This paper represents new approaches for calculating, designing, and optimizing prestressed arched trusses with a tie member. Structural systems with long spans, such as trusses, beams, frames, etc., are subjected to a considerable/substantial risk of losing load-carrying capacity because of the different types of loads used. Some traditional design methods define the values of prestressing force in the tie member and internal forces in the truss elements to avoid this load capacity loss. However, the accuracy and limits of the determination of the forces are not necessarily known. The authors offer a new type of prestressed arched truss and some new approaches in the design and calculation process to solve these disadvantages. The study’s main objectives were to design an innovative and new geometric form of prestressed arched truss, which allows the development of high-value prestressing force, to optimize a new truss for reducing self-weight, increasing load-carrying capacity compared to its analogs. The force, stiffness matrix, and simulated annealing methods were used during the study. A new advance to the optimization of prestressed arched truss suggested by the authors reduces the self-weight and improves the load capacity of the truss by 8–17%, depending on the span.