Abstract This paper proposes a new methodology for determining the geometrical parameters and the optimal distribution of small-scale linear Fresnel reflectors on flat roofs of urban buildings. This engineering problem is highly complex as it involves 21 variables; in contrast to present-day studies available in the literature, our method provides a global solution. The algorithm involves several stages, in which it uses multiple objective functionals: maximization of the used area of the roof, minimization of the cost, minimization of losses. The solution found by this method combines all the relevant aspects from the technical and/or economic point of views and obtains, as the final objective, the maximization of the absorbed annual energy for the stated problem.