Bacterial Foraging-Tabu Search Metaheuristics for Identification of Nonlinear Friction Model

<div class="floats-full-page floats-full-page-other"><h2>Table 2</h2><div class="floats-full-page-caption">ATS parameters. </div><div class="floats-full-page-content"><table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="8"><hr /></td></tr><tr><td align="left" rowspan="2">Test functions</td><td align="center"><i>N</i></td><td align="center"><span style="width: 68.525002px;"><svg height="15.65" id="M110" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 68.525002 15.65" width="68.525002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.362)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207&#10;q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.017,-0,0,-.017,11.605,11.362)"><use xlink:href="#x6F"></use></g><g transform="matrix(.017,-0,0,-.017,20.104,11.362)"><path d="M518 50v-26q-32 -4 -77 -16l-37 -11t-33 -9l-6 6v71q-56 -42 -74 -52q-43 -25 -77 -25q-55 0 -89.5 36.5t-34.5 112.5v196q0 38 -6.5 48.5t-26.5 15.5l-28 6v23q19 1 72 7q59 9 71 11q-3 -31 -3 -145v-135q0 -113 88 -113q59 0 108 48v234q0 38 -8 49t-34 15l-36 6v23&#10;q44 2 90 8q37 4 67 10v-334q0 -37 8.5 -47t38.5 -12z" id="x75"></path></g><g transform="matrix(.017,-0,0,-.017,29.13,11.362)"><use xlink:href="#x6E"></use></g><g transform="matrix(.017,-0,0,-.017,38.106,11.362)"><path d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" id="x74"></path></g>
<g transform="matrix(.012,-0,0,-.012,43.288,15.45)"><use xlink:href="#x6D"></use></g><g transform="matrix(.012,-0,0,-.012,53.033,15.45)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5&#10;t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.012,-0,0,-.012,58.256,15.45)"><path d="M474 0h-214v26q32 4 39 12t-5 28l-74 117q-39 -58 -64 -106q-16 -25 -10 -35t44 -16v-26h-186v26q46 6 64 17t48 49t85 120l-87 136q-23 36 -40 47t-58 16v26h199v-26q-31 -4 -36.5 -12.5t9.5 -29.5l59 -93q37 56 58 94q13 23 7 30t-40 11v26h183v-26q-47 -5 -65 -13.5&#10;t-45 -39.5q-24 -29 -78 -110l97 -148q28 -43 46.5 -55.5t63.5 -18.5v-26z" id="x78"></path></g>
</svg></span></td><td align="center"><i>R</i></td><td align="center">&#13;
								BT,<i> n_re_back </i></td><td align="center" colspan="3">AR</td></tr><tr><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td><td align="left">Stage I</td><td align="center">Stage II</td><td align="center">Stage III</td></tr><tr><td align="left" colspan="8"><hr /></td></tr><tr><td align="left">BF</td><td align="center">30</td><td align="center">10,000</td><td align="center">0.2</td><td align="center">5</td><td align="center"><svg height="18.299999" id="M111" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 93.974998 18.299999" width="93.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,15.775)"><path d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" id="x3C"></path></g><g transform="matrix(.017,-0,0,-.017,27.244,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.854,15.775)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,64.267,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,72.426,15.775)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,80.6,7.613)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,87.585,7.613)"><use xlink:href="#x31"></use></g>
</svg>,</td><td align="center"><svg height="18.299999" id="M112" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 93.974998 18.299999" width="93.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,15.775)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,44.854,15.775)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,64.267,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,72.426,15.775)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,80.6,7.613)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,87.585,7.613)"><use xlink:href="#x33"></use></g>
</svg>,</td><td align="center">—</td></tr><tr><td align="left">RF</td><td align="center">30</td><td align="center">10,000</td><td align="center">0.2</td><td align="center">5</td><td align="center"><span style="width: 97.162498px;"><svg height="16.049999" id="M113" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 97.162498 16.049999" width="97.162498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117&#10;t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g><g transform="matrix(.017,-0,0,-.017,15.718,15.775)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,15.775)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,48.033,15.775)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,67.446,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,75.605,15.775)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,83.775,7.613)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,90.76,7.613)"><use xlink:href="#x33"></use></g>
</svg></span></td><td align="center"><span style="width: 97.162498px;"><svg height="16.012501" id="M114" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 97.162498 16.012501" width="97.162498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.738)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,15.738)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,15.738)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,48.033,15.738)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,67.446,15.738)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,75.605,15.738)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,83.775,7.587)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,90.76,7.587)"><use xlink:href="#x34"></use></g>
</svg></span></td><td align="center">—</td></tr><tr><td align="left">SF</td><td align="center">30</td><td align="center">10,000</td><td align="center">0.8</td><td align="center">5</td><td align="center"><span style="width: 35.474998px;"><svg height="13.6375" id="M115" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 35.474998 13.6375" width="35.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x35"></use></g>
