Arg-e-Bam ͑Bam Citadel͒ was a large urban complex of ancient earthen architecture in an arid environment. This complex was renowned for its majestic size and its peculiar impression on the visitors at first sight. The Arg-e-Bam was built on approximately 20 hectares of land over a period of 1,800 years; it was abandoned 180 years ago. The Arg was a gallery of different ancient architectural elements in its original urban concept of a city in the pre-medieval era. The whole area was constructed entirely of earthen material and was heavily damaged by the 2003 Bam earthquake. The level of destruction is about 70% on major parts of this huge monument.

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In shear wall-based buildings, locating the shear wall in plan has an important role in the resistance of seismic loading. In this article, the minimum torsion is considered as one of the main goals for optimal layout of shear walls, unlike the common method that accepts a certain torsion limit. The method presented is in accordance with the principles of design codes with emphasis on reaching the least possible torsion effect. By using a multi-objective function, based on the Pareto solutions, the torsion function behaves against the cost of a structure subjected to constraints of flexural strength, shear strength, and drift. This approach has the ability to layout shear walls in irregular plans and those which have high architectural limits. Also, it can fulfill the main goal of a structural engineer in order to satisfy the requirements of an architectural plan and obtain its minimum torsion effect as well. This method has been applied to various types of regular and irregular plans according to the classification of seismic design codes. Results show that besides minimizing the cost, the torsion effect reaches the minimum possible value considered by the seismic design code, as compared with other methods.

A new method for structural optimization is presented for successive approximation of the objective function and constraints in conjunction with Lagrange multipliers approach. The focus is on presenting the methodology with simple examples. The basis of the iterative algorithm is that after each iteration, it brings the approximate location of the estimated minimum closer to the exact location, gradually. In other words, instead of the linear or parabolic term used in Taylor expansion, which works based on a short step length, an arch is used that has a constant curvature but a longer step length. Using this approximation, the equations of optimization involve the Lagrange multipliers as the only unknown variables. The equations which depend on the design variables are decoupled linearly as these variables are directly obtained. One mathematical example is solved to explain in details how the method works. Next, the method is applied to the optimization of a simple truss structure to explain how the method can be used in structural optimization. The same problems have been solved by penalty method and compared. The results from both methods have been the same. However, because of the long step length and reduction in the number of variables, the speed of convergence has been higher in the presented method.