2012-08-31T17:02:03Z pmendes@uchc.edu Mendes Pedro University of Connecticut School of Medicine

Holder table 2 function

Part of a set of benchmark functions for global optimisation

variables: 2
interval: [-10,10] (all variables)
global minima: (8.05502,9.66459), (-8.05502,9.66459), (8.05502,-9.66459), (-8.05502,-9.66459)
minimum value: -19.20850

f(x₁,x₂)=- abs( sin(x₁) cos(x₂) exp( abs( 1 - sqrt(x₁² + x₂²) / π ) ) )

The holder table function has four global minima close to the corners of the search space. In addition it has many other local minima, arranged in a regular pattern. The function is separable so in principle it could be minimized by two independent searches in one direction (each of the parameters).

Defined in: Mishra, S.K. (2006) Some new test functions for global optimization and performance of repulsive particle swarm method. Munich Personal RePEc Archive paper 2718 (http://mpra.ub.uni-muenchen.de/2718/).

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2012-08-31T17:29:26Z 2012-08-31T17:02:24Z 2012-08-31T17:02:23Z -abs(sin(<CN=Root,Model=Holder table 2 function,Vector=Values[x1],Reference=InitialValue>)*cos(<CN=Root,Model=Holder table 2 function,Vector=Values[x2],Reference=InitialValue>)*exp(abs(1-sqrt(<CN=Root,Model=Holder table 2 function,Vector=Values[x1],Reference=InitialValue>^2+<CN=Root,Model=Holder table 2 function,Vector=Values[x2],Reference=InitialValue>^2)/pi))) 0 0 0 0 <CN=Root,Model=Holder table 2 function,Vector=Values[Holder table 2 function],Reference=InitialValue> This table outputs time and the target function of the optimization.