Dekker1/dekker-phd-thesis
Archived
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

More work on the incremental chapter

Browse Source
This commit is contained in:
Jip J. Dekker 2021-02-24 17:09:07 +11:00
parent ae8be07972
commit a04e3bee7e
No known key found for this signature in database
GPG Key ID: 517DF4A00618C9C3
49 changed files with 407 additions and 237 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
Pipfile.lock generated
View File

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

2
assets/glossary.tex
View File

@ -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},
}

2
assets/mzn/2_knapsack.mzntex
View File

@ -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}{;}

2
assets/mzn/6_abs_reif_result.mzntex
View File

@ -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}{]}

2
assets/mzn/6_abs_reif_trail.mzntex
View File

@ -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}

23
assets/mzn/6_adaptive.mzn
View File

@ -1,8 +1,15 @@
predicate adaptiveUniform(array[int] of var int: x, float: initialDestrRate) =
let { var float: rate; } in
if status() = START then rate = initialDestrRate
elseif status() = UNSAT then rate = min(last_val(rate)-0.02,0.6)
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]) else true endif);
predicate adaptive_uniform(array[int] of var int: x, float: init_rate) =
let {
var float: rate;
} in if status() = START then
rate = init_rate
elseif status() = UNSAT then
rate = min(last_val(rate) - 0.02, 0.6)
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
);

25
assets/mzn/6_adaptive.mzntex
View File

@ -1,10 +1,17 @@
\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}{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{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}{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{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{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{k}{endif}\PY{l+s}{ }\PY{o}{/\PYZbs{}}
\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{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}{;}
\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}{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{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{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}{rate}\PY{l+s}{ }\PY{o}{=}\PY{l+s}{ }\PY{n+nv}{init\PYZus{}rate}
\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+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{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}

7
assets/mzn/6_basic_complete.mzn
View File

@ -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;

9
assets/mzn/6_basic_complete.mzntex
View File

@ -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}{;}

4
assets/mzn/6_basic_complete_transformed.mzn
View File

@ -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}@
@...@

6
assets/mzn/6_basic_complete_transformed.mzntex
View File

@ -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}

1
assets/mzn/6_basic_lns.mzn Normal file
View File

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

3
assets/mzn/6_basic_lns.mzntex Normal file
View File

@ -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}

2
assets/mzn/6_gbac_neighbourhood.mzntex
View File

@ -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}{(}

4
assets/mzn/6_hill_climbing.mzn
View File

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

6
assets/mzn/6_hill_climbing.mzntex
View File

@ -1,5 +1,3 @@
\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}{hill\PYZus{}climbing}\PY{p}{(}\PY{p}{)}\PY{l+s}{ }\PY{o}{=}
\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}{;}
\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{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}{;}
\end{Verbatim}

2
assets/mzn/6_incremental.mzntex
View File

@ -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}

25
assets/mzn/6_lex_minimize.mzn Normal file
View File

@ -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;

27
assets/mzn/6_lex_minimize.mzntex Normal file
View File

@ -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}

17
assets/mzn/6_lns_minisearch.mzn
View File

@ -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(
if has_sol() then post(uniform_neighbourhood(vars, destr_rate))
else true endif /\
time_limit(explore_time, minimize_bab(obj)) /\
commit() /\ print()
) /\ post(obj < sol(obj)) );
repeat (i in 1..iterations) (
scope(
if has_sol() then
post(uniform_neighbourhood(vars, destr_rate))
endif
/\ time_limit(explore_time, minimize_bab(obj))
/\ commit()
/\ print()
)
/\ post(obj < sol(obj))
);

19
assets/mzn/6_lns_minisearch.mzntex
View File

@ -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{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{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{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{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{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{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{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}{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{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{k}{endif}
\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}

9
assets/mzn/6_lns_minisearch_pred.mzn
View File

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

11
assets/mzn/6_lns_minisearch_pred.mzntex
View File

@ -1,5 +1,8 @@
\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}{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{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{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}{;}
\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}{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{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}

19
assets/mzn/6_pareto_optimal.mzn Normal file
View File

@ -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])
);

