International Journal of Civil Engineering, Vol. 12, No. 4, Transaction A: Civil Engineering, December 2014 Shape-size optimization of single-layer barrel vaults using improved magnetic charged system search A. Kaveh 1, *, B. Mirzaei 2 , A. Jafarvand 2 Received: February 2014, Revised: July 2014, Accepted: October 2014 Abstract 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. Keywords: Shape-size optimization, Barrel vaults, Improved magnetic Charged system search, Open application programming interface. 1. Introduction Optimization has become the most interesting and effective subject in the field of structural design. The presentation of many meta-heuristic algorithms in the last three decades is a continuing developmental process in the field of structural optimization. On the other hand, the increasing use of braced barrel vaults as a kind of light- weight space structures is inevitable. Optimization of barrel vaults, therefore, can be a highly effective issue in engineering design of these spatial structures. Meta-heuristics algorithms are recent generation of the optimization approaches to solve complex problems. These methods explore the feasible region based on both randomization and some specified rules through a group of search agents. Laws of natural phenomena are usually source of the rules. Genetic Algorithm (GA) is introduced by Holland [1] and Goldberg [2]. It is inspired by biological evolutions theory. Particle swarm optimization (PSO) is introduced by Eberhart and Kennedy [3]. It simulates social behavior, and it is inspired by the migration of animals in a bird flock or fish school. The particle swarm algorithm is applied to truss optimization with dynamic constraints [4]. Ant Colony Optimization (ACO) is presented by Dorigo et al. [5]. * Corresponding author: alikaveh@iust.ac.ir 1 Professor, Centre of Excellence for Structural Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran 2 Department of Civil Engineering, University of Zanjan, Zanjan, Iran It imitates foraging behavior of ant colonies. There are several other natural-inspired algorithms such as Simulated Annealing (SA) presented by Kirkpatrick et al. [6], Harmony Search (SA) introduced by Geem et al. [7], Big Bang–Big Crunch algorithm (BB–BC) presented by Erol and Eksin [8], and improved by Kaveh and Talatahari [9]. Due to good performance of these algorithms and their simple implementation, they have been widely used for solving various problems in different fields of science and engineering. One of the most recent meta-heuristic algorithms is the Charged System Search (CSS) proposed by Kaveh and Talatahari [10]. Electric laws of physics and the Newtonian laws of mechanics are used for guiding the Charged Particles (CPs) to explore the locations of the optimum. Colliding Bodies Optimization (CBO) is developed by Kaveh and Mahdavi [11] which is the first parameter independent method. Some applications of metaheuristic algorithms can be found in [12-14]. In the field of size optimization of single-layer barrel vaults frames some studies are carried out. Kaveh and Eftekhar have presented optimal design of barrel vault frames using IBB-BC algorithm [15], in which a 173-bar single layer barrel vault is optimized under both symmetrical and unsymmetrical load cases. In a study by the authors of present work, size optimization of some single layer barrel vault frames via IMCSS algorithm [16] has been presented. In a study carried out by Parke [17], several different configurations of braced barrel vaults have been investigated using the stiffness method of analysis. Three different configurations have been analysed, each with five different span/height ratios and under both cases of symmetrical and non-symmetrical imposed nodal loads. Structural Engineering