Local Search Techniques for Temporal Planning in LPG Paper by Gerevini, Serina, Saetti, Spinoni Presented by Alex.

Local Search Techniques for Temporal Planning in LPG

Paper by Gerevini, Serina, Saetti, Spinoni

Presented by Alex

Overview of Problem

• What problem are they solving?– Temporal planning (duh)– More specifically? What kinds of action

restrictions?

Overview of Techniques

• In general, what techniques do they use?– Local search, variation of Walksat– Mix of Graphplan and POP– Complicated heuristics

Outline

• Search Space

• Local search and heuristics– Search operators– Various cost metrics

• Experiments

Search Space

• What is an A-graph?

• Noop propagation– What is it?– Why is it important?

LA-graphs

• Same thing, except …– One non-noop per layer

And TA-graphs

• What is a TA-graph?– Triple (LA-graph, Time-assign’t, Ordering Cs)

• What do the time assignments represent?– Earliest time a fact can become true– Earliest time an action can finish executing

Example TA-Graph

How does it fit into Graphplan?

• Only permanent action mutexes – meaning?

• What good are action mutexes in an LA-graph?

• How much of Graphplan is left?

POP & LPG

• POP• Threats

– Promotion

– Demotion

• Causal Link• Least Commitment

• LPG• Mutexes

– LA-graph ordering

• Action-Effect edge• Topological Sort (as

opposed to total order of LA-graph)

Solution State

• What constraints does a TA-graph have to obey to be a solution?– Logical constraints (are goals and action

preconditions satisfied)– Temporal/Ordering constraints

• Time assign’ts consistent with orderings

• Ordering constraints imply mutex actions don’t co-occur

Local Search: Operators

• Every search operator fixes an “inconsistency” in the partial plan– What kinds of inconsistencies are there?

• How do you fix inconsistencies?

TA-graph, again

TA-graph with added node

Local Search: Walksat

• Proposition with k clauses and n variables – With probability p, pick a variable at random

from an unsatisfied clause and flip its value– With prob. 1-p, flip value of variable that

maximizes number of satisfied clauses

WalkPlan

• For a given inconsistency, if there is a move that increases plan quality, do it.

• Otherwise, – with probability p, pick a move at random– With probability 1-p, pick best move

• Do random restarts after too many moves

Questions about WalkPlan

• How do they pick the inconsistency to fix?

• Why do they change the Walksat algorithm?

• Where do they start search after a random restart?

Heuristics

E(a) = b * Execution_Cost(a) +

c * Temporal_Cost(a) +

d * Search_Cost(a)

Relaxed Plan

• When adding (or removing) action a, find relaxed plan for unsupported preconditions of a (or the preconditions that used to be supported by a, if removing a).

• In what way(s) is it relaxed?

Experiments

• Impressive, no?

• Are there any criticisms? caveats?– Is it fair to compare separately along the time

and quality axes? I.e., is a quickly-generated but very crappy plan better than a more slowly-generated but decent plan?

Comments

Too much low-level detail (code)

Why the spikes in the graphs?

Future Work

Gplan, TabuPlan, …

Add learning, or dynamically change heuristics

More expressive temporal action language

Handle Universally Quantified Effects