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

Schaffer F7(2) function

Part of a set of benchmark functions for global optimisation

variables: 2
interval: [-100,100] (all variables)
minimum: (0,0)
minimum value: 0

f(x₁,x₂)= (1+ sin(50* (sqrt(x₁²+x₂²))^0.2)² * sqrt(sqrt(x₁²+x₂²)) )²

The Schaffer F7 function is difficult because to reach the global minimum concentric barriers need to be overcome. which are higher closer to the minimum. There are local minima everywhere in the search space. This function is a good test for escaping local minima. This is the 2-dimensional version of the function.

Defined in: Schaffer, J.D. (1985) Some experiments in machine learning using vector evaluated genetic algorithms PhD Thesis, Vanderbilt University, Nashville, TN (USA).

CC0 1.0 Universal: To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. Please refer to CC0 Public Domain Dedication for more information.

2012-08-31T17:29:26Z 2012-08-31T17:02:24Z 2012-08-31T17:02:23Z ((1+sin(50*sqrt(<CN=Root,Model=Schaffer F7(2) function,Vector=Values[x1],Reference=InitialValue>^2+<CN=Root,Model=Schaffer F7(2) function,Vector=Values[x2],Reference=InitialValue>^2)^0.2))*sqrt(sqrt(<CN=Root,Model=Schaffer F7(2) function,Vector=Values[x1],Reference=InitialValue>^2+<CN=Root,Model=Schaffer F7(2) function,Vector=Values[x2],Reference=InitialValue>^2)))^2 0 0 0 0 <CN=Root,Model=Schaffer F7(2) function,Vector=Values[Schaffer F7(2) function],Reference=InitialValue> This table outputs time and the target function of the optimization.