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One of the most important factors that affects construction costs of highways is the earthwork cost. On the other hand, the earthwork cost strongly depends on the design of vertical alignment or project line. In this study, at first, the problem of vertical alignment optimization was formulated. To this end, station, elevation and vertical curve length in case of each point of vertical intersection (PVI) were considered as decision variables. The objective function was considered as earthwork cost and constraints were assumed as the maximum and minimum grade of tangents, minimum elevation of compulsory points, and the minimum length of vertical curves. For solving this optimization problem, the Colliding Bodies Optimization (CBO) algorithm was employed and results were compared with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). In order to evaluate the effectiveness of formulation and CBO algorithm, three different highways were designed with respect to three different terrains including level, rolling and mountainous. After designing the preliminary vertical alignment for each highway, the optimal vertical alignments were determined by different optimization algorithms. The results of this research show that the CBO algorithm is superior to GA and PSO. Percentage of optimality (saving in earthworks cost) by CBO algorithm for level, rolling and mountainous terrains was determined as 44.14, 21.42 and 22.54%, respectively.

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In recent decades, steel was used more than other materials in structural engineering. However, the safety of high-heat steel structures dramatically decreased, due to steel mechanical properties. Therefore, the design process should be done in a way that the structure has the required resistance at high temperatures and during the fire, according to the effect of heat on the performance of steel structures. In this study, the optimal design process of steel structures is considered under the fire load. In the optimal design process, the failure risk of the structure members is considered as a constraint. Therefore, the optimization process requires thermal and structural reliability analysis. A parametric model has been used to analyse the reliability of the structure in the fire limit state. The optimization process is also performed based on the Colliding Bodies Optimization (CBO) algorithm. In order to evaluate the optimal design process, 3 and 6-floors frames have been investigated. The results showed that the members' condition is effective in the structural resistance for the thermal loading. On the contrary, the structure design based on the reliability under the fire load provides a proper prediction from the behaviour of the structure and satisfies the requirements for the common state of design.

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In this study, the finite element model updating was simulated by reducing the stiffness of the members. Due to lack of access to the experimental results, the data obtained from an analytical model were used in the proposed structural damage scenarios. The updating parameters for the studied structures were defined as a reduction coefficient applied to the stiffness of the members. Parameter variations were calculated by solving an unconstrained nonlinear optimization problem. The objective function in the optimization problem was proposed based on the Multi-Degree-of-Freedom (MDOF) equations of motion as well as the dynamic characteristics of the studied structure. Only the first natural frequency of the damaged structure was used in the proposed updating process, and only one vibration mode was used in the updating problem and damage identification procedure. In addition, as elimination of high-order terms in the proposed formula introduced errors in the final response, the variations of natural frequency and vibration mode for higher-order terms were included in the free vibration equation of the proposed objective function. The Colliding Bodies Optimization (CBO) algorithm was used to solve the optimization problem. The performance of the proposed method was evaluated using the numerical examples, where different conditions were applied to the studied structures. The results of the present study showed that, the proposed method and formulation were capable of efficiently updating the dynamic parameters of the structure as well as identifying the location and severity of the damage using only the first natural frequency of the structure.