More work on the incremental chapter

Pipfile.lock

@@ -26,15 +26,15 @@
         },
         "minizinc-python": {
             "git": "https://github.com/MiniZinc/minizinc-python",
-            "ref": "5231948b09c4fe8ed3780b3c71abed75d038a759"
+            "ref": "0becdd6e346c1021b26901de44dc1fc7fd9ac48c"
         },
         "pygments": {
             "hashes": [
-                "sha256:bc9591213a8f0e0ca1a5e68a479b4887fdc3e75d0774e5c71c31920c427de435",
+                "sha256:37a13ba168a02ac54cc5891a42b1caec333e59b66addb7fa633ea8a6d73445c0",
-                "sha256:df49d09b498e83c1a73128295860250b0b7edd4c723a32e9bc0d295c7c2ec337"
+                "sha256:b21b072d0ccdf29297a82a2363359d99623597b8a265b8081760e4d0f7153c88"
             ],
             "index": "pypi",
-            "version": "==2.7.4"
+            "version": "==2.8.0"
         }
     },
     "develop": {}

assets/glossary.tex

@@ -64,7 +64,7 @@ dedicated algorithms or rewriting rules to better handle the global constraint},
 \newglossaryentry{gls-lns}{
   name={large neighbourhood search},
   description={Large Neighbourhood Search (LNS) is a meta-search algorithm that
-repeatedly restricts the search space, applying a \gls{neighbourhood}, to
+repeatedly restricts the search space, \ie applying a \gls{neighbourhood}, to
 quickly find better solutions to a problem},
 }
 

assets/mzn/2_knapsack.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{c}{\PYZpc{} Problem parameters}
 \PY{k+kt}{enum}\PY{l+s}{ }\PY{n+nv}{TOYS}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{n+nv}{football}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{tennisball}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{stuffed\PYZus{}lama}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{stuffed\PYZus{}elephant}\PY{p}{\PYZcb{}}\PY{p}{;}
 \PY{k+kt}{array}\PY{p}{[}\PY{n+nv}{TOYS}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{toy\PYZus{}joy}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{p}{[}\PY{l+m}{63}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{12}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{50}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{100}\PY{p}{]}\PY{p}{;}

assets/mzn/6_abs_reif_result.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{n+nv}{c}\PY{l+s}{ }\PY{esc}{$\mapsto$}\PY{l+s}{ }\PY{l}{true}\PY{l+s}{ }\PY{esc}{$\sep$}\PY{l+s}{ }\PY{p}{[}\PY{p}{]}
 \PY{n+nv}{x}\PY{l+s}{ }\PY{esc}{$\mapsto$}\PY{l+s}{ }\PY{n+nf}{mkvar}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m}{10}\PY{o}{..}\PY{l+m}{10}\PY{p}{)}\PY{l+s}{ }\PY{esc}{$\sep$}\PY{l+s}{ }\PY{p}{[}\PY{p}{]}
 \PY{n+nv}{y}\PY{l+s}{ }\PY{esc}{$\mapsto$}\PY{l+s}{ }\PY{n+nf}{mkvar}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m}{10}\PY{o}{..}\PY{l+m}{10}\PY{p}{)}\PY{l+s}{ }\PY{esc}{$\sep$}\PY{l+s}{ }\PY{p}{[}\PY{p}{]}

assets/mzn/6_abs_reif_trail.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{c}{\PYZpc{} Posted c}
 \PY{l}{true}\PY{l+s}{ }\PY{esc}{$\lhd$}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{p}{[}\PY{n+nv}{c}\PY{p}{]}
 \PY{c}{\PYZpc{} Propagated c = true}

assets/mzn/6_adaptive.mzn

@@ -1,8 +1,15 @@
-predicate adaptiveUniform(array[int] of var int: x, float: initialDestrRate) =
+predicate adaptive_uniform(array[int] of var int: x, float: init_rate) =
-  let { var float: rate; } in
+  let {
-  if     status() = START then rate = initialDestrRate
+    var float: rate;
-  elseif status() = UNSAT then rate = min(last_val(rate)-0.02,0.6)
+  } in if status() = START then
-  else                         rate = max(last_val(rate)+0.02,0.95)
+    rate = init_rate
-  endif /\
+  elseif status() = UNSAT then
-  forall(i in index_set(x))
+    rate = min(last_val(rate) - 0.02, 0.6)
-        (if uniform(0.0,1.0) > rate then x[i] = sol(x[i]) else true endif);
+  else
+    rate = max(last_val(rate) + 0.02, 0.95)
+  endif
+  /\ forall(i in index_set(x)) (
+    if uniform(0.0, 1.0) > rate then
+      x[i] = sol(x[i])
+    endif
+  );

assets/mzn/6_adaptive.mzntex

@@ -1,10 +1,17 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{adaptiveUniform}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{initialDestrRate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{adaptive\PYZus{}uniform}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{init\PYZus{}rate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{rate}\PY{p}{;}\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{initialDestrRate}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{rate}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{elseif}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{UNSAT}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{min}\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{rate}\PY{p}{)}\PY{o}{\PYZhy{}}\PY{l+m}{0.02}\PY{p}{,}\PY{l+m}{0.6}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{max}\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{rate}\PY{p}{)}\PY{o}{+}\PY{l+m}{0.02}\PY{p}{,}\PY{l+m}{0.95}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{init\PYZus{}rate}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{elseif}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{UNSAT}\PY{l+s}{ }\PY{k}{then}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{min}\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{rate}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+s}{ }\PY{l+m}{0.02}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{0.6}\PY{p}{)}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{(}\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+m}{1.0}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{l}{true}\PY{l+s}{ }\PY{k}{endif}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{max}\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{rate}\PY{p}{)}\PY{l+s}{ }\PY{o}{+}\PY{l+s}{ }\PY{l+m}{0.02}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{0.95}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{1.0}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{rate}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_basic_complete.mzn

@@ -1,8 +1,11 @@
 array[1..n] of var 1..n: x;  % decision variables
 var int: cost;               % objective function
-% ... some constraints defining the problem
+
+% --- some constraints defining the problem ---
+
 % The user-defined LNS strategy
-predicate my_lns() = basic_lns(uniformNeighbourhood(x,0.2));
+predicate my_lns() = basic_lns(uniform_neighbourhood(x, 0.2));
+
 % Solve using my\_lns, restart every 500 nodes, overall timeout 120 seconds
 solve ::on_restart("my_lns") ::restart_constant(500) ::timeout(120)
       minimize cost;

assets/mzn/6_basic_complete.mzntex

@@ -1,9 +1,12 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k+kt}{array}\PY{p}{[}\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{n}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{n}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{;}\PY{l+s}{ }\PY{l+s}{ }\PY{c}{\PYZpc{} decision variables}
 \PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{cost}\PY{p}{;}\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{c}{\PYZpc{} objective function}
-\PY{c}{\PYZpc{} ... some constraints defining the problem}
+
+\PY{c}{\PYZpc{} --- some constraints defining the problem ---}
+
 \PY{c}{\PYZpc{} The user-defined LNS strategy}
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{my\PYZus{}lns}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{basic\PYZus{}lns}\PY{p}{(}\PY{n+nf}{uniformNeighbourhood}\PY{p}{(}\PY{n+nv}{x}\PY{p}{,}\PY{l+m}{0.2}\PY{p}{)}\PY{p}{)}\PY{p}{;}
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{my\PYZus{}lns}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{basic\PYZus{}lns}\PY{p}{(}\PY{n+nf}{uniform\PYZus{}neighbourhood}\PY{p}{(}\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{0.2}\PY{p}{)}\PY{p}{)}\PY{p}{;}
+
 \PY{c}{\PYZpc{} Solve using my\_lns, restart every 500 nodes, overall timeout 120 seconds}
 \PY{k}{solve}\PY{l+s}{ }\PY{p}{:}\PY{p}{:}\PY{n+nf}{on\PYZus{}restart}\PY{p}{(}\PY{l+s}{\PYZdq{}}\PY{l+s}{my\PYZus{}lns}\PY{l+s}{\PYZdq{}}\PY{p}{)}\PY{l+s}{ }\PY{p}{:}\PY{p}{:}\PY{n+nf}{restart\PYZus{}constant}\PY{p}{(}\PY{l+m}{500}\PY{p}{)}\PY{l+s}{ }\PY{p}{:}\PY{p}{:}\PY{n+nf}{timeout}\PY{p}{(}\PY{l+m}{120}\PY{p}{)}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{minimize}\PY{l+s}{ }\PY{n+nv}{cost}\PY{p}{;}

assets/mzn/6_basic_complete_transformed.mzn

@@ -1,7 +1,7 @@
 var 1..5: s;@ \Vlabel{line:6:status:start}@
 constraint status(s);
 var bool b1;
-constraint int_ne_reif(s,1,b1); % b1 <-> status()!=START @\Vlabel{line:6:status:end}@
+constraint int_ne_reif(s,1,b1); @\Vlabel{line:6:status:end}@ % b1 <-> status() != START
 
 var 0.0..1.0: rnd1;@\Vlabel{line:6:x1:start}@
 constraint float_uniform(0.0,1.0,rnd1);
@@ -11,6 +11,6 @@ var bool: b3;
 constraint bool_and(b1,b2,b3);
 var 1..3: x1;
 constraint int_sol(x[1],x1);@\Vlabel{line:6:x1}@
-% (status()!=START /\ uniform(0.0,1.0)>0.2) -> x[1]=sol(x[1])
+% (status() != START /\textbackslash uniform(0.0, 1.0) > 0.2) -> x[1] = sol(x[1])
 constraint int_eq_imp(x[1],x1,b3); @\Vlabel{line:6:x1:end}@
 @...@

assets/mzn/6_basic_complete_transformed.mzntex

@@ -1,8 +1,8 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k+kt}{var}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{l+m}{5}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{s}\PY{p}{;}\PY{esc}{ \Vlabel{line:6:status:start}}
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{n+nv}{s}\PY{p}{)}\PY{p}{;}
 \PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{bool}\PY{l+s}{ }\PY{n+nv}{b1}\PY{p}{;}
-\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}ne\PYZus{}reif}\PY{p}{(}\PY{n+nv}{s}\PY{p}{,}\PY{l+m}{1}\PY{p}{,}\PY{n+nv}{b1}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{c}{\PYZpc{} b1 <-> status()!=START @\Vlabel{line:6:status:end}@}
+\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}ne\PYZus{}reif}\PY{p}{(}\PY{n+nv}{s}\PY{p}{,}\PY{l+m}{1}\PY{p}{,}\PY{n+nv}{b1}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{esc}{\Vlabel{line:6:status:end}}\PY{l+s}{ }\PY{c}{\PYZpc{} b1 <-> status() != START}
 
 \PY{k+kt}{var}\PY{l+s}{ }\PY{l+m}{0.0}\PY{o}{..}\PY{l+m}{1.0}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{rnd1}\PY{p}{;}\PY{esc}{\Vlabel{line:6:x1:start}}
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{float\PYZus{}uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+m}{1.0}\PY{p}{,}\PY{n+nv}{rnd1}\PY{p}{)}\PY{p}{;}
@@ -12,7 +12,7 @@
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{bool\PYZus{}and}\PY{p}{(}\PY{n+nv}{b1}\PY{p}{,}\PY{n+nv}{b2}\PY{p}{,}\PY{n+nv}{b3}\PY{p}{)}\PY{p}{;}
 \PY{k+kt}{var}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{l+m}{3}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x1}\PY{p}{;}
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{p}{,}\PY{n+nv}{x1}\PY{p}{)}\PY{p}{;}\PY{esc}{\Vlabel{line:6:x1}}
-\PY{c}{\PYZpc{} (status()!=START /\ uniform(0.0,1.0)>0.2) -> x[1]=sol(x[1])}
+\PY{c}{\PYZpc{} (status() != START /\textbackslash uniform(0.0, 1.0) > 0.2) -> x[1] = sol(x[1])}
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}eq\PYZus{}imp}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{p}{,}\PY{n+nv}{x1}\PY{p}{,}\PY{n+nv}{b3}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{esc}{\Vlabel{line:6:x1:end}}
 \PY{esc}{...}
 \end{Verbatim}

assets/mzn/6_basic_lns.mzn

@@ -0,0 +1 @@
+predicate basic_lns(var bool: nbh) = (status()!=START -> nbh);

assets/mzn/6_basic_lns.mzntex

@@ -0,0 +1,3 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{basic\PYZus{}lns}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{bool}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{nbh}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{p}{(}\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{o}{!=}\PY{n+nv}{START}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{nbh}\PY{p}{)}\PY{p}{;}
+\end{Verbatim}

assets/mzn/6_gbac_neighbourhood.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{c}{\PYZpc{} TODO: We probably need to unify these (at least for the thesis)}
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{random\PYZus{}allocation}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{sol}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{courses}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}

assets/mzn/6_hill_climbing.mzn

@@ -1,3 +1 @@
-predicate hill_climbing() =
+predicate hill_climbing() = status() != START -> _objective < sol(_objective);
-  if status()=START then true
-  else _objective < sol(_objective) endif;

assets/mzn/6_hill_climbing.mzntex

@@ -1,5 +1,3 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{hill\PYZus{}climbing}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{hill\PYZus{}climbing}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{!=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{o}{=}\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{l}{true}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}\PY{l+s}{ }\PY{k}{endif}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_incremental.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nv}{x}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{l+m}{10}\PY{p}{;}
 \PY{k}{constraint}\PY{l+s}{ }\PY{n+nv}{y}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_lex_minimize.mzn

@@ -0,0 +1,25 @@
+predicate lex_minimize(array[int] of var int: o) =
+  let {
+    var index_set(o): stage
+    array[index_set(o)] of var int: best;
+  } in if status() = START then
+    stage = min(index_set(o))
+  else
+    if status() = UNSAT then
+      if lastval(stage) < l then
+        stage = lastval(stage) + 1
+      else
+        complete()  % we are finished
+      endif
+    else
+      stage = lastval(stage)
+      /\ best[stage] = sol(_objective)
+    endif
+    /\ for(i in min(index_set(o))..stage-1) (
+      o[i] = lastval(best[i])
+    )
+    /\ if status() = SAT then
+        o[stage] < sol(_objective)
+    endif
+    /\ _objective = o[stage]
+  endif;

assets/mzn/6_lex_minimize.mzntex

@@ -0,0 +1,27 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{lex\PYZus{}minimize}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{o}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{o}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{stage}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{array}\PY{p}{[}\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{o}\PY{p}{)}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{best}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{stage}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{min}\PY{p}{(}\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{o}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{UNSAT}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{stage}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nv}{l}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{stage}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{stage}\PY{p}{)}\PY{l+s}{ }\PY{o}{+}\PY{l+s}{ }\PY{l+m}{1}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{complete}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{l+s}{ }\PY{c}{\PYZpc{} we are finished}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{stage}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{stage}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nv}{best}\PY{p}{[}\PY{n+nv}{stage}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{for}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nb}{min}\PY{p}{(}\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{o}\PY{p}{)}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nv}{stage}\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{o}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{best}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{SAT}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{o}\PY{p}{[}\PY{n+nv}{stage}\PY{p}{]}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{o}\PY{p}{[}\PY{n+nv}{stage}\PY{p}{]}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{p}{;}
+\end{Verbatim}

