Plots

Two contours of the function are presented below:

Description and Features

• The function is not convex.
• The function is defined on n-dimensional space.
• The function is non-separable.
• The function is differentiable.

Input Domain

The function can be defined on any positive input domain but it is usually evaluated on $x_i \in [0, 10]$ for $i=1, …, n$.

Global Minima

The function has a global minimum $f(\textbf{x}^{\ast})=0$ located at $\mathbf{x^\ast}=(0, …, 0)$.

Implementation

An implementation of the Alpine N. 1 Function with MATLAB is provided below.

The function can be represented in Latex as follows:

References:

• Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation}, Vol. 4, No. 2, pp. 150–194 (2013), arXiv:1308.4008
• M. Clerc, “The Swarm and the Queen, Towards a Deterministic and Adaptive Particle Swarm Optimization, ” IEEE Congress on Evolutionary Computation, Washington DC, USA, pp. 1951-1957, 1999.