21
assets/mzn/6_pareto_optimal.mzntex Normal file
View File

@ -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}

2
assets/mzn/6_rcpsp_neighbourhood.mzntex
View File

@ -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}

2
assets/mzn/6_restart_ann.mzntex
View File

@ -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}

21
assets/mzn/6_round_robin.mzn
View File

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

23
assets/mzn/6_round_robin.mzntex
View File

@ -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{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{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{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{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{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{l+s}{ }\PY{l+s}{ }\PY{p}{)}\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{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}{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{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{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{k}{else}
\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{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{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{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}

12
assets/mzn/6_simulated_annealing.mzn
View File

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

14
assets/mzn/6_simulated_annealing.mzntex
View File

@ -1,9 +1,11 @@
\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}{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{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}{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}
\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}{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{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{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{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{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}

12
assets/mzn/6_sol_function.mzn
View File

@ -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)
else let {
var lb(x)..ub(x): xi;
constraint int_sol(x,xi);
if is_fixed(x) then
fix(x)
else
let {
var lb(x)..ub(x): xi;
constraint int_sol(x,xi);
} in xi;
endif;
endif;

14
assets/mzn/6_sol_function.mzntex
View File

@ -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{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{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{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{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{n+nb}{fix}\PY{p}{(}\PY{n+nv}{x}\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}{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}

1
assets/mzn/6_state_access.mzn
View File

@ -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);

3
assets/mzn/6_state_access.mzntex
View File

@ -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}

7
assets/mzn/6_status.mzn
View File

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

9
assets/mzn/6_status.mzntex
View File

@ -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{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{p}{\PYZcb{}}\PY{l+s}{ }\PY{o}{in}\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{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{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}

2
assets/mzn/6_steelmillslab_neighbourhood.mzntex
View File

@ -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}{)}

1
assets/mzn/6_transformed_half_reif.mzn Normal file
View File

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

3
assets/mzn/6_transformed_half_reif.mzntex Normal file
View File

@ -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}

1
assets/mzn/6_transformed_partial.mzn Normal file
View File

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

3
assets/mzn/6_transformed_partial.mzntex Normal file
View File

@ -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}

6
assets/mzn/6_uniform_neighbourhood.mzn
View File

@ -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;

8
assets/mzn/6_uniform_neighbourhood.mzntex
View File

@ -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}

6
assets/mzn/6_uniform_slv.mzn Normal file
View File

@ -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;