assets/mzn/6_lns_minisearch.mzn

@@ -1,8 +1,13 @@
 function ann: lns(var int: obj, array[int] of var int: vars,
                   int: iterations, float: destr_rate, int: explore_time) =
-  repeat (i in 1..iterations) ( scope(
+  repeat (i in 1..iterations) (
-      if has_sol() then post(uniform_neighbourhood(vars, destr_rate))
+    scope(
-      else true endif /\
+      if has_sol() then
-      time_limit(explore_time, minimize_bab(obj)) /\
+        post(uniform_neighbourhood(vars, destr_rate))
-      commit() /\ print()
+      endif
-    ) /\ post(obj < sol(obj)) );
+      /\ time_limit(explore_time, minimize_bab(obj))
+      /\ commit()
+      /\ print()
+    )
+    /\ post(obj < sol(obj))
+  );

assets/mzn/6_lns_minisearch.mzntex

@@ -1,10 +1,15 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{function}\PY{l+s}{ }\PY{k+kt}{ann}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{lns}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{obj}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{vars}\PY{p}{,}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{iterations}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{destr\PYZus{}rate}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{explore\PYZus{}time}\PY{g+gr}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{repeat}\PY{l+s}{ }\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{iterations}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}\PY{l+s}{ }\PY{n+nf}{scope}\PY{p}{(}
+\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{repeat}\PY{l+s}{ }\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{iterations}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{has\PYZus{}sol}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nf}{post}\PY{p}{(}\PY{n+nf}{uniform\PYZus{}neighbourhood}\PY{p}{(}\PY{n+nv}{vars}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{destr\PYZus{}rate}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{scope}\PY{p}{(}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{l}{true}\PY{l+s}{ }\PY{k}{endif}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{has\PYZus{}sol}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{k}{then}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{time\PYZus{}limit}\PY{p}{(}\PY{n+nv}{explore\PYZus{}time}\PY{p}{,}\PY{l+s}{ }\PY{n+nf}{minimize\PYZus{}bab}\PY{p}{(}\PY{n+nv}{obj}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{post}\PY{p}{(}\PY{n+nf}{uniform\PYZus{}neighbourhood}\PY{p}{(}\PY{n+nv}{vars}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{destr\PYZus{}rate}\PY{p}{)}\PY{p}{)}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{commit}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{print}\PY{p}{(}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{g+gr}{)}\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{post}\PY{p}{(}\PY{n+nv}{obj}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{obj}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{g+gr}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{time\PYZus{}limit}\PY{p}{(}\PY{n+nv}{explore\PYZus{}time}\PY{p}{,}\PY{l+s}{ }\PY{n+nf}{minimize\PYZus{}bab}\PY{p}{(}\PY{n+nv}{obj}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{commit}\PY{p}{(}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{print}\PY{p}{(}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{g+gr}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{post}\PY{p}{(}\PY{n+nv}{obj}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{obj}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{g+gr}{)}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_lns_minisearch_pred.mzn

@@ -1,3 +1,6 @@
-predicate uniform_neighbourhood(array[int] of var int: x, float: destrRate) =
+predicate uniform_neighbourhood(array[int] of var int: x, float: destr_rate) =
-  forall(i in index_set(x))
+  forall(i in index_set(x)) (
-  (if uniform(0.0,1.0) > destrRate then x[i] = sol(x[i]) else true endif);
+    if uniform(0.0, 1.0) > destr_rate then
+      x[i] = sol(x[i])
+    endif
+  );

assets/mzn/6_lns_minisearch_pred.mzntex

@@ -1,5 +1,8 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{uniform\PYZus{}neighbourhood}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{destrRate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{uniform\PYZus{}neighbourhood}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{destr\PYZus{}rate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nb}{index\PYZus{}set}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
-\PY{l+s}{ }\PY{l+s}{ }\PY{p}{(}\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+m}{1.0}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{destrRate}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{l}{true}\PY{l+s}{ }\PY{k}{endif}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{1.0}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{destr\PYZus{}rate}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_pareto_optimal.mzn

@@ -0,0 +1,19 @@
+predicate pareto_optimal(var int: obj1, var int: obj2) =
+  let {
+    int: ms = 1000; % max solutions
+    var 0..ms: nsol;  % number of solutions
+    set of int: SOL = 1..ms;
+    array[SOL] of var lb(obj1)..ub(obj1): s1;
+    array[SOL] of var lb(obj2)..ub(obj2): s2;
+  } in if status() = START then
+    nsol = 0
+  elseif status() = UNSAT then
+    complete() % we are finished!
+  elseif
+    nsol = sol(nsol) + 1 /\
+    s1[nsol] = sol(obj1) /\
+    s2[nsol] = sol(obj2)
+  endif
+  /\ for(i in 1..nsol) (
+    obj1 < lastval(s1[i]) \/ obj2 < lastval(s2[i])
+  );

assets/mzn/6_pareto_optimal.mzntex

@@ -0,0 +1,21 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{pareto\PYZus{}optimal}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{obj1}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{obj2}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{ms}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{l+m}{1000}\PY{p}{;}\PY{l+s}{ }\PY{c}{\PYZpc{} max solutions}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{l+m}{0}\PY{o}{..}\PY{n+nv}{ms}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{nsol}\PY{p}{;}\PY{l+s}{ }\PY{l+s}{ }\PY{c}{\PYZpc{} number of solutions}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{set}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{SOL}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{ms}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{array}\PY{p}{[}\PY{n+nv}{SOL}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{obj1}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{obj1}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{s1}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{array}\PY{p}{[}\PY{n+nv}{SOL}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{obj2}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{obj2}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{s2}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{nsol}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{l+m}{0}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{elseif}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{UNSAT}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nf}{complete}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{c}{\PYZpc{} we are finished!}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{elseif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{nsol}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{nsol}\PY{p}{)}\PY{l+s}{ }\PY{o}{+}\PY{l+s}{ }\PY{l+m}{1}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{s1}\PY{p}{[}\PY{n+nv}{nsol}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{obj1}\PY{p}{)}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{s2}\PY{p}{[}\PY{n+nv}{nsol}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{obj2}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
+\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{for}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{nsol}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{obj1}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{s1}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZbs{}/}\PY{l+s}{ }\PY{n+nv}{obj2}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{lastval}\PY{p}{(}\PY{n+nv}{s2}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}\PY{p}{;}
+\end{Verbatim}

assets/mzn/6_rcpsp_neighbourhood.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{free\PYZus{}timeslot}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{l+s}{ }\PY{o}{=}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{slot}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{max}\PY{p}{(}\PY{n+nv}{Times}\PY{p}{)}\PY{l+s}{ }\PY{o}{div}\PY{l+s}{ }\PY{l+m}{10}\PY{p}{;}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{time}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{n+nb}{min}\PY{p}{(}\PY{n+nv}{Times}\PY{p}{)}\PY{p}{,}\PY{l+s}{ }\PY{n+nb}{max}\PY{p}{(}\PY{n+nv}{Times}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+s}{ }\PY{n+nv}{slot}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}

assets/mzn/6_restart_ann.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{c}{\PYZpc{} post predicate "pred" whenever the solver restarts}
 \PY{k}{annotation}\PY{l+s}{ }\PY{n+nf}{on\PYZus{}restart}\PY{p}{(}\PY{k+kt}{string}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{pred}\PY{p}{)}\PY{p}{;}
 \PY{c}{\PYZpc{} restart after fixed number of nodes}

