A Modification Artificial Bee Colony Algorithm for Optimization Problems

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Decreasing individuals</td><td align="center">Mean objective value</td><td align="center">Average population</td><td align="center">Time (sec)</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">1</td><td align="center">8.38 × 10<sup>−16</sup></td><td align="center">8.5</td><td align="center">0.90</td></tr><tr><td align="left"><span style="width: 36.8485ptpx;"><svg height="10.0405pt" id="M148" style="vertical-align:-0.3625994pt" version="1.1" viewbox="-0.0498162 -9.6779 36.8485 10.0405" width="36.8485pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="406" vert-adv-y="406"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,5.505,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,16.052,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,27.033,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="406" vert-adv-y="406"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,32.946,0)"><path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data></g></svg></span></td><td align="center">5.29 × 10<sup>−16</sup></td><td align="center">7.2</td><td align="center">0.84</td></tr><tr><td align="left">3</td><td align="center">1.54 × 10<sup>−11</sup></td><td align="center">4.6</td><td align="center">0.73</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Comparison result in 10 independent runs for different number of decreasing individuals per generation.

Mathematical Problems in Engineering

tab5

Table 5

Table 5: A Modification Artificial Bee Colony Algorithm for Optimization Problems 