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This paper presents a concept of combining genetic algorithms (GAs) with an approximate evaluation technique to achieve a computationally effective search and optimization procedure. The major objective of this work is to enable the use of GAs on computationally expensive problems, while retaining their basic robust search capabilities. Starting with a coarse approximation model of the problems, GAs successively use finer models, thereby allowing the proposed algorithm to find the optimal or a near-optimal solution of computationally expensive problems faster. A general methodology is proposed for combining any approximating technique with GA. The proposed methodology is also tested in conjunction with one particular approximating technique, namely the artificial neural network, on a B-spline curve fitting problem successfully. Savings in the exact function evaluation up to 32% are achieved. The computational advantage demonstrated here should encourage the use of the proposed approach to more complex and computationally demanding real-world problems.