An approach based on Hotelling’s test for multicriteria stochastic simulation–optimization

In a stochastic simulation context, iterative methods of optimization, which perform at each step of their optimization procedure a comparison between two different values of the objective function, need the use of statistical tests in order to properly evaluate and compare the simulation results. However, when the objective function to be optimized is a multicriteria function involving several performance measures, classical statistical procedures, which do not take into account the correlation between the performance measures, could reject acceptable solutions. To avoid this, we propose an efficient and rigorous statistical procedure already used in a multicriteria context, Hotelling’s T² procedure. This paper shows that this procedure is very well adapted when the problem is to compare simultaneously several criteria in a stochastic simulation–optimization context.