Travelling Salesman Problem Stewart Adam Kevin Visser May 14, 2010

The Problem Need to visit N cities with smallest total distance travelled Thought of in the 1830s Mathematicians in the 1930s realized the problem was unsolvable with the current technology

The Problem Assumptions made: ▫Must end at same city that we started at ▫Cannot visit any city twice ▫Can start the trip at any city

Conventional Approach Very long to calculate: ▫Modeling 30 cities means 30!=2.6 x 10^32 possible solutions ▫Equivalent to 8.4 x 10^24 years of trying at 1 solution/second

Genetic Algorithm Similar to wind farm problem Can’t use the same crossover or mutation methods, as that may result in duplicate cities Must converge on good solutions, but keep enough entropy in the solutions so we can pop out of local minimums ▫Solution: Morph our way out with lots of mutation ▫Solution: More elites to keep track of the better solutions

Crossover Given the parents: [7, 2, 4, 1, 9, | 5, 6, 8, 10, 3] and [4, 9, 10, 3, 7, | 5, 8, 6, 1, 2] Copy, excluding duplicates Child 1 (pass 1): [7, 2, 4, 1, 9, X, X, 10, 3, X] Fill in blanks with cities from parent 2 (in unused order) Child 1 (pass 2): [7, 2, 4, 1, 9, 5, 8, 10, 3, 6]

Mutation Swap the position of two elements More randomness! ▫When mutation happens, it randomly performs 1 or 2 “swap” passes ▫Mutation 50% of the time ▫1% of mutations are greedy (force a better solution)

Fun stuff: Videos Circle: Long

Fun stuff: Videos Circle: Short

Fun stuff: Videos Random: Local minimum

Fun stuff: Videos Test case: Stuck

Fun stuff: Videos Test case: Best

The best solution had a distance of units (shown on left). Results

Best solution != nearest city The best results always seems to form closed shapes Shapes are close as possible to the circumference of a circle (contours). No diagonal lines Results