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\title{Marvin: A Heuristic Search Planner with Online Macro-Action Learning\\
Andrew Coles {\tt andrew.coles@cis.strath.ac.uk}\\
Amanda Smith {\tt amanda.smith@cis.strath.ac.uk}\\
Department of Computer and Information Sciences,\\University of Strathclyde,\\26
Richmond Street, Glasgow, G1 1XH, UK
}




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\begin{figure}{\small\begin{algorithmic} [1]
\STATE \textbf{Procedure: EHCSearch}
\STATE open\_list = [initial\_state];
\STATE best\_heuristic = heuristic value of initial\_state;
\WHILE{open\_list not empty}
\STATE current\_state = pop state from head of open\_list;
\STATE successors = the list of states visible from current\_state;
\WHILE{successors is not empty}
\STATE next\_state = remove a state from successors;\\
\STATE h = heuristic value of next\_state;\\
\IF{next\_state is a goal state}
\STATE return next\_state;
\ENDIF
\IF{h better than best\_heuristic}
\STATE clear successors;
\STATE clear open\_list;
\STATE best\_heuristic = h;
\ENDIF
\STATE place next\_state at back of open\_list;
\ENDWHILE
\ENDWHILE
\end{algorithmic}}

\end{figure}%
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\begin{figure}{\small\begin{algorithmic} [1]
\STATE \textbf{Procedure: GreedyBFS}
\STATE insert (state=initial\_state, h=initial\_heuristic, counter=0) into search\_queue;
\STATE \WHILE{search\_queue not empty} 
	\STATE current\_queue\_entry = pop item from front of search\_queue;
	\STATE current\_state = state from current\_queue\_entry;
	\STATE current\_heuristic = heuristic from current\_queue\_entry;
	\STATE starting\_counter = counter from current\_queue\_entry;\\
\par
\STATE applicable\_actions = array of actions applicable in current\_state;
\par
\STATE \FORALL{index ?i in applicable\_actions $\geq$\  starting\_counter}
		\STATE current\_action = applicable\_actions[?i];
		\STATE successor\_state = current\_state.apply(current\_action);
\par
\STATE \IF{successor\_state is goal}
			\STATE return plan and exit;
		\ENDIF
		\STATE successor\_heuristic = heuristic value of successor\_state;
		\STATE \IF{successor\_heuristic $<$\  current\_heuristic}
			\STATE insert (current\_state, current\_heuristic, ?i + 1) at front of search\_queue;
			\STATE insert (successor\_state, successor\_heuristic, 0) at front of search\_queue;
			\STATE break for;
		\STATE \ELSE
			\STATE insert (successor\_state, successor\_heuristic, 0) into search\_queue;
		\ENDIF
	\ENDFOR
\ENDWHILE
\STATE exit - no plan found;
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\begin{figure}{\small\begin{algorithmic} [1]
\STATE \textbf{Procedure: BuildMacro}
\STATE parameters = [];
\STATE parameter\_types = [];
\STATE abstract\_steps = [];
\STATE parameter\_count = 0;
\STATE \FORALL{action ?a in the action sequence used to escape a plateau}
	\STATE abstract\_parameters = [];
	\STATE \FORALL{parameter ?p of ?a}
		\STATE \IF{?p $\in$\  parameters}
			\STATE index = parameter index of ?p in parameters;
			\STATE append (index) to abstract\_parameters;
		\STATE \ELSE
			\STATE parameters[parameter\_count] = ?p;
			\STATE parameter\_types[parameter\_count] = type of ?p;
			\STATE append (parameter\_count) to abstract\_parameters;
			\STATE increment parameter\_count;
		\ENDIF
	\ENDFOR
	\STATE append (action type of ?a, abstract\_parameters) to abstract\_steps;
\ENDFOR
\STATE return parameter\_types and abstract\_steps as a macro-action
\end{algorithmic}}

