Visual Analytics (VA) researchers frequently collaborate closely with domain experts to derive requirements and select appropriate solutions to fulfill these requirements. Despite strides made in exploring requirement and solution spaces, challenges persist due to the absence of guidance in the initial consideration space and the lack of shared problem-solving knowledge, often resulting in suboptimal solutions. To address these issues, we conducted an empirical study of VA research, with a focus on mapping the relations between requirement and solution spaces. Analyzing 220 VA papers, we formulate refined topologies for data, requirements, and solutions. We propose conceptualizing the connections between requirements, data, and solutions through knowledge graphs and utilizing solution paths to encapsulate fundamental problem-solving knowledge in visual analytics research. Through the integration of solution paths into a graph and analyzing their interconnections, we identified a subset of problem-driven design patterns that demonstrated the efficacy of our approach. By externalizing problem-solving knowledge and formulating problem-driven design patterns, our aim is to streamline the exploration of consideration space, facilitating the inclusion of "good" solutions, and establish a benchmark for shared design decisions among researchers and readers.