Solving TSP in O-Mopsi
orienteering game
Lahari Sengupta
Radu Mariescu-Istodor
Pasi Fränti
31.12.2015
Motivation
O-Mopsi as optimization problem
Classical orienteering:
• Order of targets fixed
• (N-1)  shortest path problems
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O-Mopsi:
• Solving the best order
• Travelling salesman problem
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Why it matters?
Player route: 3.1 km
Reference:
2.4 km
• Estimation of the
game length
• Estimation of the
game complexity
• Need reference
route for analysis
Differences
Basic information
Statistics
Estimated
length
Targets
Basic information
Reference route
Reference
route
Analysis of results
Comparing results
• Median finish time 32:00
• Ground truth comparison:
-
Median
32:00
Best student
18:21
Hot shot organizer 6:22
Estimated (bird)
2.0
1.5
1.3
1.0
km
km
km
km
• Is it just raw speed or optimizing?
• Is this game particularly difficult???
1.0 km
1.5 km
SciFest 2014 short
How good was the chosen order?
• Distance (50%):
• Order (30%):
affected also by the navigation
affected only by the problem solving
same
same
Distances:
Median:
Best :
Estimated:
2.0 km
1.5 km
1.0 km
Optimal route
• Reference route is not optimal !
• Length only 3.7 % difference
• Best player played the optimal route
Distances:
Optimal:
Reference:
978 m
1014 m
Complexity of game
Case study with simple game
10 target with 1 km estimated length
B&B
976 m
ACO
976 m
TS
1011 m
Greedy 1140 m
Effect of starting point
Center of the area
x,x
x,x
x,x
x,x
x,x
x,x
x,x
x,x
x,x
x,x
Removing longest edge
• Concluding solution from TSP not possible
• Counter example below
• Needs to consider all start points
Optimal
Hypothetical
Assume this
is removed
But then order
here changes
Hypotethical algorithm:
1. Solve TSP
2. Remove longest edge