Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Tight Bounds for Blind Search on the Integers
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چکیده
We analyze a simple random process in which a token is moved in the interval A = [0, n]: Fix a probability distribution µ over [1, n]. Initially, the token is placed in a random position in A. In round t, a random value d is chosen according to µ. If the token is in position a ≥ d, then it is moved to position a−d. Otherwise it stays put. Let T be the number of rounds until the token reaches position 0. We show tight bounds for the expectation of T for the optimal distribution µ, i.e., we show that minµ{Eµ(T)} = Θ ` (log n) 2 ´. For the proof, a novel potential function argument is introduced. The research is motivated by the problem of approximating the minimum of a continuous function over [0, 1] with a " blind " optimization strategy.
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تاریخ انتشار 2008