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% Title.
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\title{Swarm Intelligence Engineering for Spatial Organization Modelling}
%
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\name{Author(s) Name(s)\thanks{Thanks to XYZ agency for funding.}}
\address{Author Affiliation(s)}

\twoauthors
  {Rawan Ghnemat, Cyrille Bertelle}
   {LITIS - University of Le Havre\\
   25 rue Philippe Lebon - BP 540\\
   76058 Le Havre cedex, France}
  {G\'erard H.E. Duchamp}
   {LIPN - University of Paris XIII\\
   99 avenue Jean-Baptiste Cl\'ement\\
   93430 Villetaneuse, France}
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%  {C. Author-three, D. Author-four\sthanks{The fourth author performed the work
%   while at ...}}
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\begin{document}
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\begin{abstract}
In this paper, we propose a swarm intelligence algorithm to deal with dynamical and spatial organization emergence. The goal is to model and simulate the developement of spatial centers using multi-criteria. We combine a decentralized approach based on emergent clustering mixed with spatial constraints or attractions. We propose an extension of the ant nest building algorithm with multi-centers and adaptive process. Typically, this model is suitable to analyse and simulate urban dynamics like gentrification or the dynamics of the cultural equipment in urban area. 
\end{abstract}

\begin{keywords}
swarm intelligence, complex systems, self-organization, ant systems, spatial organization
\end{keywords}

\vspace*{0.5in}
\vspace*{-\baselineskip}
%

\section{Introduction}
\label{sec:intro} 

Many natural and artificial systems have emergent properties based on spatial development. This spatial development is the result of some mecanisms from the system behavior but the spatial development itself, is the actor of the system formation by morphogenetic feedback. Natural ecosystems or social organizations in urban dynamics are typically such emergent spatial organization. The goal of this paper is to study some computable mecanisms and algorithms able to model such spatial self-organization processes, taking into account the complexity of the phenomena.\\ 

In section \ref{sec:modcomp}, complex system concepts are defined and theirs applications to urban dynamics understanding are described. Section \ref{sec:swarmIntelligence} presents swarm intelligence algorithms as methodologies to implement the complex systems concepts, using distributed computations. Section \ref{sec:emergentSpatialOrganization} propose some specific swarm intelligence methods based on ant systems to model the spatial organizations emergence. Ant clustering is presented as the basis of the self-organization process. An algorithm based on the usage of pheromon template is proposed as an extension of this self-organization process, allowing to control some spatial constraints during the self-organization phenomenon. Using multi-template, we propose a general methodology to solve multi-criteria spatial self-organization. Experiment are given, using repast agent platform mixed with a geographical information system.   
 


\begin{figure*} [ht]
 \begin{center}
 \includegraphics[width=0.65\textwidth]{MasFromGis.png}\\
(a) Complexity of geographical space with respect of emergent organizations\\
 \includegraphics[width=0.5\textwidth]{app2mod-en.png}\\
(b) Modelling the organization detection using swarm intelligence over dynamical environments 
 \caption{Spatial organizations Complexity Description and the Conceptual Generic Model Based on Swarm Intelligence}
 \label{urbanComplexityModelling}
 \end{center}
 \end{figure*}




\section{Modelling Spatial Complexity}
\label{sec:modcomp} 

\subsection{Complex System Concepts}
\label{subsec:comsys}

\subsubsection{From Entities to Systems}
Complex system theory is based on the fact that from many applicative domains, we can find similar processes linking emergent global behavior and interaction network of constituents. The global behavior is generally not accessible using classical analytical methods.\\ 

In classical analytical methods, the global behavior of the system is the description of the equations. Simulations from these formulations, consist in obtaining the trajectories of the behavior predefined in the equation formulation. \\

In complex systems modelling, we have to model the constituents of the system and the interaction network or system which link these constiuents, using a decentralized approach. So the global behavior of the system can not be understood by the description of each constituent. In complex system modelling, the global behavior is an emergent property from the interaction network or systems between its constituents and lead to the creation of an dynamical organization of these constituents\\

