Correction to: Variable decomposition approach applied to multi-objective optimization for minimum powering of commercial ships

1 Correction to: Journal of Marine Science and Technology https://doi.org/10.1007/s00773-018-0551-5

In the original publication of the article Figs. 14, 26b, e, Eqs. (2), (23), (24), (27), (29) and (30) are incorrectly published. The correct figures and equations are provided in this article.

$$ \frac{{\delta {\rm DP}}}{{{\rm DP}}} = \frac{{\delta R}}{R} - \frac{{\delta \eta _{\rm P} }}{{\eta _{\rm P} }} $$

(2)

$$\begin{aligned} {\rm DP} & \propto \frac{{\rho \pi {D^2}}}{{16{\alpha _P}{\eta _R}}}{V_{\rm a}}^{3}\beta {C_{{\rm th}}}^{r} \\ & =\frac{{{8^r}{{(\rho \pi {D^2})}^{1 - r}}\beta {V_S}^{{3 - 2r}}}}{{16{\alpha _{\rm P}}{\eta _R}}}{(1 - {w_{\rm S}})^{3 - 2r}}{R^r}{(1 - t)^{ - r}} \\ \end{aligned} $$

(23)

$$ {\rm DP} \propto \frac{1}{{\eta _{R} }}(1 - w_{{\rm S}} )^{{3 - 2r}} R^{r} (1 - t)^{{ - r}} $$

(24)

$$\frac{1}{r}\frac{{\delta {\rm DP}}}{{{\rm DP}}} \approx \frac{{\delta R}}{R} - \frac{{\delta (1 - t)}}{{(1 - t)}}+0.439\frac{{\delta (1 - {w_{\rm S}})}}{{(1 - {w_{\rm S}})}} - 0.813\frac{{\delta {\eta _R}}}{{{\eta _R}}}$$

(27)

$$\begin{aligned} \frac{1}{r}\frac{{\delta {\rm DP}}}{{{\rm DP}}} & = - \frac{{\delta (1 - t)}}{{(1 - t)}}+\frac{{3 - 2r}}{r}\frac{{\delta (1 - {w_{\rm S}})}}{{(1 - {w_{\rm S}})}} - \frac{1}{r}\frac{{\delta {\eta _R}}}{{{\eta _R}}} \\ & \approx - \frac{{\delta (1 - t)}}{{(1 - t)}}+0.439\frac{{\delta (1 - {w_{\rm S}})}}{{(1 - {w_{\rm S}})}} - 0.813\frac{{\delta {\eta _R}}}{{{\eta _R}}} \\ \end{aligned} $$

(29)

$$\frac{1}{r}\frac{{\delta {\rm DP}}}{{{\rm DP}}} \approx - \frac{{\delta (1 - t)}}{{(1 - t)}}+0.439\frac{{\delta (1 - {w_t})}}{{(1 - {w_t})}} - 0.813\frac{{\delta {\eta _R}}}{{{\eta _R}}}$$

(30)