</svg><i>, </i><svg height="11.375" id="M116" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 50.6875 11.375" width="50.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,42.457,11.112)"><use xlink:href="#x35"></use></g>
</svg></span></td><td align="center"><span style="width: 35.474998px;"><svg height="13.6375" id="M117" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 35.474998 13.6375" width="35.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x32"></use></g>
</svg><i>, </i><svg height="11.375" id="M118" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 50.6875 11.375" width="50.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,42.457,11.112)"><use xlink:href="#x31"></use></g>
</svg></span></td><td align="center">—</td></tr><tr><td align="left">SchF</td><td align="center">30</td><td align="center">10,000</td><td align="center">50</td><td align="center">5</td><td align="center"><span style="width: 51.787498px;"><svg height="13.6375" id="M119" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 51.787498 13.6375" width="51.787498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,35.403,11.113)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,43.562,11.113)"><use xlink:href="#x30"></use></g>
</svg><i>, </i><svg height="11.375" id="M120" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 46.8125 11.375" width="46.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><use xlink:href="#x35"></use></g>
</svg></span></td><td align="center"><span style="width: 43.637501px;"><svg height="13.6375" id="M121" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 43.637501 13.6375" width="43.637501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,35.403,11.113)"><use xlink:href="#x30"></use></g>
</svg><i>, </i><svg height="11.375" id="M122" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 46.8125 11.375" width="46.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.112)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.112)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,38.582,11.112)"><use xlink:href="#x30"></use></g>
</svg></span></td><td align="center"><span style="width: 35.474998px;"><svg height="13.6375" id="M123" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 35.474998 13.6375" width="35.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x31"></use></g>
</svg><i>, </i><svg height="11.3125" id="M124" style="vertical-align:-0.1092pt" version="1.1" viewbox="0 0 38.650002 11.3125" width="38.650002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,11.113)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,11.113)"><use xlink:href="#x31"></use></g>
</svg></span></td></tr><tr><td align="left">ShuF</td><td align="center">30</td><td align="center">10,000</td><td align="center">1.0</td><td align="center">5</td><td align="center"><span style="width: 35.474998px;"><svg height="13.6375" id="M125" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 35.474998 13.6375" width="35.474998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x31"></use></g>
</svg><i>, </i><svg height="16.049999" id="M126" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 97.162498 16.049999" width="97.162498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,15.775)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,48.033,15.775)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,67.446,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,75.605,15.775)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,83.775,7.613)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,90.76,7.613)"><use xlink:href="#x32"></use></g>
</svg></span></td><td align="center"><span style="width: 45.450001px;"><svg height="13.6375" id="M127" style="vertical-align:-1.97925pt" version="1.1" viewbox="0 0 45.450001 13.6375" width="45.450001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43D"></use></g><g transform="matrix(.017,-0,0,-.017,12.54,11.113)"><use xlink:href="#x3C"></use></g><g transform="matrix(.017,-0,0,-.017,27.244,11.113)"><use xlink:href="#x2212"></use></g><g transform="matrix(.017,-0,0,-.017,37.222,11.113)"><use xlink:href="#x31"></use></g>
</svg><i>, </i><svg height="16.049999" id="M128" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 97.162498 16.049999" width="97.162498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x1D445"></use></g><g transform="matrix(.017,-0,0,-.017,15.718,15.775)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,30.422,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,48.033,15.775)"><use xlink:href="#xD7"></use></g><g transform="matrix(.017,-0,0,-.017,67.446,15.775)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,75.605,15.775)"><use xlink:href="#x30"></use></g>
<g transform="matrix(.012,-0,0,-.012,83.775,7.613)"><use xlink:href="#x2212"></use></g><g transform="matrix(.012,-0,0,-.012,90.76,7.613)"><use xlink:href="#x33"></use></g>
</svg></span></td><td align="center">—</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr" /></td></tr></table></td></tr></table></div></div>

Table 2 | Bacterial Foraging-Tabu Search Metaheuristics for Identification of Nonlinear Friction Model

title

Table 2: Bacterial Foraging-Tabu Search Metaheuristics for Identification of Nonlinear Friction Model

description

Table 2

About this journal

<p><em>Journal of Applied Mathematics</em> publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.</p>


Journal profile

Meet the editorial board

<p><em>Journal of Applied Mathematics</em> maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.</p>


Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.