assets/mzn/6_round_robin.mzn

@@ -1,11 +1,12 @@
 predicate round_robin(array[int] of var bool: nbhs) =
-    let {
+  let {
-        int: N = length(nbhs);
+      int: N = length(nbhs);
-        var -1..N-1: select; % Neighbourhood selection
+      var -1..N-1: select; % Neighbourhood selection
-    } in if status()=START then
+  } in if status()=START then
-        select= -1
+      select = -1
-    else
+  else
-        select= (last_val(select) + 1) mod N
+      select = (last_val(select) + 1) mod N
-    endif /\ forall(i in 1..N) (
+  endif
-          select=i-1 -> nbhs[i] @\Vlabel{line:6:roundrobin:post}@
+  /\ forall(i in 1..N) (
-    );
+      select = i-1 -> nbhs[i] @\Vlabel{line:6:roundrobin:post}@
+  );

assets/mzn/6_round_robin.mzntex

@@ -1,13 +1,14 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{round\PYZus{}robin}\PY{p}{(}\PY{k+kt}{array}\PY{p}{[}\PY{k+kt}{int}\PY{p}{]}\PY{l+s}{ }\PY{k+kt}{of}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{bool}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{nbhs}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{N}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{length}\PY{p}{(}\PY{n+nv}{nbhs}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{N}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nb}{length}\PY{p}{(}\PY{n+nv}{nbhs}\PY{p}{)}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{N}\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{select}\PY{p}{;}\PY{l+s}{ }\PY{c}{\PYZpc{} Neighbourhood selection}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{N}\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{select}\PY{p}{;}\PY{l+s}{ }\PY{c}{\PYZpc{} Neighbourhood selection}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{o}{=}\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{o}{=}\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{o}{=}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+m}{1}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+m}{1}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{o}{=}\PY{l+s}{ }\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{select}\PY{p}{)}\PY{l+s}{ }\PY{o}{+}\PY{l+s}{ }\PY{l+m}{1}\PY{p}{)}\PY{l+s}{ }\PY{o}{mod}\PY{l+s}{ }\PY{n+nv}{N}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{p}{(}\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{select}\PY{p}{)}\PY{l+s}{ }\PY{o}{+}\PY{l+s}{ }\PY{l+m}{1}\PY{p}{)}\PY{l+s}{ }\PY{o}{mod}\PY{l+s}{ }\PY{n+nv}{N}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{N}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{o}{=}\PY{n+nv}{i}\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{nbhs}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{esc}{\Vlabel{line:6:roundrobin:post}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{N}\PY{p}{)}\PY{l+s}{ }\PY{p}{(}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{select}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{i}\PY{o}{\PYZhy{}}\PY{l+m}{1}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{nbhs}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{l+s}{ }\PY{esc}{\Vlabel{line:6:roundrobin:post}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{)}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_simulated_annealing.mzn

@@ -1,7 +1,9 @@
-predicate simulated_annealing(float: initTemp, float: coolingRate) =
+predicate simulated_annealing(float: init_temp, float: cooling_rate) =
-  let { var float: temp; } in
+  let {
-  if status()=START then temp = initTemp
+    var float: temp;
+  } in if status() = START then
+    temp = init_temp
   else
-    temp = last_val(temp)*(1-coolingRate) /\ % cool down
+    temp = last_val(temp) * (1 - cooling_rate) % cool down
-    _objective < sol(_objective) - ceil(log(uniform(0.0,1.0)) * temp)
+    /\ _objective < sol(_objective) - ceil(log(uniform(0.0, 1.0)) * temp)
   endif;

assets/mzn/6_simulated_annealing.mzntex

@@ -1,9 +1,11 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{simulated\PYZus{}annealing}\PY{p}{(}\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{initTemp}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{coolingRate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{simulated\PYZus{}annealing}\PY{p}{(}\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{init\PYZus{}temp}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{cooling\PYZus{}rate}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{temp}\PY{p}{;}\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
-\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{o}{=}\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nv}{temp}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{initTemp}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{temp}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{k}{then}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{temp}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{init\PYZus{}temp}
 \PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{temp}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{temp}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{l+m}{1}\PY{o}{\PYZhy{}}\PY{n+nv}{coolingRate}\PY{p}{)}\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{c}{\PYZpc{} cool down}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nv}{temp}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{n+nv}{temp}\PY{p}{)}\PY{l+s}{ }\PY{o}{*}\PY{l+s}{ }\PY{p}{(}\PY{l+m}{1}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+s}{ }\PY{n+nv}{cooling\PYZus{}rate}\PY{p}{)}\PY{l+s}{ }\PY{c}{\PYZpc{} cool down}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+s}{ }\PY{n+nb}{ceil}\PY{p}{(}\PY{n+nb}{log}\PY{p}{(}\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+m}{1.0}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{o}{*}\PY{l+s}{ }\PY{n+nv}{temp}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{l+s}{ }\PY{o}{\PYZlt{}}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{l+s}{\PYZus{}}\PY{l+s}{o}\PY{l+s}{b}\PY{l+s}{j}\PY{l+s}{e}\PY{l+s}{c}\PY{l+s}{t}\PY{l+s}{i}\PY{l+s}{v}\PY{l+s}{e}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZhy{}}\PY{l+s}{ }\PY{n+nb}{ceil}\PY{p}{(}\PY{n+nb}{log}\PY{p}{(}\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+s}{ }\PY{l+m}{1.0}\PY{p}{)}\PY{p}{)}\PY{l+s}{ }\PY{o}{*}\PY{l+s}{ }\PY{n+nv}{temp}\PY{p}{)}
 \PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_sol_function.mzn

@@ -1,8 +1,10 @@
 predicate int_sol(var int: x, var int: xi);
 function int: sol(var int: x) =
-    if is_fixed(x) then fix(x)
+  if is_fixed(x) then
-    else let {
+    fix(x)
-        var lb(x)..ub(x): xi;
+  else
-        constraint int_sol(x,xi);
+    let {
+      var lb(x)..ub(x): xi;
+      constraint int_sol(x,xi);
     } in xi;
-    endif;
+  endif;

assets/mzn/6_sol_function.mzntex

@@ -1,10 +1,12 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}sol}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{xi}\PY{p}{)}\PY{p}{;}
 \PY{k}{function}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nb}{is\PYZus{}fixed}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{l+s}{ }\PY{k}{then}\PY{l+s}{ }\PY{n+nb}{fix}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{if}\PY{l+s}{ }\PY{n+nb}{is\PYZus{}fixed}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{l+s}{ }\PY{k}{then}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{n+nb}{fix}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{xi}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{else}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{,}\PY{n+nv}{xi}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{x}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{xi}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{int\PYZus{}sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{,}\PY{n+nv}{xi}\PY{p}{)}\PY{p}{;}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{xi}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{endif}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_state_access.mzn

@@ -1,5 +1,6 @@
 % Report the status of the solver (before restarting).
 enum STATUS = {START, UNKNOWN, UNSAT, SAT, OPT} @\label{ann:enum_status}@
 function STATUS: status(); @\label{ann:status}@
+
 % Provide access to the last assigned value of variable x.
 function int: last_val(var int: x);

assets/mzn/6_state_access.mzntex

@@ -1,7 +1,8 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{c}{\PYZpc{} Report the status of the solver (before restarting).}
 \PY{k+kt}{enum}\PY{l+s}{ }\PY{n+nv}{STATUS}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{n+nv}{START}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{UNKNOWN}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{UNSAT}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{SAT}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{OPT}\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{esc}{\label{ann:enum_status}}
 \PY{k}{function}\PY{l+s}{ }\PY{n+nv}{STATUS}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{esc}{\label{ann:status}}
+
 \PY{c}{\PYZpc{} Provide access to the last assigned value of variable x.}
 \PY{k}{function}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{last\PYZus{}val}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{)}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_status.mzn

@@ -1,5 +1,6 @@
 predicate status(var int: stat); @\Vlabel{line:6:status}@
 function var STATUS: status() =
-    let { var STATUS: stat;
+  let {
-            constraint status(stat);
+    var STATUS: stat;
-    } in stat;
+    constraint status(stat);
+  } in stat;

assets/mzn/6_status.mzntex

@@ -1,7 +1,8 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{stat}\PY{p}{)}\PY{p}{;}\PY{l+s}{ }\PY{esc}{\Vlabel{line:6:status}}
 \PY{k}{function}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nv}{STATUS}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nv}{STATUS}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{stat}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{n+nv}{stat}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nv}{STATUS}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{stat}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{stat}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{status}\PY{p}{(}\PY{n+nv}{stat}\PY{p}{)}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{stat}\PY{p}{;}
 \end{Verbatim}

assets/mzn/6_steelmillslab_neighbourhood.mzntex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{free\PYZus{}slab}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}\PY{l+s}{ }\PY{k+kt}{int}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{slab}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{1}\PY{p}{,}\PY{l+s}{ }\PY{n+nv}{nbSlabs}\PY{p}{)}\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}
 \PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{forall}\PY{p}{(}\PY{n+nv}{i}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{l+m}{1}\PY{o}{..}\PY{n+nv}{nbSlabs}\PY{l+s}{ }\PY{k}{where}\PY{l+s}{ }\PY{n+nv}{slab}\PY{l+s}{ }\PY{o}{!=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{assign}\PY{p}{[}\PY{n+nv}{i}\PY{p}{]}\PY{p}{)}\PY{p}{)}

assets/mzn/6_transformed_half_reif.mzn

@@ -0,0 +1 @@
+b3 -> x[1] = sol(x[1])

assets/mzn/6_transformed_half_reif.mzntex

@@ -0,0 +1,3 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{n+nv}{b3}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{p}{)}
+\end{Verbatim}

assets/mzn/6_transformed_partial.mzn

@@ -0,0 +1 @@
+(status() != START /\ uniform(0.0,1.0) > 0.2) -> x[1] = sol(x[1])

assets/mzn/6_transformed_partial.mzntex

@@ -0,0 +1,3 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{p}{(}\PY{n+nf}{status}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{!=}\PY{l+s}{ }\PY{n+nv}{START}\PY{l+s}{ }\PY{o}{/\PYZbs{}}\PY{l+s}{ }\PY{n+nf}{uniform}\PY{p}{(}\PY{l+m}{0.0}\PY{p}{,}\PY{l+m}{1.0}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZgt{}}\PY{l+s}{ }\PY{l+m}{0.2}\PY{p}{)}\PY{l+s}{ }\PY{o}{\PYZhy{}\PYZgt{}}\PY{l+s}{ }\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nf}{sol}\PY{p}{(}\PY{n+nv}{x}\PY{p}{[}\PY{l+m}{1}\PY{p}{]}\PY{p}{)}
+\end{Verbatim}

assets/mzn/6_uniform_neighbourhood.mzn

@@ -1,6 +0,0 @@
-predicate float_uniform(var float:l, var float: u, var float: r);
-function var float: uniform_nbh(var float: l, var float: u) :: impure =
-    let {
-        var lb(l)..ub(u): rnd;
-        constraint float_uniform(l,u,rnd):
-    } in rnd;

assets/mzn/6_uniform_neighbourhood.mzntex

@@ -1,8 +0,0 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
-\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{float\PYZus{}uniform}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{n+nv}{l}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{u}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{r}\PY{p}{)}\PY{p}{;}
-\PY{k}{function}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{uniform\PYZus{}nbh}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{l}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{u}\PY{p}{)}\PY{l+s}{ }\PY{p}{:}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{impure}\PY{l+s}{ }\PY{o}{=}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{l}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{u}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{rnd}\PY{p}{;}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{float\PYZus{}uniform}\PY{p}{(}\PY{n+nv}{l}\PY{p}{,}\PY{n+nv}{u}\PY{p}{,}\PY{n+nv}{rnd}\PY{p}{)}\PY{p}{:}
-\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{rnd}\PY{p}{;}
-\end{Verbatim}

assets/mzn/6_uniform_slv.mzn

@@ -0,0 +1,6 @@
+predicate float_uniform(var float:l, var float: u, var float: r);
+function var float: uniform_slv(var float: l, var float: u) :: impure =
+  let {
+    var lb(l)..ub(u): rnd;
+    constraint float_uniform(l,u,rnd):
+  } in rnd;

assets/mzn/6_uniform_slv.mzntex

@@ -0,0 +1,8 @@
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
+\PY{k}{predicate}\PY{l+s}{ }\PY{n+nf}{float\PYZus{}uniform}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{n+nv}{l}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{u}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{r}\PY{p}{)}\PY{p}{;}
+\PY{k}{function}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nf}{uniform\PYZus{}slv}\PY{p}{(}\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{l}\PY{p}{,}\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{k+kt}{float}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{u}\PY{p}{)}\PY{l+s}{ }\PY{p}{:}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{impure}\PY{l+s}{ }\PY{o}{=}
+\PY{l+s}{ }\PY{l+s}{ }\PY{k}{let}\PY{l+s}{ }\PY{p}{\PYZob{}}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k+kt}{var}\PY{l+s}{ }\PY{n+nb}{lb}\PY{p}{(}\PY{n+nv}{l}\PY{p}{)}\PY{l+s}{.}\PY{l+s}{.}\PY{n+nb}{ub}\PY{p}{(}\PY{n+nv}{u}\PY{p}{)}\PY{p}{:}\PY{l+s}{ }\PY{n+nv}{rnd}\PY{p}{;}
+\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{l+s}{ }\PY{k}{constraint}\PY{l+s}{ }\PY{n+nf}{float\PYZus{}uniform}\PY{p}{(}\PY{n+nv}{l}\PY{p}{,}\PY{n+nv}{u}\PY{p}{,}\PY{n+nv}{rnd}\PY{p}{)}\PY{p}{:}
+\PY{l+s}{ }\PY{l+s}{ }\PY{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\PY{l+s}{ }\PY{n+nv}{rnd}\PY{p}{;}
+\end{Verbatim}

assets/py/2_dyn_knapsack.pytex

@@ -1,4 +1,4 @@
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8},xleftmargin=5mm]
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1,codes={\catcode`\$=3\catcode`\^=7\catcode`\_=8\relax},xleftmargin=5mm]
 \PY{n}{toys\PYZus{}joy} \PY{o}{=} \PY{p}{[}\PY{l+m+mi}{63}\PY{p}{,} \PY{l+m+mi}{12}\PY{p}{,} \PY{l+m+mi}{50}\PY{p}{,} \PY{l+m+mi}{100}\PY{p}{]}
 \PY{n}{toys\PYZus{}space} \PY{o}{=} \PY{p}{[}\PY{l+m+mi}{32}\PY{p}{,} \PY{l+m+mi}{8}\PY{p}{,} \PY{l+m+mi}{16}\PY{p}{,} \PY{l+m+mi}{40}\PY{p}{]}
 \PY{n}{space\PYZus{}left} \PY{o}{=} \PY{l+m+mi}{64}

chapters/6_incremental.tex

@@ -55,22 +55,22 @@ still prove prohibitive, warranting direct support from the
 methods to provide this support:
 
 \begin{itemize}
-  \item Using a minimal extension of existing solvers, we can compile
+  \item We introduce the notion of restart-based \gls{meta-search} algorithms.
-        \gls{meta-search} algorithms into efficient solver-level specifications
+        Using a minimal extension to a \cml\ and its target solver, we can model
-        based on solver restart, avoiding re-compilation all-together.
+        some \gls{meta-search} algorithms and compile \gls{meta-search}
-  \item We can add an interface for adding and removing constraints in the
+        algorithms into efficient solver-level specifications based on solver
-        \gls{constraint-modelling} infrastructure and avoid re-compilation where
+        restarts, avoiding re-compilation all-together.
-        possible.
+  \item Alternatively, we can add an incremental interface for adding and
+        removing constraints to the infrastructure of the \cml. Although this
+        does not avoid the need for re-compilation, it can reduce the work to
+        only the part of the constraint model that has changed. This approach
+        can be used when an algorithm cannot be described using restart-based
+        \gls{meta-search} or required extension is not available for the solver.
 \end{itemize}
 
