3.3.3. Post-processing of the constrained Multi-objective optimization

If we were not able to run the Multi-objective with constraints optimization we can load the project for the post-processing from:
.../modeFRONTIER30x/doc/html/caeInt/star-CD/ blunt/prj_full/multiObjCon/StarCD-MultiObjCon.prj

Once we move to the Design Space tab we enter into the post-processing environment.
On the left we find a new tool bar where there are all post-processing tools for result assessment.

Clich on the Design Table icon to show the complete result database (Input and Output Variables, Objective and Constraints), see Fig. 1.
This table updates while the optimization is running and each design is written as soon as it is calculated.

When the optimization has finished we can mark the design belonging to the Pareto Frontier selecting the action Mark Mark Pareto Design > only Real from the Edit menu.

Note: Twenty-eight designs belong to the Pareto frontier, it means that all the other designs are not better of these twenty-eight for both objectives.

Note: As we can see in the initial population many designs violate constraints while after two or three generations the optimization algorithm creates design that respect the constraints and have better performance. In fact many designs of the Pareto frontier belong to last few generations.

Fig. 1: Design Table

When we want to post-process results of an optimization with a lot of output quantities (output variables, objectives, constraints) a very useful tool is the Parallel Coodinates Chart .
To see all interesting quantities of our project in a Parallel Coodinates Chart click on the and select all the Input Variables, drag among the Output Variables, all the Objectives and only the Cons_area Constraint since the Cons_mom has the same expression of the Objective obj_mom, see Fig. 2.

Fig. 2: Parallel Chart Creation

A new window will appear into the Design Space and it shows us the value of selected quantities for each design, see Fig. 3. Each desisn is a continous line and moving the arrows we can filter designs to select those that better fulfil our objectives. For example in the Fig. 3 we filtered results looking for a compromise between the three objectives (maximize both lift and aerodynamic efficency and minimize the torque)

Fig. 3: Parallel Chart : how to filter the results

If we take a look at the Scatter Chart eff vs. lift we can see in Fig. 4 that the optimization algorithm has found designs wich have high values of the eff and values of the lift better than for mono-objective and multi-objective (without constraints) optimisation. The reason of this improvement is that we have added an objective on the value of the lift so that the optimization algorithm has evaluated each design from this angle as well.

Fig. 4: Scatter Chart : eff vs. lift

If we want to know which is the most influent constraint we can create a Broken constraints Chart .
Select both constraints, Fig. 5 and when we click on Ok botton to confirm our choice a pie diagram will appear and each slice rappresents the ratio of each broken constraint respect to all broken constraints, Fig. 6.

Fig. 5: Broken Constraints Chart creation

Fig. 6: Broken Constraints Chart