%% LATEX TWICE TO GET THE REFERENCES RIGHT
%%\documentstyle[12pt]{article}
\documentstyle[12pt,epsf,psfig]{article}

\newcommand{\postscript}[2]
 {\setlength{\epsfxsize}{#2\hsize}
  \centerline{\epsfbox{#1}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newtheorem{theorem}{Theorem}
\newtheorem{itlemma}{Lemma}[section] %number by section (set in \em by default)
%%%same numbering counter as itlemmas:
\newtheorem{itproposition}[itlemma]{Proposition}
\newtheorem{itcorollary}[itlemma]{Corollary}
\newtheorem{itremark}[itlemma]{Remark}
\newtheorem{itnote}[itlemma]{Note}
\newtheorem{itobservation}[itlemma]{Observation}
\newtheorem{itdefinition}[itlemma]{Definition}
\newtheorem{itexercise}[itlemma]{Exercise}
\newtheorem{itexample}[itlemma]{Example}

\newenvironment{lemma}{\begin{itlemma}\rm}{\end{itlemma}} %no-italics
\newenvironment{remark}{\begin{itremark}\rm}{\end{itremark}} %no-italics
\newenvironment{observation}{\begin{itobservation}\rm}{\end{itobservation}} %no-italics
\newenvironment{corollary}{\begin{itcorollary}\rm}{\end{itcorollary}}
\newenvironment{proposition}{\begin{itproposition}\rm}{\end{itproposition}}
\newenvironment{definition}{\begin{itdefinition}\rm}{\end{itdefinition}}
\newenvironment{exercise}{\begin{itexercise}\rm}{\end{itexercise}}
\newenvironment{example}{\begin{itexample}\rm}{\end{itexample}}

\tolerance=1600 %allow some tolerance in extending after line.
\parskip=3pt plus 1pt minus 1pt
\overfullrule=0pt %no dark lines if overfull

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This are for choices.  They take 4 or 6 args
%% (carriage returns allowed in between}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\twoif}[4]{
\left\{ \begin{array}{ll}#1&#2\\#3&#4\end{array}\right.
}
\newcommand{\threeif}[6]{
\left\{ \begin{array}{ll}#1&#2\\#3&#4\\#5&#6\end{array}\right.
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\partmlab#1#2#3#4#5#6#7#8{\bordermatrix{&#1&#2\cr#3&#5&#6\cr
					\noalign{\medskip}#4&#7&#8\cr}}
%% For 2by2 partitioned matrices; arguments are: two labels of top, side,
%% 4 entries (row by row).  If entries are themselves matrix or pmatrix,
%% better for readability of source to define first: \def\matrix1{...} etc.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\bigframebox}[1]{\framebox{\parbox{\smallerwidth}{#1}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Warning: use \noindent before!
% AND IN TEXT, after begin doc, do:
% \newlength{\smallerwidth}  %for bigboxes
% \setlength{\smallerwidth}{\textwidth}
% \addtolength{\smallerwidth}{-8pt}        %MUST BE DONE AFTER begin doc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def \beq {\begin{eqnarray}}
\def \eeq {\end{eqnarray}}
\def \beqn {\begin{eqnarray*}}
\def \eeqn {\end{eqnarray*}}

