An Improved Sequential Multi-Objective Robust Optimisation Approach Considering Interval Uncertainty Reduction Under Mixed Uncertainties

Many engineering design optimisation problems are multi-objective and subjected to multiple constraints. These problems may encounter uncertainties in their inputs, which may cause uncontrollable variations in the objectives and constraints. Multi-objective robust optimisation (MORO) approaches aim to obtain Pareto solutions with the least sensitivity to uncertainties. In this paper, an improved sequential MORO approach considering interval uncertainty reduction under mixed uncertainties (SMORO-IM) is proposed. Firstly, it adopts the efficient sequential optimisation framework based on the worst possible point constraint cuts. Secondly, a formulation for obtaining robust optimal solutions under mixed interval and probabilistic uncertainties is employed. In addition, considering that the interval uncertainties in inputs can be reduced at allowable cost, the cost of interval uncertainty reduction is defined as an extra objective function in the proposed approach, aiming at obtaining optimal solutions with different interval uncertainties. Two numerical examples and two engineering cases are used to illustrate the effectiveness of the proposed SMORO-IM approach. The objective and feasibility robustness of the obtained optimal solutions are verified by the Monte Carlo Method.