Performance Metrics for Multiobjective Optimization Under Noise

This article discusses the challenge when evaluating multiobjective optimization algorithms under noise. It argues that it is important to take into account possible selection errors by a decision maker, due to inaccurate estimates of a solution’s true objective values. It demonstrates that commonly used performance metrics do not properly account for such errors, and proposes two alternative performance metrics that do account for such errors by adapting the popular R2 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm { IGD}}^{+}$ </tex-math></inline-formula> metrics.