Evolutionary multi-objective worst-case robust optimisation

Many real-world problems are subject to uncertainty, and often solutions should not only be good, but also robust against environmental disturbances or deviations from the decision variables. While most papers dealing with robustness aim at finding solutions with a high expected performance given a distribution of the uncertainty, we examine the trade-off between the allowed deviations from the decision variables (tolerance level), and the worst case performance given the allowed deviations. In this research work, we suggest two multi-objective evolutionary algorithms to compute the available trade-offs between allowed tolerance level and worst-case quality of the solutions, and the tolerance level is defined as robustness which could also be the variations from parameters. Both algorithms are 2-level nested algorithms. While the first algorithm is point-based in the sense that the lower level computes a point of worst case for each upper level solution, the second algorithm is envelope-based, in the sense that the lower level computes a whole trade-off curve between worst-case fitness and tolerance level for each upper level solution. Our problem can be considered as a special case of bi-level optimisation, which is computationally expensive, because each upper level solution is evaluated by calling a lower level optimiser. We propose and compare several strategies to improve the efficiency of both algorithms. Later, we also suggest surrogate-assisted algorithms to accelerate both algorithms