\newcommand{\rf}[1]{[\ref{#1}]}            %bibliographical references

\newcommand{\text}[1]{\hbox{\rm \ #1\ \/}}
\newcommand{\be}[1]{\begin{equation}\label{#1}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bl}[1]{\begin{lemma}\label{#1}}
\newcommand{\ble}[1]{\begin{lemmaex}\label{#1}}
\newcommand{\br}[1]{\begin{remark}\label{#1}}
\newcommand{\bn}[1]{\begin{note}\label{#1}}
\newcommand{\bo}[1]{\begin{observation}\label{#1}}
\newcommand{\bt}[1]{\begin{theorem}\label{#1}}
\newcommand{\bd}[1]{\begin{definition}\label{#1}}
\newcommand{\bp}[1]{\begin{proposition}\label{#1}}
\newcommand{\bc}[1]{\begin{corollary}\label{#1}}
\newcommand{\bfact}[1]{\begin{fact}\label{#1}}
\newcommand{\ber}[1]{\begin{exercise}\label{#1}}
\newcommand{\bex}[1]{\begin{example}\label{#1}}
\newcommand{\bem}[1]{\begin{example}\label{#1}}    %Yes, 2 different ones...
\newcommand{\ec}{\mybox\end{corollary}}
\newcommand{\efact}{\mybox\end{fact}}
\newcommand{\eer}{\mybox\end{exercise}}
\newcommand{\eex}{\mybox\end{example}}
\newcommand{\eem}{\mybox\end{example}}
\newcommand{\el}{\mybox\end{lemma}}
\newcommand{\ele}{\mybox\end{lemmaex}}
\newcommand{\er}{\mybox\end{remark}}
\newcommand{\en}{\mybox\end{note}}
\newcommand{\eo}{\mybox\end{observation}}
\newcommand{\et}{\qed\end{theorem}}
\newcommand{\ed}{\mybox\end{definition}}
\newcommand{\ep}{\mybox\end{proposition}}
\newcommand{\epr}{\end{proof}}
\newcommand{\bpr}{\begin{proof}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  These are just for statements, no "qed" box is put in.
%%  (Also for when I have to finish something after a displayed equation
%%        or itemized.)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\ecs}{\end{corollary}}
\newcommand{\eers}{\end{exercise}}
\newcommand{\eexs}{\end{example}}
\newcommand{\eems}{\end{example}}
\newcommand{\els}{\end{lemma}}
\newcommand{\eles}{\end{lemmaex}}
\newcommand{\ers}{\end{remark}}
\newcommand{\ens}{\end{note}}
\newcommand{\eos}{\end{observation}}
\newcommand{\ets}{\end{theorem}}
\newcommand{\eds}{\end{definition}}
\newcommand{\eps}{\end{proposition}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\qed}{\hfill \halmos} %put \qed at right margin
\newcommand{\mybox}{\hfill $\Box$} %put \qed at right margin (white square)

%%%\newcommand{\pmat}[2]{\left( \begin{array}{#1} #2 \end{array} \right) }
%%%use as e.g. \pmat{cc}{ a&b\\ a &c }  Note 'cc' for 2 Centered cols
%%%can also use \pmatrix{ a&b\cr a &c \cr} for plainTeX standard construct
%%%\setcounter{page}{27} should set the CURRENT page to 27

\def \R {\bb R} % reals
\def \C {\bb C} % complexes
\def \Z {\bb Z} % integers
\def \X {\bb X} % for this paper only!
\def \inter {{\rm int \,}}
\def \rank {{\rm rank \,}}
%%%\def \inf {{\rm inf \,}}  %better in Latex -- subscripts OK!
%%%\def \min {{\rm min \,}}
\def \im {{\rm im \,}}
\def \ker {{\rm ker \,}}
\def \norm #1{\Vert #1 \Vert}
\def \ip #1\by #2{\langle #1 , #2 \rangle}
\def \Sone {{\bf S}^1} % circle
\def \wigglearrow {\sim \mkern -6mu >}

\def \today {\ifcase \month \or January\or February\or  
  March\or April\or May\or June\or July\or August\or 
  September\or October\or November\or December\fi\   
  \number \day, \number \year}                       
\newcommand{\comment}[1]{}
\newcommand{\halmos}{\rule{1ex}{1.4ex}}
%%%alternative to \qed (see below)
\newenvironment{proof}{\noindent {\em Proof}.\ }{\hspace*{\fill}$\halmos$\medskip}

%%%\def\qed{\kern 1em \vrule height .5em width .5em depth 0em}
%%%(I now use new qed: in right margin)

