Evolutionary multi-level robust solution search for noisy multi-objective optimisation problems with different noise levels

For noisy multi-objective optimisation problems involving multiple noisy objective functions with different noise levels, this work proposes a multiobjective evolutionary algorithm for multi-level robust solution search (MOEAMRS). MOEA-MRS simultaneously finds multi-level robust solutions with different noise levels for each search direction in the objective space. Furthermore, as an extension of MOEA-MRS, we also propose a MOEA for preference-based multi-level robust solution search (MOEA-pMRS) which focuses the solutions search on a specific noise level to consider the case that the decision maker has a preference for the noise level. The experimental results using noisy DTLZ2 and multi-objective knapsack problems shows that the proposed MOEA-MRS is able to obtain multi-level robust solutions with different noise levels for each search direction in a single run of the algorithm, and the proposed MOEA-pMRS can emphasise the solution search for specific noise levels.