| Ackley |
A multimodal function with many local minima and one global minimum at the origin. Features exponential and cosine components that create a complex landscape with a nearly flat outer region. |
0 |
x* = (0, 0, ..., 0) |
| Griewank |
A multimodal function that becomes more difficult as dimensionality increases. Has one global minimum at the origin and many local minima. The cosine component creates periodic structures. |
0 |
x* = (0, 0, ..., 0) |
| Rastrigin |
A highly multimodal function with many local minima arranged in a regular pattern. Based on the sphere function with added cosine modulation to create multiple peaks and valleys. |
0 |
x* = (0, 0, ..., 0) |
| Rosenbrock |
A classic optimization benchmark known as the "banana function" due to its curved valley shape. Non-convex with one global minimum in a narrow, curved valley that is difficult to locate. |
0 |
x* = (1, 1, ..., 1) |
| Schwefel |
A deceptive multimodal function where the global minimum is far from the local minima. Features a complex structure with the global optimum located near the boundary of the search space. |
0 |
x* = (420.9687, 420.9687, ..., 420.9687) |
| Sphere |
The simplest benchmark function with a single global minimum at the origin. Unimodal and convex, making it relatively easy to optimize and useful for testing basic algorithm performance. |
0 |
x* = (0, 0, ..., 0) |
