Abstract-The automation of software architecture design is an important goal in software engineering. A plethora of automated design exploration techniques have been devised in the last decades to handle the complexity of making design decision in large scale, complex software systems. The common aim of these methods is the optimisation of quality attributes, such as reliability and safety. The majority of approaches use heuristic methods, such as local search or genetic algorithms, which use gradients in the fitness space to guide the search to the local optimum. When problems are constrained, search gradients are disrupted by infeasible regions, which may have a great impact on the difficulty of solving optimisation problems.Discovering the conditions under which a search heuristic will succeed or fail is critical for understanding the strengths and weaknesses of different software architecture optimisation methods. This paper investigates how to adequately characterize the features of constrained problem instances that have impact on difficulty in terms of algorithmic performance, and how such features can be defined and measured for the component deployment optimisation problem. We employ fitness landscape characterisation metrics that measure uniformity of the gradients in the search space, and investigate how two different constraints shape the search space, and as a result affect the performance of software architecture optimisation approaches.