Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

The above algorithm considers two depth cut-off levels. If the stack contains
nodes whose children all have ‘f’ value lower than the cut-off value c, then
these children are pushed into the stack to satisfy the depth first criteria of
iterative deepening algorithms. However, when it fails, i.e., ‘f’ value of one or
more child n’ of n exceeds the cut-off level c, then the c’ value of the node n
is set to min (c’, f(n’)). The algorithm terminates when either i) the goal is
identified (successful termination) or ii) the stack is empty and the cut-off
value c’ = ∝.
The main advantage of IDA* over A* lies in the memory requirement.
The A* requires an exponential amount of memory because of no restriction
on depth cut-off. The IDA* on the other hand expands a node n only when all
its children n’ have f (n’) value less than the cut-off value c. Thus it saves a
considerable amount of memory.
Another important point to note is that IDA* expands the same nodes
expanded by A* and finds an optimal solution when the heuristic function
used is optimal.
4.3.3 Heuristic Search on AND-OR Graphs
The second classical problem, where the heuristic search is applicable, is the
backward reasoning problem implemented on AND-OR graphs. Before
describing the technique of pruning an AND-OR graph, let us first understand
the process of expanding an unconstrained graph. Consider the problem of
acquiring a TV set. One has to identify the possible ways one can acquire the
TV set. So, here the goal is “to acquire a TV set” and the terminals of the
graph describe the possible means by which it can be achieved. The details of
the possibility space are given in fig. 4.10.
For heuristic search on AND-OR graph, we use an algorithm, called an AO*
algorithm. The major steps of the AO* algorithm are presented below.
1. Given the Goal node, hereafter called the starting state, find the
possible offsprings of the starting state, such that the Goal can be
derived from them by AND / OR clauses.
3. Estimate the h’ values at the leaves and find the leaf (leaves) with
minimum h’. The cost of the parent of the leaf (leaves) is the minimum
of the cost of the OR clauses plus one or the cost of the AND clauses
plus the number of AND clauses. After the children with minimum h’
are estimated, a pointer is attached to point from the parent node to
its promising children.