designvariable

A design variable is a controllable parameter in a mathematical model used in design optimization. It represents a degree of freedom that can be adjusted to improve objective performance while satisfying constraints. Design variables are distinguished from state variables, which describe system behavior in a given design, and from parameters, which are fixed constants.

In formal optimization problems, the design variable vector x appears in the objective function f(x) and in constraint functions g_i(x) ≤ 0 and h_j(x) = 0. The aim is to find x within a feasible design space X that minimizes or maximizes the objective. Design variables can be continuous (real-valued), discrete (integer or binary), or mixed-integer, leading to different classes of optimization problems.

Examples include selecting cross-sectional areas in structural design, shape parameters in aerodynamic optimization, or component values in electronic circuit design. In computer-aided design (CAD) and CAE workflows, design variables parameterize a geometric model, and changes to them propagate through simulations to evaluate performance.

The collection of all admissible design variables forms the design space. Sensitivity analysis examines how small changes in design variables affect outcomes. In multidisciplinary design optimization, variables may come from multiple disciplines, and constraints reflect manufacturing, cost, and feasibility considerations. Alternatives naming include decision variables or control variables.