The general form of the approximate RSM function ex- pressing the relation among process parameters and the res- ponses is as follows:

approximation。

To solve the optimization problem, the non-sort dominated genetic algorithm II (NSGA II) [8] is employed in solving trade-offs among objective functions。 The NSGA II is a mul- ti-objective, exploratory technique that is well-suited for highly non-linear design spaces。

The algorithm is adopted to search Pareto-optimal solu- tions in multi-objective optimization problems。 Non- dominated sorting genetic algorithm II (NSGA II) is a multi- objective evolutionary algorithm that was developed by Deb。 As compared to other optimization algorithms, such as neural network or PSO, this algorithm is reliable and cheaper。   The

schematic view of NSGA-II on a flow chart is shown in Fig-

The procedure of NSGA II can be roughly described    ac-

Where β0, βi, βii and βij are called regression coefficients;  ε is an approximate error; x1 to x5 denote TM, TME, Pt, Pp, and tc, respectively; fk denotes the responses including clamping force and warpage value。 The accuracy approximate model which expresses the relation between inputs and responses is often assessed by the coefficient of determination or R- squared analysis。

Prior to the optimization process, relationships between process parameters and objective functions should be created。 Thus, DOE or space sampling techniques are employed to establish experiments-matrix design。 After acquisition of numerical data, an approximation process is carried out in order to establish a mathematical model。 Based on the simu- lation data, analysis of variance (ANOVA) is conducted to validate not only the effect of process parameters on the desi- rability but also the significance of response variables。 The optimization process was resolved based on explicit equa- tions in regression  that  were  obtained through  the previous

cording to the following steps:

(Step 1) Identify NGSA II parameters including population size, crossover and mutation probability, termina- tion criteria, and design variable ranges。

(Step 2)  Initialize population within boundary conditions。 (Step 3) Sorting population based on non-domination criteria。 (Step 4) Computation of crowding distance。 Once the sorting

is complete, the crowding distance is calculated for each inpidual。 The inpiduals in the population are selected based on rank and crowding distance。

(Step 5) Employing genetic results with intermediate popula- tion。

(Step 6) Combining offspring population and current genera- tion。 Calculation of the inpiduals for the next gen- eration based on the rank and crowding distance。

(Step 7) Go to step 3 and repeat until termination criteria are satisfied。

Figure 4。 Schematic of the NSGA-II procedure [6]。

Table 1。 Material properties of GTX810。

Melt density (g/m3) 1。2465

Solid density (g/m3) 1。3493

Eject temperature (°C) 231

Maximum shear stress (MPa) 0。45

Maximum shear rate (1/s) 50000

Thermal conductivity (W/m°C) 0。23

Elasticity module (MPa) 3869。81

Poisson ratio 0。4232

Many researchers have demonstrated that NSGA II is an efficient technique for solving complex optimization prob- lems [9-11]。 In NSGA II, each objective is treated separately, and a Pareto front is constructed through selection of feasible, non-dominated designs。 Pareto plots allow the designer to reach compensable solutions according to customized re- quirements。 Ultimately, numerical experiments test the relia- bility of the optimal parameters and the proposed methods。