21.4.5.3. Robust Design Optimization & DFSS

Unlike the deterministic optimization, the formulation of robust design optimization & DFSS is somewhat complicated.

Minimize \(\alpha \cdot f\left( \mathbf{x} \right)+{{k}_{0}}\cdot {{\sigma }_{0}}\left( \mathbf{x} \right)\)

Subject to

\({{h}_{i}}\left( \mathbf{x} \right)=0,\text{ }i=1,2,...,l\)

\({{g}_{j}}\left( \mathbf{x} \right)+{{k}_{j}}{{\sigma }_{j}}\left( \mathbf{x} \right)\le 0,\text{ }j=1,2,...,m\)

\(\mathbf{x}\pm \sigma \in \Omega\)

where, \({{\sigma }_{j}}\left( \mathbf{x} \right),\text{ }j=0,1,...,m\) are the standard deviation of \(f\) and \({{g}_{j}}\). The value of \(\alpha\) and \({{k}_{i}}\) are user defined parameters. If users define \(\alpha =0\) and \({{k}_{0}}=1\), the design objective is a minimization of the variance of \(f\left( \mathbf{x} \right)\). Also, if users define \({{k}_{j}}=6\), the inequality constraints are DFSS constraints.

Reference

  1. Fletcher, R., Practical method of optimization, John Wiley & Sons, Chichester, 1987.

  2. Vanderplaats, G.N., Numerical optimization techniques for engineering design, McGraw-Hill, 1984.

  3. Osyczka, A., Multicriterion optimization in engineering, Ellis Horwood Limited, 1984.