A Methodology to Determine the Subset of Heuristics for Hyperheuristics through Metalearning for Solving Graph Coloring and Capacitated Vehicle Routing Problems

<table class="table-group" id="tab7"><tr><td><table class="table"><tr><td class="thead-hr" colspan="14"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center">Statistics</td><td class="align_center"><svg height="10.2124pt" id="M199" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g></svg> value</td><td 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628 43 643 122L719 524C735 610 741 615 822 622L828 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.507,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg></span></td><td class="align_center"><span style="width: 19.6072ptpx;"><svg height="11.8174pt" id="M210" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 19.6072 11.8174" width="19.6072pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M828 650H570L564 622C646 614 650 609 634 524L604 366H253L281 524C296 608 308 615 382 622L388 650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.507,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="14"><hr/></td></tr><tr><td class="align_left">F</td><td class="align_center">255.72</td><td class="align_center">0</td><td class="align_center">4.64</td><td class="align_center">6.40</td><td class="align_center">2.18</td><td class="align_center">4.68</td><td class="align_center">3.33</td><td class="align_center">10.01</td><td class="align_center">7.52</td><td class="align_center">2.48</td><td class="align_center">7.40</td><td class="align_center">6.47</td><td class="align_center">10.89</td></tr><tr><td class="align_left">FA</td><td class="align_center">77.86</td><td class="align_center">0</td><td class="align_center">374.88</td><td class="align_center">461.35</td><td class="align_center">209.30</td><td class="align_center">370.94</td><td class="align_center">340.22</td><td class="align_center">820.66</td><td class="align_center">575.50</td><td class="align_center">212.84</td><td class="align_center">568.01</td><td class="align_center">505.86</td><td class="align_center">829.45</td></tr><tr><td class="align_left">Q</td><td class="align_center">99.04</td><td class="align_center">0</td><td class="align_center">5.27</td><td class="align_center">6.49</td><td class="align_center">1.91</td><td class="align_center">5.24</td><td class="align_center">3.68</td><td class="align_center">9.99</td><td class="align_center">6.84</td><td class="align_center">2.44</td><td class="align_center">7.11</td><td class="align_center">6.13</td><td class="align_center">10.90</td></tr><tr class="table-tr"><td colspan="14"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Statistic test results for graph coloring instances for Friedman (F), Friedman Aligned (FA), and Quade (Q).</div>

Complexity

tab7

Table 7

Table 7: A Methodology to Determine the Subset of Heuristics for Hyperheuristics through Metalearning for Solving Graph Coloring and Capacitated Vehicle Routing Problems 

Table 7 | A Methodology to Determine the Subset of Heuristics for Hyperheuristics through Metalearning for Solving Graph Coloring and Capacitated Vehicle Routing Problems 