables <math display="inline"><semantics> <msub> <mi>A</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> (right-hand graph) and corresponding contour lines (left-hand graph). We note a periodicity of the maxima and the minima of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> with respect to the variable <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math>. (<b>f</b>) Dependence of the function <math display="inline"><semantics> <msup> <mi>χ</mi> <mn>2</mn> </msup> </semantics></math> on the variables <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> (right-hand graph) and corresponding contour lines (left-hand graph).</p>
Full article ">Figure 2
<p>Strategy selection curve; (<b>a</b>) Selection probability <math display="inline"><semantics> <msub> <mi>α</mi> <mi>t</mi> </msub> </semantics></math>, (<b>b</b>) Distribution of strategy selection.</p>
Full article ">Figure 3
<p>Convergence curves for the functions <math display="inline"><semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>3</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>5</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>F</mi> <mn>8</mn> </msub> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and 30. The horizontal and vertical axis represent the iterations and the mean error values for the 31 independent repetitions.</p>
Full article ">Figure 3 Cont.
<p>Convergence curves for the functions <math display="inline"><semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>3</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>5</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi>F</mi> <mn>8</mn> </msub> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and 30. The horizontal and vertical axis represent the iterations and the mean error values for the 31 independent repetitions.</p>
Full article ">Figure 4
<p>Convergence curves for the functions <math display="inline"><semantics> <msub> <mi>F</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>3</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>F</mi> <mn>5</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>F</mi> <mn>8</mn> </msub> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and 30. The horizontal and vertical axis represent the iterations and the mean error values for the 31 independent repetitions.</p>
Full article ">Figure 5
<p>Convergence curves of the error measure in the solution for the <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function. The horizontal and vertical axis represent the iterations and the mean error values for the 31 independent iterations.</p>
Full article ">Figure 6
<p>Box and whisker plots of the best global fit values obtained by HE-DEPSO and the DEPSO, SHADE, CoDE, DE, and PSO algorithms in the 31 independent repetitions in the <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> function. The horizontal axis shows the algorithms to be compared, and the vertical axis shows the global fit values.</p>
Full article ">Figure 7
<p>Allowed regions for <math display="inline"><semantics> <msub> <mi>A</mi> <mi>u</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>A</mi> <mi>d</mi> </msub> </semantics></math> constrained based on current experimental data with different levels of precision: <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics></math> (black dots), <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> (blue dots), and <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> (orange dots).</p>
Full article ">Figure 8
<p>Allowed regions for <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mn>2</mn> </msub> </semantics></math> constrained based on current experimental data with different levels of precision: <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> </mrow> </semantics></math> (black dost), <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> (blue dots), and <math display="inline"><semantics> <mrow> <msup> <mi>χ</mi> <mn>2</mn> </msup> <mo>&lt;</mo> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> (orange dots).</p>
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<p>Predictions for <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>c</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>u</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>u</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Predictions for <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>c</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>t</mi> <mi>b</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>u</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Predictions for <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>t</mi> <mi>d</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>t</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>u</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi>d</mi> </msub> <mo>=</mo> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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18 pages, 7434 KiB  
Article
Prediction of Jacking Force for Construction of Long-Distance Rectangular Utility Tunnel Using Differential Evolution–Bidirectional Gated Re-Current Unit–Attention Model
by Tianshuang Liu, Juncheng Liu, Yong Tan and Dongdong Fan
Buildings 2024, 14(10), 3169; https://doi.org/10.3390/buildings14103169 - 5 Oct 2024
Viewed by 384
Abstract
Most of the current machine learning algorithms are applied to predict the jacking force required in micro-tunneling; in contrast, few studies about long-distance, large-section jacking projects have been reported in the literature. In this study, an intelligent framework, consisting of a differential evolution [...] Read more.
Most of the current machine learning algorithms are applied to predict the jacking force required in micro-tunneling; in contrast, few studies about long-distance, large-section jacking projects have been reported in the literature. In this study, an intelligent framework, consisting of a differential evolution (DE), a bidirectional gated re-current unit (BiGRU), and attention mechanisms was developed to automatically identify the optimal hyperparameters and assign weights to the information features, as well as capture the bidirectional temporal features of sequential data. Based on field data from a pipe jacking project crossing underneath a canal, the model’s performance was compared with those of four conventional models (RNN, GRU, BiGRU, and DE–BiGRU). The results indicated that the DE–BiGRU–attention model performed best among these models. Then, the generalization performance of the proposed model in predicting jacking forces was evaluated with the aid of a similar case at the site. It was found that fine-tuning parameters for specific projects is essential for improving the model’s generalization performance. More generally, the proposed prediction model was found to be practically useful to professionals and engineers in making real-time adjustments to jacking parameters, predicting jacking force, and carrying out performance evaluations. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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<p>Schematic diagram of the DE algorithm.</p>
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<p>Schematic diagram of the GRU cell structure.</p>
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<p>Schematic diagram of the BiGRU structure.</p>
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<p>Flowchart of the proposed framework for predicting jacking force dynamically.</p>
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<p>In situ photo of the project.</p>
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<p>Soil stratigraphy along the longitudinal side of the project.</p>
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<p>Cutting head of the pipe jacking machine.</p>
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<p>Data preprocessing: (<b>a</b>) outlier elimination and (<b>b</b>) denoising.</p>
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<p>The calculated Pearson correlation coefficients between jacking parameters.</p>
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<p>Prediction results of (<b>a</b>) the DE–BiGRU–attention model; (<b>b</b>) the DE–BiGRU model; (<b>c</b>) the BiGRU model; (<b>d</b>) the GRU model; and (<b>e</b>) the RNN model.</p>
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<p>Prediction results of (<b>a</b>) the DE–BiGRU–attention model; (<b>b</b>) the DE–BiGRU model; (<b>c</b>) the BiGRU model; (<b>d</b>) the GRU model; and (<b>e</b>) the RNN model.</p>
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<p>Prediction of jacking force for the right pipe using (<b>a</b>) the trained DE–BiGRU–attention model; (<b>b</b>) the trained DE–BiGRU model.</p>
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18 pages, 1667 KiB  
Article
An Improved NSGA-III with a Comprehensive Adaptive Penalty Scheme for Many-Objective Optimization
by Xinghang Xu, Du Cheng, Dan Wang, Qingliang Li and Fanhua Yu
Symmetry 2024, 16(10), 1289; https://doi.org/10.3390/sym16101289 - 1 Oct 2024
Viewed by 593
Abstract
Pareto dominance-based algorithms face a significant challenge in handling many-objective optimization problems. As the number of objectives increases, the sharp rise in non-dominated individuals makes it challenging for the algorithm to differentiate their quality, resulting in a loss of selection pressure. The application [...] Read more.
