The tools available to achieve the given objectives are Moldflow MPI for the injection molding simulations, and modeFRONTIER for the automation of the multiobjective optimization, and as data postprocessor.
The Moldflow MPI model and the process assumptions
The part has been modeled in Moldflow MPI by using a midplane model, including about 37.000 triangular elements. The hot runner system has been defined by beam elements. The mesh of the panel and of the hot runners is shown in fig. 3. Mesh diagnostics commands have been used to detect and fix model errors, such as high aspect ratio or overlapping elements.
JCI provided indications on the characteristics of the injection molding machine: an important aspect to be considered is that the clamp force value for this part should be under 1350 tons. A few preliminary Moldflow MPI analyses clarified that it is extremely difficult to respect such clamp force limits when using only three injection points for the mold. This is mainly due to the relatively long flow lengths within the part when using only 3 gates: hence the maximum pressure, and particularly the clamp force, are too high for the considered machine. Therefore, the number of injection points has been set to a constant value of five in the subsequent optimization, even though it is possible to consider the number of injection points as a variable within a modeFRONTIER project.
The thickness of the part is approximately constant around 2.8 mm: such a value was obtained by the customer itself as a good compromise between cost, structural and processing needs. For this reason, thickness has not been included as a free parameter to be investigated, even though it would be possible within a modeFRONTIER optimization.
Optimization parameters
Among all the process parameters controlling part quality and clamp force, 8 have been selected as the most sensitive ones, and subsequently set up as “input variables” in the modeFRONTIER optimization workflow linked to the Moldflow MPI model.

Fig. 4 – Typical packing profile 
The packing profile has been parameterized giving modeFRONTIER the opportunity to control the packing pressure, packing time (time during which constant packing pressure is applied) and decay time (time from packing pressure to zero pressure). A typical packing profile is shown in fig. 4.
This is important not only with respect to the clamp force, but also in order to control the warpage of the part.
JCI recommended to use a packing pressure of about 25 – 35 MPa for this material. To better study the influence of packing pressure on design objectives, packing pressure values between 20 and 50 MPa have been considered.
The total cycle time has been determined after a few introductive analyses, taking into account the characteristics of the injection molding machine: its value is around 45s, including approximately 14s of mold opening time. Since the order of magnitude of the filling time is about 5s, as found out after some preliminary analyses, about 26s are consequently available for the packing and the cooling of the part.
Considering also other characteristics of the process (such as redosing time), it has been decided to investigate the influence of the total packing time on the design objectives (in particular with the aim to achieve warpage reduction), by assigning two independent input variables to the packing time and the decay time, both can span from 0 to 20s, without exceeding a maximum of 20s together. This is possible in the modeFRONTIER workflow by assigning a constraint to the sum of the independent variables.

