  Well placement optimization is commonly performed using population-based
global stochastic search algorithms. These optimizations are computationally
expensive due to the large number of multiphase flow simulations that must be
conducted. In this work, we present an optimization framework in which these
simulations are performed with low-fidelity (LF) models. These LF models are
constructed from the underlying high-fidelity (HF) geomodel using a global
transmissibility upscaling procedure. Tree-based machine-learning methods,
specifically random forest and light gradient boosting machine, are applied to
estimate the error in objective function value (in this case net present value,
NPV) associated with the LF models. In the offline (preprocessing) step,
preliminary optimizations are performed using LF models, and a clustering
procedure is applied to select a representative set of 100--150 well
configurations to use for training. HF simulation is then performed for these
configurations, and the tree-based models are trained using an appropriate set
of features. In the online (runtime) step, optimization with LF models, with
the machine-learning correction, is conducted. Differential evolution is used
for all optimizations. Results are presented for two example cases involving
the placement of vertical wells in 3D bimodal channelized geomodels. We compare
the performance of our procedure to optimization using HF models. In the first
case, 25 optimization runs are performed with both approaches. Our method
provides an overall speedup factor of 46 relative to optimization using HF
models, with the best-case NPV within 1% of the HF result. In the second case
fewer HF optimization runs are conducted (consistent with actual practice), and
the overall speedup factor with our approach is about 8. In this case, the
best-case NPV from our procedure exceeds the HF result by 3.8%