Pareto dominance-based algorithms face a significant challenge in handling many-objective optimization problems. As the number of objectives increases, the sharp rise in non-dominated individuals makes it challenging for the algorithm to differentiate their quality, resulting in a loss of selection pressure. The application of the penalty-based boundary intersection (PBI) method can balance convergence and diversity in algorithms. The PBI method guides the evolution of individuals by integrating the parallel and perpendicular distances between individuals and reference vectors, where the penalty factor is crucial for balancing these two distances and significantly affects algorithm performance. Therefore, a comprehensive adaptive penalty scheme was proposed and applied to NSGA-III, named caps-NSGA-III, to achieve balance and symmetry between convergence and diversity. Initially, each reference vector’s penalty factor is computed based on its own characteristic. Then, during the iteration process, the penalty factor is adaptively adjusted according to the evolutionary state of the individuals associated with the corresponding reference vector. Finally, a monitoring strategy is designed to oversee the penalty factor, ensuring that adaptive adjustments align with the algorithm’s needs at different stages. Through a comparison involving benchmark experiments and two real-world problems, the competitiveness of caps-NSGA-III was demonstrated. Full article
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<p>Illustration of distances <math display="inline"><semantics> <msub> <mi>d</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>d</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>Illustration of the limitation of the fixed <math display="inline"><semantics> <mi>θ</mi> </semantics></math> value in SPS using boundary weight vector.</p>
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<p>Illustration of the limitation of the fixed <math display="inline"><semantics> <mi>θ</mi> </semantics></math> value in SPS using intermediate reference vector.</p>
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<p>Parallel coordinates of the non-dominated fronts obtained by the six algorithms on the 15-objective DTLZ4 instance.</p>
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<p>Parallel coordinates of the non-dominated fronts obtained by the six algorithms on the 15-objective WFG4 instance.</p>
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<p>Analysis of the impact of <math display="inline"><semantics> <mi>α</mi> </semantics></math> on caps-NSGA-III for the WFG1, WFG2, WFG3, and WFG8 problems. The blue line represents <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, the orange line represents <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, and the yellow line represents <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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18 pages, 4642 KiB  
Article
Sustainable Operation Strategy for Wet Flue Gas Desulfurization at a Coal-Fired Power Plant via an Improved Many-Objective Optimization
by Jianfeng Huang, Zhuopeng Zeng, Fenglian Hong, Qianhua Yang, Feng Wu and Shitong Peng
Sustainability 2024, 16(19), 8521; https://doi.org/10.3390/su16198521 - 30 Sep 2024
Viewed by 551
Abstract
Coal-fired power plants account for a large share of the power generation market in China. The mainstream method of desulfurization employed in the coal-fired power generation sector now is wet flue gas desulfurization. This process is known to have a high cost and [...] Read more.
Coal-fired power plants account for a large share of the power generation market in China. The mainstream method of desulfurization employed in the coal-fired power generation sector now is wet flue gas desulfurization. This process is known to have a high cost and be energy-/materially intensive. Due to the complicated desulfurization mechanism, it is challenging to improve the overall sustainability profile involving energy-, cost-, and resource-relevant objectives via traditional mechanistic models. As such, the present study formulated a data-driven many-objective model for the sustainability of the desulfurization process. We preprocessed the actual operation data collected from the desulfurization tower in a domestic ultra-supercritical coal-fired power plant with a 600 MW unit. The extreme random forest algorithm was adopted to approximate the objective functions as prediction models for four objectives, namely, desulfurization efficiency, unit power consumption, limestone supply, and unit operation cost. Three metrics were utilized to evaluate the performance of prediction. Then, we incorporated differential evolution and non-dominated sorting genetic algorithm-III to optimize the multiple parameters and obtain the Pareto front. The results indicated that the correlation coefficient (R2) values of the prediction models were greater than 0.97. Compared with the original operation condition, the operation under optimized parameters could improve the desulfurization efficiency by 0.25% on average and reduce energy, cost, and slurry consumption significantly. This study would help develop operation strategies to improve the sustainability of coal-fired power plants. Full article
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<p>Proportions of coal mine risks.</p>
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<p>Schematic diagram of a wet flue gas desulfurization system.</p>
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<p>The investigated WFGD system at Chaozhou, China.</p>
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<p>The basic structure of the ERF algorithm.</p>
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<p>Distribution of reference points with <span class="html-italic">M</span> = 3.</p>
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<p>The procedure of NSGA-III-DE algorithm.</p>
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<p>Correlation coefficients between variables.</p>
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<p>Testing results of prediction model for (<b>a</b>) desulfurization efficiency, (<b>b</b>) unit power consumption, and (<b>c</b>) limestone supply.</p>
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<p>Pareto-optimal front of four-objective optimization.</p>
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<p>Optimized objective values of test samples: (<b>a</b>) desulfurization efficiency, (<b>b</b>) unit power consumption, (<b>c</b>) limestone supply, and (<b>d</b>) unit operation cost.</p>
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26 pages, 2093 KiB  
Article
Assessment of Femoral Head Sphericity Using Coordinate Data through Modified Differential Evolution Approach
by Syed Hammad Mian, Zeyad Almutairi and Mohamed K. Aboudaif
Mathematics 2024, 12(19), 2989; https://doi.org/10.3390/math12192989 - 25 Sep 2024
Viewed by 377
Abstract
Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is [...] Read more.
Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is applied to assess the form error. Since the traditional least-squares approach is susceptible to overestimation, it leads to unreasonable rejections. This paper implements a modified differential evolution (DE) algorithm to estimate the minimum zone femoral head sphericity. In this algorithm, opposition-based learning is considered for population initialization, and an adaptive scheme is enacted for scaling factor and crossover probability. The coefficients of the correlation factor and the uncertainty propagation are also measured so that the result’s uncertainty can be determined. Undoubtedly, the credibility and plausibility of inspection outcomes are strengthened by evaluating measurement uncertainty. Several data sets are used to corroborate the outcome of the DE algorithm. CMM validation shows that the modified DE algorithm can measure sphericity with high precision and consistency. This algorithm allows for an adequate initial solution and adaptability to address a wide range of industrial problems. It ensures a proper balance between exploitation and exploration capabilities. Thus, the suggested methodology, based on the computational results, is feasible for the online deployment of the sphericity evaluation. The adopted DE strategy is simple to use, has few controlling variables, and is computationally less expensive. It guarantees a robust solution and can be used to compute different form errors. Full article
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<p>Computation of the form error.</p>
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<p>Minimum zone (<b>a</b>) roundness error; (<b>b</b>) cylindricity error [<a href="#B21-mathematics-12-02989" class="html-bibr">21</a>,<a href="#B22-mathematics-12-02989" class="html-bibr">22</a>].</p>
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<p>Classification of the form evaluation algorithms.</p>
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<p>Flowchart illustrating the DE procedure.</p>
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<p>Variation of control parameters: (<b>a</b>) Scale factor; (<b>b</b>) Crossover probability.</p>
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<p>(<b>a</b>) Bridge-type CMM; (<b>b</b>) Set up to capture coordinate points; (<b>c</b>) Hip-stem implant.</p>
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<p>Evolution Process: (<b>a</b>) Data Set 1; (<b>b</b>) Data Set 2; (<b>c</b>) Data Set 3; (<b>d</b>) Femoral Head.</p>
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33 pages, 5556 KiB  
Article
Multi-Layer Objective Model and Progressive Optimization Mechanism for Multi-Satellite Imaging Mission Planning in Large-Scale Target Scenarios
by Xueying Yang, Min Hu, Gang Huang and Feiyao Huang
Appl. Sci. 2024, 14(19), 8597; https://doi.org/10.3390/app14198597 - 24 Sep 2024
Viewed by 360
Abstract
With the continuous increase in the number of in-orbit satellites and the explosive growth in the demand for observation targets, satellite resource allocation and mission scheduling are faced with the problems of declining benefits and stagnant algorithm performance. This work proposes a progressive [...] Read more.
