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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. 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}. 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{}. 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. 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. 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. 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. 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. Although \gls{half-reif} is not a new technique, there are still numerous open questions.
In particular, our research raises the questions about its effectiveness for \gls{mip} solvers. 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 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. 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 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}. 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}. 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{}. 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. \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. 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. 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. 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. 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{}. \paragraph{Summary} In conclusion, this thesis presented an architecture for the \gls{rewriting} of \cmls{}.