Damavandi objective function.
This class defines the Damavandi global optimization problem. This 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.
Deb 1 objective function.
This class defines the Deb 1 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: . The number of global minima is that are evenly spaced in the function landscape, where represents the dimension of the problem.
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.
Deb 3 objective function.
This class defines the Deb 3 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: . The number of global minima is that are evenly spaced in the function landscape, where represents the dimension of the problem.
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.
Decanomial objective function.
This class defines the Decanomial function global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Gavana, A. Global Optimization Benchmarks and AMPGO
Deceptive objective function.
This class defines the Deceptive global optimization problem. This is a multimodal minimization problem defined as follows:
Where is a fixed non-linearity factor; in this exercise, . The function is given by:
Here, represents the number of dimensions and for .
Global optimum: for for
Gavana, A. Global Optimization Benchmarks and AMPGO
Todo
this function was taken from the Gavana website. The following code is based on his code. His code and the website don’t match, the equations are wrong.
Deckkers-Aarts objective function.
This class defines the Deckkers-Aarts global optimization problem. This 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
jamil solution and global minimum are slightly wrong.
DeflectedCorrugatedSpring objective function.
This class defines the Deflected Corrugated Spring function global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise, and .
Here, represents the number of dimensions and for .
Global optimum: for for
Gavana, A. Global Optimization Benchmarks and AMPGO
Todo
website has a different equation to the gavana codebase. The function below is different to the equation above. Also, the global minimum is wrong.
De Jong Function No. 5
DeVilliers-Glasser 1 objective function.
This class defines the DeVilliers-Glasser 1 function global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise, and .
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.
DeVilliers-Glasser 2 objective function.
This class defines the DeVilliers-Glasser 2 function global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise, and .
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.
Dixon and Price objective function.
This class defines the Dixon and Price global optimization problem. This 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
Gavana code not correct. i array should start from 2.
Dolan objective function.
This class defines the Dolan global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Gavana, A. Global Optimization Benchmarks and AMPGO
DropWave objective function.
This class defines the DropWave global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Gavana, A. Global Optimization Benchmarks and AMPGO