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By Maksimov V. I.

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Finally, it turned out that the type of heuristic evaluation function assumed by our search method is indeed much simpler to obtain for RBC problems than admissible heuristics. In fact, by applying techniques from statistical regression to a training set of optimally solved configuration problems 1 we were able to derive very good estimations h of the cost function h* [9]. For each node ry of the search tree, h(ry) is an estimation of the cost of the demand d - A x x(ry) that remains of the original demand d (associated with the root of the tree).

ACM, 47, 452-482 Buckley J. J. (1988) Possibility and necessity in optimization, Fuzzy Sets and Systems, 25, 1-13. , Farreny H. (1982). Fuzzy pattern matching. Kybernetes, 11, 103-116. Cohen M. -Y. (1980) Rational behavior under complete ignorance. Econometrica, 48, 1280-1299. , Thomason R. (1999). Background to qualitative decision theory. P. (1991). Impediments to universal preference-based default theories. Artificial Intelligence, 49, 97- 128. Dubois D. (1986). Belief structures, possibility theory and decomposable confidence measures on finite sets.

As will be seen, these methods allow for estimating the quality of a solution eventually found when following a path without referring to other search paths, or other solutions already encountered. Consider a path p = (TJl, ... ,TJK) with path profile f(p) = (f(TJd,··· ,f(TJK)). , the change of which has to be detected, is the expected value E(F(TJk)). Depending on the information available about {Lo and {Ll, the expected values before and after a change, different algorithms can be applied. Generally, it must be assumed that neither {La nor {Ll is known.

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A Boundary Control Problem for a Nonlinear Parabolic Equation by Maksimov V. I.

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