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This paper presents the design and an initial performance evaluation of the query optimizer generator designed for the EXODUS extensible database system. Algebraic transformation rules are translated into an executable query optimizer, which transforms query trees and selects methods for executing operations according to cost functions associated with the methods. The search strategy avoids exhaustive search and it modifies itself to take advantage of past experience. Computational results show that an optimizer generated for a relational system produces access plans almost as good as those produced by exhaustive search, with the search time cut to a small fraction.