Multi-objective constrained black-box optimization using radial basis function surrogates

This article presents a framework for a surrogate-based stochastic search algorithm for multi-objective and constrained black-box optimization where the objective and constraint function values are outputs of computationally expensive computer simulations. Unlike many other approaches, the proposed framework is not population-based and handles constraints without explicitly using a penalty function. In each iteration, the algorithm constructs or updates response surface models or surrogate models of the objective and constraint functions. Then, it generates multiple random trial points according to some probability distribution over the search space. The surrogate models for the objective and constraint functions are then used to identify the trial points that are predicted to be feasible and nondominated. From this set of trial points, two criteria are used to select the next sample point where the expensive objective and constraint functions will be evaluated. These criteria are the minimum distance of the predicted objective vector of a trial point from the current set of nondominated objective vectors and also the minimum distance of the trial point from previous sample points. The proposed framework is implemented using radial basis function (RBF) surrogate models and compared with alternative methods, including NSGA-II and Uniform Random Search on 28 benchmark test problems. The numerical results indicate that the proposed method is promising for computationally expensive multi-objective and constrained black-box optimization.