With the continuous increase in the number of in-orbit satellites and the explosive growth in the demand for observation targets, satellite resource allocation and mission scheduling are faced with the problems of declining benefits and stagnant algorithm performance. This work proposes a progressive optimization mechanism and population size adaptive strategy for an improved differential evolution algorithm (POM-PSASIDEA) in large-scale multi-satellite imaging mission planning to address the above challenges. (1) MSIMPLTS based on Multi-layer Objective Optimization is constructed, and the MSIMPLTS is processed hierarchically by setting up three sub-models (superstructure, mesostructure, and understructure) to achieve a diversity of resource selection and step-by-step refinement of optimization objectives to improve the task benefits. (2) Construct the progressive optimization mechanism, which contains the allocation optimization, time window optimization, and global optimization phases, to reduce task conflicts through the progressive decision-making of the task planning scheme in stages. (3) A population size adaptive strategy for an improved differential evolution algorithm is proposed to dynamically adjust the population size according to the evolution of the population to avoid the algorithm falling into the local optimum. The experimental results show that POM-PSASIDEA has outstanding advantages over other algorithms, such as high task benefits and a high task allocation rate when solved in a shorter time. Full article
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<p>MSIMP basic mission scenarios: (<b>a</b>) The sequence of multi-satellite imaging mission assignments. (<b>b</b>) The visible time window allocation scheme for each satellite and the target task.</p>
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<p>Observation time window conflict diagram.</p>
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<p>Progressive optimization mechanism.</p>
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<p>Allocation optimization phase process.</p>
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<p>Time window optimization phase.</p>
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<p>Geographic distribution of the 100 target tasks.</p>
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<p>Initial task planning scheme.</p>
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<p>Schematic of the distribution of the final MSIMPLTS-MLOO mission planning scheme.</p>
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<p>Performance analysis of the MSIMPLTS-MLOO model for solving different instances of MSIMPLTS in a large-scale target task scenario: (<b>a</b>) MSIMPLTS-MLOO model when solving different instances of MSIMPLTS; (<b>b</b>) mission benefits in the local region and the global region.</p>
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<p>Benefit analysis of the POM-PSASIDEA algorithm for solving different instances of MSIMPLTS in a large-scale target task scenario. (<b>a</b>) Task benefit convergence for task number 100. (<b>b</b>) Task benefit convergence for task number 150. (<b>c</b>) Task benefit convergence for task number 200. (<b>d</b>) Task benefit convergence for task number 250. (<b>e</b>) Task benefit convergence for task number 300. (<b>f</b>) Task benefit convergence for task number 350.</p>
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<p>Benefit analysis of the POM-PSASIDEA algorithm for solving different instances of MSIMPLTS in a large-scale target task scenario. (<b>a</b>) Task benefit convergence for task number 100. (<b>b</b>) Task benefit convergence for task number 150. (<b>c</b>) Task benefit convergence for task number 200. (<b>d</b>) Task benefit convergence for task number 250. (<b>e</b>) Task benefit convergence for task number 300. (<b>f</b>) Task benefit convergence for task number 350.</p>
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<p>Experiments comparing the performance of the POM-PSASIDEA algorithm with other algorithms. (<b>a</b>) Max fitness of different algorithms in the local area scenario. (<b>b</b>) Max fitness of different algorithms in the global area scenario. (<b>c</b>) Average fitness of different algorithms in the local area scenario. (<b>d</b>) Average fitness of different algorithms in the global area scenario. (<b>e</b>) Min fitness of different algorithms in the local area scenario. (<b>f</b>) Min fitness of different algorithms in the global area scenario.</p>
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22 pages, 494 KiB  
Article
Vehicle Trajectory Prediction Based on Adaptive Edge Generation
by He Ren and Yanyan Zhang
Electronics 2024, 13(18), 3787; https://doi.org/10.3390/electronics13183787 - 23 Sep 2024
Viewed by 597
Abstract
With the rapid evolution of intelligent driving technology, vehicle trajectory prediction has become a pivotal technique for enhancing road safety and traffic efficiency. In this domain, high-definition vector maps and graph neural networks (GNNs) play a vital role, supporting precise vehicle positioning and [...] Read more.
With the rapid evolution of intelligent driving technology, vehicle trajectory prediction has become a pivotal technique for enhancing road safety and traffic efficiency. In this domain, high-definition vector maps and graph neural networks (GNNs) play a vital role, supporting precise vehicle positioning and optimizing path planning, thereby improving the performance of intelligent driving systems. However, high-definition vector maps and traditional GNNs still encounter several challenges in trajectory prediction, such as high computational resource demands, long training times, and limited modeling capabilities for dynamic traffic environments and complex interactions. To address these challenges, this paper proposes an adaptive edge generator method, this method dynamically constructs and optimizes the connections between nodes in the GNN architecture, effectively enhancing the accuracy and efficiency of trajectory prediction. Specifically, we classify nodes into dynamic and static nodes based on their attributes, and devise differentiated edge construction strategies accordingly. For dynamic nodes, we introduce a relative angle factor, enabling the attention model to comprehensively consider the distance and intersection status between nodes, resulting in more accurate computation of edge weights. For static nodes, we utilize a length threshold to assess the feasibility of establishing connections between vehicles and lane lines, determining whether a connection should be established. Through this approach, we successfully reduce the algorithmic complexity, increase computational speed, and maintain high trajectory prediction accuracy. Tests on the Argoverse motion prediction dataset demonstrate that trajectory prediction utilizing the adaptive edge generator achieves an average displacement error (ADE) of 0.6681, a final displacement error (FDE) of 0.9864, and a miss rate (MR) of 0.0952. Furthermore, the model parameters are significantly reduced, validating the effectiveness of the proposed vehicle trajectory prediction method based on the adaptive edge generator. Full article
(This article belongs to the Section Artificial Intelligence)
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<p>Map of selected map scenes and vehicle locations in the Argoverse dataset.</p>
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<p>General block diagram of adaptive edge generator; dynamic nodes include dynamic information such as vehicles, and static nodes include static information such as lane lines; these generate edges and weights through different rules.</p>
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<p>The input includes the vehicle’s movement direction, calculated from the previous and current time steps, along with the coordinates of the vehicle and other objects. Additionally, the hidden layer processes the relative angles between vehicles and the hidden information from the previous layer. The hidden layer decides how to connect the nodes and uses the decoder to predict the final output.</p>
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<p>Vehicle scenario construction diagram for some cases.</p>
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<p>Schematic of dynamic edge generation for specific scenarios.</p>
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<p>The number of total nodes compared with the number of updated nodes.</p>
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<p>Qualitative results of the adaptive edge generator, with past trajectories shown in red, real trajectories in green, the method in this paper in blue, and the VectorNet method in black. Compared with the VectorNet method, the method proposed in this paper can successfully predict the turning and acceleration performance of complex intersections. (<b>a</b>) Predicted intersection turn; (<b>b</b>) prediction of complex intersections; (<b>c</b>) predicted intersection turn; (<b>d</b>) prediction of acceleration.</p>
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22 pages, 4873 KiB  
Article
Path Planning for Wall-Climbing Robots Using an Improved Sparrow Search Algorithm
by Wenyuan Xu, Chao Hou, Guodong Li and Chuang Cui
Actuators 2024, 13(9), 370; https://doi.org/10.3390/act13090370 - 20 Sep 2024
Viewed by 485
Abstract
Traditional path planning algorithms typically focus only on path length, which fails to meet the low energy consumption requirements for wall-climbing robots in bridge inspection. This paper proposes an improved sparrow search algorithm based on logistic–tent chaotic mapping and differential evolution, aimed at [...] Read more.
