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

Update background section

Browse Source
This commit is contained in:
Jip J. Dekker 2021-04-12 17:07:50 +10:00
parent 8c6f4572e8
commit 29b31b2a09
No known key found for this signature in database
GPG Key ID: 517DF4A00618C9C3
3 changed files with 31 additions and 32 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

16
assets/mzn/back_knapsack.mzn
View File

@ -1,15 +1,15 @@
% Problem parameters
enum TOYS;@\Vlabel{line:back-knap-toys}@
array[TOYS] of int: toy_joy;@\Vlabel{line:back-knap-joy}@
array[TOYS] of int: toy_space;@\Vlabel{line:back-knap-space}@
int: space_left;@\Vlabel{line:back-knap-left}@
enum TOYS;@\Vlabel{line:back:knap:toys}@
array[TOYS] of int: toy_joy;@\Vlabel{line:back:knap:joy}@
array[TOYS] of int: toy_space;@\Vlabel{line:back:knap:space}@
int: space_left;@\Vlabel{line:back:knap:left}@
% Decision variables
var set of TOYS: selection;@\Vlabel{line:back-knap-sel}@
var int: total_joy = sum(toy in selection)(toy_joy[toy]);@\Vlabel{line:back-knap-tj}@
var set of TOYS: selection;@\Vlabel{line:back:knap:sel}@
var int: total_joy = sum(toy in selection)(toy_joy[toy]);@\Vlabel{line:back:knap:tj}@
% Constraints
constraint sum(toy in selection)(toy_space[toy]) < space_left;@\Vlabel{line:back-knap-con}@
constraint sum(toy in selection)(toy_space[toy]) < space_left;@\Vlabel{line:back:knap:con}@
% Goal
solve maximize total_joy;@\Vlabel{line:back-knap-obj}@
solve maximize total_joy;@\Vlabel{line:back:knap:obj}@

1
assets/packages.tex
View File

@ -82,6 +82,7 @@ style=apa,
\newcommand{\Vlabel}[1]{\label[line]{#1}\hypertarget{#1}{}}
\newcommand{\lref}[1]{\hyperlink{#1}{\FancyVerbLineautorefname~\ref*{#1}}}
\newcommand{\Lref}[1]{\hyperlink{#1}{\FancyVerbLineautorefname~\ref*{#1}}}
\newcommand{\lrefrange}[2]{\FancyVerbLineautorefname{}s~\hyperlink{#1}{\ref*{#1}}--\hyperlink{#2}{\ref*{#2}}}
\newcommand{\Lrefrange}[2]{Lines~\hyperlink{#1}{\ref*{#1}}--\hyperlink{#2}{\ref*{#2}}}

46
chapters/2_background.tex
View File

@ -130,20 +130,20 @@ Let us introduce the language by modelling the problem from
\end{listing}
The model starts with the declaration of the \glspl{parameter}.
\Lref{line:back-knap-toys} declares an enumerated type that represents all
\Lref{line:back:knap:toys} declares an enumerated type that represents all
possible toys, \(T\) in the mathematical model in the example.
\Lref{line:back-knap-joy,line:back-knap-space} declare arrays mapping from toys
\Lref{line:back:knap:joy,line:back:knap:space} declare arrays mapping from toys
to integer values, these represent the functional mappings \(joy\) and
\(space\). Finally, \lref{line:back-knap-left} declares an integer
\(space\). Finally, \lref{line:back:knap:left} declares an integer
\gls{parameter} to represent the car capacity as an equivalent to \(C\).
The model then declares its \glspl{variable}. \Lref{line:back-knap-sel} declares
The model then declares its \glspl{variable}. \Lref{line:back:knap:sel} declares
the main \gls{variable} \mzninline{selection}, which represents the selection of
toys to be packed. \(S\) in our earlier model. We also declare the variable
\mzninline{total_joy}, on \lref{line:back-knap-tj}, which is functionally
\mzninline{total_joy}, on \lref{line:back:knap:tj}, which is functionally
defined to be the summation of all the joy for the toy picked in our selection.
Finally, the model contains a constraint, on \lref{line:back-knap-con}, to
Finally, the model contains a constraint, on \lref{line:back:knap:con}, to
ensure we do not exceed the given capacity and states the goal for the solver:
to maximise the value of the variable \mzninline{total_joy}.
@ -157,30 +157,30 @@ primitive constraints.
Given the assignments
\begin{mzn}
TOYS = {football, tennisball, stuffed_lama, stuffed_elephant};
toy_joy = [63, 12, 50, 100];
toy_space = [32, 8, 16, 40];
space_left = 64;
TOYS = {football, tennisball, stuffed_elephant};
toy_joy = [63, 12, 100];
toy_space = [32, 8, 40];
space_left = 44;
\end{mzn}
is the result of flattening for \mzninline{n=2}:
the following model is the result of flattening:
\begin{mzn}
var 1..2: x_1_1;
var 1..2: x_1_2;
var 1..2: x_2_1;
var 1..2: x_2_2;
constraint all_different([x_1_1, x_1_2]);
constraint all_different([x_2_1, x_2_2]);
constraint all_different([x_1_1, x_2_1]);
constraint all_different([x_1_2, x_2_2]);
var 0..1: selection_0;
var 0..1: selection_1;
var 0..1: selection_2;
var 0..175: total_joy:: is_defined_var;
constraint int_lin_le([32,8,40],[selection_0,selection_1,selection_2],44);
constraint int_lin_eq([63,12,100,-1],[selection_0,selection_1,selection_2,total_joy],0):: defines_var(total_joy);
solve maximize total_joy;
\end{mzn}
This \emph{flat} problem will be passed to some \gls{solver}, which will attempt
to determine an assignment to each decision variable \verb|x_i_j| that satisfies
all constraints, or report that there is no such assignment.
to determine an assignment to each decision variable \mzninline{solection_i} and
\mzninline{total_joy} that satisfies all constraints and maximises
\mzninline{total_joy}, or report that there is no such assignment.
\section{The current \glsentrytext{minizinc} interpreter}%
\section{The Current \glsentrytext{minizinc} Interpreter}%
\label{sec:back-mzn-interpreter}
\section{Other Constraint Modelling Languages}%
@ -191,5 +191,3 @@ all constraints, or report that there is no such assignment.
\section{Constraint Logic Programming}%
\label{sec:back-clp}