Digitization leads to large and complex data sets that can be used as input for optimization problems, especially for choice-based optimization problems, which is the integration of a discrete choice model into an optimization problem. We consider a high-dimensional estimation problem and a location problem under the multinomial logit (MNL) model. We integrate the machine learning methods Lasso and Ridge regression into the maximum likelihood method to estimate the MNL model. For complex data sets, this improves the estimation results and, based on that, the optimization results. We consider realistically designed synthetic location problem instances. The results are used to analyze the quality of the solutions to the location problems depending on the estimation methods used.