I wrote a simple genetic algorithm that can solve traveling salesman problem with 5 cities. I want to see how it does on a problem with more cities, something like 10, 25, 50, 100, but I can't find a sample date for the problem to try it on. Basically, I am looking for 2D lists or matrices with distances between cities. It would be nice if there is a solution. Where should I look?
Thank You in Advance
The Traveling Salesman Problem (TSP) is believed to be an intractable problem and have no practically efficient algorithm to solve it. The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space.
Travelling Salesman Problem (TSP) : Given a set of cities and distances between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point.
In fact, TSP belongs to the class of combinatorial optimization problems known as NP-complete. This means that TSP is classified as NP-hard because it has no “quick” solution and the complexity of calculating the best route will increase when you add more destinations to the problem.
The dynamic programming or DP method guarantees finding the best answer to TSP. However, its time complexity would exponentially increase with the number of cities. The time complexity with the DP method asymptotically equals N² × 2^N where N is the number of cities.
For next incomes, i'll paste some more "small" cases:
You can find more tests in here. but the file is ".tsp" extension and you should do a simple parse that translate to the matrix of distances.
(distance in miles)
6 cities, expected: 1248.0
9999 64 378 519 434 200
64 9999 318 455 375 164
378 318 9999 170 265 344
519 455 170 9999 223 428
434 375 265 223 9999 273
200 164 344 428 273 9999
15 cities, expected: 1194.0
-1 141 134 152 173 289 326 329 285 401 388 366 343 305 276
141 -1 152 150 153 312 354 313 249 324 300 272 247 201 176
134 152 -1 24 48 168 210 197 153 280 272 257 237 210 181
152 150 24 -1 24 163 206 182 133 257 248 233 214 187 158
173 153 48 24 -1 160 203 167 114 234 225 210 190 165 137
289 312 168 163 160 -1 43 90 124 250 264 270 264 267 249
326 354 210 206 203 43 -1 108 157 271 290 299 295 303 287
329 313 197 182 167 90 108 -1 70 164 183 195 194 210 201
285 249 153 133 114 124 157 70 -1 141 147 148 140 147 134
401 324 280 257 234 250 271 164 141 -1 36 67 88 134 150
388 300 272 248 225 264 290 183 147 36 -1 33 57 104 124
366 272 257 233 210 270 299 195 148 67 33 -1 26 73 96
343 247 237 214 190 264 295 194 140 88 57 26 -1 48 71
305 201 210 187 165 267 303 210 147 134 104 73 48 -1 30
276 176 181 158 137 249 287 201 134 150 124 96 71 30 -1
Hugeeee 29 cities, expected: 27603
imagem: western sahara
-1 74 4110 3048 2267 974 4190 3302 4758 3044 3095 3986 5093 6407 5904 8436 6963 6694 6576 8009 7399 7267 7425 9639 9230 8320 9300 8103 7799
74 -1 4070 3000 2214 901 4138 3240 4702 2971 3021 3915 5025 6338 5830 8369 6891 6620 6502 7939 7326 7193 7351 9571 9160 8249 9231 8030 7725
4110 4070 -1 1173 1973 3496 892 1816 1417 3674 3778 2997 2877 3905 5057 5442 4991 5151 5316 5596 5728 5811 5857 6675 6466 6061 6523 6165 6164
3048 3000 1173 -1 817 2350 1172 996 1797 2649 2756 2317 2721 3974 4548 5802 4884 4887 4960 5696 5537 5546 5634 7045 6741 6111 6805 6091 5977
2267 2214 1973 817 -1 1533 1924 1189 2498 2209 2312 2325 3089 4401 4558 6342 5175 5072 5075 6094 5755 5712 5828 7573 7222 6471 7289 6374 6187
974 901 3496 2350 1533 -1 3417 2411 3936 2114 2175 3014 4142 5450 4956 7491 5990 5725 5615 7040 6430 6304 6459 8685 8268 7348 8338 7131 6832
4190 4138 892 1172 1924 3417 -1 1233 652 3086 3185 2203 1987 3064 4180 4734 4117 4261 4425 4776 4844 4922 4971 5977 5719 5228 5780 5302 5281
3302 3240 1816 996 1189 2411 1233 -1 1587 1877 1979 1321 1900 3214 3556 5175 4006 3947 3992 4906 4615 4599 4700 6400 6037 5288 6105 5209 5052
4758 4702 1417 1797 2498 3936 652 1587 -1 3286 3374 2178 1576 2491 3884 4088 3601 3818 4029 4180 4356 4469 4497 5331 5084 4645 5143 4761 4787
3044 2971 3674 2649 2209 2114 3086 1877 3286 -1 107 1360 2675 3822 2865 5890 4090 3723 3560 5217 4422 4257 4428 7000 6514 5455 6587 5157 4802
3095 3021 3778 2756 2312 2175 3185 1979 3374 107 -1 1413 2725 3852 2826 5916 4088 3705 3531 5222 4402 4229 4403 7017 6525 5451 6598 5142 4776
