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2: for x ∈ searchSpace do if good(x) then success(x) fi od; failure() 2. Search 43 To improve the search, one can use a set called options that contains only the objects that may be interesting to test at a certain step of the search instead of the whole search space. This set will be modified during the search by the procedure modify(options). The most important function in the search algorithm will be a selector function that we denote by selectFrom(options) which performs the selection of a new object from options to test at each search step.
Initial value of the beam can be any element of the search space from which the solution is accessible by means of the search operators. The beam is updated at every search step on the basis of the knowledge obtained during the search. The beam is always a finite set, even when the search space is infinite. The beam is analogous to the set open in the breadth-first search algorithm, except that the beam need not be a complete border between the attended and unattended nodes. The beam is not only extended, but also decreased, using heuristics, if it grows too large.
17: F((a1, . . , ai), (V1, . . ,Vn), D) = if i == n then (a1, . . , an) fi; L: while not empty(Vi+1) do x=selectFrom (Vi+1 ); if accept (a1, . . ,Dn)); 2. 6. Search on and-or trees Another, and a slightly more complicated backtracking search algorithm is the search on an and-or tree that has interleaved layers of or-nodes and and-nodes. Search is successful in an and-node if and only if it is successful in all its immediate descendants. It is successful in an or-node if and only if it is successful in some of its immediate descendants.