From b84118430fa712e54118565175a8098496849101 Mon Sep 17 00:00:00 2001 From: "Jip J. Dekker" Date: Sun, 25 Jul 2021 10:24:58 +1000 Subject: [PATCH] Grammar pass over Conclusions --- chapters/6_conclusions.tex | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/chapters/6_conclusions.tex b/chapters/6_conclusions.tex index 8018f26..ab78fb3 100644 --- a/chapters/6_conclusions.tex +++ b/chapters/6_conclusions.tex @@ -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{}.