-Although it might sound like the first option is always the best one, it should
-be noted that this option cannot always be used. It might not be possible to
-extend the target \gls{solver} (or it might not be allowed in case of some
-proprietary \glspl{solver}). Furthermore, the modelling of \gls{meta-search}
-algorithms using solver restarts is limited \textbf{TODO: in some way}.
-
 The rest of the chapter is organised as follows. \Cref{sec:6-modelling}
-discusses the declarative modelling of \gls{meta-search} algorithms using \cmls.
+discusses the declarative modelling of restart-based \gls{meta-search}
+algorithms that can be modelled directly in a \cml.
 \Cref{sec:6-solver-extension} introduces the method to compile these
 \gls{meta-search} specifications into efficient solver-level specifications that
 only require a small extension of existing \glspl{solver}.
@@ -81,7 +81,7 @@ and remove constraints from an existing model while avoiding recompilation.
 Finally, \Cref{sec:6-conclusion} presents the conclusions.
 
 
-\section{Modelling of Meta-Search}
+\section{Modelling of Restart-Based Meta-Search}
 \label{sec:6-modelling}
 
 This section introduces a \minizinc\ extension that enables modellers to define
@@ -198,9 +198,9 @@ workaround, we currently pass the name of the predicate to be called for each
 restart as a string (see the definition of the new \mzninline{on_restart}
 annotation in \cref{lst:6-restart-ann}).
 
-The second component of our \gls{lns} definition is the \emph{restarting strategy},
+The second component of our \gls{lns} definition is the \emph{restarting
-defining how much effort the solver should put into each neighbourhood (\ie\
+  strategy}, defining how much effort the solver should put into each
-restart), and when to stop the overall search.
+neighbourhood (\ie\ restart), and when to stop the overall search.
 
 We propose adding new search annotations to \minizinc\ to control this behaviour
 (see \cref{lst:6-restart-ann}). The \mzninline{restart_on_solution} annotation
@@ -212,7 +212,7 @@ search when no solution is found. The \mzninline{timeout} annotation gives an
 overall time limit for the search, whereas \mzninline{restart_limit} stops the
 search after a fixed number of restarts.
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_restart_ann.mzn}
   \caption{\label{lst:6-restart-ann} New annotations to control the restarting
     behaviour}
@@ -222,14 +222,14 @@ search after a fixed number of restarts.
 
 Although using just a restart annotations by themselves allows us to run the
 basic \gls{lns} algorithm, more advanced \gls{meta-search} algorithms will
-require more then just reapplying the same \gls{neighbourhood} time after time.
+require more then reapplying the same \gls{neighbourhood} time after time. It
-It is, for example, often beneficial to use several \gls{neighbourhood}
+is, for example, often beneficial to use several \gls{neighbourhood} definitions
-definitions for a problem. Different \glspl{neighbourhood} may be able to
+for a problem. Different \glspl{neighbourhood} may be able to improve different
-improve different aspects of a solution, at different phases of the search.
+aspects of a solution, at different phases of the search. Adaptive \gls{lns}
-Adaptive \gls{lns} \autocite{ropke-2006-adaptive, pisinger-2007-heuristic},
+\autocite{ropke-2006-adaptive, pisinger-2007-heuristic}, which keeps track of
-which keeps track of the \glspl{neighbourhood} that led to improvements and
+the \glspl{neighbourhood} that led to improvements and favours them for future
-favours them for future iterations, is the prime example for this approach. A
+iterations, is the prime example for this approach. A simpler scheme may apply
-simpler scheme may apply several \glspl{neighbourhood} in a round-robin fashion.
+several \glspl{neighbourhood} in a round-robin fashion.
 
 In \minisearch\, these adaptive or round-robin approaches can be implemented
 using \emph{state variables}, which support destructive update (overwriting the
@@ -252,7 +252,7 @@ like \mzninline{sol}, has versions for all basic variable types) allows
 modellers to access the last value assigned to a variable (the value is
 undefined if \mzninline{status()=START}).
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_state_access.mzn}
   \caption{\label{lst:6-state-access} Functions for accessing previous solver
     states}
@@ -272,59 +272,58 @@ parametric over the neighbourhoods they should apply. For example, since
 strategy \mzninline{basic_lns} that applies a neighbourhood only if the current
 status is not \mzninline{START}:
 
-\mzninline{predicate basic_lns(var bool: nbh) = (status()!=START -> nbh);}
+\highlightfile{assets/mzn/6_basic_lns.mzn}
 
 In order to use this predicate with the \mzninline{on_restart} annotation, we
-cannot simply pass \mzninline{basic_lns(uniformNeighbourhood(x,0.2))}. First of
+cannot simply pass \mzninline{basic_lns(uniform_neighbourhood(x, 0.2))}. First
-all, calling \mzninline{uniformNeighbourhood} like that would result in a
+of all, calling \mzninline{uniform_neighbourhood} like that would result in a
 \emph{single} evaluation of the predicate, since \minizinc\ employs a
 call-by-value evaluation strategy. Furthermore, the \mzninline{on_restart}
 annotation only accepts the name of a nullary predicate. Therefore, users have
 to define their overall strategy in a new predicate. \Cref{lst:6-basic-complete}
 shows a complete example of a basic \gls{lns} model.
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_basic_complete.mzn}
   \caption{\label{lst:6-basic-complete} Complete \gls{lns} example}
 \end{listing}
 
 We can also define round-robin and adaptive strategies using these primitives.
-%\paragraph{Round-robin \gls{lns}}
+\Cref{lst:6-round-robin} defines a round-robin \gls{lns} meta-heuristic, which
-\Cref{lst:6-round-robin} defines a round-robin \gls{lns} meta-heuristic, which cycles
+cycles through a list of \mzninline{N} neighbourhoods \mzninline{nbhs}. To do
-through a list of \mzninline{N} neighbourhoods \mzninline{nbhs}. To do this, it
+this, it uses the decision variable \mzninline{select}. In the initialisation
-uses the decision variable \mzninline{select}. In the initialisation phase
+phase (\mzninline{status()=START}), \mzninline{select} is set to \mzninline{-1},
-(\mzninline{status()=START}), \mzninline{select} is set to \mzninline{-1}, which
+which means none of the neighbourhoods is activated. In any following restart,
-means none of the neighbourhoods is activated. In any following restart,
 \mzninline{select} is incremented modulo \mzninline{N}, by accessing the last
 value assigned in a previous restart (\mzninline{last_val(select)}). This will
 activate a different neighbourhood for each restart
 (\lref{line:6:roundrobin:post}).
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_round_robin.mzn}
   \caption{\label{lst:6-round-robin} A predicate providing the round robin
     meta-heuristic}
 \end{listing}
 
 %\paragraph{Adaptive \gls{lns}}
-For adaptive \gls{lns}, a simple strategy is to change the size of the neighbourhood
+For adaptive \gls{lns}, a simple strategy is to change the size of the
-depending on whether the previous size was successful or not.
+neighbourhood depending on whether the previous size was successful or not.
 \Cref{lst:6-adaptive} shows an adaptive version of the
-\mzninline{uniformNeighbourhood} that increases the number of free variables
+\mzninline{uniform_neighbourhood} that increases the number of free variables
 when the previous restart failed, and decreases it when it succeeded, within the
 bounds $[0.6,0.95]$.
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_adaptive.mzn}
   \caption{\label{lst:6-adaptive} A simple adaptive neighbourhood}
 \end{listing}
 
