Flowsheet simulations of chemical processes on an industrial scale require the solution of large systems of nonlinear equations, so that solvability becomes a practical issue. Additional constraints from technical, economic, environmental, and safety considerations may further limit the feasible solution space beyond the convergence requirement. A priori, the design variable domains for which a simulation converges and fulfills the imposed constraints are usually unknown and it can become very time-consuming to distinguish feasible from infeasible design variable choices by simply running the simulation for each choice. To support the exploration of the design variable space for such scenarios, an adaptive sampling technique based on machine learning models has recently been proposed. However, that approach only considers the exploration of the convergent domain and ignores additional constraints. In this paper, we present an improvement which particularly takes the fulfillment of constraints into account. We successfully apply the proposed algorithm to a toy example in up to 20 dimensions and to an industrially relevant flowsheet simulation.