System architecting is one of the first stages of the engineering problem-solving process. Pivotal decisions regarding the system's overall configuration are taken in this phase. Consequently, decision support tools like system architecture optimization are needed to effectively assess the architectural design space. However, system architecture optimization problems include several features that make them challenging to tackle with traditional optimization techniques, including multiple objectives and mixed-discrete, hierarchical design spaces.

This work examines three algorithms capable of handling the mixed-discrete and multi-objective nature of system architecture optimization problems: genetic algorithms (such as NSGA-II), Bayesian optimization (BO), and the Deep Deterministic Policy Gradient (DDPG) reinforcement learning framework. These algorithms act as the engines that power three strategies capable of addressing hierarchical design spaces: \textit{global exploration}, \textit{nested optimization}, and \textit{decision chain}. While global exploration optimizes all design variables in a single loop and uses imputation on the inactive variables, the nested optimization method divides the problem into multiple hierarchical optimization loops. In contrast, the decision chain approach reframes the problem into a sequential decision-making process within an environment where an agent's actions alter design instances.

Test problems of varying complexity are used to evaluate the suitability of these algorithms and strategies. First, an airfoil optimization problem demonstrates the basic functionality of the selected algorithms with satisfactory results comparable to those found in the literature for the same problem. Next, a mixed-discrete version of the ZDT1 multi-objective problem is evaluated for different problem sizes and proportions of continuous and discrete variables. In this family of problems, the NSGA-II algorithm emerges as the most reliable and best-performing. At the same time, DDPG struggles with many variables, and Bayesian optimization runs into computational performance issues when dealing with large discrete combinatorial spaces.

Later, the architecture optimization strategies are evaluated on two versions of the Goldstein problem, a hierarchical and multi-objective test case. In the first version, which only considers eight architectures, all three strategies show competency in solving the optimization problem, but the global exploration strategy consistently shows the best performance. The decision chain strategy is discarded from further study at this stage due to relatively low performance and implementation difficulties. The second version of the Goldstein problem can be adjusted to different degrees of hierarchy and numbers of architectures. In this case, global exploration rises again as the best-performing strategy.

Finally, a real-world aileron structural optimization study at GKN Fokker shows that the implemented global exploration and nested strategies can find better designs than a random sampling of the design space. The best design for this test problem is achieved with a two-level nested strategy, combining NSGA-II in the outer loop and Bayesian optimization in the inner loop.

In conclusion, this research proposes three adaptive strategies powered by various algorithms to solve system architecture optimization problems. The findings suggest a preference for global exploration when a complete design vector can be pre-established. Otherwise, the nested optimization strategy, which can combine different algorithms' strengths and does not need a predefined design vector, emerges as the most suitable choice for more complex scenarios.