Traditional path planning algorithms typically focus only on path length, which fails to meet the low energy consumption requirements for wall-climbing robots in bridge inspection. This paper proposes an improved sparrow search algorithm based on logistic–tent chaotic mapping and differential evolution, aimed at addressing the issue of the sparrow search algorithm’s tendency to fall into local optima, thereby optimizing path planning for bridge inspection. First, the initial population is optimized using logistic–tent chaotic mapping and refracted opposition-based learning, with dynamic adjustments to the population size during the iterative process. Second, improvements are made to the position updating formulas of both discoverers and followers. Finally, the differential evolution algorithm is introduced to enhance the global search capability of the algorithm, thereby reducing the robot’s energy consumption. Benchmark function tests verify that the proposed algorithm exhibits superior optimization capabilities. Further path planning simulation experiments demonstrate the algorithm’s effectiveness, with the planned paths not only consuming less energy but also exhibiting shorter path lengths, fewer turns, and smaller steering angles. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Histogram of chaotic mapping: (<b>a</b>) tent mapping; (<b>b</b>) logistic mapping; (<b>c</b>) logistic–tent mapping.</p>
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<p>Scatter plot of chaotic mapping: (<b>a</b>) tent mapping; (<b>b</b>) logistic mapping; (<b>c</b>) logistic–tent mapping.</p>
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<p>Lyapunov exponent analysis of logistic–tent mapping.</p>
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<p>Convergence curves of standard and chaos-based SSA variants: (<b>a</b>) Sphere; (<b>b</b>) Rosenbrock; (<b>c</b>) Rastrigin; (<b>d</b>) Ackley. Figure labels: TSSA (SSA with tent map), LSSA (SSA with logistic map), LTSSA (SSA with logistic–tent map).</p>
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<p>Refractive inverse learning schematic.</p>
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<p>Relationship between the unit circle and the sinusoidal function curve.</p>
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<p>Convergence curves on the test functions of each algorithm.</p>
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<p>Convergence curves on the test functions of each algorithm.</p>
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<p>Convergence curves on the test functions of each algorithm.</p>
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<p>Map of the two complexity levels of the environment: (<b>a</b>) Environment 1; (<b>b</b>) Environment 2.</p>
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<p>Simulation of path planning for each algorithm in Environment 1: (<b>a</b>) PSO; (<b>b</b>) GWO; (<b>c</b>) SSA; (<b>d</b>) LDESSA. The starting point is shown as a green dot, and the end point is shown as a red dot.</p>
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<p>Simulation of path planning for each algorithm in Environment 2: (<b>a</b>) PSO; (<b>b</b>) GWO; (<b>c</b>) SSA; (<b>d</b>) LDESSA. The starting point is shown as a green dot, and the end point is shown as a red dot.</p>
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<p>Simulation of path planning for each algorithm in Environment 2: (<b>a</b>) PSO; (<b>b</b>) GWO; (<b>c</b>) SSA; (<b>d</b>) LDESSA. The starting point is shown as a green dot, and the end point is shown as a red dot.</p>
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<p>Cost function convergence curve: (<b>a</b>) Environment 1; (<b>b</b>) Environment 2.</p>
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63 pages, 2957 KiB  
Article
Hybrid Four Vector Intelligent Metaheuristic with Differential Evolution for Structural Single-Objective Engineering Optimization
by Hussam N. Fakhouri, Ahmad Sami Al-Shamayleh, Abdelraouf Ishtaiwi, Sharif Naser Makhadmeh, Sandi N. Fakhouri and Faten Hamad
Algorithms 2024, 17(9), 417; https://doi.org/10.3390/a17090417 - 20 Sep 2024
Viewed by 490
Abstract
Complex and nonlinear optimization challenges pose significant difficulties for traditional optimizers, which often struggle to consistently locate the global optimum within intricate problem spaces. To address these challenges, the development of hybrid methodologies is essential for solving complex, real-world, and engineering design problems. [...] Read more.
