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

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

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.

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

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

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

Narrow Exit Path Search Space(2)

Plan Quality

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)

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

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

Domains Arvand-LS Arvand Roamer Probe LAMA LAMA FF FD-AT-2 FDSS-2 barman(20) elevators(20) floortile(20) nomystery(20) openstacks(20) parcprinter(20) parking(20) pegsol(20) scanalyzer(20) sokoban(20) tidybot(20) transport(20) visitall(20) woodworking(20) Total(280) Coverage Results of IPC-2011 Benchmark

Domains Arvand-LS Arvand Roamer Probe LAMA-2011 LAMA FF FD-AT-2 FDSS-2 barman(20) elevators(20) floortile(20) nomystery(20) openstacks(20) parcprinter(20) parking(20) , pegsol(20) scanalyzer(20) sokoban(20) tidybot(20) transport(20) visitall(20) woodworking(20) Total(280) Quality Results of IPC-2011 Benchmark

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

Coverage Results of Large Problems Domains Arvand-LS Arvand Roamer Probe LAMA2011 FD-AT-2 FDSS-2 FF LPG large-elevator(20) large-openstacks(20) large-visitall(20) large-woodworking(20) total(80)

Quality Results of Large Problems

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