Travelling Salesman Problem Stewart Adam Kevin Visser May 14, - - PowerPoint PPT Presentation

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

• f 948.33 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