The purpose of this paper is to propose a new method for the automatic composition of both encoding schemes and search operators for system architecture optimization. The method leverages prior work that identified a set of six patterns that appear often in system architecture decision problems (down-selecting, combining, assigning, partitioning, permuting, and connecting). First, the user models the architecture space as a directed graph, where nodes are decisions belonging to one of the aforementioned patterns, and edges are dependencies between decisions that affect architecture enumeration (e.g., the outcome of decision 1 affects the number of alternatives available for decision 2). Then, based on a library of encoding scheme and operator fragments that are appropriate for each pattern, an algorithm automatically composes an encoding scheme and corresponding search operators by traversing the graph. The method is demonstrated in two case studies: a study integrating three architectural decisions for constructing a portfolio of earth observing satellite missions, and a study integrating eight architectural decisions for designing a guidance navigation and control system. Results suggest that this method has comparable search performance to hand-crafted formulations from experts. Furthermore, the proposed method drastically reducing the need for practitioners to write new code.