The New Horizons mission has returned hyperspectral data for Pluto’s surface consisting of complex, not directly modelisable spectra. A radiative transfer model that accurately represents the complexity of the putative surface structure and mix of components poses a high-dimensional inverse problem, with 50-60 independent variables. We develop an efficient resolution method using progressive metaheuristics, and present the most accurate quantitative data on Pluto’s surface composition to date.