<p>Long span enclosures for which the roof is barrel vaulted and supported by prestressed cables have recently been popular in many long-span enclosures. However, the present design practice does not consider the energy distribution in between reliability and modal dynamics as single tasks. Such separation leaves some gaps such as stiffness tuning based on static assumptions; other pathways of energy are rarely even quantified, and probabilistic safety is just added at the end. The present study fills out that void and creates a completely associated optimization scheme for barrel vaulted structures with cables, where every stage strengthens and checks subsequent sets. The approach commences with a sequential modal frequency sensitivity analysis model, associating geometry, material properties, and cable pretension with frequency shifts, sensitivity-weighted stiffness values being produced, substantiating the way with which cables determine the first three vibration modes-all within an array of relations. These critical and information-structured sensitivity measures feed a hybrid energy flow allocation model where bending, axial, and cable energies are iteratively balanced, applied reductions to bending concentration in the direction of approximately 15%. These maps of energy flow are then introduced into an evolutionary constraint propagation network model embedding nonlinear equilibrium conditions into an improved shuffled Jaya algorithm where peak stresses are estimated to reduce in the order of 10–13%, with rod and cable force effectiveness improved. With regard to structural reliability, it is examined using a surrogate-assisted dynamic reliability mapping model integrating stochastic load patterns coupled with surrogate predictors, where nearly 20% of the surface changes from low-to-high reliability zones. Finally, a multi-stage adaptive cable force redistribution model reads its map of reliability to re-tune the forces on the cables that generates a rise of about 8% in stiffness and a decrease in probability of failure of around 25%. The attractive thing with chaining these models is that one integrated framework brings together modal control, energy balance, optimization of equilibrium, and probabilistic safety as a continuum in adaptive design using cables endowed with barrel vaults, thus yielding vaults with demonstrably higher stability, reliability, and long-term efficiency.</p>