Although controller devices highly improve the seismic performance of civil structures, they usually incur enormous financial costs. A variety of sequential methods for minimizing the cost function have been proposed in the literature. In most of these methods, the control system is optimally designed after the best structural configuration is provided. However, such sequential procedures are unable to yield the best overall design. This paper discusses a combined structural and control optimization approach in which the structural mass and controlled system energy are simultaneously minimized. To this end, a twofold objective function is defined by linearly combining the structural mass and linear quadratic regulator (LQR) performance index. It is shown that the optimal value of this objective function depends on the initial condition, and to circumvent this problem, an alternative objective function is introduced which allows for solving the problem of initial condition dependency. Given the complexity of the problem, a variable neighborhood search (VNS) metaheuristic method is developed. The performance of the developed method is demonstrated through case studies involving the determination of structural responses for shear-type frames. The case studies are presented for evaluating and comparing the effectiveness of the proposed simultaneous technique and the conventional sequential method. The responses of the structures are determined under an array of strong ground motions. The results of the comparative analyses revealed that the simultaneously optimized cases using the proposed methodology had superior dynamic performance compared to the sequentially optimized cases.

尽管控制器设备可以极大地改善土木结构的抗震性能，但它们通常会产生巨大的财务成本。文献中已经提出了各种使成本函数最小的顺序方法。在大多数这些方法中，控制系统是在提供最佳结构配置后进行优化设计的。但是，这样的顺序过程无法产生最佳的总体设计。本文讨论了一种结构与控制相结合的优化方法，该方法同时将结构质量和受控系统能量最小化。为此，通过线性组合结构质量和线性二次调节器（LQR）性能指标来定义双重目标函数。结果表明，该目标函数的最优值取决于初始条件，为了解决这个问题，引入了一个替代目标函数，该函数可以解决初始条件依赖性问题。考虑到问题的复杂性，开发了一种可变邻域搜索（VNS）元启发式方法。通过案例研究证明了所开发方法的性能，其中涉及确定剪切型框架的结构响应。案例研究用于评估和比较所提出的同步技术和常规顺序方法的有效性。在一系列强烈的地面运动下确定了结构的响应。比较分析的结果表明，与顺序优化的案例相比，使用所提出的方法同时优化的案例具有更好的动态性能。