Complex and nonlinear optimization challenges pose significant difficulties for traditional optimizers, which often struggle to consistently locate the global optimum within intricate problem spaces. To address these challenges, the development of hybrid methodologies is essential for solving complex, real-world, and engineering design problems. This paper introduces FVIMDE, a novel hybrid optimization algorithm that synergizes the Four Vector Intelligent Metaheuristic (FVIM) with Differential Evolution (DE). The FVIMDE algorithm is rigorously tested and evaluated across two well-known benchmark suites (i.e., CEC2017, CEC2022) and an additional set of 50 challenging benchmark functions. Comprehensive statistical analyses, including mean, standard deviation, and the Wilcoxon rank-sum test, are conducted to assess its performance. Moreover, FVIMDE is benchmarked against state-of-the-art optimizers, revealing its superior adaptability and robustness. The algorithm is also applied to solve five structural engineering challenges. The results highlight FVIMDE’s ability to outperform existing techniques across a diverse range of optimization problems, confirming its potential as a powerful tool for complex optimization tasks. Full article
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<p>Illustration of sample objective space from CEC2022 Benchmark Functions (F1–F4).</p>
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<p>Convergence diagram over CEC2022 benchmark functions (F1–F6).</p>
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<p>Convergence diagram over CEC2022 benchmark functions (F7–F12).</p>
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<p>Tension/compression spring design problem.</p>
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<p>The welded beam design problem.</p>
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<p>Cantilever beam design problem.</p>
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<p>Three-bar truss design problem.</p>
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<p>Error measure box plot analysis over CEC2022 benchmark functions (F1–F6).</p>
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<p>Error measure box plot analysis over CEC2022 benchmark functions (F7–F12).</p>
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<p>Error measure box plot analysis over CEC2017 benchmark functions (F1–F6).</p>
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<p>Error measure box plot analysis over CEC2017 benchmark functions (F7–F12).</p>
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<p>Error measure box plot analysis over CEC2017 benchmark functions (F13–F18).</p>
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<p>Error measure box plot analysis over CEC2017 benchmark functions (F19–F24).</p>
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<p>Error measure box plot analysis over CEC2017 benchmark functions (F25–F30).</p>
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21 pages, 5729 KiB  
Article
An Effective Training Method for Counterfactual Multi-Agent Policy Network Based on Differential Evolution Algorithm
by Shaochun Qu, Ruiqi Guo, Zijian Cao, Jiawei Liu, Baolong Su and Minghao Liu
Appl. Sci. 2024, 14(18), 8383; https://doi.org/10.3390/app14188383 - 18 Sep 2024
Viewed by 417
Abstract
Due to the advantages of a centralized critic to estimate the Q-function value and decentralized actors to optimize the agents’ policies, counterfactual multi-agent (COMA) stands out in most multi-agent reinforcement learning (MARL) algorithms. The sharing of policy parameters can improve sampling efficiency [...] Read more.
Due to the advantages of a centralized critic to estimate the Q-function value and decentralized actors to optimize the agents’ policies, counterfactual multi-agent (COMA) stands out in most multi-agent reinforcement learning (MARL) algorithms. The sharing of policy parameters can improve sampling efficiency and learning effectiveness, but it may lead to a lack of policy diversity. Hence, to balance parameter sharing and diversity among agents in COMA has been a persistent research topic. In this paper, an effective training method for a COMA policy network based on a differential evolution (DE) algorithm is proposed, named DE-COMA. DE-COMA introduces individuals in a population as computational units to construct the policy network with operations such as mutation, crossover, and selection. The average return of DE-COMA is set as the fitness function, and the best individual of policy network will be chosen for the next generation. By maintaining better parameter sharing to enhance parameter diversity, multi-agent strategies will become more exploratory. To validate the effectiveness of DE-COMA, experiments were conducted in the StarCraft II environment with 2s_vs_1sc, 2s3z, 3m, and 8m battle scenarios. Experimental results demonstrate that DE-COMA significantly outperforms the traditional COMA and most other multi-agent reinforcement learning algorithms in terms of win rate and convergence speed. Full article
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<p>CTDE framework vs. DTDE framework.</p>
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<p>Parameter sharing model.</p>
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<p>Parameter independence model.</p>
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<p>Policy network coding method.</p>
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<p>Flowchart of DE-COMA.</p>
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<p>DE-COMA initialization module.</p>
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<p>DE-COMA interaction module.</p>
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<p>DE-COMA RL update module.</p>
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<p>DE-COMA differential evolution update module.</p>
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<p>Training convergence plots of win rates for six algorithms on StarCraft II 2s_vs_1sc (<b>a</b>), 2s3z (<b>b</b>), 3m (<b>c</b>), 8m (<b>d</b>).</p>
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<p>Training convergence plots of average return for six algorithms on StarCraft II 2s_vs_1sc (<b>a</b>), 2s3z (<b>b</b>), 3m (<b>c</b>), 8m (<b>d</b>).</p>
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<p>2s3z scenario action sampling.</p>
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<p>2s_vs_1sc scenario action sampling.</p>
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<p>3m scenario action sampling.</p>
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<p>8m scenario action sampling.</p>
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24 pages, 918 KiB  
Article
Quality of Service-Aware Multi-Objective Enhanced Differential Evolution Optimization for Time Slotted Channel Hopping Scheduling in Heterogeneous Internet of Things Sensor Networks
by Aida Vatankhah and Ramiro Liscano
Sensors 2024, 24(18), 5987; https://doi.org/10.3390/s24185987 - 15 Sep 2024
Viewed by 382
Abstract
The emergence of the Internet of Things (IoT) has attracted significant attention in industrial environments. These applications necessitate meeting stringent latency and reliability standards. To address this, the IEEE 802.15.4e standard introduces a novel Medium Access Control (MAC) protocol called Time Slotted Channel [...] Read more.
The emergence of the Internet of Things (IoT) has attracted significant attention in industrial environments. These applications necessitate meeting stringent latency and reliability standards. To address this, the IEEE 802.15.4e standard introduces a novel Medium Access Control (MAC) protocol called Time Slotted Channel Hopping (TSCH). Designing a centralized scheduling system that simultaneously achieves the required Quality of Service (QoS) is challenging due to the multi-objective optimization nature of the problem. This paper introduces a novel optimization algorithm, QoS-aware Multi-objective enhanced Differential Evolution optimization (QMDE), designed to handle the QoS metrics, such as delay and packet loss, across multiple services in heterogeneous networks while also achieving the anticipated service throughput. Through co-simulation between TSCH-SIM and Matlab, R2023a we conducted multiple simulations across diverse sensor network topologies and industrial QoS scenarios. The evaluation results illustrate that an optimal schedule generated by QMDE can effectively fulfill the QoS requirements of closed-loop supervisory control and condition monitoring industrial services in sensor networks from 16 to 100 nodes. Through extensive simulations and comparative evaluations against the Traffic-Aware Scheduling Algorithm (TASA), this study reveals the superior performance of QMDE, achieving significant enhancements in both Packet Delivery Ratio (PDR) and delay metrics. Full article
(This article belongs to the Special Issue Advanced Applications of WSNs and the IoT)
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<p>Sample tree topology showing sink, transmitting nodes, and flows.</p>
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<p>Simple wireless network topology with an example TSCH schedule.</p>
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<p>QoS-oriented Multi-objective Differential Evolution Optimization flowchart.</p>
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<p>Sample of six pool statuses corresponding to six time slots.</p>
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<p>Process of mapping the generated matrix values to sensors for TSCH schedule creation: (<b>a</b>) random matrix generation, (<b>b</b>) normalization, (<b>c</b>) mapping the sensor’s position in the pool, and (<b>d</b>) assign nodes and matching pairs.</p>
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<p>Co-simulation: sequence diagram of QMDE using Matlab and TSCH-SIM.</p>
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<p>Optimization progress in scenario 5 with 64 nodes.</p>
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<p>Slotframe size of QMDE algorithm in various scenarios.</p>
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<p>Evaluation of delay between applications in (<b>a</b>) Scn 1, (<b>b</b>) Scn 2, (<b>c</b>) Scn 3, (<b>d</b>) Scn 4, and (<b>e</b>) Scn 5.</p>
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<p>Evaluation of PDR for two applications in (<b>a</b>) Scn 1, (<b>b</b>) Scn 2, (<b>c</b>) Scn 3, (<b>d</b>) Scn 4, and (<b>e</b>) Scn 5.</p>
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<p>Time complexity of QMDE algorithm in various scenarios.</p>
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<p>Delay comparison between QMDE and TASA in (<b>a</b>) Scn 1, (<b>b</b>) Scn 2, (<b>c</b>) Scn 3, (<b>d</b>) Scn 4, and (<b>e</b>) Scn 5.</p>
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<p>PDR comparison between QMDE and TASA in (<b>a</b>) Scn 1, (<b>b</b>) Scn 2, (<b>c</b>) Scn 3, (<b>d</b>) Scn 4, and (<b>e</b>) Scn 5.</p>
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35 pages, 3759 KiB  
Article
Hybrid Artificial Protozoa-Based JADE for Attack Detection
by Ahmad k. Al Hwaitat and Hussam N. Fakhouri
Appl. Sci. 2024, 14(18), 8280; https://doi.org/10.3390/app14188280 - 13 Sep 2024
Viewed by 400
Abstract
This paper presents a novel hybrid optimization algorithm that combines JADE Adaptive Differential Evolution with Artificial Protozoa Optimizer (APO) to solve complex optimization problems and detect attacks. The proposed Hybrid APO-JADE Algorithm leverages JADE’s adaptive exploration capabilities and APO’s intensive exploitation strategies, ensuring [...] Read more.
This paper presents a novel hybrid optimization algorithm that combines JADE Adaptive Differential Evolution with Artificial Protozoa Optimizer (APO) to solve complex optimization problems and detect attacks. The proposed Hybrid APO-JADE Algorithm leverages JADE’s adaptive exploration capabilities and APO’s intensive exploitation strategies, ensuring a robust search process that balances global and local optimization. Initially, the algorithm employs JADE’s mutation and crossover operations, guided by adaptive control parameters, to explore the search space and prevent premature convergence. As the optimization progresses, a dynamic transition to the APO mechanism is implemented, where Levy flights and adaptive change factors are utilized to refine the best solutions identified during the exploration phase. This integration of exploration and exploitation phases enhances the algorithm’s ability to converge to high-quality solutions efficiently. The performance of the APO-JADE was verified via experimental simulations and compared with state-of-the-art algorithms using the 2022 IEEE Congress on Evolutionary Computation benchmark (CEC) 2022 and 2021. Results indicate that APO-JADE achieved outperforming results compared with the other algorithms. Considering practicality, the proposed APO-JADE was used to solve a real-world application in attack detection and tested on DS2OS, UNSW-NB15, and ToNIoT datasets, demonstrating its robust performance. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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<p>Objective space of CEC2022 benchmark functions (F1–F6).</p>
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<p>APO-JADE convergence diagram on CEC2022 benchmark (F1–F6).</p>
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<p>APO-JADE convergence diagram on CEC2022 benchmark (F7–F12).</p>
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<p>APO−JADE search history diagram on CEC2022 benchmark (F1–F6).</p>
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<p>APO−JADE search history diagram on CEC2022 benchmark (F7–F12).</p>
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<p>APO-JADE average fitness diagram on CEC2022 (F1–F6).</p>
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<p>APO-JADE average fitness diagram on CEC2022 (F7–F12).</p>
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<p>APO-JADE box-plot diagram on CEC2022 benchmark (F1–F6).</p>
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<p>APO-JADE box-plot diagram on CEC2022 benchmark (F7–F12).</p>
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<p>APO-JADE heat map diagram on CEC2022 benchmark suite (F1–F6).</p>
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<p>APO-JADE heat map diagram on CEC2022 benchmark (F7–F12).</p>
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21 pages, 4763 KiB  
Article
MCMC Methods for Parameter Estimation in ODE Systems for CAR-T Cell Cancer Therapy
by Elia Antonini, Gang Mu, Sara Sansaloni-Pastor, Vishal Varma and Ryme Kabak
Cancers 2024, 16(18), 3132; https://doi.org/10.3390/cancers16183132 - 11 Sep 2024
Viewed by 625
Abstract
Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges [...] Read more.
Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges to be addressed, for instance, the associated severe toxicities, such as cytokine release syndrome. To model CAR-T cell dynamics, focusing on their proliferation and cytotoxic activity, we developed a mathematical framework using ordinary differential equations (ODEs) with Bayesian parameter estimation. Bayesian statistics were used to estimate model parameters through Monte Carlo integration, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. This paper explores MCMC methods, including the Metropolis–Hastings algorithm and DEMetropolis and DEMetropolisZ algorithms, which integrate differential evolution to enhance convergence rates. The theoretical findings and algorithms were validated using Python and Jupyter Notebooks. A real medical dataset of CAR-T cell therapy was analyzed, employing optimization algorithms to fit the mathematical model to the data, with the PyMC library facilitating Bayesian analysis. The results demonstrated that our model accurately captured the key dynamics of CAR-T cell therapy. This conclusion underscores the potential of parameter estimation to improve the understanding and effectiveness of CAR-T cell therapy in clinical settings. Full article
(This article belongs to the Section Cancer Immunology and Immunotherapy)
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<p>Different CAR-T cell phenotypes and their effect on patients, every dynamic is labeled with the kinetic parameters from <a href="#cancers-16-03132-t001" class="html-table">Table 1</a> and <a href="#cancers-16-03132-t002" class="html-table">Table 2</a>. After CAR-T cell infusion, they spread throughout the body (<math display="inline"><semantics> <msub> <mi>C</mi> <mi>D</mi> </msub> </semantics></math>), with some settling in blood and tumor areas. These engrafted cells are known as effector. CAR-T cells (<math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math>), they expand upon antigen contact (<b><span style="color: #FFE082">—</span></b>,<b><span style="color: #7FD6F9">—</span></b>) and differentiate into memory CAR-T cells (<math display="inline"><semantics> <msub> <mi>C</mi> <mi>M</mi> </msub> </semantics></math>), before becoming exhausted and either dying naturally or through a tumor immunosuppressive mechanism. Both effector CAR-T cells and those that are rapidly spreading can kill cancer cells. The memory CAR-T cells eventually die off, yet they can quickly react to cancer cells. When these memory cells come into contact with cancer cells, they turn back into effector CAR-T cells and quickly help to fight the cancer. However, over time, these cells can become worn out and stop working. The cancer cells (T), which are recognized by the CAR-T cells, grow based on what they have available in their environment and are killed off by the cytotoxic effect of the working CAR-T cells (<b><span style="color: #B599CC">—</span></b>). The net growth in cancer cells is determined by how fast they multiply and naturally they die, represented by the logistic function (<b><span style="color: #FFCEC6">—</span></b>) [<a href="#B17-cancers-16-03132" class="html-bibr">17</a>].</p>
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<p>Plot of medical data for patient 28.</p>
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<p>Comparison between the plots of the total CAR-T cells (<b><span style="color: #282DED">—</span></b>) obtained with the parameters from the article (<b>a</b>) and the <tt>least_squares</tt> method (<b>b</b>). The medical data (<span style="color: #282DED">•</span>) from <a href="#cancers-16-03132-t005" class="html-table">Table 5</a>.</p>
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<p>Comparison between the trace plots of kinetic parameters obtained with SMC (<b>a</b>), Metropolis (<b>b</b>), DEMetropolis (<b>c</b>), and DEMetropolisZ (<b>d</b>). Each plot was obtained with 10,000 draws and 16 chains in parallel.</p>
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<p>Comparison between the total CAR-T cell plots of the different trajectories for each of the algorithms (<span style="color: #282DED">—</span>). SMC (<b>a</b>), Metropolis (<b>b</b>), DEMetropolis (<b>c</b>), and DEMetropolisZ (<b>d</b>) and the medical data (<span style="color: #282DED">•</span>) from <a href="#cancers-16-03132-t005" class="html-table">Table 5</a>.</p>
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<p>Forest plots of marginal probabilities (“dispersion coefficient” = (97.5th percentile value − 2.5th percentile value)/mean value) of every kinetic parameter. These plots compare four methods: DEMetropolisZ (<b><span style="color: #282DED">—</span></b>), DEMetropolis (<b><span style="color: #F97C16">—</span></b>), Metropolis algorithm (<b><span style="color: #338C05">—</span></b>), and sequential Monte Carlo, SMC (<b><span style="color: #C10C8E">—</span></b>).</p>
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<p>DEMetropolisZ pair plot of the posterior correlations.</p>
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