3986 3915 2997 2317 2325 3014 2203 1321 2178 1360 1413 -1 1315 2511 2251 4584 2981 2778 2753 4031 3475 3402 3531 5734 5283 4335 5355 4143 3897
5093 5025 2877 2721 3089 4142 1987 1900 1576 2675 2725 1315 -1 1323 2331 3350 2172 2275 2458 3007 2867 2935 2988 4547 4153 3400 4222 3376 3307
6407 6338 3905 3974 4401 5450 3064 3214 2491 3822 3852 2511 1323 -1 2350 2074 1203 1671 2041 1725 1999 2213 2173 3238 2831 2164 2901 2285 2397
5904 5830 5057 4548 4558 4956 4180 3556 3884 2865 2826 2251 2331 2350 -1 3951 1740 1108 772 2880 1702 1450 1650 4779 4197 2931 4270 2470 2010
8436 8369 5442 5802 6342 7491 4734 5175 4088 5890 5916 4584 3350 2074 3951 -1 2222 2898 3325 1276 2652 3019 2838 1244 1089 1643 1130 2252 2774
6963 6891 4991 4884 5175 5990 4117 4006 3601 4090 4088 2981 2172 1203 1740 2222 -1 684 1116 1173 796 1041 974 3064 2505 1368 2578 1208 1201
6694 6620 5151 4887 5072 5725 4261 3947 3818 3723 3705 2778 2275 1671 1108 2898 684 -1 432 1776 706 664 756 3674 3090 1834 3162 1439 1120
6576 6502 5316 4960 5075 5615 4425 3992 4029 3560 3531 2753 2458 2041 772 3325 1116 432 -1 2174 930 699 885 4064 3469 2177 3540 1699 1253
8009 7939 5596 5696 6094 7040 4776 4906 4180 5217 5222 4031 3007 1725 2880 1276 1173 1776 2174 -1 1400 1770 1577 1900 1332 510 1406 1002 1499
7399 7326 5728 5537 5755 6430 4844 4615 4356 4422 4402 3475 2867 1999 1702 2652 796 706 930 1400 -1 371 199 3222 2611 1285 2679 769 440
7267 7193 5811 5546 5712 6304 4922 4599 4469 4257 4229 3402 2935 2213 1450 3019 1041 664 699 1770 371 -1 220 3583 2970 1638 3037 1071 560
7425 7351 5857 5634 5828 6459 4971 4700 4497 4428 4403 3531 2988 2173 1650 2838 974 756 885 1577 199 220 -1 3371 2756 1423 2823 852 375
9639 9571 6675 7045 7573 8685 5977 6400 5331 7000 7017 5734 4547 3238 4779 1244 3064 3674 4064 1900 3222 3583 3371 -1 620 1952 560 2580 3173
9230 9160 6466 6741 7222 8268 5719 6037 5084 6514 6525 5283 4153 2831 4197 1089 2505 3090 3469 1332 2611 2970 2756 620 -1 1334 74 1961 2554
8320 8249 6061 6111 6471 7348 5228 5288 4645 5455 5451 4335 3400 2164 2931 1643 1368 1834 2177 510 1285 1638 1423 1952 1334 -1 1401 648 1231
9300 9231 6523 6805 7289 8338 5780 6105 5143 6587 6598 5355 4222 2901 4270 1130 2578 3162 3540 1406 2679 3037 2823 560 74 1401 -1 2023 2617
8103 8030 6165 6091 6374 7131 5302 5209 4761 5157 5142 4143 3376 2285 2470 2252 1208 1439 1699 1002 769 1071 852 2580 1961 648 2023 -1 594
7799 7725 6164 5977 6187 6832 5281 5052 4787 4802 4776 3897 3307 2397 2010 2774 1201 1120 1253 1499 440 560 375 3173 2554 1231 2617 594 -1
The sources I've found online are quite huge. I might be doing something wrong, but 10 places (cities) take ~0.6s and 11 places take ~7s. The smallest known-solution dataset I could find was 15 places (and considered "small", the "classical" one being 48 places) but perhaps those are for optimized (non-brute force) algorithms. In the end I made my own table with real-world cities:
m
a
a h
s h s u
t a e i g l
r a e t e s
i c r t l e b b a e
c h l a e c o e n o p
h e e r e h n r n h e
t n n d n t n g e e n
maastricht 0 29 20 21 16 31 100 12 4 31 18
aachen 29 0 15 29 28 40 72 21 29 41 12
heerlen 20 15 0 15 14 25 81 9 23 27 13
sittard 21 29 15 0 4 12 92 12 25 13 25
geleen 16 28 14 4 0 16 94 9 20 16 22
echt 31 40 25 12 16 0 95 24 36 3 37
bonn 100 72 81 92 94 95 0 90 101 99 84
hulsberg 12 21 9 12 9 24 90 0 15 25 13
kanne 4 29 23 25 20 36 101 15 0 35 18
ohe 31 41 27 13 16 3 99 25 35 0 38
epen 18 12 13 25 22 37 84 13 18 38 0
Optimal (by program): cities 0-7-4-3-9-5-2-6-1-10-8-0 = 253km
maastricht -> hulsberg -> geleen -> sittard -> ohe -> kanne -> echt
-> heerlen -> bonn -> aachen -> epen -> kanne -> maastricht
The data format readable by the program is a partial table (because it's symmetrical):
29 20 21 16 31 100 12 4 31 18
15 29 28 40 72 21 29 41 12
15 14 25 81 9 23 27 13
4 12 92 12 25 13 25
16 94 9 20 16 22
95 24 36 3 37
90 101 99 84
15 25 13
35 18
38
For me this takes ~6.7 seconds to process on a 3rd gen i7 (i7-3630QM). Program is written in C++, single-threaded and simply brute-forces the possibilities. For testing it might be more practical to remove one place, then it takes ~660ms (0.7s) which is still enough to see if code changes make much of a difference.
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