Parsopoulos objective function.
This class defines the Parsopoulos global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional Parsopoulos function
Global optimum: This function has infinite number of global minima in R2,
at points ,
where
and
In the given domain problem, function has 12 global minima all equal to zero.
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.
Pathological objective function.
This class defines the Pathological global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and
for
.
Two-dimensional Pathological function
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.
Paviani objective function.
This class defines the Paviani global optimization problem. This is a multimodal minimization problem defined as follows:
with 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
think Gavana web/code definition is wrong because final product term shouldn’t raise x to power 10.
Peaks objective function.
Two-dimensional Peaks function
Penalty 1 objective function.
This class defines the Penalty 1 global optimization problem. This is a imultimodal minimization problem defined as follows:
Where, in this exercise:
And:
Here, represents the number of dimensions and
for
.
Two-dimensional Penalty01 function
Global optimum: for
for
Gavana, A. Global Optimization Benchmarks and AMPGO
Penalty 2 objective function.
This class defines the Penalty 2 global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
Here, represents the number of dimensions and
for
.
Two-dimensional Penalty02 function
Global optimum: for
for
Gavana, A. Global Optimization Benchmarks and AMPGO
PenHolder objective function.
This class defines the PenHolder global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional PenHolder function
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.
PermFunction 1 objective function.
This class defines the PermFunction1 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and
for
.
Two-dimensional PermFunction01 function
Global optimum: for
for
Mishra, S. Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions. Munich Personal RePEc Archive, 2006, 1005
Todo
line 560
PermFunction 2 objective function.
This class defines the Perm Function 2 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and
for
.
Two-dimensional PermFunction02 function
Global optimum: for
for
Mishra, S. Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions. Munich Personal RePEc Archive, 2006, 1005
Todo
line 582
Picheny objective function.
Two-dimensional Picheny function
Pinter objective function.
This class defines the Pinter global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
Where and
.
Here, represents the number of dimensions and
for
.
Two-dimensional Pinter function
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.
Plateau objective function.
This class defines the Plateau global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and
for
.
Two-dimensional Plateau function
Global optimum: for
for
Gavana, A. Global Optimization Benchmarks and AMPGO
Powell objective function.
This class defines the Powell global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and
for
.
Global optimum: for
for
Powell, M. An iterative method for finding stationary values of a function of several variables Computer Journal, 1962, 5, 147-151
Power sum objective function.
This class defines the Power Sum global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise,
Here, for
.
Global optimum: for
Gavana, A. Global Optimization Benchmarks and AMPGO
Price 1 objective function.
This class defines the Price 1 global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional Price01 function
Global optimum: for
or
or
or
.
Price, W. A controlled random search procedure for global optimisation Computer Journal, 1977, 20, 367-370
Price 2 objective function.
This class defines the Price 2 global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional Price02 function
Global optimum: for
Price, W. A controlled random search procedure for global optimisation Computer Journal, 1977, 20, 367-370
Price 3 objective function.
This class defines the Price 3 global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional Price03 function
Global optimum: for
,
,
,
.
Price, W. A controlled random search procedure for global optimisation Computer Journal, 1977, 20, 367-370
Todo
Jamil #96 has an erroneous factor of 6 in front of the square brackets
Price 4 objective function.
This class defines the Price 4 global optimization problem. This is a multimodal minimization problem defined as follows:
with for
.
Two-dimensional Price04 function
Global optimum: for
,
and
Price, W. A controlled random search procedure for global optimisation Computer Journal, 1977, 20, 367-370