This dissertation investigates black-box optimization methods and their applicationsto complex engineering decision problems. Many modern optimization tasks involve objectives that are expensive to evaluate, analytically unknown, or dependent on simulation results. When such problems also include constraints, uncertainties, or multiple objectives, conventional deterministic optimization becomes impractical. The research focuses on developing efficient algorithms for these settings and applying them to representative problems in power system operation. The first part of the dissertation presents the LEAP-BO algorithm, a high- dimensional Bayesian optimization method that improves sampling efficiency under limited evaluation budgets. LEAP-BO introduces a local exploration and adaptive progression strategy that balances global and local search without relying on problem- specific assumptions. Analytical reasoning and numerical experiments confirm its consistent improvement over baseline BO methods in moderate- to high-dimensional problems. The second part develops the Interactive Multi-Objective Wish-List (IMOWL) framework, which provides a mathematical foundation for verifying the achievability of user preferences in multi-objective optimization. Based on this theory, the IMOWL- BO algorithm is implemented to perform interactive optimization with adaptive stopping and preference verification. The method demonstrates reliable convergence and efficiency on benchmark problems with conflicting objectives. The final part applies the black-box optimization perspective to stochastic power- system problems. A Bayesian-optimization-based, impact-driven scenario-reduction approach is proposed to select representative uncertainty scenarios according to their influence on operational feasibility rather than statistical similarity. The reduced sets improve the capability to preserve constraint-satisfaction accuracy especially for problems with high level of nonlinearity between scenarios and their impact on constraints. Building on this, a BO-assisted frequency-secure optimal power flow (OPF) framework is developed. The formulation incorporates stochastic OPF with frequency- security constraints, renewable-generation uncertainty, and operational contingencies. A reduced-set preparation stage, based on the proposed impact-driven scenario- reduction method, is introduced to identify the most influential scenarios in an offline study mode. The resulting reduced set is then used in real-time OPF to improve compliance with frequency-security limits, such as rate-of-change-of-frequency and frequency-nadir, while maintaining computational tractability. Together, these studies form a unified investigation that spans algorithmic design, theoretical analysis, and practical application. The results show that Bayesian- optimization-based strategies can be effectively adapted for high-dimensional, multi- objective, and uncertainty-driven problems, providing practical improvements in efficiency and reliability for black-box optimization in engineering systems.