2013-03-28T02:47:52Z pmendes@uchc.edu Mendes Pedro University of Connecticut School of Medicine

Colville function

Part of a set of benchmark functions for global optimisation

variables: 4
interval: [-10,10] (all variables)
minimum: (1,1,1,1)
minimum value: 0

f(x₁,...,x₄)= (x₁-1)² + 100 (x₁²-x₂)² + 10.1 (x₂-1)² + (x₃-1)² + 100 (x₃²-x₄)² + 10.1 (x₄-1)² + 19.8 (x₄-1)/x₂

The Colville function resides inside a long, narrow, and parabolic shaped valley. It serves as a test for premature convergence.

Defined in: De Jong, K. A. (1975) An analysis of the behavior of a class of genetic adaptive systems. PhD Thesis, University of Michigan.

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2013-03-28T02:48:47Z 2013-03-28T02:51:41Z 2013-03-28T02:51:50Z 100*(<CN=Root,Model=Colville Function,Vector=Values[x2],Reference=InitialValue>-<CN=Root,Model=Colville Function,Vector=Values[x1],Reference=InitialValue>^2)^2+(1-<CN=Root,Model=Colville Function,Vector=Values[x1],Reference=InitialValue>)^2+90*(<CN=Root,Model=Colville Function,Vector=Values[x4],Reference=InitialValue>-<CN=Root,Model=Colville Function,Vector=Values[x3],Reference=InitialValue>^2)^2+(1-<CN=Root,Model=Colville Function,Vector=Values[x3],Reference=InitialValue>)^2+10.1*((<CN=Root,Model=Colville Function,Vector=Values[x2],Reference=InitialValue>-1)^2+(<CN=Root,Model=Colville Function,Vector=Values[x4],Reference=InitialValue>-1)^2)+19.8*(<CN=Root,Model=Colville Function,Vector=Values[x2],Reference=InitialValue>-1)*(<CN=Root,Model=Colville Function,Vector=Values[x4],Reference=InitialValue>-1) 0 42 0 0 0 0 <CN=Root,Model=Colville Function,Vector=Values[Colville function],Reference=InitialValue> This table outputs time and the target function of the optimization.