信息素的局部更新策略
每只蚂蚁在构造出一条从起点到终点的路径后,蚁群算法还要求根据路径的总长度来更新这条路径所包含的每条边上信息素的浓度(在旅行商问题中每座城市是图中的一个节点,城市两两间有一条边相连)。下面给出了蚁群算法更新信息素的公式:
aaarticlea/png;base64,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" alt="" width="381" height="141" />
.
上面的第一个公式体现了信息素的更新值的计算,其中,Ck代表第k只蚂蚁所构造的路径的总长度,Q是凭经验设定的一个参数,通常置为1。component(i,j)表示从城市i到城市j的一条边,m是蚂蚁的总数。上面的第二个公式是说i和j这条边的信息素值tau等于这条边上原有的信息素加上在上一次构造路径活动中所有经过这条边的蚂蚁贡献的信息素更新值(即第一个公式)。
假设三只蚂蚁构造的路径长度如下所示:
Tour 1: 450
Tour 2: 380
Tour 1: 460
则它们的信息素的更新值相加结果为:componentNewPheromone = (Q / 450) + (Q / 380) + (Q / 460)
最后把它加到各个蚂蚁的路径中每条边原来的信息素值之上:
componentPheromone = componentPheromone + componentNewPheromone
上述信息素更新过程的伪代码如下所示:
for ant in colony do //蚁群中每条蚂蚁都逐个更新自己路径经过边上的的信息素
tour = ant.getTour(); //蚂蚁计算路径的总长度
pheromoneToAdd = getParam('Q') / tour.distance(); //蚂蚁计算信息素的更新值
for cityIndex in tour do //回溯路径中的每个城市
if lastCity(cityIndex) do // 如果当前城市是路径上的最后一个城市,取出它和第一个城市间的边
edge = getEdge(cityIndex, )
else do
edge = getEdge(cityIndex, cityIndex+) //否则,取当前城市和路径上下一个城市间的边
end if
currentPheromone = edge.getPheromone(); //获得边上之前的信息素
edge.setPheromone(currentPheromone + pheromoneToAdd)//原有信息素加上更新值后得到新信息素
end for // ant路径上所有的边的信息素更新完毕
end for //蚁群中所有蚂蚁都处理完毕
信息素的挥发
在自然界中蚂蚁遗留下来的信息素经过一段时间后会挥发,我们在算法中也模拟上述过程,具体公式如下:
aaarticlea/png;base64,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" alt="" />
rho是一个人为设定的参数,称为挥发率,一般为0-1间的数。
相应的伪代码如下所示:
for edge in edges
updatedPheromone = ( - getParam('rho')) * edge.getPheromone()
edge.setPheromone(updatedPheromone)
end for
精英蚂蚁策略
精英蚂蚁是对蚁群算法的一种改进,所谓精英蚂蚁是指当全部蚂蚁都构造完各自的路径之后,所有路径中最短的那条路径所对应的蚂蚁。精英蚂蚁策略的公式如下所示,它和上面的信息素局部更新公式的唯一区别在于精英蚂蚁在像其它蚂蚁一样更新完自己路径上的信息素后,还要再重复一遍信息素的更新过程,只不过这次要把更新值乘上一个参数e,e通常选在0和1之间。
