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I've written an iterative deepening algorithm, it works except when I add cycle checking, the algorithm returns a deeper solution than it should. But when I don't check for cycles it does work correctly, but it takes too long. Can anyone please spot the bug?

(defun rec-depth-limited (problem node cutoff closed)

(if (= cutoff 0)

(if (funcall (problem-goalp problem) node)

node)

(if (visited-p node closed)

nil

(progn

;; when i remove the next line, it works correctly

(setf (gethash (node-state node) closed) t)

(loop for child in (expand node (problem-actions problem)) do

(let ((result (rec-depth-limited problem child (1- cutoff) closed)))

(if result

(return result))))))))

(defun iterative-deepening (problem)

"Iterative deepening search"

(let ((cutoff 0))

(loop

(format t "~%cut-off: ~A" cutoff)

(let ((solution (rec-depth-limited

problem

(make-node :state (problem-state problem))

cutoff

(make-hash-table :test #'equalp)))) ;solve problem up to cutoff

(if (null  solution)

(return solution))))))

(defun visited-p (node table)

"Checks if the state in the node was visited before by checking

if it exists in the table"

(nth-value 1 (gethash (node-state node) table)))

Edit: here is the expand function

(defun expand (node actions)

"Expands a node, returns a list of the new nodes"

(remove-if #'null (apply-actions node actions)));apply all actions on all nodes

(defun apply-actions (node actions)

"Applies all actions to a state, returns a list of new states"

(mapcan #'(lambda (action)

(mapcar #'(lambda (tile) (funcall action tile node))

(node-state node)))

actions))

This is one of the actions, they are all the same except for minor changes

(defun slide-right (tile node)

"slide the tile one cell to the right. returns nil if not possible,

otherwise returns a node with the new state"

(when (can-slide-right-p tile (node-state node));if can slide right

(and visualize (format t "~%slide ~A to the right" (tile-label tile)))

(let*  ((newstate (mapcar #'copy-tile (node-state node)));copy the current state

(depth (node-depth node))

(newcol (incf (tile-col (find tile newstate :test #'equalp))));update state

(cost (1+ (node-cost node))))

(make-node :state newstate ;create new node with the new state

:parent node

:depth (1+ depth)

:action (concatenate 'string

"slide "

(tile-label tile)

" right" )

:cost cost))))

Predicates

(defun can-slide-right-p (tile state)

"returns T if the specified tile can be sled one cell to the right"

(let  ((row (tile-row tile))

(end (+ (tile-col tile) (tile-length tile))) ;col at which tile ends after being sled

(orient (tile-orientation tile)))

(and (equal orient 'H)

(or (tile-is-mouse tile) (< end *board-w*))

(empty-cell-p row end state))))

(defun spans-cell-p (row col tile)

"returns T if the specified tile spans the specified cell"

(if (equal (tile-orientation tile) 'H)

(horizontally-spans-cell-p row col tile)

(vertically-spans-cell-p row col tile)))

(defun horizontally-spans-cell-p (row col tile)

"Tests if the specified horizontal tile spans the specified cell"

(let ((tile-col (tile-col tile))

(tile-row (tile-row tile))

(tile-len (tile-length tile)))

(and (= tile-row row) (>= col tile-col) (< col (+ tile-col tile-len)))))

(defun vertically-spans-cell-p (row col tile)

"Tests if the specified vertical tile spans the specified cell"

(let  ((tile-col (tile-col tile))

(tile-row (tile-row tile))

(tile-len (tile-length tile)))

(and (= tile-col col) (>= row tile-row) (< row (+ tile-row tile-len)))))

by (108k points)

A confined depth-first search with cycle detection may return a longer path when the first path that leads to the goal is longer than any other shorter path that includes the same state. Iterative Deepening search (IDS) with a lookup table a brute force approach, where the search tree is rebuilt during each iteration of increasing depth. The search was augmented by a lookup table of all positions 6 moves away from the solution. In the implementation, this was not all that different from the bi-directional search. I ran one search from the goal position for 6 moves to fill in the entries in the "lookup table." The table was implemented as the same binary search tree I used for indexing positions in the bi-directional search.

Let D be a goal state:

A -- B -- C -- D

\

C -- D

With a depth limit of 2, if the top branch is visited first, B and C will be visited and saved in the hash table. When the bottom branch is visited, it won't expand past C, because it was marked as visited.

A feasible solution is to set the hash value to the minimum depth where the state was found. This presents the state known as visited for a certain depth and beyond, but it'll be possible to expand it again if visited with less depth.

(defun visited-p (node table)

(let ((visited-depth (gethash (node-state node) table)))

(and visited-depth

(>= (node-depth node) visited-depth))))

(defun set-visited (node table)

(let ((visited-depth (gethash (node-state node) table)))

(setf (gethash (node-state node) table)

(if visited-depth

(min visited-depth (node-depth node))

(node-depth node)))))

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