A Hybrid Bat Algorithm with Path Relinking for Capacitated Vehicle Routing Problem

<table>Changing curve of frequency <svg height="12.225" id="M102" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.6375 12.225" width="11.6375" 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="M54 437h47v21q0 48 11 83q23 72 77 118q55 46 110 53q53 -3 79 -34q13 -16 5 -35q-5 -13 -19 -24t-27 3q-37 37 -81 37q-34 0 -53 -29q-24 -37 -23 -153v-40h118q5 -7 1.5 -21t-11.5 -19h-108v-287q0 -55 13 -67t73 -18v-25h-236v26q49 5 60 16.5t11 60.5v294h-70l-4 11z
" id="x66"></path></g><g transform="matrix(.017,-0,0,-.017,5.247,12.162)"><path d="M181 342h2q63 107 121 107q24 0 41 -16t17 -34q0 -34 -32 -49q-17 -7 -26 2q-21 20 -43 20q-20 0 -42 -22t-38 -63v-183q0 -50 12.5 -62t69.5 -16v-26h-230v26q47 5 58 17t11 61v207q0 49 -9 60.5t-53 16.5v23q74 12 141 40v-109z" id="x72"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: A Hybrid Bat Algorithm with Path Relinking for Capacitated Vehicle Routing Problem 