We present a constraint-based methodology which is successfully applied to a variety of engineering problems from a wide range of disciplines. Initially conceived from investigations of the engineering design process, the methodology has helped design engineers to identify and understand the initial limitations placed upon a system. Written as a set of algebraic expressions, the design objectives and design constraints can be formulated and minima found using numerical optimization techniques. These solutions provide initial configurations for the system, corresponding to how "true" all of the constraints are. A bespoke constraint-based modelling environment has been created which embodies the methodology. This is able to resolve large systems, comprising over 100 degrees-of-freedom, using an assortment of optimization routines-direct, gradient and evolutionary algorithms. These algorithms are appropriate for a number of problem types and their inclusion increase the scope of applicability of the methodology which is demonstrated using case studies from a number of engineering domains. Machines and mechanisms; human modelling; force and flow; structural geology and discrete disassembly processes are all studied using constraint-based formulations. The contribution of the paper lies in thus proving that complex (heterogeneous) systems-of-systems can be solved if the connectivity between the systems is expressed using constraint-rules.