ZDT3 Function

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Description

Builds and returns the two-objective ZDT3 test problem. For m objective it is defined as follows

f(\mathbf{x}) = ≤ft(f_1(\mathbf{x}_1), f_2(\mathbf{x})\right)

with

f_1(\mathbf{x}_1) = \mathbf{x}_1, f_2(\mathbf{x}) = g(\mathbf{x}) h(f_1(\mathbf{x}_1), g(\mathbf{x}))

where

g(\mathbf{x}) = 1 + \frac{9}{m - 1} ∑_{i = 2}^m \mathbf{x}_i, h(f_1, g) = 1 - √{\frac{f_1(\mathbf{x})}{g(\mathbf{x})}} - ≤ft(\frac{f_1(\mathbf{x})}{g(\mathbf{x})}\right)\sin(10π f_1(\mathbf{x}))

and \mathbf{x}_i \in [0,1], i = 1, …, m. This function has some discontinuities in the Pareto-optimal front introduced by the sine term in the h function (see above). The front consists of multiple convex parts.

Usage

1
makeZDT3Function(dimensions)

Arguments

dimensions

[integer(1)]
Number of decision variables.

Value

[smoof_multi_objective_function]

References

E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000

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