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\begin{figure}{\small\begin{algorithmic}[1]
\STATE \textbf{Procedure: test-action-applicability}
\STATE reset\_satisfaction\_counters();\STATE \FORALL{predicate ?p in the state}
	\STATE \FORALL{(ground action ?a, tree node ?c) pair having ?p as a negative precondition child node}
		\STATE tree\_node\_to\_update = ?c;
		\STATE \WHILE{tree\_node\_to\_update is still valid}
			\STATE old\_value = value in tree\_node\_to\_update;
			\STATE value in tree\_node\_to\_update = old\_value + 1;			\STATE \IF{value in tree\_node\_to\_update $>$\  0 \&\& old\_value = 0}
				\STATE tree\_node\_to\_update = parent of tree\_node\_to\_update;
			\STATE \ELSE
				\STATE tree\_node\_to\_update = invalid;
			\ENDIF
		\ENDWHILE
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	\STATE \FORALL{(ground action ?a, tree node ?c) pair having ?p as a positive precondition child node}
		\STATE tree\_node\_to\_update = ?c;
		\STATE \WHILE{tree\_node\_to\_update is still valid}
			\STATE old\_value = value in tree\_node\_to\_update;
			\STATE value in tree\_node\_to\_update = old\_value -1;			\STATE \IF{value in tree\_node\_to\_update = 0 \&\& old\_value $>$\  0}
				\STATE tree\_node\_to\_update = parent of tree\_node\_to\_update;
			\STATE \ELSE 
				\STATE tree\_node\_to\_update = invalid;
			\ENDIF
		\ENDWHILE
	\ENDFOR
\ENDFOR
\STATE applicable\_actions = $\emptyset$;
\STATE \FORALL{ground action ?a}
	\STATE \IF{root tree node is satisfied}
		\STATE add ?a to applicable\_actions;	\ENDIF
\ENDFOR
\end{algorithmic}}

\end{figure}%
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\begin{figure}\small {
0: (activate-trans philosopher-1 philosopher forks--pid-wfork state-1 state-6) [1]\\
1: (activate-trans philosopher-2 philosopher forks--pid-wfork state-1 state-6) [1]\\
2: (activate-trans philosopher-3 philosopher forks--pid-wfork state-1 state-6) [1]\\
3: (activate-trans philosopher-4 philosopher forks--pid-wfork state-1 state-6) [1]\\
4: (activate-trans philosopher-0 philosopher forks--pid-wfork state-1 state-6) [1]\\
\par
\textbf{5: Macro-Action A Derived Here, using philosopher-4, philosopher-3, forks-4 and forks-3\\}
\par
16: (activate-trans philosopher-3 philosopher forks--pid-rfork state-6 state-3) [1]\\
\par
\textbf{17: Macro-Action A, using philosopher-2, philosopher-1, forks-2- and forks-1\\}
\par
28: (activate-trans philosopher-1 philosopher forks--pid-rfork state-6 state-3) [1]\\
\par
\textbf{29: Macro-Action B Derived Here, using philosopher-3 and -forks-3-\\}
\par
32: (activate-trans philosopher-3 philosopher forks-\_\_-pidp1\_\_11\_-rfork state-3 state-4) [1]\\
\par
\textbf{33: Macro-Action B, using philosopher-1 and -forks-1-\\}
\par
36: (activate-trans philosopher-1 philosopher forks-\_\_-pidp1\_\_11\_-rfork state-3 state-4) [1]\\
\par
37: (queue-write philosopher-0 forks--pid-wfork forks-0- fork) [1]\\
38: (advance-empty-queue-tail forks-0- queue-1 qs-0 qs-0 fork empty zero one) [1]\\
39: (perform-trans philosopher-0 philosopher forks--pid-wfork state-1 state-6) [1]\\
40: (activate-trans philosopher-0 philosopher forks--pid-rfork state-6 state-3) [1]\\
\par
\textbf{41: Macro-Action B, using philosopher-0 and -forks-0-\\}
\par
44: (activate-trans philosopher-0 philosopher forks-\_\_-pidp1\_\_5\_-rfork state-3 state-4) [1]\\
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