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The strategy for optimizing the shape design of automotive mufflers is presented. The main goal is to obtain the basic dimensions of the acoustic muffler with the TL been maximized in the interest band frequency. The Finite Element Method with quadratic elements and the method of the four modified parameters are used to calculate the necessary parameters to evaluate the TL's numeric value. The minimizing (or maximizing) problem is solved using the method of the viable directions of Zoutendijk due to its robustness. Numerical experiments performed with asymmetric expansion chambers with extended inlet/outlet show results for the shape optimization with and without constraints.