Because metamodeling technique is an approximate technology, there are errors between the predicted values obtained by the regression model and the true values obtained by simulation/experiment at the ‘‘optimum’’ point。 Therefore, evalu- ating optimum design point is required。 This is a remarkable difference between direct simulation-based optimization meth- od and metamodel-based optimization method。 If the error between the predicted and actual values at the optimum point is acceptable, the optimization process is finished successfully。 The advantage of metamodel-based optimization approach is that the designer can initiatively choose the numbers of experiment or simulations。 This advantage is extremely important when optimizing process parameter for molding complex and large parts with many elements。

A comparison between the two proposed optimization methods in terms of simulation cost, number of iterations or sim- ulation time, response nonlinearity, molded part geometry, and the accuracy of optimization result is summarized in Table 1 in order to make a guideline for selecting the appropriate optimization    framework。

4。 Case studies

To show the feasibility of the proposed optimization frameworks, two examples of application are implemented。 This sec- tion also investigates the characteristics of some of optimization    methods。

4。1。 Case study 1: highly nonlinear response  problem

The molded part is a tray made by PP material as shown in Fig。 6。 We used Moldflow software for flow and warpage sim- ulation。 The molded part was modeled by CAD software, imported to Moldflow environment, and meshed with triangular

Fig。 6。  A plastic tray with a bounding-box dimension 400 × 250 × 20 mm and 2。5 mm thickness。

Table 2

Comparison of optimization results obtained from different optimization  approaches。

Variable Unit Lower range Upper range RBF (1) ANN (2) GA (3) Gradient based (4) GA then gradient (5)

Tm °C 30 60 35。5 36。6 31。7 30。0 30。0

Ti °C 220 260 223。3 221。7 220。3 220。0 220。0

ti s 1 2 1。3 1。3 1。6 2。0 1。2

Pp MPa 60 90 61。6 89。5 63。3 60。6 60。0

tp s 4