aaarticlea/png;base64,iVBORw0KGgoAAAANSUhEUgAAAqcAAADBCAIAAAB9tY49AAAbxklEQVR4nO3dv9GrOLzG8W3g0NgWQBtkWwAdUMAOBZCTEjskdbIzZM4o4F5u8MzR1ZFAyDbG4tX3E+zs8WtjSWB++s9f/wMAAPLw1/8CAIA8/LUAAIA8EPUBAMgFUR8AgFwQ9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPUBAMgFUR8AgFwQ9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPUBAMgFUR8AgFwQ9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPUBAMgFUR8AgFwQ9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPUBAMgFUR8AgFwQ9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPUBAMgFUR8AgFwQ9QEAyAVR/8sej0fbtkVRTNP07bQAAH44ov7XzPPc931RFHVdPx6Pbydn0zAMVVVRLwGAH4Co/x3zPCuUDsPw7bTsU+3k26kAALyLqP8FJuTfbrfTvrEsy5d7FJTaY5OES5umqaqqj3b/tG172g8EyAdR/wuapimKouu6mDff7/e2bcuyLIqiKIqyLLuum+f5qW/suq7ve+fFeZ6HYVBipGma+/2uPzVNY94Zn9ozKZF1XRMbTjZNU1mWnx7xeTweRVEELnXVPOq61tX77I9C2rat61r1Wv83gg+h2L+IqH+2aZoib1KPx0N3tL7vTTN9HEd9PP6e+3g8yrK0XzFTCsqyHIZBBzcvmv86CVb9QNWCZVnu93tVVYq7H60T6O5v10KkbVtNhKQf4ljjOAauLl0P4zjaL26doxjq+qqqyv9TVVW7Vbqu6zQ55oWvNlSrNtd2ysJn51r8Yl+9kNLMcpqpikHUP5ti6u79UffWqqr8ykF8vUHqurbv0WqobU0pUPKKojD1DL2iX6YCv143RxiG4aNx936/+7f1eZ5NBSXBfojr0tXVtu3qXxWh/QJfPUdPfePqZ1WxC39c1+Q77UVdS5eoO4bPzrWsFrt/IaWZ5TRTFYmofzbTfA+8JxDyJf5Od7/f/Z9QoKtAdW37I/agvhP1VRuYpslp+R3OT63uDpdonF2L6nBbLey+78uyXL0s32n3bH227/vVPgCbuQ5f/nb1n73ZW3CO8Nm5lq1idy6GNLOcZqoiEfXPpptUIEyaKnDgNqo27u4NcVkWe/zVHDm8cMB5g92YtuvmZkJATDIOpxJIecXjRem0rhasaoRn3ul2F4+YWuw736IxgkuspgmcncuJLPY0s5xmqiIR9U9l4m7gctFYdbjvyPTDh7+u73u7M1ZX6m6bxpmoZddRzNjEMAz6uX5rUZ/d64ADabbH6p80q/TMxOxeXbfb7eX5BIYGvC4xRhs4O5cTWexpZjnNVEUi6p9K/dKBG5maU7s/hpior9V6pjPWtIp222rOwIGJ+qqbmxdVe9AePuEDvux2u2mir0mzmb5nhCsx0zS1bauZ3lVV+V0sWiLRNI3e47yh6zrNWJymaZqmpmn0TtWl+r6v67osS73BfEqLC/Q2zZHUt6+OyMQkoO/7eZ7NtGfn6+xDmePUdW13eu8eRz2WDvvgujL9LPjnKJ4Kp2masixXP25fcqtMFdmcmq1C3ioZ84vzP3LUebndbpr02rbtOI5O61ZpE/+LZPfs7CZ4i06f0na73Zy0PZVN31PF7lxIkVneOv6H8huTqvQR9U+liyYQqPSG3Tiqlm64stm2rX1N6wZaPL/ASTUV3ZXMZ7uuM/ep11ZMxXyvCkozIew/Rc4YV5ZNGPC7BxQzTCmp4Whul7pZK/v2ZGN9uwkwql3Zp6zv+77vTQ1PxzfTD19OgO6G/tfpRZWSiZ0aNH32OIHRSv3J6aMKnKNdSrMOuPVx3XYDB9F5MTsHqGprF3K4ZJbfZe50rR17XswEHX/JiRJjwlW