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In this paper we address the problem of constrained nonlinear optimization problems in engineering design. The proposed approach uses a genetic algorithm based strategy in conjunction with fuzzy constraints and fitness functions to represent and solve parametric design optimization problems. It is shown, via some classic examples from the engineering design literature, that this approach is effective and leads to improved performance both computationally as well as in terms of the proximity of the solution to the Pareto optimal front. The paper concludes with a discussion of the relevant issues in the proposed approach and suggestions for extension of this effort towards addressing multi-constraint problems.