Solving TSP in O-Mopsi orienteering game Radu Mariescu-Istodor 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 O-Mopsi: Solving the best order Travelling salesman problem ? ? ? ? ? ? ? ?

Why it matters? Estimation of the game length 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

Analysis of results

Comparing results 1.0 km 1.5 km Median finish time 32:00 SciFest 2014 short Comparing results Median finish time 32:00 Ground truth comparison: Median 32:00 2.0 km Best student 18:21 1.5 km Hot shot organizer 6:22 1.3 km Estimated (bird) 1.0 km Is it just raw speed or optimizing? Is this game particularly difficult??? 1.0 km 1.5 km

How good was the chosen order? Distance (50%): affected also by the navigation Order (30%): affected only by the problem solving same not same not same same same same not same Distances: Median: 2.0 km Best : 1.5 km Estimated: 1.0 km

Optimal route Reference route is not optimal ! Length only 3.7 % difference Best player played the optimal route not not Distances: Optimal: 978 m Reference: 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 Need results for different start points x,x x,x

Need beter example where optimal order changes Removing longest edge Concluding solution from TSP not possible Counter example below Needs to consider all start points Need beter example where optimal order changes Optimal Hypothetical Assume this is removed But then order here changes Hypotethical algorithm: Solve TSP Remove longest edge