Testfunksjoner

Testfunksjoner, or test functions, are mathematical functions used to evaluate and compare optimization algorithms and numerical methods. They provide controlled problem landscapes with known properties and, in many cases, known global optima. By applying an algorithm to these functions, researchers can study convergence speed, robustness to noise, sensitivity to dimensionality, and behavior on multimodal or non-convex landscapes. The term is common in optimization and numerical analysis, and sometimes appears in related fields such as machine learning as benchmark problems.

Testfunksjoner are categorized along several dimensions: unimodal versus multimodal (one local minimum versus many), separable versus non-separable (dimensions that interact or not), convex versus non-convex, continuous versus discontinuous, differentiable versus non-differentiable, and noisy or constrained. Common benchmark functions include the Rosenbrock function (a narrow, curved valley leading to a global minimum), the Rastrigin function (many local minima in a roughly flat space), the Ackley function (a rugged landscape with a global optimum at the origin), the Griewank function, and Himmelblau’s function. In higher dimensions, these functions are often extended to 2–50 variables or more.

Practically, researchers report the function name, dimensionality, global optimum value and location, and performance metrics such as time to convergence, function evaluations, and solution quality. Testfunksjoner serve as a baseline before applying algorithms to real-world problems, helping to benchmark and compare methods in a standardized way.