Kriging-based infill sampling criterion for constraint handling in multi-objective optimization

This paper proposes a novel infill sampling criterion for constraint handling in multi-objective optimization of computationally expensive black-box functions. To reduce the computational burden, Kriging models are used to emulate the objective and constraint functions. The challenge of this multi-objective optimization problem arises from the fact that the epistemic uncertainty of the Kriging models should be taken into account to find Pareto-optimal solutions in the feasible domain. This is done by the proposed sampling criterion combining the Expected HyperVolume Improvement of the front of nondominated solutions and the Probability of Feasibility of new candidates. The proposed criterion is non-intrusive and derivative-free, and it is oriented to: (1) problems in which the computational cost is mainly from the function evaluation rather than optimization, and (2) problems that use complex in-house or commercial software that cannot be modified. The results using the proposed sampling criterion are compared with the results using Multi-Objective Evolutionary Algorithms. These results show that the proposed sampling criterion permits to identify both the feasible domain and an approximation of the Pareto front using a reduced number of computationally expensive simulations. Copyright Springer Science+Business Media New York 2016