-\subsection{Meta-heuristics}
+\subsection{Optimisation strategies}
 
 The \gls{lns} strategies we have seen so far rely on the default behaviour of
-\minizinc\ solvers to use branch-and-bound for optimisation: when a new solution
+\minizinc\ solvers to use a branch-and-bound method for optimisation: when a new
-is found, the solver adds a constraint to the remainder of the search to only
+solution is found, the solver adds a constraint to the remainder of the search
-accept better solutions, as defined by the objective function in the
+to only accept better solutions, as defined by the objective function in the
 \mzninline{minimize} or \mzninline{maximize} clause of the \mzninline{solve}
 item. When combined with restarts and \gls{lns}, this is equivalent to a simple
 hill-climbing meta-heuristic.
@@ -336,25 +335,42 @@ branch-and-bound constraint on restart. It will still use the declared objective
 to decide whether a new solution is the globally best one seen so far, and only
 output those (to maintain the convention of \minizinc\ solvers that the last
 solution printed at any point in time is the currently best known one).
-%
+
 With \mzninline{restart_without_objective}, the restart predicate is now
 responsible for constraining the objective function. Note that a simple
 hill-climbing (for minimisation) can still be defined easily in this context as:
 
-{
+\highlightfile{assets/mzn/6_hill_climbing.mzn}
-  \scriptsize
-  \highlightfile{assets/mzn/6_hill_climbing.mzn}
-}
 
 It takes advantage of the fact that the declared objective function is available
-through the built-in variable \mzninline{_objective}.
+through the built-in variable \mzninline{_objective}. A more interesting example
-%
+is a simulated annealing strategy. When using this strategy, the solutions that
-A simulated annealing strategy is also easy to
+the solver finds are no longer required to steadily improve in quality. Instead,
-express:
+we ask the solver to find a solution that is a significant improvement over the
+previous solution. Over time we decrease the amount by which we require the
+solution needs to improve until we are just looking for any improvements. This
+\gls{meta-search} can help improving the qualities of solutions quickly and
+thereby reaching the optimal solution quicker. This strategy is also easy to
+express using our restart-based modelling:
 
 \highlightfile{assets/mzn/6_simulated_annealing.mzn}
 
-\section{Compilation of Meta-Search}
+Using the same methods it is also possible to describe optimisation strategies
+with multiple objectives. An example of such a strategy is lexicographic search.
+Lexicographic search can be employed when there is a strict order between the
+importance of different variables. It required that, once a solution is found,
+each subsequent solution must either improve the first objective, or have the
+same value for the first objective and improve the second objective, or have the
+same value for the first two objectives and improve the third objective, and so
+on. We can model this strategy restarts as such:
+
+\highlightfile{assets/mzn/6_lex_minimize.mzn}
+
+Another optimisation
+
+\highlightfile{assets/mzn/6_pareto_optimal.mzn}
+
+\section{Compilation of Meta-Search Specifications}
 \label{sec:6-solver-extension}
 
 The neighbourhoods defined in the previous section can be executed with
@@ -380,7 +396,7 @@ in terms of standard \minizinc\ expressions, with the exception of a few new
 built-in functions. When the neighbourhood predicates are evaluated in the
 \minisearch\ way, the \minisearch\ runtime implements those built-in functions,
 computing the correct value whenever a predicate is evaluated.
-%
+
 Instead, the compilation scheme presented below uses a limited form of
 \emph{partial evaluation}: parameters known at compile time will be fully
 evaluated; those only known during the solving, such as the result of a call to
@@ -403,7 +419,7 @@ performs four simple steps:
         \mzninline{sol}, \mzninline{status}, and \mzninline{last_val} as
         returning a \mzninline{var} instead of a \mzninline{par} value; and
         rename calls to random functions, e.g., \mzninline{uniform} to
-        \mzninline{uniform_nbh}, in order to distinguish them from their
+        \mzninline{uniform_slv}, in order to distinguish them from their
         standard library versions.
   \item Convert any expression containing a call from step 2 to \mzninline{var}
         to ensure the functions are compiled as constraints, rather than
@@ -416,10 +432,11 @@ performs four simple steps:
 These transformations will not change the code of many neighbourhood
 definitions, since the built-in functions are often used in positions that
 accept both parameters and variables. For example, the
-\mzninline{uniformNeighbourhood} predicate from \cref{lst:6-lns-minisearch-pred}
+\mzninline{uniform_neighbourhood} predicate from
-uses \mzninline{uniform(0.0,1.0)} in an \mzninline{if} expression, and
+\cref{lst:6-lns-minisearch-pred} uses \mzninline{uniform(0.0, 1.0)} in an
-\mzninline{sol(x[i])} in an equality constraint. Both expressions can be
+\mzninline{if} expression, and \mzninline{sol(x[i])} in an equality constraint.
-translated to \flatzinc\ when the functions return a \mzninline{var}.
+Both expressions can be translated to \flatzinc\ when the functions return a
+\mzninline{var}.
 
 \subsection{Compiling the new built-ins}
 
@@ -433,7 +450,7 @@ simply replaces the functional form by a predicate \mzninline{status} (declared
 in \lref{line:6:status}), which constrains its local variable argument
 \mzninline{stat} to take the status value.
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_status.mzn}
   \caption{\label{lst:6-status} MiniZinc definition of the \mzninline{status} function}
 \end{listing}
@@ -451,7 +468,7 @@ question becomes known at compile time, we use that value instead. Otherwise, we
 replace the function call with a type specific \mzninline{int_sol} predicate,
 which is the constraint that will be executed by the solver.
 %
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_sol_function.mzn}
   \caption{\label{lst:6-int-sol} MiniZinc definition of the \mzninline{sol}
     function for integer variables}
@@ -467,7 +484,7 @@ able to generate the most efficient \flatzinc\ code for expressions involving
 \paragraph{Random number functions}
 
 Calls to the random number functions have been renamed by appending
-\texttt{\_nbh}, so that the compiler does not simply evaluate them statically.
+\texttt{\_slv}, so that the compiler does not simply evaluate them statically.
 The definition of these new functions follows the same pattern as for
 \mzninline{sol}, \mzninline{status}, and \mzninline{last_val}. The MiniZinc
 definition of the \mzninline{uniform_nbh} function is shown in
@@ -479,13 +496,13 @@ Note that the function accepts variable arguments \mzninline{l} and
 \mzninline{u}, so that it can be used in combination with other functions, such
 as \mzninline{sol}.
 
-\begin{listing}[t]
+\begin{listing}
-  \highlightfile{assets/mzn/6_uniform_neighbourhood.mzn}
+  \highlightfile{assets/mzn/6_uniform_slv.mzn}
   \caption{\label{lst:6-int-rnd} MiniZinc definition of the
     \mzninline{uniform_nbh} function for floats}
 \end{listing}
 
-\subsection{Solver support for \gls{lns} \glsentrytext{flatzinc}}
+\subsection{Solver support for restart-based built-ins}
 
 We will now show the minimal extensions required from a solver to interpret the
 new \flatzinc\ constraints and, consequently, to execute \gls{lns} definitions
@@ -500,10 +517,10 @@ new constraints the solver needs to:
 \begin{itemize}
   \item \mzninline{status(s)}: record the status of the previous restart, and
         fix \mzninline{s} to the recorded status.
-  \item \mzninline{sol(x,sx)} (variants): constrain \mzninline{sx} to be equal
+  \item \mzninline{sol(x, sx)} (variants): constrain \mzninline{sx} to be equal
         to the value of \mzninline{x} in the incumbent solution. If there is no
         incumbent solution, it has no effect.
-  \item \mzninline{last_val(x,lx)} (variants): constrain \mzninline{lx} to take
+  \item \mzninline{last_val(x, lx)} (variants): constrain \mzninline{lx} to take
         the last value assigned to \mzninline{x} during search. If no value was
         ever assigned, it has no effect. Note that many solvers (in particular
         SAT and LCG solvers) already track \mzninline{last_val} for their
@@ -527,30 +544,33 @@ implemented these extensions for both Gecode (110 new lines of code) and Chuffed
 
 For example, consider the model from \cref{lst:6-basic-complete} again.
 \Cref{lst:6-flat-pred} shows a part of the \flatzinc\ that arises from compiling
-\mzninline{basic_lns(uniformNeighbourhood(x, 0.2))}, assuming that
+\mzninline{basic_lns(uniform_neighbourhood(x, 0.2))}, assuming that
 \mzninline{index_set(x) = 1..n}.
 
