%
% A Template for a Technical Report
%


\documentclass[11pt, conference, onecolumn, compsoc]{IEEEtran}
% Draft Mode for a Manuscript
% \documentclass[11pt, conference, onecolumn, compsoc, draftcls]{IEEEtran}

% Place IEEEtran.cls into the directory where a LaTeX source file of
% your paper resides in.
% Or manually specify the path to it like:
% \documentclass[11pt, conference, onecolumn, compsoc, draftcls]{../sty/IEEEtran}


% List LaTeX packages to be used
\usepackage{amsmath}	% use AMS math packages
\usepackage{amsfonts}	% if you want the AMS fonts
\usepackage{amssymb}	% if you want extra symbols
\usepackage{times}	% use Times font instead of Computer Modern font
\usepackage{epsfig}	% allow included Postscript
\usepackage{enumerate}	% use non-arabic numbers for labeling items 


\begin{document}

% paper title can use linebreaks \\ within to get better formatting as desired
% Give an appropriate title, e.g., An Algorithm for Searching on an Array
\title{A Title of Your Paper}


% author names and affiliations
% use a multiple column layout for up to two different
% affiliations

% \author{\IEEEauthorblockN{Authors Name/s per 1st Affiliation (Author)}
% \IEEEauthorblockA{line 1 (of Affiliation): dept. name of organization\\
% line 2: name of organization, acronyms acceptable\\
% line 3: City, Country\\
% line 4: Email: name@xyz.com}
% \and
% \IEEEauthorblockN{Authors Name/s per 2nd Affiliation (Author)}
% \IEEEauthorblockA{line 1 (of Affiliation): dept. name of organization\\
% line 2: name of organization, acronyms acceptable\\
% line 3: City, Country\\
% line 4: Email: name@xyz.com}
% }

\author{\IEEEauthorblockN{Your Full Name}
\IEEEauthorblockA{Department of Information and Computer Sciences\\
University of Hawaii at Manoa\\
Honolulu, Hawaii, U.S.A.\\
account@hawaii.edu}
}


% make the title area
\maketitle

\thispagestyle{plain}	
\pagestyle{plain}
\pagenumbering{arabic}


\begin{abstract}
An abstract is a paragraph of 100--200 words that
summarize the topic discussed in this paper and
the major achievement(s) of the paper
in order to attract attention of potential readers.
DO NOT USE LISTS, TABLES, OR FIGURES IN ABSTRACT.
The following is an example paragraph:
This paper addresses a problem of searching on a sorted array
of n distinct nonnegative integers.
We present %a recursive
an algorithm for the search problem.
The worst-case time complexity $t(n)$ of the algorithm is analyzed
and shown to be % $\Theta(\log n)$
$o(n)$
by solving a recurrence system on $t(n)$.
A na\"{i}ve algorithm scans the entire array
and results in $\Theta(n)$ time complexity.
Hence, our algorithm improves the order of magnitude
of the time complexity.
Then, the extra space required by the algorithm beside its input
is analyzed and shown to be $O(1)$.
Thus, it implies an optimum bound of the space complexity
for the problem.
\end{abstract}

\begin{IEEEkeywords}
algorithm; search; time complexity; space complexity; % recursion;
optimum bound
\end{IEEEkeywords}



\section{Introduction}
\label{Sintro}

% \input{intro.tex}	% `\input' command imports another tex source file

%% Introduction typically includes the following.
%% o Background
%% o An Introduction of the Paper's Topic to Readers
%% o Related Work (Survey of Previously Presented Results on Relevant Topics)
%% o Achievement(s) of the Paper
%% o Outline of the Paper


%% Here is an example of Introduction (irrelevant to the topic of Assignment 1)

%% Background
In recent years, {\em genetic algorithms}
({\em GAs})~\cite{Beasley93a,Beasley93b,Goldberg89}
have widely been recognized as an effective solving technique
for complex problems in the real world~\cite{Goldberg94}.
For example, a bibliography~\cite{Alander96}
on applications of GAs even limited to only engineering
includes over 1,400 papers as of April 1996.
As GAs are getting a larger spectrum of applications,
it becomes more crucial to develop a methodology for
the design of GAs.

