Coordination of Pheromone Deposition Might Solve Time-Constrained Travelling Salesman Problem

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:8.96em"/><col style="width:8.52em"/><col style="width:9.71em"/><col style="width:5.86em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center">Strict ACO model</td><td class="align_center">Tolerant ACO model</td><td class="align_center">Ant System</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">Equation <a href="https://static.hindawi.com/articles/complexity/volume-2018/6498218/figures/#eq6" target="_blank"><i><svg height="11.5695pt" id="M90" style="vertical-align:-2.26812pt" version="1.1" viewbox="-0.0498162 -9.30138 18.1852 11.5695" width="18.1852pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.738,0)"><path d="M114 480C175 497 250 537 253 615C255 675 211 710 176 710C157 710 133 696 132 670C131 660 137 654 143 653C173 645 194 628 192 596C190 554 152 526 104 508L114 480Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.531,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></i></a></td><td class="align_center">45</td><td class="align_center">42</td><td class="align_center">0</td></tr><tr><td class="align_left"><span style="width: 100.009ptpx;"><svg height="9.49473pt" id="M91" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 100.009 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class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The number of trials of the shortest tour of each model by replacing a certain equation. <i>Eil</i> 51 was used for these analyses. One hundred trials are conducted.</div>

Complexity

tab3

Table 3

Table 3: Coordination of Pheromone Deposition Might Solve Time-Constrained Travelling Salesman Problem 