8
assets/mzn/6_uniform_slv.mzntex Normal file
View File

@ -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}

2
assets/py/2_dyn_knapsack.pytex
View File

@ -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}

218
chapters/6_incremental.tex
View File

@ -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
\gls{meta-search} algorithms into efficient solver-level specifications
based on solver restart, avoiding re-compilation all-together.
\item We can add an interface for adding and removing constraints in the
\gls{constraint-modelling} infrastructure and avoid re-compilation where
possible.
\item We introduce the notion of restart-based \gls{meta-search} algorithms.
Using a minimal extension to a \cml\ and its target solver, we can model
some \gls{meta-search} algorithms and compile \gls{meta-search}
algorithms into efficient solver-level specifications based on solver
restarts, avoiding re-compilation all-together.
\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},
defining how much effort the solver should put into each neighbourhood (\ie\
restart), and when to stop the overall search.
The second component of our \gls{lns} definition is the \emph{restarting
strategy}, defining how much effort the solver should put into each
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.
It is, for example, often beneficial to use several \gls{neighbourhood}
definitions for a problem. Different \glspl{neighbourhood} may be able to
improve different aspects of a solution, at different phases of the search.
Adaptive \gls{lns} \autocite{ropke-2006-adaptive, pisinger-2007-heuristic},
which keeps track of the \glspl{neighbourhood} that led to improvements and
favours them for future iterations, is the prime example for this approach. A
simpler scheme may apply several \glspl{neighbourhood} in a round-robin fashion.
require more then reapplying the same \gls{neighbourhood} time after time. It
is, for example, often beneficial to use several \gls{neighbourhood} definitions
for a problem. Different \glspl{neighbourhood} may be able to improve different
aspects of a solution, at different phases of the search. Adaptive \gls{lns}
\autocite{ropke-2006-adaptive, pisinger-2007-heuristic}, which keeps track of
the \glspl{neighbourhood} that led to improvements and favours them for future
iterations, is the prime example for this approach. A simpler scheme may apply
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
all, calling \mzninline{uniformNeighbourhood} like that would result in a
cannot simply pass \mzninline{basic_lns(uniform_neighbourhood(x, 0.2))}. First
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 cycles
through a list of \mzninline{N} neighbourhoods \mzninline{nbhs}. To do this, it
uses the decision variable \mzninline{select}. In the initialisation phase
(\mzninline{status()=START}), \mzninline{select} is set to \mzninline{-1}, which
means none of the neighbourhoods is activated. In any following restart,
\Cref{lst:6-round-robin} defines a round-robin \gls{lns} meta-heuristic, which
cycles through a list of \mzninline{N} neighbourhoods \mzninline{nbhs}. To do
this, it uses the decision variable \mzninline{select}. In the initialisation
phase (\mzninline{status()=START}), \mzninline{select} is set to \mzninline{-1},
which 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
depending on whether the previous size was successful or not.
For adaptive \gls{lns}, a simple strategy is to change the size of the
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
is found, the solver adds a constraint to the remainder of the search to only
accept better solutions, as defined by the objective function in the
\minizinc\ solvers to use a branch-and-bound method for optimisation: when a new
solution is found, the solver adds a constraint to the remainder of the search
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:
{
\scriptsize
\highlightfile{assets/mzn/6_hill_climbing.mzn}
}
\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}.
%
A simulated annealing strategy is also easy to
express:
through the built-in variable \mzninline{_objective}. A more interesting example
is a simulated annealing strategy. When using this strategy, the solutions that
the solver finds are no longer required to steadily improve in quality. Instead,
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}
uses \mzninline{uniform(0.0,1.0)} in an \mzninline{if} expression, and
\mzninline{sol(x[i])} in an equality constraint. Both expressions can be
translated to \flatzinc\ when the functions return a \mzninline{var}.
\mzninline{uniform_neighbourhood} predicate from
\cref{lst:6-lns-minisearch-pred} uses \mzninline{uniform(0.0, 1.0)} in an
\mzninline{if} expression, and \mzninline{sol(x[i])} in an equality constraint.
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]
\highlightfile{assets/mzn/6_uniform_neighbourhood.mzn}
\begin{listing}
\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
block of code (\lrefrange{line:6:x1:start}{line:6:x1:end}) represents the
decomposition of the expression
\mzninline{b1} that is true if-and-only-if the status is not \mzninline{START}.
The second block of code (\lrefrange{line:6:x1:start}{line:6:x1:end}) represents
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
\mzninline{b3} is constrained to be the conjunction \mzninline{status()!=START
/\ uniform(0.0,1.0)>0.2}. \lref{line:6:x1} constrains \mzninline{x1} to be the
value of \mzninline{x[1]} in the previous solution. Finally, the half-reified
constraint in \lref{line:6:x1:end} implements \mzninline{b3 -> x[1]=sol(x[1])}.
is constrained to be true if-and-only-if the random number is greater than
\(0.2\); while \mzninline{b3} is constrained to be the conjunction of the two.
\lref{line:6:x1} constrains \mzninline{x1} to be the value of \mzninline{x[1]}
in the previous solution. Finally, the half-reified constraint in
\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.
Now \mzninline{s} is not 1, and \mzninline{b1} will be set to
\mzninline{true}. The \mzninline{float_random} propagator assigns
\mzninline{rnd1} a new random value and, depending on whether it is greater
than \mzninline{0.2}, the Boolean variables \mzninline{b2}, and consequently
\mzninline{b3} will be assigned. If it is \mzninline{true}, the constraint
in line \lref{line:6:x1:end} will become active and assign \mzninline{x[1]}
to its value in the previous solution.
When the solver restarts, all of the special propagators are re-executed. Now
\mzninline{s} is not 1, and \mzninline{b1} will be set to \mzninline{true}. The
\mzninline{float_random} propagator assigns \mzninline{rnd1} a new random value
and, depending on whether it is greater than \mzninline{0.2}, the Boolean
variables \mzninline{b2}, and consequently \mzninline{b3} will be assigned. If
it is \mzninline{true}, the constraint in line \lref{line:6:x1:end} will become
active and assign \mzninline{x[1]} 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
how these Boolean conditions are compiled and evaluated.
solution has been recorded yet, but we use this simple example to illustrate how
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
calls is straightforward, since \nanozinc\ is already processed call-by-call.
as well as to \emph{remove} calls from an existing \nanozinc\ program. Adding
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.}

10
dekker_thesis.tex
View File

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