The use of trade-off analysis as part of optimising designs has been an emerging technique for a number of years. However, only recently has much work been done with respect to systematically deriving the understanding of the system problem to be optimised and using this information as part of the design process. As systems have become larger and more complex then a need has arisen for suitable approaches. The system problem consists of design choices, measures for individual values related to quality attributes and weights to balance the relative importance of each individual quality attribute. In this paper, a method is presented for establishing an understanding of a system problem using the goal structuring notation (GSN). The motivation for this work is borne out of experience working on embedded systems in the context of critical systems where the cost of change can be large and the impact of design errors potentially catastrophic. A particular focus is deriving an understanding of the problem so that different solutions can be assessed quantitatively, which allows more definitive choices to be made. A secondary benefit is it also enables design using heuristic search approaches which is another area of our research. The overall approach is demonstrated through a case study which is a task allocation problem.