Advanced Harmony Search with Ant Colony Optimization for Solving the Traveling Salesman Problem

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Parameters</td><td align="center">Values</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">HMS</td><td align="center">100~200</td></tr><tr><td align="left">HMCR</td><td align="center">0.9</td></tr><tr><td align="left">PAR</td><td align="center">0.4</td></tr><tr><td align="left"><span style="width: 9.2875004px;"><svg height="12.175" id="M45" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 9.2875004 12.175" width="9.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M516 277q0 -126 -140 -231q-36 -27 -75.5 -42.5t-63.5 -15.5q-38 0 -73 43q-10 -44 -18 -106q-18 -134 -32 -151q-12 -16 -40 -25t-46 -10l-5 14q22 38 84 406q16 92 44.5 146.5t88.5 95.5q68 47 136 47q63 0 101.5 -47.5t38.5 -123.5zM432 259q0 61 -27 101t-79 40
t-82 -49t-49 -148l-24 -127q42 -36 88 -36q79 0 126 61.5t47 157.5z" id="x1D70C"></path></g>
</svg></span></td><td align="center">0.05</td></tr><tr><td align="left"><span style="width: 9.7749996px;"><svg height="7.9499998" id="M46" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 9.7749996 7.9499998" width="9.7749996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" id="x1D6FC"></path></g>
</svg></span></td><td align="center">0.8</td></tr><tr><td align="left"><span style="width: 10px;"><svg height="16.6625" id="M47" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 10 16.6625" width="10" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" id="x1D6FD"></path></g>
</svg></span></td><td align="center">1.0</td></tr><tr><td align="left"><span style="width: 20.2125px;"><svg height="14.0375" id="M48" style="vertical-align:-4.10045pt" version="1.1" viewbox="0 0 20.2125 14.0375" width="20.2125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
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<g transform="matrix(.012,-0,0,-.012,10.138,13.838)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg></span></td><td align="center">0.01</td></tr><tr><td align="left">Iteration</td><td align="center">1000</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameters settings of the proposed algorithm.

Journal of Applied Mathematics

tab1

Table 1

Table 1: Advanced Harmony Search with Ant Colony Optimization for Solving the Traveling Salesman Problem 