Responses

Total  defection (mm)

3。15

2。74

2。93

3。54a

2。72

Cooling  time (s) 12。3 12。3 11。7 11。5 11。5

a   One of the local  optimum。

elements。 An API program was coded in order to automatically perform the simulation task。 The integration between opti- mization controller and flow simulation was implemented using iSight    software。

The problem is finding the optimum values of five important process parameters including mold temperature (Tm), melt temperature (Ti), injection time (ti), packing pressure (Pp), and packing time (tp)。 The value ranges of these parameters are determined from the recommended ranges given by the plastic manufacturer (Table   2)。

The optimization problem is stated as   follows:

- Minimize the warpage W ¼ f ðTm ; Ti ; Pp; tp ; ti Þ ð1Þ

-  Subject  to : 30 6 Tm  6 60;      220 6 T1  6  260 ð2Þ

60 6 Pp 6 90;    4 6 tp 6 7

1 6 ti  6 2

Both the previously mentioned optimization methods that cover gradient-based, non-gradient based, and hybrid optimi- zation techniques are adopted。 The first method applies the indirect or metamodel-based optimization approaches including RSM, RBF, and ANN。 The second method applies the direct optimization approaches including GA, gradient-based optimiza- tion technique, and hybrid of GA and gradient-based optimization    technique。

For gradient-based optimization, firstly, the RSM metamodel was used with 36 numerical experiments organized by L36 orthogonal array。 The fitness plot of the RSM model shows a very good prediction of cooling time (R2 = 1。0); however, the warpage response is too low (R2 = 0。62, see Fig。 7)。 The low value of R2 for the response of warpage is caused by a highly non- linear behavior of warpage due to low stiffness and corner effect of the molded part。 Therefore, RSM method is inadequate metamodel for this  example。

RBF is subsequently used instead of RSM model。 The value of R-squared of RBF model is higher than those of RSM (0。72 compared to 0。62, Figs。 7 and 8) because RBF model can fit the nonlinearity better。 ANN model was also applied in this exam- ple。 The quality of ANN model depends on the quality of training data set。 In this case study, training data-set is 60 design points sampled by Latin hypercube technique。 The columns marked with (1) and (2) in Table 2 show the optimization results obtained by RBF and ANN approaches。

The direct simulation-based optimization methods were tested with non-gradient based GA, gradient based and hybrid optimization techniques。 Non-gradient based GA method gives a relatively significant result, in general, because it gives low values of considered outputs (2。93 mm of warpage and 11。7 s of cooling time)。 The history plot of optimization process using direct GA optimization method is shown in Fig。 9。 However, the number of simulations is confined in a predetermined value of 200 runs for this case study due to the computing cost of each simulation and the budget of time。 Therefore, the real