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Grammar pass over Conclusions

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chapters/6_conclusions.tex
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@ -74,7 +74,7 @@ To determine whether a \constraint{} has to be \gls{reified}, this analysis dete
Crucially, our analysis considers the possibility of identifiers being used in multiple positions and user-defined functions.
Depending on the context of a \constraint{}, we can decide if a \gls{reif} can be avoided, if a \gls{half-reif} can be used, or if we have to use a full \gls{reif}.
We noted that \gls{half-reif} interacts with some of the existing simplification techniques in the architecture and propose alterations to accommodate them.
We noted that \gls{half-reif} interacts with some existing simplification techniques in the architecture and propose alterations to accommodate them.
Foremost, \gls{cse} can no longer always reuse the same results for identical \constraints{}, it must now consider the context of the \constraint{}.
For \constraints{} were \gls{cse} is triggered in multiple contexts, we propose rules to either use the result that is acceptable in both contexts, or create such a result.
Using this adjustment we ensure that identical \constraints{} are not duplicated and re-use the same \gls{cvar}, even when they occurred in different contexts.
@ -92,14 +92,15 @@ Additionally, we implemented two \glspl{propagator} for \gls{half-reif} \constra
In our experiments, we reaffirmed the effectiveness of the \glspl{propagator}, but we showed mixed results for the use of automatic \gls{half-reif} on a bigger scale.
While it was clearly beneficial for \gls{sat}, other \solvers{} did not seem to enjoy the same benefit and in some cases were even negatively impacted.
Although \gls{half-reif} is not a new technique, there is still a lot left to explore.
In particular, our research raises the questions about its effectiveness for \gls{mip} solvers.
Although \gls{half-reif} is not a new technique, there are still numerous open questions.
In particular, our research was unable to determine the effectiveness of \gls{half-reif} for \gls{mip} solvers.
It is clear that the use of \gls{half-reif} is beneficial in some cases, but it seems to have a negative effect in other cases.
It is thus important that we achieve a better understanding of when the latter occurs.
As also discussed by \textcite{feydy-2011-half-reif}, we see that \gls{cp} solvers are sometimes negatively impacted because \glspl{half-reif} do not fix their \gls{cvar}, requiring more search.
As a solution to this problem we could consider a form in between \gls{half-reif} and full \gls{reif}.
In this form the propagator would set the \gls{cvar} to \mzninline{true} if the \constraint{} holds, but does not propagate the negation of the \constraint{} when it is set to \mzninline{false}.
The downside of this form is that it is no longer equivalent to a logical implication (and, for example, \gls{chain-compression} would no longer be applicable), but \glspl{propagator} for this form are still easy to design/implement and they ensure that the \gls{cvar} is fixed through \gls{propagation}.
The downside of this form is that it is no longer equivalent to a logical implication, which means that measures such as \gls{chain-compression} would no longer be applicable.
However, \glspl{propagator} for this form are still easy to design/implement, and they ensure that the \gls{cvar} is fixed through \gls{propagation}.
Finally, automated \gls{half-reif} in \minizinc{} will allow new solving performance improvements by allowing \solver{} implementers to experiment with \glspl{decomp} or \glspl{propagator} for \gls{half-reified} \constraints{}.
\paragraph{Incremental Solving} Using a \cml{} as the interface for a \gls{meta-optimization} toolchain can be very intuitive and open up new opportunities.
@ -136,7 +137,7 @@ It is, however, still a significant improvement over repeatedly \gls{rewriting}
The improvements offered by these new methods may spark future research.
Primarily, they will allow and promote using \gls{meta-optimization} algorithms in \cmls{} for new problems.
It could even be worthwhile to revisit existing applications of incremental constraint modelling.
The utilisation of the presented methods might offer a significant improvement in performance, allowing the solving of more complex problems.
The utilization of the presented methods might offer a significant improvement in performance, allowing the solving of more complex problems.
Finally, new \gls{meta-optimization} techniques could require extensions of the methods presented.
\paragraph{Summary} In conclusion, this thesis presented an architecture for the \gls{rewriting} of \cmls{}.