GAs can be regarded as a paradigm of algorithms in the sense that
the GAs are parameterized and applicable to a variety of
problems by instantiating the paradigm.
There are the following 4 major components to be designed in GAs.
\begin{enumerate}
  \item	Coding:  The representation of potential solutions
	which is a mapping scheme from a problem to the GA paradigm
  \item	Fitness Function:  The quantified measure for quality
	of solutions which enables to differentiate ``good''
	solutions from ``bad'' solutions
  \item	Configuration:  A combination of operators which are
	applied to a population
  \item	Parameters:  Population size, population structure,
	operators' parameters (such as mutation rate),
	termination condition, etc.
\end{enumerate}
In an optimization problem, the fitness function is usually given
{\em a priori} as an objective function,
although the objective function may slightly be modified
so that constraints are incorporated into the fitness function
appropriately.

%% Motivation
Practitioners need a systematic way to design and implement
``good'' GAs for their particular problems quickly.
To design good algorithms, we should be able to compare
algorithms for the same problem and choose the best one
with respect to a certain criterion.
For deterministic, sequential algorithms
(what we traditionally call ``algorithms''),
there are well-defined criteria such as space and time
complexities.
These criteria were generalized and applied to
randomized algorithms as {\em average-case\/}
computational complexities though,
they are not suitable for evaluating the performance of GAs
accurately.

%% Previous Approaches and Related Work
The performance of GAs has been studied in terms of
resultant fitness values and convergence primarily.
For example, a number of papers investigated
correlations between convergence speed and
a particular parameter such as the population size
and mutation rate.
In many applications of optimization in practice
(not necessarily real-time applications),
however,
a goal is to find a solution as good as possible
``within a certain amount of time''~\cite{Nakano94}.
With such a constraint on computational cost, it is not
much critical to seek for convergence of a population.
Furthermore, some applications such as robot path planning
which will be discussed in Section~\ref{Sanalysis}
require the diversity of a population rather than the convergence
in order to utilize the adaptivity of a GA.
In addition, there may be a trade-off between solution quality
and convergence,
since a higher pressure (i.e., speed) to convergence tends to
increase the possibility of premature convergence at a local
optimum.

% Major Contributions
This paper proposes four performance measures of GAs:
The {\em likelihood of optimality},
the {\em average fitness value},
the {\em likelihood of evolution leap}, and
the {\em adaptivity}.
The measures are defined so that they can be observed
in simulation of GAs.
They enable us to compare between different configurations
of a GA for the same optimization problem and
between different parameter settings in each configuration.
Then, we present a case study in which a GA for robot path
planning was tuned by using the measures in order to use it
in motion planning of an underwater vehicle being developed
at the University of Hawaii~\cite{Choi95}.
The performance of the GA was optimized through performance
evaluation by using the proposed measures.
With this experience in tuning of the GA by simulation,
we propose a {\em process of tuning} based on techniques for
{\em experimental design}.
The process of tuning leads us to
a systematic way for design and tuning of a GA.
This is a step toward the development of a tool for
automatic tuning of GAs.

%% Organization of the Paper
This paper is organized as follows.
Section 2 presents the terminology on GAs,
defines the four performance measures, and
introduces basic concepts of experimental design.
Section 3 presents the case study which explains
how we tuned a GA for robot path planning and
shows simulation results on the performance of the GA.
Section 4 proposes the process of tuning and
discusses applications of techniques for experimental design
to the process.
Finally, Section 5 summarizes the paper.



\section{Preliminaries}
\label{Sprelim}

% \input{prelim.tex}

%% Preliminaries may include the following.
%% o Necessary Definitions
%% o Necessary Notations
%% o Basic Concepts Necessary for an Algorithm

\newpage
\vspace*{4in}


\section{Algorithm Design}
\label{Sdesign}

\subsection{Key Idea}
\label{SSkey}

% \input{key.tex}

\newpage
\vspace*{2in}


\subsection{Pseudocode}
\label{SSpseudo}

% \input{pseudocode.tex}

\newpage
\vspace*{4in}


\subsection{Correctness Proof}
\label{SScorrect}

% \input{correct.tex}

\newpage
\vspace*{2in}
\newpage



\section{Computational Complexity Analysis}
\label{Sanalysis}

\subsection{Time Complexity}
\label{SStime}

% \input{time.tex}

\newpage
\vspace*{2in}


\subsection{Space Complexity}
\label{SSspace}

% \input{space.tex}

\newpage


\subsection{Comparison with a Na\"{i}ve Algorithm}
\label{SScompare}

% \input{comparison.tex}

\vspace*{4in}



\section{Conclusion}
\label{Sconc}

%% A summary of achievement(s) in this paper possibly with concluding remarks
%% o Remaining open questions
%% o Future directions

%% Here is an example of Conclusion (irrelevant to the topic of Assignment 1)

This paper proposed the four performance measures of a GA:
The likelihood of optimality, the average fitness value,
the likelihood of evolution leap, and the adaptivity.
The case study was presented in which a configuration of the GA
for robot path planning was chosen, parameters of the GA
were tuned and the performance was optimized through
performance evaluation by using the measures.
Finally, we proposed the process of systematic tuning
based on techniques for the design of experiments.
This is a step toward the development of a tool
for automatic tuning of GAs~\cite{Smith96,SmithThesis}.

