---

Barrel vaults are attractive space structures that cover large area without intermediate supports. In this paper, the charged

search system (CSS) optimization algorithm is employed for optimal design of barrel vaults. This method utilizes the governing

laws of Coulomb and Gauss from electrostatics and the Newtonian law of mechanics. The results demonstrate the efficiency of

the discrete CSS algorithm compared to other meta-heuristic algorithms.

---

In this paper, the problem of simultaneous shape and size optimization of single-layer barrel vault frames which contains both of discrete and continuous variables is addressed. In this method, the improved magnetic charged system search (IMCSS) is utilized as the optimization algorithm and the open application programming interface (OAPI) plays the role of interfacing analysis software with the programming language. A comparison between the results of the present method and some existing algorithms confirms the high ability of this approach in simultaneous shape and size optimization of the practical and large-scale spatial structures.