Robust multi-modal optimisation

Abstract

Robust and multi-modal optimisation are two important topics that have received significant attention from the evolutionary computation community over the past few years. However, the two topics have usually been investigated independently and there is a lack of work that explores the important intersection between them. This is because there are real-world problems where both formulations are appropriate in combination. For instance, multiple 'good' solutions may be sought which are distinct in design space for an engineering problem - where error between the computational model queried during optimisation and the real engineering environment is believed to exist (a common justification for multi-modal optimisation) - but also engineering tolerances may mean a realised design might not exactly match the inputted specification (a robust optimisation problem). This paper conducts a preliminary examination of such intersections and identifies issues that need to be addressed for further advancement in this new area. The paper presents initial benchmark problems and examines the performance of combined state-of-the-art methods from both fields on these problems.