Find the shortest tour through the following cities (TSP). Provided is the x-coo

Question

Find the shortest tour through the following cities (TSP). Provided is the x-coordinates of the cities and the y-coordinates of the cities. This is a "one-way" TSP, meaning that the start end end cities will be different. The coordinates are x = (214 18 188 242 94 270 25 11 139 248 56 167 216 108 54 45 41 28 259 156 136 71 148 149 56 48) and y = (229 115 152 78 27 14 4 214 31 245 46 125 234 206 271 43 260 43 105 200 43 247 160 156 234 158). Provide the length of the shortest tour. As an example, the first city will have coordinates (214, 229).

Explanation / Answer

From the above graph it is clearly seen that there where 2 pairs of points are very close to each other ,

So, definitely they have the shortest distance between them.

Those pair of points with their city number are:

23(148,160) and 24(149,156)

1(214,229) and 13(216,234)

so, the distance between city 23 and 24 = [(149-148)2 + (156-160)2]1/2 = 4.123 unit

and   the distance between city 1 and 13 = [(216-214)2 + (234-229)2]1/2  = 5.385 unit

Hence the shortest distance is found to be between city 23 and 24 with 4,123 unit.

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