Salomon objective function.
This class defines the Salomon 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.
Sargan objective function.
This class defines the Sargan 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.
SawtoothXY objective function.
Schaffer 1 objective function.
This class defines the Schaffer 1 global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for for
Mishra, S. Some new test functions for global optimization and performance of repulsive particle swarm method. Munich Personal RePEc Archive, 2006, 2718
Schaffer 2 objective function.
This class defines the Schaffer 2 global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for for
Mishra, S. Some new test functions for global optimization and performance of repulsive particle swarm method. Munich Personal RePEc Archive, 2006, 2718
Schaffer 3 objective function.
This class defines the Schaffer 3 global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Mishra, S. Some new test functions for global optimization and performance of repulsive particle swarm method. Munich Personal RePEc Archive, 2006, 2718
Schaffer 4 objective function.
This class defines the Schaffer 4 global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Mishra, S. Some new test functions for global optimization and performance of repulsive particle swarm method. Munich Personal RePEc Archive, 2006, 2718
Schmidt-Vetters objective function.
This class defines the Schmidt-Vetters global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for
Todo
equation seems right, but [7.07083412 , 10., 3.14159293] produces a lower minimum, 0.193973
Schwefel 1 objective function.
This class defines the Schwefel 1 global optimization problem. This is a unimodal minimization problem defined as follows:
Where, in this exercise, .
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.
Schwefel 2 objective function.
This class defines the Schwefel 2 global optimization problem. This is a unimodal 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.
Schwefel 4 objective function.
This class defines the Schwefel 4 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for:math:x_i = 1 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.
Schwefel 6 objective function.
This class defines the Schwefel 6 global optimization problem. This is a unimodal 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.
Schwefel 20 objective function.
This class defines the Schwefel 20 global optimization problem. This is a unimodal 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
Jamil #122 is incorrect. There shouldn’t be a leading minus sign.
Schwefel 21 objective function.
This class defines the Schwefel 21 global optimization problem. This is a unimodal 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.
Schwefel 22 objective function.
This class defines the Schwefel 22 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.
Schwefel 26 objective function.
This class defines the Schwefel 26 global optimization problem. This 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
Schwefel 36 objective function.
This class defines the Schwefel 36 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.
Shekel 5 objective function.
This class defines the Shekel 5 global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
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
this is a different global minimum compared to Jamil#130. The minimum is found by doing lots of optimisations. The solution is supposed to be at [4] * N, is there any numerical overflow?
Shekel 7 objective function.
This class defines the Shekel 7 global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
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
this is a different global minimum compared to Jamil#131. This minimum is obtained after running lots of minimisations! Is there any numerical overflow that causes the minimum solution to not be [4] * N?
Shekel 10 objective function.
This class defines the Shekel 10 global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
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
Found a lower global minimum than Jamil#132... Is this numerical overflow?
Shubert 1 objective function.
This class defines the Shubert 1 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for (and many others).
Gavana, A. Global Optimization Benchmarks and AMPGO
Todo
Jamil#133 is missing a prefactor of j before the cos function.
Shubert 3 objective function.
This class defines the Shubert 3 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for (and many others).
Gavana, A. Global Optimization Benchmarks and AMPGO
Todo
Jamil#134 has wrong global minimum value, and is missing a minus sign before the whole thing.
Shubert 4 objective function.
This class defines the Shubert 4 global optimization problem. This is a multimodal minimization problem defined as follows:
Here, represents the number of dimensions and for .
Global optimum: for (and many others).
Gavana, A. Global Optimization Benchmarks and AMPGO
Todo
Jamil#135 has wrong global minimum value, and is missing a minus sign before the whole thing.
Simpleton objective function.
SineEnvelope objective function.
This class defines the SineEnvelope global optimization problem. This 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
Todo
Jamil #136
Sinusoidal objective function.
Six Hump Camel objective function.
This class defines the Six Hump Camel global optimization problem. This is a multimodal minimization problem defined as follows:
with for .
Global optimum: for or
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.
Sodp objective function.
This class defines the Sum Of Different Powers global optimization problem. This 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
Sphere objective function.
This class defines the Sphere 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
Jamil has stupid limits
SphericalSinc objective function.
Spike objective function.
Step objective function.
This class defines the Step 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.
Step objective function.
This class defines the Step 2 global optimization problem. This 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
Step 3 objective function.
Stochastic objective function.
This class defines the Stochastic global optimization problem. This is a multimodal minimization problem defined as follows:
The variable is a random variable uniformly distributed in .
Here, represents the number of dimensions and for .
Global optimum: for for
Gavana, A. Global Optimization Benchmarks and AMPGO
StretchedV objective function.
This class defines the Stretched V global optimization problem. This is a multimodal minimization problem defined as follows:
Where, in this exercise:
Here, represents the number of dimensions and for .
Global optimum: for when .
Adorio, E. MVF - “Multivariate Test Functions Library in C for Unconstrained Global Optimization”, 2005
Todo
All the sources disagree on the equation, in some the 1 is in the brackets, in others it is outside. In Jamil#142 it’s not even 1. Here we go with the Adorio option.
StyblinskiTang objective function.
This class defines the Styblinski-Tang 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.