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

Sphere function

Part of a set of benchmark functions for global optimisation

variables: 3
interval: [-2.56,5.12] (all variables)
minimum: (0,0,0)

f(x1,x2,x3)=x1²+x2²+x3²

This is a 3-dimensional convex function (spherical). It is the easiest 3D function to minimize. It is separable, in that each parameter could be minimized independently. It serves as a test case for convergence velocity.

First defined (in this context) by: 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 <CN=Root,Model=Sphere function,Vector=Values[x1],Reference=InitialValue>^2+<CN=Root,Model=Sphere function,Vector=Values[x2],Reference=InitialValue>^2+<CN=Root,Model=Sphere function,Vector=Values[x3],Reference=InitialValue>^2 0 0 0 0 0 <CN=Root,Model=Sphere function,Vector=Values[Sphere function],Reference=InitialValue> This table outputs time and the target function of the optimization.