@@ -23,7 +23,7 @@ Again, just like in our previous example, we shall consider agent and variable t
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@@ -23,7 +23,7 @@ Again, just like in our previous example, we shall consider agent and variable t
In our example, the cost function will be defined as a maximisation of the surveillance space covered.
In our example, the cost function will be defined as a maximisation of the surveillance space covered.
In this case, Daleks who are the only ones capable of covering an area should be highly rewarded for doing so, and areas which can be covered by two Daleks who can also cover another area should ultimately be surveiled only by one of them.
In this case, Daleks who are the only ones capable of covering an area should be highly rewarded for doing so, and areas which can be covered by two Daleks who can also cover another area should ultimately be surveiled only by one of them.
Considering the position of the 5 Daleks, we can model the prolem as the following constraints graph:
Considering the position of the 5 Daleks, we can model the prolem as the following constraints graph (see \ref{fig:dalek}):
\begin{figure}
\begin{figure}
\centering
\centering
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@@ -46,7 +46,7 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
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@@ -46,7 +46,7 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
\label{fig:dalek}
\label{fig:dalek}
\end{figure}
\end{figure}
With utility functions modeled as follows, translating the necessity to cover a maximal number of zones.
With utility functions modeled as given in \ref{tab:dalek-utilities}, translating the necessity to cover a maximal number of zones.
\begin{table}[ht]
\begin{table}[ht]
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@@ -227,11 +227,6 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
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@@ -227,11 +227,6 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
\end{tabular}
\end{tabular}
\caption{Binary utility functions according to surveillance directions}
\caption{Binary utility functions according to surveillance directions}
\label{tab:dalek-utilities}
\label{tab:dalek-utilities}
\end{table}
\end{table}
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@@ -420,6 +415,9 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
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@@ -420,6 +415,9 @@ Considering the position of the 5 Daleks, we can model the prolem as the followi
\subsection{Modelling of the problem with SCADCOP API}
\subsection{Modelling of the problem with SCADCOP API}
This problem can be modelled as follows with the scadcop library.