 \Lrefrange{line:6:status:start}{line:6:status:end} define a Boolean variable
-\mzninline{b1} that is true iff the status is not \mzninline{START}. The second
+\mzninline{b1} that is true if-and-only-if the status is not \mzninline{START}.
-block of code (\lrefrange{line:6:x1:start}{line:6:x1:end}) represents the
+The second block of code (\lrefrange{line:6:x1:start}{line:6:x1:end}) represents
-decomposition of the expression
+the decomposition of the expression
+
+\highlightfile{assets/mzn/6_transformed_partial.mzn}
 
-\mzninline{(status() != START /\ uniform(0.0,1.0) > 0.2) -> x[1] = sol(x[1])}
-%
 which is the result of merging the implication from the \mzninline{basic_lns}
 predicate with the \mzninline{if} expression from
 \mzninline{uniformNeighbourhood}. The code first introduces and constrains a
 variable for the random number, then adds two Boolean variables: \mzninline{b2}
-is constrained to be true iff the random number is greater than 0.2; while
+is constrained to be true if-and-only-if the random number is greater than
-\mzninline{b3} is constrained to be the conjunction \mzninline{status()!=START
+\(0.2\); while \mzninline{b3} is constrained to be the conjunction of the two.
-  /\ uniform(0.0,1.0)>0.2}. \lref{line:6:x1} constrains \mzninline{x1} to be the
+\lref{line:6:x1} constrains \mzninline{x1} to be the value of \mzninline{x[1]}
-value of \mzninline{x[1]} in the previous solution. Finally, the half-reified
+in the previous solution. Finally, the half-reified constraint in
-constraint in \lref{line:6:x1:end} implements \mzninline{b3 -> x[1]=sol(x[1])}.
+\lref{line:6:x1:end} implements
+
+\highlightfile{assets/mzn/6_transformed_half_reif.mzn}
+
 We have omitted the similar code generated for \mzninline{x[2]} to
 \mzninline{x[n]}. Note that the \flatzinc\ shown here has been simplified for
 presentation.
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_basic_complete_transformed.mzn}
   \caption{\label{lst:6-flat-pred} \flatzinc\ that results from compiling \\
     \mzninline{basic_lns(uniformNeighbourhood(x,0.2))}.}
@@ -562,28 +582,28 @@ and \mzninline{b3} to \mzninline{false}. Therefore, the implication in
 \lref{line:6:x1:end} is not activated, leaving \mzninline{x[1]} unconstrained.
 The neighbourhood constraints are effectively switched off.
 
-When the solver restarts, all of the special propagators are re-executed.
+When the solver restarts, all of the special propagators are re-executed. Now
-Now \mzninline{s} is not 1, and \mzninline{b1} will be set to
+\mzninline{s} is not 1, and \mzninline{b1} will be set to \mzninline{true}. The
-\mzninline{true}. The \mzninline{float_random} propagator assigns
+\mzninline{float_random} propagator assigns \mzninline{rnd1} a new random value
-\mzninline{rnd1} a new random value and, depending on whether it is greater
+and, depending on whether it is greater than \mzninline{0.2}, the Boolean
-than \mzninline{0.2}, the Boolean variables \mzninline{b2}, and consequently
+variables \mzninline{b2}, and consequently \mzninline{b3} will be assigned. If
-\mzninline{b3} will be assigned. If it is \mzninline{true}, the constraint
+it is \mzninline{true}, the constraint in line \lref{line:6:x1:end} will become
-in line \lref{line:6:x1:end} will become active and assign \mzninline{x[1]}
+active and assign \mzninline{x[1]} to its value in the previous solution.
-to its value in the previous solution.
 
 Furthermore, it is not strictly necessary to guard \mzninline{int_uniform}
-against being invoked before \mzninline{status()!=START}, since the
+against being invoked before the first solution is found, since the
 \mzninline{sol} constraints will simply not propagate anything in case no
-solution has been recorded yet, but we use this simple example to illustrate
+solution has been recorded yet, but we use this simple example to illustrate how
-how these Boolean conditions are compiled and evaluated.
+these Boolean conditions are compiled and evaluated.
 
 \section{An Incremental Interface for Constraint Modelling Languages}
 \label{sec:6-incremental-compilation}
 
 In order to support incremental flattening, the \nanozinc\ interpreter must be
 able to process \nanozinc\ calls \emph{added} to an existing \nanozinc\ program,
-as well as to \emph{remove} calls from an existing \nanozinc\ program. Adding new
+as well as to \emph{remove} calls from an existing \nanozinc\ program. Adding
-calls is straightforward, since \nanozinc\ is already processed call-by-call.
+new calls is straightforward, since \nanozinc\ is already processed
+call-by-call.
 
 Removing a call, however, is not so simple. When we remove a call, all effects
 the call had on the \nanozinc\ program have to be undone, including results of
@@ -854,7 +874,7 @@ periods, which is done via the variables \mzninline{period_of} in the model.
 \cref{lst:6-free-period} shows the neighbourhood chosen, which randomly picks one
 period and frees all courses that are assigned to it.
 
-\begin{table}[t]
+\begin{table}
     \centering
     \input{assets/table/6_gbac}
     \caption{\label{tab:6-gbac}\texttt{gbac} benchmarks}
@@ -868,7 +888,7 @@ Gecode. However, \gls{lns} again significantly improves over standard Chuffed.
 
 \subsubsection{\texttt{steelmillslab}}
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_steelmillslab_neighbourhood.mzn}
   \caption{\label{lst:6-free-bin}\texttt{steelmillslab}: Neighbourhood that frees
     all orders assigned to a selected slab.}
@@ -884,7 +904,7 @@ that randomly selects a slab and frees the orders assigned to it in the
 incumbent solution. These orders can then be freely reassigned to any other
 slab.
 
-\begin{table}[t]
+\begin{table}
     \centering
     \input{assets/table/6_steelmillslab}
     \caption{\label{tab:6-steelmillslab}\texttt{steelmillslab} benchmarks}
@@ -901,7 +921,7 @@ outperforms \gecodeStd on this problem, once we use \gls{lns}, the learning in
 % RCPSP/wet
 \subsubsection{\texttt{rcpsp-wet}}
 
-\begin{listing}[t]
+\begin{listing}
   \highlightfile{assets/mzn/6_rcpsp_neighbourhood.mzn}
   \caption{\label{lst:6-free-timeslot}\texttt{rcpsp-wet}: Neighbourhood freeing
     all tasks starting in the drawn interval.}

dekker_thesis.tex

@@ -39,11 +39,11 @@ following publication:
 \end{refsection}
 
 \mainmatter{}
-\include{chapters/1_introduction}
+% \include{chapters/1_introduction}
-\include{chapters/2_background}
+% \include{chapters/2_background}
-\include{chapters/3_paradigms}
+% \include{chapters/3_paradigms}
-\include{chapters/4_rewriting}
+% \include{chapters/4_rewriting}
-\include{chapters/5_half_reif}
+% \include{chapters/5_half_reif}
 \include{chapters/6_incremental}
 
 \backmatter{}