ANN model is preferred to use in conjunction with GA optimization technique。 Shen et al。 [25] optimized injection mold- ing process parameters using a combination of artificial neural network and GA method。 Chen et al。 [26,27] optimized pro- cess parameters for multi-input multi-output (MIMO) and multi-input single-output (MISO) plastic injection molding via soft computing with ANN and GA。 Ozcelik and Erzurumlu [28] compared the warpage optimization in the plastic injection molding using ANOVA, ANN and GA。 Other authors [29–34] also used ANN and GA for optimizing process parameter in injec- tion molding in order to improve the quality of molded part。 Most of these authors concluded that ANN and GA hybrid strat- egy is a robust approach。 However, most of them did not mention the way to select the number of experiments which is used to obtain training data for ANN model。 The number of input parameters varies from 4 to 6 in most of these studies, but the number of experiment changes in a large range (from 27 [28] to 252 [25])。 It is clear that if the number of experiments is too high, the simulation or physical experiment cost is extremely    elevated。

2。3。3。 Kriging model

Kriging, a kind of metamodel, is considered as an appropriate model for deterministic and high nonlinear when the num- ber of process parameters is moderate [3,35]。 However, this method has low attraction to the researchers in the field of injec- tion molding because of its complexity compared with RSM or because of its reputation in comparison with ANN。 Very few studies used Kriging method。 Gao and Wang [36,37] introduced an effective warpage optimization method in injection molding based on the Kriging  model。

2。3。4。 Radial basis function model

RBF is also a common metamodel, but it is not widely used in process parameters compared to other models。 Li et al。 ap- plied the radial basis function to optimize the packing profile of the injection molding process [38]。 They used the gradient- based optimization algorithm namely sequential quadratic programming。 The Latin hyper cube sampling technique was used for DOE。 This technique offers the designer a freedom for choosing the number of experiment。

Although a large amount of works that devoted effort to process parameters optimization, there are still some consider- able issues。 The existence of many approaches shows that the process parameters optimization for injection molding is quite complex and perse。 The level of complication depends on the optimization objective, the geometry of the molded part, materials, and the number of design variables。 In addition, the selection of optimization techniques and optimization meth- ods mainly depends on the experience and subjective choice of researchers。 In the literature, there is no guideline or a gen- eralization of the optimization method that is used to optimize injection molding process parameters。 Thus, general frameworks for simulation-based optimization applied to injection molding are proposed in order to facilitate and accelerate the design and optimization  process。

3。 Proposed frameworks  for  optimizing  molding parameters

3。1。 Optimization method for optimizing molding parameters using direct numerical optimization    models

A framework for optimizing molding parameters using direct numerical optimization model includes a framework for automated simulation and a schematic procedure of the direct simulation-based optimization。 The optimization process is based on the direct numerical optimization method。 Both gradient based and non-gradient based optimization techniques can be used to find the optimum solution。 Numerical optimization is a searching process in which the optimization loop is terminated when the convergence is reached (optimum solution is found), or the termination criteria are active。 Because the computing cost of CAE simulation is usually expensive for large and complex parts, the common termination criterion is the predefined maximum number of  simulations。