A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution

<table class="table-group" id="tab13"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td align="left">Algorithm</td><td align="center">NBIPOP-aCMA</td><td align="center">fk-PSO</td><td align="center">SPSO2011</td><td align="center">SPSOABC</td><td align="center">PVADE</td><td align="center">HBD</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td align="left">Ranking</td><td align="center"><b>1.80</b></td><td align="center">3.61</td><td align="center">5.29</td><td align="center">3.34</td><td align="center">3.95</td><td align="center"><b><i>3.02</i></b></td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Average ranking of six algorithms by the Friedman test for CEC2013 functions at <svg height="9.21094pt" id="M435" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 39.1241 9.21094" width="39.1241pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,14.163,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,25.901,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,32.404,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>.

Mathematical Problems in Engineering

tab13

Table 13

Table 13: A Hybrid Backtracking Search Optimization Algorithm with Differential Evolution 