Noisy multiobjective optimization on a budget of 250 evaluations

We consider methods for noisy multiobjective optimization, specifically methods for approximating a true underlying Pareto front when function evaluations are corrupted by Gaussian measurement noise on the objective function values. We focus on the scenario of a limited budget of function evaluations (100 and 250), where previously it was found that an iterative optimization method - ParEGO - based on surrogate modeling of the multiobjective fitness landscape was very effective in the non-noisy case. Our investigation here measures how ParEGO degrades with increasing noise levels. Meanwhile we introduce a new method that we propose for limited-budget and noisy scenarios: TOMO, deriving from the single-objective PB1 algorithm, which iteratively seeks the basins of optima using nonparametric statistical testing over previously visited points. We find ParEGO tends to outperform TOMO, and both (but especially ParEGO), are quite robust to noise. TOMO is comparable and perhaps edges ParEGO in the case of budgets of 100 evaluations with low noise. Both usually beat our suite of five baseline comparisons. © Springer-Verlag 2009.