Mathematical Programming Computation

, Volume 10, Issue 4, pp 597–629 | Cite as

RBFOpt: an open-source library for black-box optimization with costly function evaluations

  • Alberto Costa
  • Giacomo NanniciniEmail author
Full Length Paper


We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the solution methodology implemented in the open-source library RBFOpt, available on COIN-OR. The algorithm is based on the Radial Basis Function method originally proposed by Gutmann (J Glob Optim 19:201–227, 2001., which builds and iteratively refines a surrogate model of the unknown objective function. The two main methodological contributions of this paper are an approach to exploit a noisy but less expensive oracle to accelerate convergence to the optimum of the exact oracle, and the introduction of an automatic model selection phase during the optimization process. Numerical experiments show that RBFOpt is highly competitive on a test set of continuous and mixed-integer nonlinear unconstrained problems taken from the literature: it outperforms the open-source solvers included in our comparison by a large amount, and performs slightly better than a commercial solver. Our empirical evaluation provides insight on which parameterizations of the algorithm are the most effective in practice. The software reviewed as part of this submission was given the Digital Object Identifier (DOI)


Black-box optimization Derivative-free optimization Global optimization Radial basis function Open-source software Mixed-integer nonlinear programming 

Mathematics Subject Classification

90C56 90C30 65K05 97N80 



The authors are grateful for partial support by the SUTD-MIT International Design Center under grant IDG21300102. The research of A. C. was partially conducted at the Future Resilient Systems and the Future Cities Laboratory at the Singapore-ETH Centre (SEC). The SEC was established as a collaboration between ETH Zurich and National Research Foundation (NRF) Singapore (FI 370074011, FI 370074016) under the auspices of the NRF’s Campus for Research Excellence and Technological Enterprise (CREATE) program.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and The Mathematical Programming Society 2018

Authors and Affiliations

  1. 1.Future Cities Laboratory ProgramETH ZurichSingaporeSingapore
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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