Ackley01 objective function.
The Ackley01 global optimization problem is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for for
Adorio, E. MVF - “Multivariate Test Functions Library in C for Unconstrained Global Optimization”, 2005
Todo
the -0.2 factor in the exponent of the first term is given as -0.02 in Jamil et al.
Ackley02 objective function.
The Ackley02 global optimization problem is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
Ackley03 objective function.
The Ackley03 global optimization problem is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
Todo
I think the minus sign is missing in front of the first term in eqn3 in Jamil. This changes the global minimum
Ackley04 objective function.
Adjiman objective function.
The Adjiman global optimization problem is a multimodal minimization problem defined as follows:
with, and .
Global optimum: for
Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
Alpine01 objective function.
The Alpine01 global optimization problem is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for for
Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
Alpine02 objective function.
The Alpine02 global optimization problem is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for for
Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194.
Todo
eqn 7 in has the wrong global minimum value.
AMGM objective function.
The AMGM (Arithmetic Mean - Geometric Mean Equality) global optimization problem is a multimodal minimization problem defined as follows
Here, represents the number of dimensions and for .
Global optimum: for for
Gavana, A. Global Optimization Benchmarks and AMPGO