Builds and returns the two-objective ZDT6 test problem. For \(m\) objective it is defined as follows $$f(\mathbf{x}) = \left(f_1(\mathbf{x}), f_2(\mathbf{x})\right)$$ with $$f_1(\mathbf{x}) = 1 - \exp(-4\mathbf{x}_1)\sin^6(6\pi\mathbf{x}_1), f_2(\mathbf{x}) = g(\mathbf{x}) h(f_1(\mathbf{x}_1), g(\mathbf{x}))$$ where $$g(\mathbf{x}) = 1 + 9 \left(\frac{\sum_{i = 2}^{m}\mathbf{x}_i}{m - 1}\right)^{0.25}, h(f_1, g) = 1 - \left(\frac{f_1(\mathbf{x})}{g(\mathbf{x})}\right)^2$$ and \(\mathbf{x}_i \in [0,1], i = 1, \ldots, m\). This function introduced two difficulities (see reference): 1. the density of solutions decreases with the closeness to the Pareto-optimal front and 2. the Pareto-optimal solutions are nonuniformly distributed along the front.
makeZDT6Function(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