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

Schaffer F6 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)= 0.5 + (sin(sqrt(x₁²-x₂²))² - 0.5) / (1 + 0.001 (x₁² + x₂²))²

The Schaffer F6 function is difficult because the global minimum is surrounded by concentric maxima which are higher closer to the minimum. This is a good test for escaping local minima.

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

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2012-08-31T17:29:26Z 2012-08-31T17:02:24Z 2012-08-31T17:02:23Z 0.5+(sin(sqrt(<CN=Root,Model=Schaffer F6 function,Vector=Values[x1],Reference=InitialValue>^2-<CN=Root,Model=Schaffer F6 function,Vector=Values[x2],Reference=InitialValue>^2))^2-0.5)/(1+0.001*(<CN=Root,Model=Schaffer F6 function,Vector=Values[x1],Reference=InitialValue>^2+<CN=Root,Model=Schaffer F6 function,Vector=Values[x2],Reference=InitialValue>^2))^2 0 0 0 0 <CN=Root,Model=Schaffer F6 function,Vector=Values[Schaffer F6 function],Reference=InitialValue> This table outputs time and the target function of the optimization.