Theory-Lesson 5 Flashcards
Ideal DV vector
The ideal DV vector is obtained by minimizing each of the OFs individually, subject to the constraints. The ideal design is represented by the so-called utopia point. Unfortunately, this point does not belong to the feasible domain and usually we should choose the point closest to this one.
Nadir solution
The nadir solution is the exact opossite of the utopia point. It corresponds to the maximum value of the OF over the Pareto-optimal set.
Discrepancy
In order to avoid having too many input samples, we can perform random samples, derived from the initial ones, to lower the computational cost of the analysis. It’s always preferable to have a uniform grid.
-Discrepancy is a measure for the deviation of a sequence from a uniform distribution, that is the discrepancy measures how evenly a generated set of points is distributed in a given space.
-Usually, the lower the number of points, the higher the discrepancy.
Weighted Sum method
-NOT VERY TIME CONSUMING
-CAN’T NE RELIABLE IF THE PARETO OPTIMAL SET IS NOT CONVEX
This method is a scalarization method in order to find the Pareto optimal set out of a set of OFs. Each OF is assigned with a weight wi , o<=wi<=1 and Σwi=1.
We systematically vary the weights and thus, different Pareto-optimal points are generated. The weights are not relevant to the importance of the OFs, they are just generated randomly.
Constraints method
-MOST EFFECTIVE TECHNIQUE BUT MORE COMPLEX TO SOLVE NUMERICALLY
We consider just one OF and we convert the other ones into inequality constraints.
In each iteration, we vary the value of all the constraints and we obtain some optimal points. In the end of the iterations, we obtain the Pareto-optimal set for all OFs. If the solutions are not unique for some values of e, then the Pareto-optimal points must be selected by direct comparison.
-By varying the weights, we compute a different minimum for the OF and a different non-dominated solution.
What is local-pareto optimality?
A solution xi is local pareto-optimal if there exists δ>0 such that xi is pareto-optimal in the circle centered at xi with radius δ.
