From a43620b68fa09cb6229f2b4eba101f7a03fb5174 Mon Sep 17 00:00:00 2001 From: "Jip J. Dekker" Date: Thu, 11 Mar 2021 13:03:51 +1100 Subject: [PATCH] Convert math contexts in remaining chapters --- chapters/2_background.tex | 10 +++++----- chapters/6_incremental.tex | 16 ++++++++-------- 2 files changed, 13 insertions(+), 13 deletions(-) diff --git a/chapters/2_background.tex b/chapters/2_background.tex index b086ce5..c428950 100644 --- a/chapters/2_background.tex +++ b/chapters/2_background.tex @@ -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) \(z\). diff --git a/chapters/6_incremental.tex b/chapters/6_incremental.tex index e53d1c6..e9267ba 100644 --- a/chapters/6_incremental.tex +++ b/chapters/6_incremental.tex @@ -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}.