Confidence-based Robust Optimisation of Engineering Design Problems

Abstract

Robust optimisation refers to the process of combining good performance with low sensitivity to possible perturbations. Due to the presence of different un- certainties when optimising real problems, failure to employ robust optimisation techniques may result in finding unreliable solutions. Robust optimisation techniques play key roles in finding reliable solutions when considering possible uncertainties during optimisation. Evolutionary optimisation algorithms have become very popular for solving real problems in science and industry mainly due to simplicity, gradient-free mechanism, and flexibility. Such techniques have been employed widely as very reliable alternatives to mathematical optimisation approaches for tackling diffi- culties of real search spaces such as constraints, local optima, multiple objectives, and uncertainties. Despite the advances in considering the first three difficulties in the literature, there is significant room for further improvements in the area of robust optimisation, especially combined with multi-objective approaches. Finding optimal solutions that are less sensitive to perturbations requires a highly systematic robust optimisation algorithm design process. This includes designing challenging robust test problems to compare algorithms, performance metrics to measure by how much one robust algorithm is better than another, and computationally cheap robust algorithms to find robust solutions for optimi- sation problems. The first two phases of a systematic algorithm design process, developing test functions and performance metrics, are prerequisite to the third phase, algorithm development. Firstly, this thesis identifies the current gaps in the literature relating to each of these phases to establish a systematic robust algorithm design process as follows: The need for more standard and challenging robust test functions for both single- and multi-objective algorithms. The need for more standard performance metrics for quantifying the per- formance of robust multi-objective algorithms. The need for more investigation and analysis of the current robustness metrics. High computational cost of the current robust optimisation techniques that rely on additional function evaluations. Low reliability of the current robust optimisation techniques that rely on the search history (sampled points during optimisation).