Test functions for optimization
Test functions (a.k.a. artificial landscapes) are the standardized objective functions used to evaluate optimizers — "useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance." This is the independent, academic counterpart to andrey-dik's ad-hoc Skin/Forest/Megacity/Hilly suite (population-optimization-benchmark). Source: Wikipedia.
The standard single-objective functions
- Sphere — simple unimodal baseline.
- Rosenbrock — a narrow curved valley; tests navigation of ill-conditioned ridges (cf. cma-es's affine-invariance strength).
- Rastrigin — highly multimodal, a lattice of local minima.
- Ackley — smooth outer region, multimodal interior.
- Griewank — smooth trend plus periodic oscillations.
- Himmelblau — four identical global minima.
The unimodal-vs-multimodal and separable-vs-non-separable axes are why no optimizer wins everywhere: a method tuned for smooth valleys (Rosenbrock) may fail on a multimodal lattice (Rastrigin). The article also distinguishes single-objective from multi-objective (MOP) test suites (e.g. Zitzler–Deb–Thiele, Kursawe) that probe Pareto-front approximation.
Why it matters here
Standardized functions "enable fair comparison of different optimization algorithms," and are the basis of academic suites like CEC / BBOB(COCO) — the independent yardstick the wiki's open questions call for to corroborate Dik's rankings (notably cma-es, which rates near the top on BBOB despite Dik's ~38/45 — a recorded tension). The very existence of these landscapes is a constructive proof of the no-free-lunch-theorem: benchmarks are designed to expose where each optimizer breaks.
Related
population-optimization-benchmark · no-free-lunch-theorem · metaheuristic-optimization · cma-es · differential-evolution · andrey-dik