Finding Robust Solutions to Multi-objective Optimisation Problems Using Polynomial Chaos

If an optimal solution is very sensitive to perturbations, then it may not be the most appropriate solution to use. In situations where natural variation is inevitable, it is therefore necessary to find a robust optimal solution. This paper examines emerging techniques for finding robust solutions to multiobjective optimisation problems. One of the major concerns in robust optimisation is that accounting for the robustness of solutions makes the problem much more computationally expensive. It is shown that the polynomial chaos approach addresses this key issue by decomposing the stochastic process into its deterministic and random process parts. A practical problem, design of an electrical RLC circuit, is used to illustrate the effectiveness of the approach.