Metamodel-based simulation optimization considering a single stochastic constraint

In this paper, we consider a simulation optimization problem with a single stochastic constraint where (i) the objective and constraint functions cannot be mathematically evaluated but they can be estimated via stochastic simulation and (ii) the number of solutions is very large (i.e., possibly infinite). To solve the problem, we propose metamodel-based frameworks which represent an extension of the metamodel approach in conjunction with the deterministic mathematical programming technique, and ranking and selection procedures. The firstly proposed framework uses ranking and selection procedures to identify the feasibility of a solution, and it selects the optimal solution among the visited promising solutions (with a prespecified statistical guarantee). In the stage of metamodel fitting, the regression metamodels are developed separately for the response values of the objective and the constraint. The other proposed frameworks adopt the penalty function approach, and fit appropriate metamodels for an aggregated objective function. Experimental results are provided to show the efficiency of the developed algorithms when compared to other existing approach.