singlecriterion

Singlecriterion refers to optimization problems or decision models that involve a single objective to be optimized, as opposed to multi-criteria or multi-objective problems that consider several objectives simultaneously. In mathematical form, a singlecriterion problem typically seeks to minimize or maximize a scalar function f(x) over a feasible set X defined by constraints, with x representing decision variables.

The singlecriterion framing emphasizes a unique target, such as cost, time, energy, or profit, which guides the selection of the best feasible solution. This contrasts with multi-criteria approaches, where trade-offs among conflicting objectives are analyzed, often leading to a set of Pareto-optimal solutions rather than a single optimum.

Common solution methods depend on the nature of the objective and the feasible region. Linear singlecriterion problems use linear programming techniques; quadratic and other convex problems can employ convex optimization methods. Nonlinear singlecriterion problems may require gradient-based algorithms, Lagrangian methods, or sequential approximation. When the feasible region is discrete or combinatorial, integer programming or mixed-integer programming techniques are used. In some cases, unknown parameters or uncertainty lead to stochastic or robust singlecriterion optimization, where the objective is optimized under probabilistic or worst-case considerations.

Applications span engineering, economics, logistics, and operations where a single measure is prioritized—such as minimizing production cost, maximizing revenue, or reducing completion time. The term is sometimes written as “single-criterion” or “single criterion,” and may appear in literature as a contrast to multi-criteria optimization.