This work presents an investigation on numerical optimization technique coupled with Reynolds-averaged Navier-Stokes analysis of flow and heat transfer for design of rib-roughened surface in case of single Surface roughened in two-dimensional channel, Standard k-v model is used as a turbulence closure. The objective function is defined as a function of heat transfer coefficient and friction drag coefficient with weighting factor. And, the ratio of width-to-height of the rib and the ratio of pitch-to-height are selected its design variables. Three different weighting factors and two sets of initial Values of the design variables in each case are tested. In Case Of double design variable, the histories of design variables and objective function are complicated, and the number Of iterations is very sensitive to the initial Values of design variables. However. overall performance of the optimization process is proved quite reliable.