A mixed-integer constrained extension of the radial basis function (RBF) interpolation algorithm for computationally costly global non-convex optimization is presented. Implementation in TOM-LAB (http://tomlab.biz) solver rbfSolve is discussed. The algorithm relies on mixed-integer nonlinear (MINLP) sub solvers in TOMLAB, e.g. OQNLP, MINLPBB or the constrained DIRECT solvers (glcDirect or glcSolve). Depending on the initial experimental design, the basic RBF algorithm sometimes fails and make no progress. A new method how to detect when there is a problem is presented. We discuss the causes and present a new faster and more robust Adaptive RBF (ARBF) algorithm. Test results for unconstrained problems are discussed.