Builds and returns the two-objective ZDT3 test problem. For \(m\) objective it is defined as follows $$f(\mathbf{x}) = \left(f_1(\mathbf{x}_1), f_2(\mathbf{x})\right)$$ 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 $$g(\mathbf{x}) = 1 + \frac{9}{m - 1} \sum_{i = 2}^m \mathbf{x}_i, h(f_1, g) = 1 - \sqrt{\frac{f_1(\mathbf{x})}{g(\mathbf{x})}} - \left(\frac{f_1(\mathbf{x})}{g(\mathbf{x})}\right)\sin(10\pi f_1(\mathbf{x}))$$ and \(\mathbf{x}_i \in [0,1], i = 1, \ldots, m\). 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.
makeZDT3Function(dimensions)[smoof_multi_objective_function]
[integer(1)]
Number of decision variables.
E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000