MD(A)O stands for multidisciplinary design (analysis and) optimization. Basically, MDAO involves using computer simulations and mathematics to model, analyze, and semi-automatically design, the best possible systems. "Systems" might include aircraft, spacecraft, buildings, or really any entity that can be modeled and where we care about performance.
M (Multidisciplinary) - This means that multiple analysis disciplines are involved in the simulation or design process. Examples of disciplines might include aerodynamics, structures, weights, stability & control, and cost / finance.
D (Design) - The ultimate goal of MDAO is to produce good designs. In a broad sense, the design of a product is the input to an analysis code, and the outputs are metrics which tell us how well the design performs and whether it is feasible.
A (Analysis) - Many people in the field will use "A" in MDAO to explicitly state that all MDAO codes perform some kind of analysis. When a simulation is used to analyze a design rather than perform numeric optimization, the term MDA can be used.. My lab at Michigan prefers to simply use MDO since optimization implies that analysis is being performed.
O (Optimization) - Broadly used, the word optimization simply means the process of making something better. In the context of MDAO, optimization refers to a set of specialized mathematical techniques that are used to find the "best" (optimal) design possible that meets a set of requirements. It is typical in MDAO (especially where geometry is a design variable) to use the techniques of constrained nonlinear optimization (or nonlinear programming).
The header image of my site is a 2D rendering of the 3D Rosenbrock Function (also known as the "banana function") which is a challenging test case for an optimizer because it has subtle valleys to find.
Some challenges in MDAO include: