J Glob Optim (2017) 69:117–136
GOSAC: global optimization with surrogate
approximation of constraints
· Joshua D. Woodbury
Received: 24 March 2016 / Accepted: 10 January 2017 / Published online: 28 January 2017
© Springer Science+Business Media New York (outside the USA) 2017
Abstract We introduce GOSAC, a global optimization algorithm for problems with com-
putationally expensive black-box constraints and computationally cheap objective functions.
The variables may be continuous, integer, or mixed-integer. GOSAC uses a two-phase opti-
mization approach. The ﬁrst phase aims at ﬁnding a feasible point by solving a multi-objective
optimization problem in which the constraints are minimized simultaneously. The second
phase aims at improving the feasible solution. In both phases, we use cubic radial basis
function surrogate models to approximate the computationally expensive constraints. We
iteratively select sample points by minimizing the computationally cheap objective function
subject to the constraint function approximations. We assess GOSAC’s efﬁciency on compu-
tationally cheap test problems with integer, mixed-integer, and continuous variables and two
environmental applications. We compare GOSAC to NOMAD and a genetic algorithm (GA).
The results of the numerical experiments show that for a given budget of allowed expensive
constraint evaluations, GOSAC ﬁnds better feasible solutions more efﬁciently than NOMAD
and GA for most benchmark problems and both applications. GOSAC ﬁnds feasible solutions
with a higher probability than NOMAD and GOSAC.
This material is based upon work supported by the U.S. Department of Energy, Ofﬁce of Science, Ofﬁce of
Advanced Scientiﬁc Computing Research, Applied Mathematics program under Contract Number
Electronic supplementary material The online version of this article (doi:10.1007/s10898-017-0496-y)
contains supplementary material, which is available to authorized users.
Joshua D. Woodbury
Lawrence Berkeley National Laboratory, Computational Research Division, Center for
Computational Sciences and Engineering, Berkeley, CA, USA
Swiss Re, Armonk, NY, USA