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Commit da2d7dbe authored by snuverink_j's avatar snuverink_j
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compile optimiser chapter: commented out unknown definition (to be fixed...

compile optimiser chapter: commented out unknown definition (to be fixed properly\!) and unused nomenclature definitions
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......@@ -56,14 +56,14 @@ Additionally, depending in which of the two spaces the algorithm uses to
% \input{../figures/tex/design_objective_space}
\end{tikzpicture}
\end{center}
\caption{The (often non-linear) mapping $f : \mathbb{R}^n \rightarrow
\mathbb{R}^M$ from design to objective space. The dashed lines represent
\caption{The (often non-linear) mapping $f : \R^n \rightarrow
\R^M$ from design to objective space. The dashed lines represent
the constraints in design space.
%and the set of solutions (Pareto front) in objective space.
}
\label{fig:des_to_obj}
\end{figure}
\nomenclature{$\mathbb{R}$}{reel numbers}
%\nomenclature{$\R$}{real numbers}
A special subset of multi-objective optimization problems where all objectives
and constraints are linear, called \textit{Multi-objective linear programs},
......@@ -88,17 +88,17 @@ A solution is said to dominate another solution if it is no worse than the
A more formal description of the dominance relation is given in
Definition~\ref{def:dom}~\cite{deb:09}.
\begin{mydef} \label{def:dom}
A point $\mathbf{x}_1$ is dominating $\mathbf{x}_2$, if both properties
\begin{itemize}
\item $f_m(\mathbf{x}_1) \geq f_m(\mathbf{x}_2) \text{,} \;\; \forall m \in
\{ 1, \dots, M \}$
\item $f_m(\mathbf{x}_1) > f_m(\mathbf{x}_2) \text{,} \;\; \exists m \in
\{1, \dots, M\}$
\end{itemize}
hold. We denote this as $\mathbf{x}_1 \preceq \mathbf{x}_2$.
\end{mydef}
\nomenclature{$\preceq$}{dominance relation operator}
%\begin{mydef} \label{def:dom}
%A point $\mathbf{x}_1$ is dominating $\mathbf{x}_2$, if both properties
%\begin{itemize}
% \item $f_m(\mathbf{x}_1) \geq f_m(\mathbf{x}_2) \text{,} \;\; \forall m \in
% \{ 1, \dots, M \}$
% \item $f_m(\mathbf{x}_1) > f_m(\mathbf{x}_2) \text{,} \;\; \exists m \in
% \{1, \dots, M\}$
%\end{itemize}
%hold. We denote this as $\mathbf{x}_1 \preceq \mathbf{x}_2$.
%\end{mydef}
%\nomenclature{$\preceq$}{dominance relation operator}
The properties of the dominance relation include transitivity
%
......
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