Many problems in structural engineering can be defined as optimization problems and be solved by adopting proper optimization algorithms. This dissertation focuses on two optimization problems in structural engineering, namely, Performance-based Design Optimization (PDO) and Structural Model Updating (SMU).In recent years, there have been many studies on the sustainability and resilience of building systems during their life-cycle. In particular, the holistic design framework using a Performance-Based Engineering (PBE) approach combined with the Multi-Attribute Utility Theory (MAUT), namely PBE-MAUT, is developed to provide a robust evaluation of the building performance in terms of sustainability and resiliency attributes. In PDO, the PBE-MAUT allows engineers to rank the design alternatives through the Generalized Expected Utility (GEU) (objective function to be maximized) containing the information about the risk attitude (or perception) of the decision makers. This dissertation proposes the PDO framework for seismic hazard using two meta-heuristic algorithms, namely, Genetic Algorithm (GA), abbreviated as PDO-GA and Bayesian Optimization Algorithm (BOA), abbreviated as PD-BOA. In this framework, probabilistic approaches are used to quantify the uncertainties in the different stages of the Performance-Based Earthquake Engineering (PBEE). For the seismic hazard, artificial accelerograms compatible with the response spectrum are generated by evolutionary Power Spectral Density (PSD) for seismic loading. For the structural analysis, distributions of the Engineering Demand Parameters (EDPs) are determined by using the Kernel Density Maximum Entropy Method (KDMEM), which provides the least biased probability density function from available data sets. For the combined damage analysis and loss estimation, GEU is used to evaluate the utility of the design alternatives based on the MAUT. The proposed framework adopts a Probability of Improvement (PI) function for the acquisition function of BOA. A hypothetical three-bay, five-story steel Moment Resisting Frame (MRF) building and three-bay, nine-story steel MRF building examples demonstrate the performances of the proposed framework. Numerical models are very powerful tools used in simulation, damage detection, and evaluating physical structures. Accurate modeling of complex structures, however, remains challenging due to incomplete information (uncertainties) about the existing structure, which results in a difference between the responses of the numerical model and the measured responses of the actual "instrumented" structure. SMU is a process for improving the accuracy of a numerical model by reducing or even closing the gap between its prediction and the measured response of its physical counterpart through model parameter optimization. In this dissertation, the ABAQUS-Python Model Updating framework for overhead box beam highway sign structures is proposed. This is a Python-based framework that uses the ABAQUS software to create and analyze Finite Element (FE) models. The performance of the proposed framework is demonstrated by application to a single-post butterfly type overhead box beam sign structure on the California State Route 113, near the city of Davis, CA.