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Solving TSP in O-Mopsi orienteering game

Explore solving the Travelling Salesman Problem in the O-Mopsi orienteering game, analyzing route optimization, complexity, and the impact of starting points.

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Solving TSP in O-Mopsi orienteering game

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  1. Solving TSP in O-Mopsi orienteering game Lahari Sengupta Radu Mariescu-Istodor Pasi Fränti 31.12.2015

  2. Motivation

  3. 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 ? ? ? ? ? ? ? ?

  4. 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

  5. Basic informationStatistics Estimated length Targets

  6. Basic informationReference route Reference route

  7. Analysis of results

  8. 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

  9. 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

  10. 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

  11. Complexity of game

  12. Case study with simple game10 target with 1 km estimated length B&B 976 m ACO 976 m TS 1011 m Greedy 1140 m

  13. Effect of starting pointCenter 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

  14. 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

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