Fig. 5 – Position and number of valve gates 

Fig. 6 – Desired position for the last point to fill. 
In this case, the positions of the injection points (see fig. 5) could not be changed significantly, due to customer requests and constraints related to the mold and part geometry. Instead, it was possible to use hot runners with valve gate control, and hence search for the optimal valve gates’ opening times. Considering that in general, it is not convenient that a single valve gate opens before the flow front reaches the valve itself (to avoid weld line forming) and that injection starts from gate1, the delayed opening times of valve gates number 25 were controlled by modeFRONTIER as independent input variables. This allowed the optimizer to control the flow pattern and the balance of fill without changing the injection gates’ positions.
Delay time ranges for gates 2 and 3 were set to 02s, the ones for gates 4 and 5 to 01.5s.
Moreover, the melt temperature has been considered as an input variable, because of its influence on flow pattern, clamp force (melt temperature influences viscosity of material and hence injection pressure and clamp force during filling) and warpage of the part. The melt temperature has been set free to vary between 220 and 260°C.
Mold temperature has been set as a constant of 40°C, since all the preliminary analyses proved that any change of mold temperature in the material’s recommended range had only secondary effects on the results of interest, with respect to the other variables.
Optimization objectives
In order to describe and control the part quality, besides warpage minimization, another important parameter to consider is a proper filling pattern. Controlling flow pattern and positioning weld lines in the least sensitive areas are important design objectives which allow to obtain good quality parts. In the present case, it has been agreed with the customer to control the position of the last zone to fill: it is important to note that this part (where a weld line is likely to form) is located in an hidden area of the medallion after having been assembled into the whole door structure. The zone recommended by the customer is shown in fig. 6:
Within modeFRONTIER it is possible to extract from any Moldflow MPI analysis the position of the lastfilledpoint, and to assign as objective the minimization of the distance of such node from the wanted zone.
Another important result from the Moldflow MPI analyses is the flow front temperature which provides important indications on the quality of the part. A big difference between minimum flow front temperature and melt temperature can lead to bad quality weld lines, flux hesitations and short shots in the most serious cases. In the modeFRONTIER project, a constraint has been assigned to the minimum flow front temperature result: if more than 10°C lower than melt temperature, the solution is going to be penalized within the optimization loop.
In summary, the following 8 independent input variables have been set:
 packing pressure;
 packing time and decay time;
 melt temperature;
 delay times for valve gates 25.
while the 3 objectives to be pursued simultaneously by the multiobjective optimizer have been:
 minimize the clamp force in Z direction (mold open direction);
 minimize the difference between maximum and minimum value of outofplane (Z direction) deformation;
 minimize the distance of the last filled node from the desired zone.
Additionally, a constraint has been set to the difference between minimum flow front temperature and melt temperature; some small bosses with low thickness, present in the part, were not included in this verification.

Fig. 7 – modeFRONTIER optimization workflow (with under development version of the Moldflow MPI node, updated at the present paper first release). 
The representation of the whole optimization process is the modeFRONTIER workflow depicted in fig. 7.
Integration of Moldflow MPI and optimization strategy
After the creation of the workflow of fig. 7, modeFRONTIER is ready to search for the best combination of input parameters, building and driving automatically several Moldflow MPI studies towards the optimum.
In particular, the link between the Moldflow MPI project and modeFRONTIER has been managed via Moldflow’s API, and hence without any ASCII file creation. In this way, it is possible to let modeFRONTIER control  as input parameters  virtually any process parameter defined in the Moldflow study, as well as other entities, such as gate numbers and positions, shape and thickness of some parts, eventually linking any external CAD system. The multidisciplinary nature of modeFRONTIER allows the user to set up mixed optimizations, connecting to the process simulation also other analyses, such as fiber orientations, FEM analyses, and so on  thus linking in other commercial CAE tools or inhouse codes in the same optimization loop.
Despite of the fact that the optimization described here, only involves process parameters, the space of the possible solutions combining the 8 defined parameters is wide, actually in the range of 1016 different responses. Therefore, due to a time constraint of one weekend on a single processor machine as total optimization time, a very efficient optimization stochastic algorithm, available in modeFRONTIER, has been chosen.
This algorithm, named MOGT (MultiObjectiveGameTheory), is based on the work of John Nash on the game theory. In a competitive game, there may be several conflicting objectives to be achieved. Each player can optimize a certain variable subset assigned to him/her with respect to the unique objective, using a fast monoobjective strategy. In any case, all the variables that are not under his/her own control, are the result of a previous optimization step carried out by all the other players. Hence, they obviously influence his/her search.


Fig. 8 – Initial design and selected optimal solution within the two main objectives’ space. 
Tab. 1 – Comparison between the initial design and the selected optimal solution, as input variable values and as objective improvements. 
The solution is an equilibrium point that occurs when the choices of the two players do not change in the following steps. This choice represents the best compromise for the objectives: it is a unique solution, however, this solution depends on the way the variables’ space has been split among the players.
For this reason, the modeFRONTIER’s MOGT implements an adaptive mechanism that allows to redistribute the variables to be optimized from one player to another, dynamically during the progress of the optimization, and accordingly to the statistical influence analysis of each variable.
The result is a robust stochastic algorithm able to approach the Pareto Frontier (the whole set of nondominated solutions of multiobjective problems) within a few attempts which is extremely useful for engineering problems with a limited solution time.
In the described project, a maximum number of Moldflow studies of about 60 was available by leaving the solver to work automatically, driven by modeFRONTIER’s MOGT, all over a weekend using a single processor workstation.
Optimization results
The results obtained by the MOGT algorithm have been visualized by applying the modeFRONTIER post processing charts. With regard to the two main objectives, the minimization of warpage and clamp force, the scatter chart shown in Fig. 8 has been particularly useful. It represents each of the Moldflow study results by means of a marker. Each green bubble shown is a solution respecting assigned constraints on total packing time and minimum flow front temperature, while a yellow marker does not.

