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

Step(5) function

Part of a set of benchmark functions for global optimisation

variables: 5
interval: [-5.12,5.12] (all variables)
minimum: (-5.12,-5.12,-5.12,-5.12,-5.12)
minimum value: -30

f(x₁,...,x₅)= 6*5+SUM(i=1,5) floor(x_i)

Step is a representative of the problem of flat surfaces. Step is a piecewise continuous step function. Flat surfaces are obstacles for optimization algorithms, because they do not give any information as to which direction is favorable. Unless an algorithm has variable step sizes, it can get stuck on one of the fl̄at plateaus. The background idea of the step function is to make the search more difficult by introducing small plateaus to the topology of an underlying continuous function.

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 30+floor(<CN=Root,Model=Step(5) function,Vector=Values[x1],Reference=InitialValue>)+floor(<CN=Root,Model=Step(5) function,Vector=Values[x2],Reference=InitialValue>)+floor(<CN=Root,Model=Step(5) function,Vector=Values[x3],Reference=InitialValue>)+floor(<CN=Root,Model=Step(5) function,Vector=Values[x4],Reference=InitialValue>)+floor(<CN=Root,Model=Step(5) function,Vector=Values[x5],Reference=InitialValue>) 2013-10-10T00:56:42Z 0 30 0 0 0 0 0 <CN=Root,Model=Step(5) function,Vector=Values[Step(5) function],Reference=InitialValue> This table outputs time and the target function of the optimization.