A Study on Multi-level Robust Solution Search for Noisy Multi-objective Optimization Problems

For noisy multi-objective optimization problems involving multiple noisy objective functions, we aim to develop a two-stage multi-criteria decision-making system considering not only the objective values but also the noise level of each solution. In the first stage, the decision maker selects a solution with a preferred balance of objective values from the obtained Pareto optimal solutions without considering the noise level. In the second stage, for the preferred balance of objective values, this system shows several solutions with different levels of the noise and guides the decision-making considering the noise level of solutions. For the two-stage multi-criteria decision-making system, in this work we propose an algorithm to simultaneously find multi-level robust solutions with different noise levels for each search direction in the objective space. The experimental results using noisy DTLZ2 and multi-objective knapsack problems shows that the proposed algorithm is able to obtain multi-level robust solutions with different noise levels for each search direction in a single run of the algorithm.