---

Genetic Algorithm is known as a generalized method of stochastic search and has been successfully applied to various types of optimization problems. By GA s it is expected to improve the solution at the expense of additional computational effort. One of the key points which controls the accuracy and convergence rate of such a process is the selected method of coding/decoding of the original problem variables and the discrete feasibility space to be searched by GAS. In this paper, a direct index coding (DIC) is developed and utilized for the discrete sizing optimization of structures. The GA operators are specialized and adopted for this kind of encoded chromosomes and are compared to those of traditional GA S. The well-known lO-bar truss example from literature is treated here as a comparison benchmark, and the outstanding computational efficiency and stability of the proposed method is illustrated. The application of the proposed encoding method is not limited to truss structures and can also be directly applied to frame sizing problems.

---

Well-known seismic design codes have offered an alternative equivalent static procedure for practical purposes instead of verifying design trials with complicated step-y-step dynamic analyses. Such a pattern of base-shear distribution over the building height will enforce its special stiffness and strength distribution which is not necessarily best suited for seismic design. The present study, utilizes a hybrid optimization procedure to seek for the best stiffness distribution in moment-resistant building frames. Both continuous loading pattern and discrete sizing variables are treated as optimization design variables. The continuous part is sampled by Harmony Search algorithm while a variant of Ant Colony Optimization is utilized for the discrete part. Further search intensification is provided by Branch and Bound technique. In order to verify the design candidates, static, modal and time-history analyses are applied regarding the code-specific design spectra. Treating a number of building moment-frame examples, such a hyper optimization resulted in new lateral loading patterns different from that used in common code practice. It was verified that designing the moment frames due to the proposed loading pattern can result in more uniform story drifts. In addition, locations of the first failure of columns were transmitted to the upper/less-critical stories of the frame. This achievement is important to avoid progressive collapse under earthquake excitation.

---

Tuned mass dampers are common solutions for passive control of bridge responses against dynamic loads. The present work concerns non-uniform support excitation of earthquakes as the dynamic loading source and studies TMD performance in controlling consequent vertical response of simply supported steel bridges. Charged system search as a recent meta-heuristic is successfully utilized to optimize TMD parameters whereas the dynamic response is evaluated via rigorous step-by-step time-history finite element analysis. As another issue, superiority of multiple TMD’s over single TMD is investigated for the present problem after unifying their parameters via optimization. Treating a bridge model as the case study under a number of real-world recorded earthquakes, the error of uniform support excitation under such a non-uniform case is evaluated. Superior efficiency of the utilized charged system search over popular genetic algorithm is observed for this problem. The results also revealed that how advantageous is the application of optimally designed multiple TMD in controlling dynamic vibration modes of such a distributed mass structure