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We present HOMERUN (Highly Optimized Multi-cloud Emission-line Ratios Usingphoto-ionizatioN), a new approach to modelling emission lines from photoionizedgas that can simultaneously reproduce all observed line intensities from a widerange of ionization levels and with high accuracy. Our approach is based on theweighted combination of multiple single-cloud photoionization models and,contrary to previous works, the novelty of our approach consists in using theweights as free parameters of the fit and constraining them with the observeddata. One of the main applications of HOMERUN is the accurate determination ofgas-phase metallicities and we show that a critical point is to allow for avariation of the N/O and S/O abundance ratios which can significantly improvethe quality of the fit and the accuracy of the results. Moreover, our approachprovides a major improvement compared to the single-cloud, constant-pressuremodels commonly used in the literature. By using high-quality literaturespectra of H ii regions where 10 to 20 emission lines (including severalauroral lines) are detected with high signal-to-noise ratio, we show that alllines are reproduced by the model with an accuracy better than 10%. Inparticular, the model is able to simultaneously reproduce [O i], [O ii], [Oiii], [S ii], and [S iii] emission lines which, to our knowledge, is anunprecedented result. Finally, we show that the gas metallicities estimatedwith our models for HII regions in the Milky Way are in agreement with thestellar metallicities than the estimates based on the Te-method. Overall, ourmethod provides a new accurate tool to estimate the metallicity and thephysical conditions of the ionized gas. It can be applied to many differentscience cases from HII regions to AGN and wherever there are emission linesfrom photoionized gas.

HOMERUN a new approach to photoionization modelling. I -- reproducing  observed emission lines with percent accuracy and obtaining accurate physical  properties of the ionized gas