A novel Kriging-assisted multi-objective optimisation method considering infeasibility ratio under input uncertainty

Abstract

Many real-life engineering applications come with various sources of uncertainty. Uncertainty can also impact the feasibility of solutions in constrained optimisation. Classic robust optimisation approaches often significantly increase the computational burden and might overlook different tolerable risks, resulting in conservative sub-optimal solutions. We reformulate the classic constrained problem as a multi-objective optimisation problem and propose a Kriging-assisted multi-objective optimisation method that trades off Infeasibility Ratio (IR) with robust performance: (1) a formulation to approximate IR is developed and introduced as an additional objective and (2) an acquisition function balancing exploration (refining feasible boundaries) and exploitation of promising areas with multiple designs is proposed. Furthermore, a new quality metric has been developed to effectively measure the convergence and diversity of the obtained Pareto solution set. The proposed framework is tested on five numerical problems and applied to an engineering case: the design of a honeycomb vibration isolator. A comparison study with other optimisation methods is conducted to verify its effectiveness and performance with promising results.