Fig. 9 – Initial design (left) and selected optimal solution (right), Z axis deflection 

Fig.10 – Initial design (left) and selected optimal solution (right), clamp force 

Fig. 11 – Initial design (left) and selected optimal solution (right), filling time plot 
The green dotted line groups the most interesting solutions. In particular, number 44 was selected as the most interesting compromise between the two main objectives.
Table 1 illustrates the comparison between the initial solution and the optimized one. As shown right, the improvements were considerable and simultaneously obtained with respect to all the three objectives. On the left, we can see the peculiar parameters’ combination which guarantees such results. Packing pressure has been reduced (beneficial in reducing clamp force) with respect to the initial design, but not abated to the minimum allowed in the defined range. In the same way, the total packing time has been increased but not up to the maximum allowed, testifying again the conflicting nature of the objectives. A peculiar combination of delay times for the controlled gates has been detected. This is to control the flow pattern with respect to the flow front temperature, pressure and deflection.
Fig.9 shows the improvements obtained with the warpage behavior of the part, mainly due to deformation reduction in the highlighted critical zones. Fig.10 compares the clamp force history of the initial and optimized process: a reduction of the peak value is clear.
Fig.11 shows how the lastfilled zone (grey cells) has been moved towards the ideal orange box defined for aesthetic reasons.
Parameter sensitivity analyses and optimization data post processing
After an optimization process, the visualization and exploitation of all the collected data represents a key issue. For example, a major topic is detecting sensitivities, main effects and interactions of the various parameters on the major outputs/objectives. modeFRONTIER offers several powerful tools to meet these challenges.
In particular, the plot in fig. 12 shows the result of a correlation analysis over a reduced factorial Design of Experiment plan performed as part of the same study described in the previous chapters. Correlation indexes are normalized between 1 (perfect positive correlation) and –1 (perfect negative correlation). Therefore, if an input parameter has an absolute index value close to 0 regarding a particular output, it means that its firstorder influence on the same is quite negligible, as it follows from the correlation definition:
While the clamp force is dominated by the packing pressure value, the chart shows that decreasing this last factor has not a huge but still a negative effect on the warpage (0.22 correlation). The reduction of the warpage is widely controlled by the packing time (increasing is beneficial) and by the gates’ delay times.
The melt temperature, within the assigned variation limits, appears not to be a primary factor with regard to both the objectives.

Fig. 12 – Correlation indexes for each input
parameter (lines) over the two main objectives (columns), modeFRONTIER’s correlation matrix. 
Interactions analysis can also be performed. In this case, the response is a rather strong interaction between melt temperature and packing pressure (see fig. 12), which from fig. 11 seem to be the least effective parameters over the warpage itself, if varied separately.
In fact, the interaction chart highlights how a simultaneous increase of melt temperature amplifies the effect of a simultaneous increase of packing pressure in terms of reduction of warpage.
modeFRONTIER provides many other modules, that allow the designer to take decisions and find satisfactory tradeoffs between several objectives, but also tools to cluster and group multidimensional data, to perform robust design analyses, and to speed up the optimization campaigns integrating metamodelling techniques (Response Surfaces).

Fig. 13 – Interaction effects on the warpage of the two factors “melt temperature” and “packing
pressure”, modeFRONTIER interaction chart 
Conclusions
Moldflow MPI and modeFRONTIER have been coupled in a multiobjective optimization. Thanks to the efficient MOGT algorithm, the initial design has been improved, with only 44 attempts (Moldflow calculations) reducing clamp force by 30% and warpage by 29%  simultaneously.
modeFRONTIER couples easily Moldflow MPI with any CAD, FEM or other inhouse CAE software to drive the process and/or product design towards a multicriteria optimal solution.