Human activities are currently at an unsustainable level and a significant reduction in greenhouse gas emissions is essential to limit global warming. Industry, which accounts for a large share of these emissions, has an important role to play, particularly in its energy consumption for heat production. One of the issues of this transformation is to assess, among all the possible energy solutions, those that are most likely to achieve the objective of reducing emissions of greenhouse gases without incidentally increasing other environmental impacts. The study proposes a method for classifying nondominated solutions found using an optimisation model based on life cycle analysis (LCA), energy and economic indicators. This is complemented by integrating constraints represented by sustainability limits, i.e. an acceptable level of impact defined by planetary boundaries. A case study of a paper industry process in Italy is presented to highlight the capability of the method. For this example, the ranking shows that-with the current LCA weighting factors-waste heat recovered using a heat pump powered by electricity has the highest ranking. However, a scoring for which exceeding sustainable levels is penalized gives a higher ranking to solutions composed of a mix of several energy sources. Moreover, if one focuses only on the global warming indicator, the most effective solutions far exceed sustainable levels for other indicators. It is therefore necessary to adopt a comprehensive environmental approach to avoid shifting environmental burdens to other impact categories. On the other hand, no solution compatible with all sustainable levels has been found. It is therefore necessary to go further by proposing a global approach detailing the level of impact that each sector can have while ensuring an overall sustainable level.