---

A two-stage optimization method is presented by employing the evolutionary structural optimization (ESO) and ant colony optimization (ACO), which is called ESO-ACO method. To implement ESO-ACO, size optimization is performed using ESO, first. Then, the outcomes of ESO are employed to enhance ACO. In optimization process, the weight of double layer grid is minimized under various constraints which artificial ground motion is used to calculate the structural responses. The presence or absence of elements in bottom and web grids and also cross-sectional areas are selected as design variables. The numerical results reveal the computational advantages and effectiveness of the proposed method.

---

For reliability-based topology optimization (RBTO) of double layer grids, a two-stage optimization method is presented by applying “Solid Isotropic Material with Penalization” and “Ant Colony Optimization” (SIMP-ACO method). To achieve this aim, first, the structural stiffness is maximized using SIMP. Then, the characteristics of the obtained topology are used to enhance ACO through six modifications. As numerical examples, reliability-based topology designs of typical double layer grids are obtained by ACO and SIMP-ACO methods. Their numerical results reveal the effectiveness of the proposed SIMPACO method for the RBTO of double layer grids.

---

Endurance Time Method (ET) is a dynamic analysis in which structures are subjected to intensifying accelerograms that are optimized in a way that seismic performance of structures can be estimated at different hazard levels with the best possible accuracy. For the currently available ET accelerograms, regardless of the shaking characteristic, an excitation level is recognized as a representative of a specific hazard level, when the acceleration and the displacement spectrum produced by the ET accelerograms up to that excitation level will be compatible with the acceleration and the displacement spectrum associated with that hazard level. This study compares the shaking characteristics of the current ET accelerograms with the ground motions. For this purpose, distribution of plastic cycles and the equivalent number of the cycles are considered as shaking properties of a motion. This study suggests a procedure to achieve the best possible consistency between the equivalent number of cycles of the current ET records and the ground motions. Moreover, a procedure to generate the new generation and optimization of the ET accelerograms which are more consistent with the ground motions are suggested.

---

In this paper, for topology optimization of double layer grids, an efficient optimization method is presented by combination of Imperialist Competitive Algorithm (ICA) and Gravitational Search Algorithm (GSA) which is called ICA-GSA method. The present hybrid method is based on ICA but the moving of countries toward their relevant imperialist is done using the law of gravity of GSA. In topology optimization process, the weight of the structure is minimized subjected to displacements of joints, internal stress and slenderness ratio of members constraints. Through numerical example, topology optimization of a typical large-scale double layer grid is obtained by ICA, GSA and ICA-GSA methods. The numerical results indicate that the proposed algorithm, ICA-GSA, executes better than ICA, GSA and the other methods presented in the literatures for topology optimization of largescale skeletal structures.

---

Endurance Time method is a time history dynamic analysis in which structures are subjected to increasing excitations. These excitations are known as endurance time excitation functions (ETEF). This study proposes a new method for generating ETEFs. In the proposed method, a new basis function for representing ETEFs is introduced. This type of ETEFs representation creates an intelligent space for this ETEFs simulating optimization problem. The proposed method is then applied in order to simulate new ETEFs. To investigate the efficiency of this proposed optimization space, newly generated ETEFs are compared with those simulated by conventional approaches. Results show an improvement in the accuracy of ETEFs as well as the reduction in the required computational time.