4lhM4O+EEb1GFWKdAR7BvKfHZ9D1b7FsX0laWd4//0fxeelB/IeqfbLf3Xpfy7qR03TsCx7nf706dQJPyLjFlSaqq0t3QT7ZuGeHJjM6oofkxb71B7CqX+gZM8HamR9hJUuyxD/J4PHRrsE/lawnQ7cx+m79pkl6x2zr2TTD+OIHRytV7feAc7VLdyBx89ZYdPqyqX87sQqeQwyWz/P5J2nfwA8+LDm4vdnVqq2VZmgya7Gzld+vs7CZ4lT4VSFt8Nn3PFvvWhbSV5d3jfzS/lx7UX4j6J1NQD0xgUYAJ1yLNkv1Aj5bf36WP7E77T+dSVlIV4J0C0Q840JTxY7xeNOFh9Q3Ln9MVlQBn94Lld/mbb3cWnineL79vDc4MCXPw+AR0XWe/zV/n5vQPPR4Pp9Aij7Nsj1Zude8HztGupml0sfnLRsJfaqxW/uwC3C0Z8/4XLozd8tSh7NCr9DhTZRV7brfbPM/TNAV6zlYTFpNg31ba7JKJv2wcLxT71oW0mrWY4380v+HKWfp+QtS/0ONhdqP17huW31WHwA9PXVWrRw5Hfd1nk1oOp8w6t0Kd7kAFZXf3Q6dHVFZnXSgB9nc53bB+m16cW4Nzd45PQFVVdqeO/3UqDTO6qZGd1eZR+DiBJci6q25dGKvnKN5Wz034S5ffZWj/6lUhM4W8WzL+Pf3A8+Ivr/UrgmZjQQlUZLfOTnyC/U/5aXvhsvG9UOziXEhbWY684D+U30uv1JefEPWXizweJmZ3HV33gTud+T1vXeVbW+7HbH6p1djBTJxqa/w+fEczbwjUAlffoKvI/j2rM98fK7EbDas1Tv/W4Bz8qQT4/Y1+F0L4rhdznN1h49Ujv7Mrn31w/5oPfKlUVeWcGmcEbbdkthrfB54XO1/+QIZ2xTaxP/Dr2zo7kQl2+JvirX57TDZ9LxT7snYhhbP8VK/kgfm9+qD+kkLU1zzeN2eEXeLxME5DZJUzAU3Tv9u2Vfns7rGz/DlcatudJ5jgvjemJ18XiV6M2QYuslrgvOjfGnTK/Nu9ecUei73f7+az/q3BGYl8KgHmFfvrTJnsZjbyOHbrZ5omu30TmFW3eo6eEhjUD7eo/Dc4gXa3ZEzjW7PDtj5yyHnxo9o4jvYM2fBNbOvsRCbY4XzKrqT6g1nhbO4efCsvdrEvaxfSU1kOOzC/gZ/JVXw/6u+2bmMUV9iWVRXwcLiyJyj1fa+wcb/fu67TlRp+6knggSXhB/3pck+tAmviwe12M1Fntx2zbAQSLb3T//t3WMVp50bmTyBwJvvoDbr2zIykxbuqVVOx0/xUAsw/7R2ItYxi9VBOZiOPU5alqZLWfz7TqNhuzfvnSF8duemNWRDhvO5Mntj6aru4VIDhQl7+LBlzTzeJP/C8OBeh3hPoV9AisUBmV89OZIIdThRUdm63m7brfiqbvheKfVm7kOKzvHgX/OfyG/iZXMWXo75Z/vjONtpffzxMpJi9eBdr4omZnGwyuPu0PU0L2vqrCfxt25p7jXmmX4KzIlRJ0piFE1DDQcWZ3aN+VPsgTlDZulGquOwy133BlJXpnXZ2Prav6sfjoUEB+zjxCfDvSvo60+BwKiKqL9qZjTyOqZJqTbOdjMB1658js2nj6vsdW4P6WsQf/qy9X+/qArzdkjFZNiu1Djwv9vaRSl7xZy9dWZYmwXpDoNd66+xEJtgvOnNhm5uwWhf2Z2Oy6Xuh2Je1Cymc5fAF/7n8Bn4mV/HNqG92mw+0JGJ8/fEwkVSZjdk94/F42E/X9SeUrYZ2J/Bs0Vw/HVk7zCRbXVWt39lyxL97rhrHUbFWU378UaRxHNVxrTGU1VtY4fUhaVcQ88/H46FX7K5ae4cDHX+1jhKZAPuupAaNv1OKCspkdhgGJ7Mxx1Hg0Wym8Mdt/jkyO0Osvt+xOqgfv/WvtlWp67ppmtVfVrhk1DDQ5WFePPC8aEK4ju+XiT5lpqSFB6oDZycmwT5TdGZTGrsW8lQ2V1P7bLH7F1Igy7sX/OfyG0jVVXwz6mt9ZP/7ka/vHMf8nJovPR5mV8zu+gH2nVGXrP8eu4f5p9qdnJwCXdJfv+QOFNN8tKkDKfLI/tnUbipPpC957895BI7ytajf973uC2b1+cv1piLJx8M4YqbyBdi3Xe0l6bxhGIZLLybZpcsjZlD/6/xxgatzmmW7tMfZ7ttWV3AlOKv0fauz1oGv+E7U185xzqD1y7/zIsnHwzgiB/W3qIi6rltdG721Wu/HMLtv+oMdqVGnTgoVzQNpLUnkm2+3W6BappNo74pqV2F1Jb8zyycRGuYwF2r61y3y8YWo70zOWjY2kFE/drHN/vi3Hg8TSQ39d5JhZ9xvMThzUn4eUy8s0l6sYbqXts7URalqHvNODbiGN5hT/PPXNSzL0jRN4h05kUw2l7XKDfBFX4j6bds6N25VhO1BL80210QYTVRRFDfs+6k9eerMx8NEillkv0tTSMqy9APJ4/FIamudTzCTd3525SZlkYuUtN468AZNt/YnaS7L0rbtzwj5i/VsN800/GEDFri0s6O+ZlY7L6qNboeupmnsmsFTHYzvMM9/3BU5McesU/hc597tdvtJE8eQpq05pEfxH0EL4BNOjfoa8vSbvGYxq3nFDmOKxJe7I2gVqUYuftLELgDAdZ0a9bd27ApP6FPsTHAPmTANW1wu2QCAH+y8qK+HTGz9NTD7aWub7sRpR7atqgwAAOc7KeprxllgbFstY3/gMLy7hTMuYNh79cQzXQ67Igc4zQ64BH4AQApOivq7E4A1oc+f6Bd+rGFd11uDAoms74p5ui4AAOc4I+qbPahjOJ+1H2t4UcrC5WYjAgB+no9H/fhuc3Ha7sXeo2nTF/OAXQAATvDlJ+3uejweft/4PM/a/sLpOdfrqYVYov6B9MxczZYoimLrSWurNJ+UmRYAcpZ61F+lh8upF8FeGqetQLX97ReT53gn6s/zrL33Fa4y35lOj29omkYjPmbP5tVpH+M4+ssmzZMPz0huHJ7GBuBMl4z6Cn7aotW8qHi/vDqB/3Nefu6Odho2H1QtJ9vAr62c/NUTq881UVltLQn5+nMZbDrLdAUBOMclo/7y+7a+2rub2j1U+w08u2muMug/sODHb7m/SiF/tUGsVR5OgN9a+qHjJLK+w2ArJwCnuWrU1+jssiz+3PjUJsyrS/nZO7vqCk4T1uQ6K+bhCKtLOdRWdipDW0s/NCLAYwsAZOuqUV993dM0Oe0/DeqnszheMenZUL3atE1wTPocCuFbOyOtlrBfDxDVpdK5PADgZFeN+prd5nfVpjaor/j97ECy2vROB7UqNEmNSZ9g9znF6sw3HT/+WlDzTjOor0c4VlXVNM3qYe/3e9M0ehqssxNU13VmRmHbtjqO6TwYx1GjMObcPR4Ps9BAeTGVOT2Mtaoq50Tr281zop2eiUDaAGDXVaP+ltSmQ2vPwaeStNWhrUP9mAeQR1KuAzU5ddrbMznCg/p2GVZV5XQJmMWf5uP2kpDb7aZnpes4eo8Zdrnf71pFoiPoI1rBoXfqUObNSrP9ZvMeE8uV/Zi0AUCMHxL1dTPV7TipuVEvTODf6h5Q73R4Y+OfRzE1UG1Ssdi9PuFBfftQTsQ1X2c3oO3Iqpa3LjNVHfT/OlmmTW/XQpwlBkrD8nv16eJNPi3L0vxT9T9TLwmnDQBi/KioX6S3+8oLqVJgcAYvwjPafjDleqvaZPr/7WKJH9R3ylmdBKa+9Xg8VAMzNa26rud5dh79fL/fdUwlchiGsizNtziJ6fte1Q692Tm+yW/TNLfbbZ7naZp0qN20AUCMHxL102Tm3z0Vqlc3j9NNP6kViecIR311gNvFEl6pb79TzXS7EqCSN0PmbdsOw+CfO7+HwNAZN6nVV9gVCx3TOZSdBr1imEH9yLQBQBhR/4Nem8C/+pHV+X05CET91f6P8KC+fRzNy/O/azeUBqpfqoWYI6hXwJ6OV5al6SRY3ZVPWw6b2G9SmGdPD4DDEfU/6LUGuj+on+COcqdZHe8Qjd87Ad4e1J+myXxQx7F7UMqy7LpOPfZ6JaaK5myY6CjL0q5JKDGmKT9Nk/1XVRHGcTRpGMexaRrzfnt7hheqjwDgI+p/kCLNs7Pu1Ytrv6LgkdQsxdOYGW3OIvutHfjtuFvXtXmDBvXN21QhG8dR0/L14uomSM6eEGq+b03UcCp5zgGd7n2TpNvtpiqdQrs50VpbGJ82ANhF1P+g13bgdyaL+Y3U3Jg9ixT4p2lSwYb3Y9ZqeL3o96WbFXF1XZui1pR4E5jVBC/L0i58fyTeZjfuzUJBHV+h3ZlLqOmB5ivKsjR1RH3cdOnHpA0AdhH1P0g3/Rfuyxpy1rytvu/ZS05b06g8q6oahmGrTMy6x7Zt7a51p5YwTZP6VJzeAsVmM2nO/6LwkI0eA6hzZ3byKctSrXbnUPouex8etd3NfD1nFH83bQCwi6j/QS9HfSTLLKUDgCsi6n+QeoOTehQQACBnRP0PUm+zPxMNAICvIOp/lpr7uW2eDwBIE1H/s+Z51jQ0fzIXAAAnI+qfYRxHPZ712wkBAGSNqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA+kaJ7nuq6Lorjf73VdN01TVVXTNMMwdF1XVVXf999OI4DrIeoDKaqqap7noiiKopjneVmWaZqKoui6blmWcRyLovh2GgFcD1EfSNE4jsuymJC//Bnp+763/wQAkYj6QKKcBn3TNOafVVXR1gfwAqI+kCg7zC/LUhRF0zTm/7uum6bpfr9/KXUALomoDyTKjOKbf6rbX30A0zTVdT1N0/cSCOB6iPpAojSBX/9/v99Nu1+z/JqmYRo/gGcR9QEAyAVRHwCAXBD1AQDIBVEfAIBcEPWBVBQf8Hg8vp0tAAkh6gOp0Mb7Utf1/Rm3263v+6ZpyrK0o/7tdvt2tgAkhKgPpOLxeNgB++UdePTAHh2kbdtjEwng0oj6QELatrWb++8cSpv5lGV5VNoidV2n9J/8vd81DIO2SWbfJCSOqA8kxDxnT7QZ38u0t8/5Q/sZRv3l9yORvp0KYAdRH0iLgoe831Jv2/apof15nvu+f/NpfsWfewmn75Bc80gkXAJRH0jLPM/2jLxhGN452jRNT3UYaELAOw/10cjCtR4L9H6ulwvWdZAnoj6QnNvtZvfzv9kGjTcMg77xnR3+zaMC9XygqqqOS+BHHJLraZp0EGXffoBCVVVN09R1TZ0AKSDqAylSd7GcEy0Ut/S95pG+LzA1FYW6xDu9j8q1xmUU7O1HJJveGtUtDkkz8A6iPvARh0zEM06YkVdV1TiOil7vzCdQEFVNpe/7d0Yo3izDGEfl2h7Ud6K+agPPDrUAH0LUB443z/P7Pdv2pj3vNENj9H2vlf0alX95WMF8/P1h8kPKMOyoXC9/DurbSxhUA1BN6JA0A28i6gPHG8fx/W75ozbt2XW/38uyVMAz49OvfZ1p5poO7ZeTfUgZBhyY62VZCmuZpamlDcOgrg4W9SEdRH08YZ5nexsZ30Hf89+/f//973/HHOusNP+h67pDtsI1O94Ub2/as0VLBuxop69