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According to a comprehensive literature review, very few studies consider life-cycle environmental impacts in small-scale hybrid renewable energy system optimization. This paper aims to fill this gap by providing a multi-objective design framework for household-scale systems based on the technical modeling of several typical components. Solar photovoltaic, wind turbine, solar heat collector, heat pump, heat storage, battery, and as a novelty, heat insulation thickness are considered. Backup power is either drawn from the grid or produced by a diesel generator in grid-connected and off-grid scenarios, respectively.\nSingle objective optimization using genetic algorithm resulted in the least cost and the least environmental footprint options in a case study of three different locations across Europe. Then, Pareto-optimal solutions between the two extremities were explored with a multi-objective genetic algorithm.\nSingle objective results show substantial differences between environmental and economic optima, while multi-objective optimization proved to be an efficient tool to investigate the trade-offs between the two conflicting goals. Solar photovoltaics is proved to be the most competitive technology to reduce environmental impacts in the case of grid-connected systems. Off-grid systems, however, benefit the most from a balanced mix of different renewable energy sources.\nLife-cycle impacts in the design of systems involving renewables is proven to be relevant while potential applications of the framework are also revealed. 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