Based on the results presented in this paper,
we are developing a GA for 3D online motion planning of the
{\em Semi-Autonomous Underwater Vehicle for Intervention Missions\/}
(SAUVIM)~\cite{Sugihara97}
that is capable of exploring up to 6,000 m in a deep ocean
and manipulating objects with two arms.


%
% Acknowledgment Section
%
% If acknowledgement is written, uncomment the line \section*{Acknowledgment}
% Use `section*' (that does not print a section number) instead of `section'

% \section*{Acknowledgment}

% The authors would like to thank...



%
% References Section
%

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)

\begin{thebibliography}{99}

% \input{references.tex}

%%
%% List of Citations of References
%% (in the order of occurrences of their citations in the main text)
%%

\bibitem{Beasley93a}
D.\ Beasley, D.\ R.\ Bull and R.\ R.\ Martin,
``An overview of genetic algorithms: Part 1, fundamentals,''
{\em University Computing\/}, vol.\ 15, no.\ 2, pp.\ 58--69, 1993.
%[Online].
%Available:
%{\tt http://ralph.cs.cf.ac.uk/papers/GAs/ga\_overview1.pdf}

\bibitem{Beasley93b}
D.\ Beasley, D.\ R.\ Bull and R.\ R.\ Martin,
``An overview of genetic algorithms: Part 2, research topics,''
{\em University Computing\/}, vol.\ 15, no.\ 2, pp.\ 170--181, 1993.
%[Online].
%Available:
%{\tt http://ralph.cs.cf.ac.uk/papers/GAs/ga\_overview2.pdf}

\bibitem{Goldberg89}
D.\ E.\ Goldberg,
{\em Genetic Algorithms in Search, Optimization, and Machine Learning\/},
Reading, MA: Addison-Wesley, 1989.

\bibitem{Goldberg94}
D.\ E.\ Goldberg,
``Genetic and evolutionary algorithms come of age,''
{\em Commun.\ ACM\/}, vol.\ 37, no.\ 3, pp.\ 588--597, Mar.\ 1994.

\bibitem{Alander96}
J.\ T.\ Alander,
``An indexed bibliography of genetic algorithms in engineering,''
Univ.\ of Vaasa, Finland, Tech.\ Rep.\ No.\ 94-1-ENG,
1996.
%[Online].
%Available:
%{\tt ftp://ftp.uwasa.fi/cs/report94-1/}

\bibitem{Nakano94}
R.\ Nakano, Y.\ Davidor and T.\ Yamada,
``Optimal population size under constant computation cost,''
in {\em Parallel Problem Solving from Nature --- PPSN III\/},
ser.\ Lecture Notes in Computer Science,
Berlin, Germany: Springer-Verlag, 1994, vol.\ 866.

\bibitem{Choi95}
S.\ K.\ Choi, J.\ Yuh and G.\ Y.\ Takashige,
``Design of an omni-directional intelligent navigator,''
in {\em Underwater Robotic Vehicles:  Design and Control\/},
J.\ Yuh, Ed.,
TSI Press, 1995.

\bibitem{Smith96}
J.\ Smith and K.\ Sugihara,
``GA toolkit on the Web,''
in {\em Proc.\ First Online Workshop on Soft Computing\/},
Aug.\ 1996.

\bibitem{SmithThesis}
J.\ Smith,
``Parallel genetic algorithm toolkit for the World Wide Web,''
M.S.\ Thesis, Dept.\ of Information and Computer Sciences,
Univ.\ of Hawaii at Manoa, Honolulu, HI, Dec.\ 1996.

\bibitem{Sugihara97}
K.\ Sugihara and J.\ Yuh,
``GA-based motion planning for underwater robotic vehicles,''
in {\em Proc.\ 10th International Symposium on
Unmanned Untethered Submersible Technology (UUST-10)\/},
Durham, NH,
Sept.\ 1997, pp.\ 406-415.

\end{thebibliography}



%
% Optional Appendices
%

% \appendix


\end{document}