The Concert Tour Problem - to find the shortest route through each of "n" cities...
a.k.a. The Traveling Salesman Problem

The Exhaustive Search (probably 1000 times too conservative)

 Computational Effort 30 Cities 50 Cities 75 Cities (n-1)! / 2 paths 4.42 e+30 paths 3.04 e+62 paths 1.65 e+107 paths / 2 e+9 paths/second/one 2GHz desktop 2.21 e+21 seconds 1.52 e+53 seconds 8.26 e+97 seconds / 60 seconds/minute 3.68 e+19 minutes 2.53 e+51 minutes 1.37 e+96 minutes / 60 minutes/hour 6.14 e+17 hours 4.22 e+49 hours 2.29 e+94 hours / 24 hours/day 2.55 e+16 days 1.7 e+48 days 9.57 e+92 days / 365 days/year 7.00 e+13 years 4.82 e+45 years 2.62 e+90 years / 4.5 e+9 years/age-of-the-earth 1.55 e+4 ages of the earth 1.07 e+36 ages of the earth 5.82 e+80 ages of the earth / 2.55 e+0 age-of-the-(earth/universe) 6.10 e+3 ages of the universe 4.20 e+35 ages of the universe 2.28 e+80 ages of the universe / 10 e+30 cubic inches/sun 4.20 e+5 sun's volume of computers, each computer one square inch for the age of the universe / 10 e+78 atoms/universe 22.85 e+0 universes with 1 computer per atom in the universe for the age of the universe In "plain" English It would take one 2GHz desktop computer 6,000 times the age of the Universe in order to consider each possible path. It would take enough 2GHz desktop computers, each one cubic inch in volume, to fill 42,000 Suns, the age of the Universe in order to consider each possible path. It would take 23 Universes full of 2GHz desktop computers, each the size of one atom, the age of the Universe in order to consider each possible path.

Traveling Salesman Problem using Genetic Algorithms
http://www.lalena.com/ai/tsp/