Design Optimization

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(:title Robust Optimization Under Uncertainty:) (:keywords robust optimization, constrained optimization, GRG, SQP, genetic algorithms, continuous optimization, mathematical modeling, discrete optimization, nonlinear, optimization, engineering optimization, interior point, active set, differential, algebraic, modeling language, university course:) (:description Robust optimization methods for systems with uncertain inputs, constraints, or mathematical models.:)

Chapter 8: Robust Optimization

In the “real” world, almost all designs are subject to variation. Such variation can arise from multiple sources, including manufacturing processes, material properties, changing operating conditions, or the environment. We can also have uncertainty associated with our computer model. We may not know some assumed values as well as we would like (e.g. heat transfer coefficients, friction coefficients), and our assumptions about boundary conditions might also be faulty. For example, loads or temperatures might be different than we assumed.

The consequences of variation are almost always bad. Variation in product dimensions can lead to assemblies which assemble poorly or not at all, or function improperly. Failure to take into account variation can lead to product failure, poor performance and customer dissatisfaction. A famous quality researcher, Genichi Taguchi, has promoted the idea that any deviation from a desired target value results in a loss to the customer.

Optimized designs may be particularly vulnerable to variation. This is because optimized designs often include active or binding constraints. Such constraints are on the verge of being violated. Slight variations in problem parameters can cause designs to become infeasible.

Thus it should be clear that we should not only be interested in an optimal design, but also in an optimal design which is robust. A robust design is a design which can tolerate variation. Fortuitously, a general approach to robust design can be formulated in terms of optimization techniques, further extending the usefulness of these methods. In this section we learn how to apply optimization methods to determine a robust design.