\def\vbar{\mathchoice{\vrule height6.3ptdepth-.5ptwidth.8pt\kern-.8pt}
   {\vrule height6.3ptdepth-.5ptwidth.8pt\kern-.8pt}
   {\vrule height4.1ptdepth-.35ptwidth.6pt\kern-.6pt}
   {\vrule height3.1ptdepth-.25ptwidth.5pt\kern-.5pt}}
\def\fudge{\mathchoice{}{}{\mkern.5mu}{\mkern.8mu}}
\def\bbc#1#2{{\rm \mkern#2mu\vbar\mkern-#2mu#1}}
\def\bbb#1{{\rm I\mkern-3.5mu #1}}
\def\bba#1#2{{\rm #1\mkern-#2mu\fudge #1}}
\def\bb#1{{\count4=`#1 \advance\count4by-64 \ifcase\count4\or\bba A{11.5}\or
   \bbb B\or\bbc C{5}\or\bbb D\or\bbb E\or\bbb F \or\bbc G{5}\or\bbb H\or
   \bbb I\or\bbc J{3}\or\bbb K\or\bbb L \or\bbb M\or\bbb N\or\bbc O{5} \or
   \bbb P\or\bbc Q{5}\or\bbb R\or\bbc S{4.2}\or\bba T{10.5}\or\bbc U{5}\or
%%%   \bbb P\or\bbc Q{5}\or\bbb R\or\bba S{8}\or\bba T{10.5}\or\bbc U{5}\or
   \bba V{12}\or\bba W{16.5}\or\bba X{11}\or\bba Y{11.7}\or\bba Z{7.5}\fi}}
%
%
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
%%% read as: theFOOTNOTE (i.e. the command  executed when doing a footnote) is
%%% now to be set as a FOOTNOTESYMBOL (type of number) value of counter
%%% FOOTNOTE (Instead of Roman).  See LaTeX manual pp.91-92 as well as 175.
\def\bi{\begin{itemize}}
\def\ei{\end{itemize}}
\def\ben{\begin{enumerate}}
\def\een{\end{enumerate}}
\def\st{\, | \,}

\newcommand{\myboxineq}{\eqno\Box} %put \qed at margin (white square) in eqn
\newcommand{\qedineq}{\eqno\halmos} %put \qed at margin in eqn

\topmargin -0.5in %default is 0.0, i.e. 1 inch from top.  Now it is 0.5
\textheight 9in
\oddsidemargin 0.25in %more reasonable margins!  (This is 1.25; can use <0 too)
\evensidemargin 0.25in %(same as above)
\textwidth 6.25in %(could use also -.5,-.5,7.5 for instance)
\tolerance=1600 %allow some tolerance in extending after line.
\parskip=3pt plus 1pt minus 1pt
\overfullrule=0pt %no dark lines if overfull

%%%% FROM HERE, macros special for paper
\def\mm{m}
\def\pp{p}
\def\proj{\pi _1} % projection on first group of coordinates
\def\x{u}  % vector argument
\def\SEC{(SEC)}
\def\SECo{(SEC$^0$)}
\def\INV{(INV)}
\def\Fp{{\cal F}_\pp}
\def\Fpm{{\cal F}_\pp^\mm}  %there is a 3,3 and a 2,1 in text

\def\Rm{\R^m}
\def\Rn{\R^n}
\newcommand{\ball}[2]{{\bb B}(#1,#2)}
\newcommand{\cball}[2]{\overline {\bb B} (#1,#2)}
\def\Fnm{{\cal F}_n^\mm}
\def\clos{{\rm clos\,}}
\def\inter{{\rm int\,}}

\def\CCF{compatible class of functions}
\begin{document}

\begin{flushright}
{\sl Thesis-Outline}
\end{flushright}
\vspace{2cm}
\begin{center} 
\hrule
\hrule
\hrule
\hrule
\hrule
\hrule
\hrule
\hrule
\hrule
\hrule
\vspace{.05cm}
\hrule
\vspace{.25cm}
{\bf 
Mean Field Annealing, Simulated Annealing, and non-Euclidean
Combinatorial Optimization  Problems: The case of Academic Course
Scheduling.
}
\vspace{.25cm}
\hrule
\vspace{.05cm}
\hrule
\hrule
\hrule
\hrule
\hrule
\vspace{2.5cm}

