Forecasting often involves high-dimensional predictors which have nonlinear relationships with the outcome of interest. Nonparametric additive index models can capture these relationships, while addressing the curse of dimensionality. This paper introduces a new algorithm, Sparse Multiple Index (SMI) Modelling, tailored for estimating high-dimensional nonparametric/semi-parametric additive index models, while limiting the number of parameters to estimate, by optimising predictor selection and predictor grouping. The SMI Modelling algorithm uses an iterative approach based on mixed integer programming to solve an $\ell_0$-regularised nonlinear least squares optimisation problem with linear constraints. We demonstrate the performance of the proposed algorithm through a simulation study, along with two empirical applications to forecast heat-related daily mortality and daily solar intensity.