Searching and gradualness.
Consider the elements of the power set S as the alternatives in a search space. Each element of the set has a value and the goal of a search is to find an element with near-minimum value. If high-valued elements of cardinality i (recall that elements of S are themselves sets) are subsets of high-valued elements of cardinality i + 1, then the search space has a king of gradualness that should facilitate search. A search algorithm might generate a series, S' (1), . . . S' (k) of samples in S, where all the elements in S' (i) have cardinality i. I propose a class of search algorithms, where each algorithm A(j) generates S' (i + 1) by emphasizing the j lowest-valued elements in S' (i). I then define search space gradualness and search algorithm performance and formally relate gradualness and performance.
D005075:Biological Evolution; D008433:Mathematics; D008954:Models, Biological