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Convert math contexts in remaining chapters

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Jip J. Dekker 2021-03-11 13:03:51 +11:00
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10
chapters/2_background.tex
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@ -76,9 +76,9 @@ problems. Its expressive language and extensive library of constraints allow
users to easily model complex problems.
Let us introduce the language by modelling the well-known \emph{Latin squares}
problem \autocite{wallis-2011-combinatorics}: Given an integer $n$, find an
$n \times n$ matrix, such that each row and column is a permutation of values
$1 \ldots n$. A \minizinc\ model encoding this problem could look as follows:
problem \autocite{wallis-2011-combinatorics}: Given an integer \(n\), find an
\(n \times n\) matrix, such that each row and column is a permutation of values
\(1 \ldots n\). A \minizinc\ model encoding this problem could look as follows:
\begin{mzn}
int: n;
@ -123,5 +123,5 @@ all constraints, or report that there is no such assignment.
This type of combinatorial problem is typically called a \gls{csp}. \minizinc
also supports the modelling of \gls{cop}, where a \gls{csp} is augmented with an
\gls{objective} $z$. In this case the goal is to find an assignment that
satisfies all constraints while minimising (or maximising) $z$.
\gls{objective} \(z\). In this case the goal is to find an assignment that
satisfies all constraints while minimising (or maximising) \(z\).

16
chapters/6_incremental.tex
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@ -309,7 +309,7 @@ neighbourhood depending on whether the previous size was successful or not.
\Cref{lst:6-adaptive} shows an adaptive version of the
\mzninline{uniform_neighbourhood} that increases the number of free variables
when the previous restart failed, and decreases it when it succeeded, within the
bounds $[0.6,0.95]$.
bounds \([0.6,0.95]\).
\begin{listing}
\mznfile{assets/mzn/6_adaptive.mzn}
@ -674,7 +674,7 @@ trailing.
Assume that we added a choice point before posting the constraint
\mzninline{c}. Then the trail stores the \emph{inverse} of all modifications
that were made to the \nanozinc\ as a result of \mzninline{c} (where
$\mapsfrom$ denotes restoring an identifier, and $\lhd$ \texttt{+}/\texttt{-}
\(\mapsfrom\) denotes restoring an identifier, and \(\lhd\) \texttt{+}/\texttt{-}
respectively denote attaching and detaching constraints):
% \mznfile{assets/mzn/6_abs_reif_trail.mzn}
@ -758,8 +758,8 @@ problem:
\mznfile{assets/mzn/6_gbac_neighbourhood.mzn}
When this predicate is called with a previous solution \mzninline{sol}, then
every \mzninline{period_of} variable has an $80\%$ chance to be fixed to its
value in the previous solution. With the remaining $20\%$, the variable is
every \mzninline{period_of} variable has an \(80\%\) chance to be fixed to its
value in the previous solution. With the remaining \(20\%\), the variable is
unconstrained and will be part of the search for a better solution.
In a non-incremental architecture, we would re-flatten the original model plus
@ -864,14 +864,14 @@ challenge~\autocite{stuckey-2010-challenge, stuckey-2014-challenge} (\texttt{gba
the \minizinc\ Challenge is shown for every instance (\emph{best known}).
For each solving method we measured the average integral of the model objective
after finding the initial solution ($\intobj$), the average best objective found
($\minobj$), and the standard deviation of the best objective found in
percentage (\%), which is shown as the superscript on $\minobj$ when running
after finding the initial solution (\(\intobj\)), the average best objective found
(\(\minobj\)), and the standard deviation of the best objective found in
percentage (\%), which is shown as the superscript on \(\minobj\) when running
\gls{lns}.
%and the average number of nodes per one second (\nodesec).
The underlying search strategy used is the fixed search strategy defined in the
model. For each model we use a round robin evaluation (\cref{lst:6-round-robin})
of two neighbourhoods: a neighbourhood that destroys $20\%$ of the main decision
of two neighbourhoods: a neighbourhood that destroys \(20\%\) of the main decision
variables (\cref{lst:6-lns-minisearch-pred}) and a structured neighbourhood for
the model (described below). The restart strategy is
\mzninline{::restart_constant(250)} \mzninline{::restart_on_solution}.