Saleh Elmohamed\\
Northeast Parallel Architectures Center,\\
Syracuse University\\
Syracuse, NY 13244\\
saleh@npac.syr.edu\\
\end{center}


\vfill
\centerline{\today}
\vfill

\newpage

\pagestyle{plain}
\pagestyle{myheadings}
\markright{\sl Thesis-Outline}

\section{A rough outline of the chapters}
\begin{enumerate}
\item The first chapter (goto ch. 2 or 3)
\begin{itemize}
\item Introduction
\item Background
\item Motivation
\end{itemize}

\item The second chapter (goto ch. 4 or 5 or 6)
\begin{itemize}
\item The timetabling problem
\item Type of constraints and data involved
\item Representation of the problem's constraints
\end{itemize}

\item The third chapter (goto ch. 4 or 5)
\begin{itemize}
\item Heuristics and Methods
\begin{itemize}
\item Mean Field Annealing [MFA] (a neural networks approach)
\begin{itemize}
\item Description of the Method
\item On the Network Topology and Simulation
\end{itemize}
\item Simulated Annealing [SA]
\begin{itemize}
\item The Algorithm, description of its steps
\item Cooling and adaptive cooling schedules
\end{itemize}
\item Expert Systems [ES]
\item Graph Coloring heuristics
\end{itemize}
\end{itemize}

\item The fourth chapter (goto ch. 5 or 7)
\begin{itemize}
\item More on Simulated Annealing and cooling schedules
\item Handling timetabling constraints on SA
\end{itemize}

\item The fifth chapter (goto ch. 4 or 7)
\begin{itemize}
\item More on Mean Field Annealing 
\item Handling timetabling constraints on MFA
\end{itemize}

\item The sixth chapter (goto ch. 7)
\begin{itemize}
\item More on graph coloring representation
\item Mapping of timetabling into graph coloring
\end{itemize}

\item The seventh chapter (goto ch. 1)
\begin{itemize}
\item Simulation results
\begin{itemize}
\item Comparison of figures and plots/graphs
\item What to deduce from such results (or what have we learned so
far?) 
\end{itemize}
\end{itemize}

\item Appendix A
\begin{itemize}
\item Sample code and modules
\begin{itemize}
\item SA modules, $\ldots$
\item MFA modules, $\ldots$
\item ES modules, $\ldots$
\item GC modules, $\ldots$
\end{itemize}
\end{itemize}

\item Appendix B
\begin{itemize}
\item On the WWW optimization set of tools
\item List of tools
\item How they are related?
\item Others $\ldots$ ?
\end{itemize}

\item References

\end{enumerate}

\section{A set of educational tools in optimization on the web}

\begin{itemize}
\item Our current optimization paper using simulated annealing,
mean field annealing, and graph coloring heuristics will be converted
to an html document... Also, this paper and other two (one addressing
various theoretical issues of feedforward neural nets, and the other
talks about a biologically inspired alternative algorithm to
back-prop) will be made available as SCCS documents.

\item A glossary of terms, concepts and a roadmap of pointers and
references are to be added to the aforementioned html document. The
target is to make it part of the educational roadmaps on {\it
http://www.npac.syr.edu/roadmap/}.

\item Pointers to other useful pages and references are to be
included.

\item Pointers to other optimization methods tackling timetabling or
scheduling in general are also to be included.

\item When this page becomes available I'll make it accessible from my
homepage as well as be part of the aforementioned roadmap.

\item Roadmap to physical optimization using heuristics such as
genetic algorithms, tabu search, neural nets, and simulated annealing.

\item Roadmap to data mining
\begin{enumerate}
\item Methods and heuristics used.
\item Other ongoing work and literature.
\end{enumerate}


\end{itemize}
\end{document}

