49 lines
4.5 KiB
TeX
49 lines
4.5 KiB
TeX
\noindent{}In previous chapters we explored \gls{rewriting} as a definitive linear process, but to solve real-world problems \gls{meta-optimisation} algorithms are often used.
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These algorithms usually require solving similar problems repeatedly, with only slight modifications, thousands of times.
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Examples of these methods are:
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\begin{itemize}
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\item Multi-objective search \autocite{jones-2002-multi-objective}.
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Optimising multiple objectives is often not supported directly in solvers.
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Instead, it can be solved using a \gls{meta-optimisation} approach: find a solution to a (single-objective) problem, then add more \constraints{} to the original problem and repeat.
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\item \gls{lns} \autocite{shaw-1998-local-search}.
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This is a very successful \gls{meta-optimisation} algorithm to quickly improve solution quality.
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After finding a (sub-optimal) solution to a problem, \constraints{} are added to restrict the search in the \gls{neighbourhood} of that \gls{sol}.
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When a new \gls{sol} is found, the \constraints{} are removed, and \constraints{} for a new \gls{neighbourhood} are added.
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\item Online Optimisation \autocite{jaillet-2021-online}.
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These techniques can be employed when the problem rapidly changes.
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An \instance{} is continuously updated with new data, such as newly available jobs to be scheduled or customer requests to be processed.
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\item Diverse Solution Search \autocite{hebrard-2005-diverse}.
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Here we aim to provide a set of solutions that are sufficiently different from each other in order to give human decision makers an overview of the possible \glspl{sol}.
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Diversity can be achieved by repeatedly solving a problem instance with different \glspl{objective}.
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\item Interactive Optimisation \autocite{belin-2014-interactive}.
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In some scenarios it can be useful to allow a user to directly provide feedback on \gls{sol} found by the \solver{}.
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The feedback in the form of \constraint{} are added back into the problem, and a new \gls{sol} is generated.
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Users may also take back some earlier feedback and explore different aspects of the problem to arrive at the best \gls{sol} that suits their needs.
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\end{itemize}
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All of these examples have in common that a \instance{} is solved, new \constraints{} are added, the resulting \instance{} is solved again, and the \constraints{} may be removed again.
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The usage of these algorithms is not new to \cmls{} and they have proven to be very useful \autocite{schrijvers-2013-combinators, rendl-2015-minisearch, schiendorfer-2018-minibrass, ek-2020-online, ingmar-2020-diverse}.
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In its most basic form, a simple scripting language is sufficient to implement these algorithms, by repeatedly \gls{rewriting} and solving the adjusted \instances{}.
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While improvements of the \gls{rewriting} process, such as the ones discussed in previous chapters, can increase the performance of these approaches, the overhead of rewriting an almost identical model may still prove prohibitive.
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It warrants direct support from the \cml{} architecture.
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In this chapter we introduce two methods to provide this support:
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\begin{itemize}
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\item We introduce the notion of \gls{rbmo} algorithms.
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Using a minimal extension to a \cml{} and its target \solver{}, we can model \gls{meta-optimisation} methods and rewrite them into efficient \glspl{slv-mod}.
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The \solver{} will then incrementally execute the methods through the use of \solver{} \glspl{restart}
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This method avoids the need of repeatedly \gls{rewriting} the \instance{} all together.
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\item Alternatively, we extend our architecture with an incremental interface for adding and removing \constraints{}.
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Although this method does not avoid repeatedly \gls{rewriting} the \instance{}, it uses \gls{incremental-rewriting} to reduce the \gls{rewriting} to the changes to the \instance{}.
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This approach can be used when an incremental method cannot be described using \gls{rbmo} or when the required extensions are not available for the target \solver{}.
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\end{itemize}
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The rest of the chapter is organised as follows.
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\Cref{sec:6-modelling} discusses the declarative modelling of \gls{rbmo} methods in a \cml{}.
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\Cref{sec:6-solver-extension} introduces the method to rewrite these \gls{meta-optimisation} definitions into efficient \glspl{slv-mod} and the minimal extension required from the target \gls{solver}.
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\Cref{sec:6-incremental-compilation} introduces the alternative method that extends our architecture with an incremental \constraint{} modelling interface.
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\Cref{sec:inc-experiments} reports on the experimental results of both approaches.
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