1. Planning via Random Walk- Driven Local Search Fan Xie Hootan Nakhost Martin Müller Presented by: Hootan Nakhost

2. Outline Random Walks Planning Problems of Random Walks Random Walk-Driven Local Search Experiments Conclusion and Future Works

3. Arvand Planner [Nakhost and Müller 2009] Exploration using random walks to overcome the problem of local minima and plateaus. Jumping greedily exploits the knowledge gained by the random walks.

4. Aras: Plan Improving Postprocessor [Nakhost et al. 2011] Expand a neighbor search space along the input plan. Output the shortest path in the neighbor search space

5. Problems of Random Walks Fails in Narrow Exit Path Search Space (we will explain later) Poor Plan Quality

6. Narrow Exit Path Search Space Coverage(20) Arvand2.2 Lama18 Probe15 FDSS-218

7. Narrow Exit Path Search Space(2)

8. Plan Quality

9. Random Walk-Driven Local Search Local Greedy Best First search (local GBFS) Perform one random walk from the node going to be expanded Keep the best random walk (lowest h) Jump to the best state (in GBFS or end-point of random walk)

10. Random Walk-Driven Local Search For every node in the open list, it has two heuristic value: h n : the heuristic value of the node itself h r : the heuristic value of the end-point of the random walk starting from the node Nodes in the open list are ordered by a linear combination of h n and h r (W = 100 in our experiments) : W * h n + h r

11. Analysis of RW-LS Advantage: – A small local search can help escape some small Narrow-Exit-Path-Search-Space – Generally, generates better solutions Disadvantage: – Slow down speed

12. Domains Arvand-LS Arvand Roamer Probe LAMA- 2011 LAMA- 2011-FF FD-AT-2 FDSS-2 barman(20)9.6016.820 17414 elevators(20)20 13.420 181618 floortile(20)1.21.8145496 nomystery(20)141910711 81613 openstacks(20)20 1220 171914 parcprinter(20)20 71320 1420 parking(20)8.63.8515 11419 pegsol(20)20 1920 scanalyzer(20)2017.6201820 1720 sokoban(20)8.42.212.41518 15 18 tidybot(20)1717.8151816 1116 transport(20)1814161314 12913 visitall(20)20 18 20 446 woodworking(20)20 18.620 1320 Total(280)216.8196.2192.2213239200176217 Coverage Results of IPC-2011 Benchmark

13. Domains Arvand-LS Arvand Roamer Probe LAMA-2011 LAMA- 2011-FF FD-AT-2 FDSS-2 barman(20)9.560.0014.2217.9816.78 14.122.5513.15 elevators(20)18.797.639.577.579.20 8.87 13.9911.76 floortile(20)1.201.800.892.134.22 3.42 8.965.21 nomystery(20)13.1618.119.656.7910.84 7.8915.6112.28 openstacks(20)15.259.7817.2010.6118.59 15.9318.0811.94 parcprinter(20)18.5617.616.0511.2919.82 18.3413.6418.24 parking(20)6.632.853.047.3212.82 6,793.8417.14 pegsol(20)19.9619.9117.6918.4119.90 19.2319.7814.46 scanalyzer(20)18.9415.4116.6314.8317.6016.5915.1417.81 sokoban(20)7.892.1712.1511.8316.64 17.6114.9216.08 tidybot(20)15.0115.8512.9516.4014.04 9.6313.7813.19 transport(20)16.2610.5413.366.7611.027.107.517.67 visitall(20)11.517.5917.4317.5718.07 1.403.351.73 woodworking(20)16.3616.0911.0517.8715.26 15.289.7119.14 Total(280)189.08145.34161.86167.36204.78162.21160.87179.80 Quality Results of IPC-2011 Benchmark

14. Larger Problems Easy domains with scalable generators are scaled to get larger problems: DomainsParameterMinMaxStep ElevatorNum of Passengers (60)2030515 OpenstacksNum of Products (250)25063020 Visit-AllGrid size (50)48862 Woodworkingnumber of parts(23)251054 The number in parentheses are the max number used in the IPC-2011 benchmark

15. Coverage Results of Large Problems Domains Arvand-LS Arvand Roamer Probe LAMA2011 FD-AT-2 FDSS-2 FF LPG large-elevator(20)20.018.81.24.0 1.02.03.00.4 large-openstacks(20)16.017.610.00.08.00.0 1.00.0 large-visitall(20)20.012.60.0 13.00.0 large-woodworking(20)18.010.454.011.03.011.03.08.6 total(80)74.059.416.28.036.04.013.07.09.0

16. Quality Results of Large Problems

17. Conclusion and Future Work Contribution: – RW-LS: A strong algorithm combining local search and random walks, implemented in the Planner Arvand-LS. – Motivated and Developed larger problems Future work: – Make it a global search algorithm – Make it one entry in a portfolio planner – Add multi-heuristic into the algorithm