zprZFFqNJp1rPy7K8nOwXyvB+v7dtq/kETdMENsw5NteLFfV1ysyLyr728HkqL8CHEPURSz2uZVnWda252bqpGW+uMfvtv3///vXrn0MOdVqaXVVVHTIS72za84lN9du2dZrUGlmwxxTii7H4s8mrpwm8lrCnynCeZ2f1ndZBbL3/2Fwvv+dhNE3TNI0ZJui6Tq/UdX3aQgwgjKiPWE3T2DfKvu8/0foc/vn169dhDf1z0uxQO/Koox27aY9jHEe/DarWqv1d5xfjs2WokGzXMExngy/ZXAMnIOojlj0DWUPOWw3lrZ5ze27zmuGfX7+Kojgs5ken+dUEb37psc+8sTfteWdNuUMdCX43uNktwLwSf+qP8lQZag6BCcnzPCsLq10jKecaOAFRH69QA3Rr3HSrX7fv+835Wf/9+/evX4EB1LCY7oFAml9J8G+RKXynmWhPjD+wk79pmtUwFp7aFj71r3mzDNXQr6pKHe/K19boQDq5Br6CqI9XqPV5+GH/+/fvoiiOGtR3fCjNvqqqDg8Phz/PbRiGQEVE8W81Op5TjE+VoVIb8/7Ecw2cgKiPp6m381MryP/79+8DB/Z/+2yaLepAPvaYhzc0H49HWZaBuXKa2ub3sYeLUVHTf/3ZgZJny3Drex2J5xo4B1EfT9Mwqt/VrHnUunXaM5bN/OroXu7hn6Pj/mqaj0vw/xvH8di6hVaOHdt5UNd1eKRAU9v8KW9bp94c9uWBEtuzZbgaX3US7dOaeK6BcxD18TTdZP02U1VV2nnUiVJVVc3zHJhTfYLVNH8iwV3XHTjn6xMh314UsMv57NapP9azZahVc+Yjms1XVZUdp9PPNXAOoj6ettUI1vTyqqrs1pLC5/LtDs/VNH8iwQcO6rdtq/rHIUcTM2ctktOK3Tr1x3qhDO/3u7OS3i63S+QaOAdRH097PB5boUi319WnjHz31rmV5sMTfNSS+k+E/PetFuPhAyWHb0vwpnNyDZyDqI8jmSeP+T20RZLLnY9NsOkneIe2hEsw5G85dqDkkDI8QcrjWUAAUR9HKoqi7/tpmpzZWLoJJhjGUkvwUSF/HMfTFpenPLLzOXnmGj8AUR9H0nbl/tTlZG+CSSVYIb9t2zdD/jRNJ3cVJDuy81F55hpXR9THGYpT1sof6PwEm5D/5nEUij7xnJ6Ay43sHCLPXOPqiPr4IDMjurjIbqbfSvA0TWVZvh/ytbL8/NlwqQ2UnCPPXOPqiPr4oK2lUMn6SoLVOn8n5GuFunlIz/mlndRAyWnyzDWujqgPfJMJ+ffnafc39TMbSQ0nX25k5xB55hpXQdQHvubZ3WNipDCScrmRnUPkmWtcDlEf+A77+blHeX9mwCFMeq4ysnOIPHONyyHqAwCQC6I+AAC5IOoDAJALoj4AALkg6gMAkAuiPpCErus0A/zN42gR/yFJAvDzEPWBVLwZ9ed5VtWBlWMAthD1gVQURfFyM12bwxzSWwDgByPqA0nQpj1vNtOJ+gDCiPpAEswjW6Zp0mNdXjjIO70FAHJA1AeSoGb6PM9N09R1bZrsdte9bxxHcwTt6s+gPoAAoj6QhKIozGNb+74fhuHZI/R9T/c+gDCiPvB99pN4Xm6s65G7xyYMwA9D1Ae+zwzqD8Og/1Hsn+c50L3vDOEXPNYdwB6iPvB9RVHUdb38bvQvy6J/xtOgvj3MDwA+oj7wfXbAVg0gvp/fme73bHUBQFaI+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5IKoDwBALoj6AADkgqgPAEAuiPoAAOSCqA8AQC6I+gAA5OL/AMYRwF1qFIAjAAAAAElFTkSuQmCC" alt="" />