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Constrained optimization of high-dimensional numerical problems plays animportant role in many scientific and industrial applications. Functionevaluations in many industrial applications are severely limited and noanalytical information about objective function and constraint functions isavailable. For such expensive black-box optimization tasks, the constraintoptimization algorithm COBRA was proposed, making use of RBF surrogate modelingfor both the objective and the constraint functions. COBRA has shown remarkablesuccess in solving reliably complex benchmark problems in less than 500function evaluations. Unfortunately, COBRA requires careful adjustment ofparameters in order to do so.  In this work we present a new self-adjusting algorithm SACOBRA, which isbased on COBRA and capable to achieve high-quality results with very fewfunction evaluations and no parameter tuning. It is shown with the help ofperformance profiles on a set of benchmark problems (G-problems, MOPTA08) thatSACOBRA consistently outperforms any COBRA algorithm with fixed parametersetting. We analyze the importance of the several new elements in SACOBRA andfind that each element of SACOBRA plays a role to boost up the overalloptimization performance. We discuss the reasons behind and get in this way abetter understanding of high-quality RBF surrogate modeling.

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control