The process of simulation-based optimization using direct numerical optimization models should be automatic in order to accelerate the optimization process。 A framework for automated simulation applied to direct numerical optimization methods is proposed in Fig。 2。 This framework includes two components: optimizer and CAE (computer aided engineering) components。 The simulation result obtained from CAE component is sent directly to the optimizer。 Subsequently, the opti- mizer evaluates the result and modifies the input parameters (design variables) in every iteration based on a selected opti- mization technique。 If the gradient-based optimization technique is used, finite difference method is applied to determine the gradient and search direction。 If non-gradient based optimization technique is selected, for example GA, the design vari- ables are modified according the strategy of this optimization technique。 All the tasks in this framework are absolutely auto- matic without the intervention of the user (namely designer) at any stage during the optimization process。

To build the proposed framework, it is necessary to couple the two tools: plastic injection molding simulation tool (CAE software) and a programing tool (or integration software) that is used to connect two tools and to solve the optimization

Fig。 2。 A framework for automated simulation applied to direct numerical optimization methods。

problem。 The selection of implementing software depends on the available tools and inpidual choices of the designer。 They can use any standard programming languages such as Visual Basic, Visual C, MATLAB, or process integration and design opti- mization tools such as iSight and PIAnO to connect the CAE components and the optimizer, control the integration loop, and resolve the optimization  problem。

How the optimizer component works in the proposed framework is also important。 The schematic procedure for optimiz- ing injection process parameters in conjunction with direct simulation-based optimization is described in Fig。 3。 Firstly, the objective functions such as warpage, shrinkage, or residual stress are determined。 Secondly, the designer identifies the de- sign variables such as melt temperature (Ti), mold temperature (Tm), fill time (ti), packing time (tp), and packing pressure (Pp) as well as constraints。 The constraints are usually the range of design variables and some boundary conditions related to the specification of the molding machine。 Thirdly, the simulation is carried out in order to obtain the values of the objective func- tions。 The loop of evaluating the simulation results, modifying design variables, and running simulation in Fig。 3 is termi-

nated when the stop criteria or the convergence of the optimization process is met。 Finally, the optimum  solution is obtained after the optimization search is  stopped。

The quality of ‘‘optimum solution’’ depends on some factors in which an initial start point of the numerical search is important。 The number of iteration sometimes depends on an arbitrary initial starting point。 However, no one knows what the best initial point is when he starts the searching process。 Another problem is that the local optimum can be reached in- stead of global optimum when gradient-based optimization technique is used。 When the behavior of the response of the out- put is high nonlinear, the optimization process may be trapped in a local optimum。 In addition, if the number of design variables increases, direct optimization method requires a lot of iterations and the total simulation cost may be high。 Assum- ing that the flow and warpage simulation take an hour to complete and the optimization process terminates after 240 iter- ations, it takes 10 days to finish the optimization process。 These problems are the disadvantages of direct simulation-based optimization method。

The optimization method for optimizing molding parameters using direct numerical optimization model is suitable for problems with low simulation cost。 High performance computer nowadays can facilitate the application of this optimization method。 In addition, hybrid optimization techniques which combine non-gradient based and gradient-based algorithm can ensure a global optimum with a moderate number of simulations for high nonlinear problems。