This dynamical and emergent organization retro-acts on its own components. Two kinds of feedback allow to describe these phenomenon. The positive feedback means that the emergence increases the organization constitution. the negative feedback means that the emergence has regulator properties which finally stop the increasing organization constitution and allow the system stabilization.\\

\subsubsection{Spatial emergence from system and environment interaction}

Another major aspect of complex systems concern that they can be considered as open systems. This means that they are crossed by energetical fluxes that make them evolve in continuous way. From these energetical fluxes, complex systems can evolve through critical states, using bifurcation schema and attractors behaviors. One of the major vector or support of these energetical fluxes is the environment itself where the complex systems and theirs entities evolve. In many natural and artificial systems, the environement has some spatial effects which interact on the whole complexity of the phenomenon. This spatial environment can be modified by the system but he can also be the catalyst of its own evolution. Understanding and modelling the deeply structural effect of the interaction between the systems and its spatial environment is the goal of the study presented in the following.

\subsection{Application to urban dynamics}

Social and human developments are typical complex systems. Urban development and dynamics are the perfect systems illustration where spatial emergence, self-organi\-za\-tion and structural interaction between the system and its components occur. In the figure \ref{urbanComplexityModelling}, we focuss our attention on the emergence of organizational systems from geographical systems. The continuous dynamic development of the organization feed-back on the geographical system which contains the organization components and their environment. The right part of this figure explains our analysis methodology which consiste to describe many applicatives problems by dynamical graphs or environments, to detect organizations over these dynamical environment, using swarm intelligence processes and to model the feed-back process of these emergent organization on the system constituents and its environment. To analyse or simulate urban dynamics, nowadays, we can use the greta amount of geographical database directly available for computational treatment within Geographical Information Systems. On the organizational level description, the new development of multiagent systems (MAS) allow nowadays to develop suitable models and efficient simulations.\\

The applications we focuss with the models that we will propose in teh following concerns specifically the multi-center (or multi-organizational) phenomona inside urban development. As an artificial ecosystems, the city development has to deal with many challenges, specifically for sustainable development, mixing economical, social and environmental aspects. The decentralized methodology proposed in the following allows to deal with multi-criteria problems, leading to propose a decision making assistance, based on simulation analysis. \\

Gentrification (to be completed)\\

Cultural dynamics (to be completed)\\
 

\section{Swarm Intelligence and Spatial Environment}
\label{sec:swarmIntelligence}

Decentralized algorithms have been implemented for many years for various purposes. In this algorithm category, multi-agent systems can be considered as generic methods \cite{weiss}. Agent-based programming deals with two main categories of agent concepts: cognitive agents and reactive agents. The first category concerns sophisticated entities able to integrate, for example, knowledge basis or communications systems. Generally, efficient computations, based on these cognitive architectures, implement few agents. The second category of agents, based on reactive architecture, is expected to be used inside numerous entity-based systems. The goals of programs using such architectures, is to deal with emergent organizations using specific algorithms called emergent computing algorithms. Swarm Intelligence is the terminology used to point out such reactive agent-based methods where each entity is built with the same basis of behavior, but reacts in autonoumous way. Swarm Optimization methods concern the problems of optimization where the computation of a function extramum is based on the concept of swarm intelligence.\\ 

Ant Colony Optimization (ACO) methods \cite{bonabeau99} is a bio-inpirated method family where the basic entities are virtual ants which cooperate to find the solution of graph-based problems, like network routing problems, for example. Using indirect communications, based on pheromon deposites over the environment (here a graph), the virtual ants react in elementary way by a probabilistic choice of path weighted with two coefficients, one comes from the problem heuristic and the other represent the pheromon rate deposit by all the ants until now. The feed-back process of the whole system over the entities is modelled by the pheromon action on the ants themselves.\\ 

Particule Swarm Optimization (PSO) is a metaheuristic method initially proposed by J. Kennedy and R. Ebenhart \cite{kennedy95}.This method is initialized with a virtual particle set which can move over the space of the solutions corresponding to a specific optimization problem. The method can be considered like an extension of a bird flocking model, like the BOIDS simulation from C.W. Reynolds \cite{reynolds87}. In PSO algorithm, each virtual particle moves according to its current velocity, its best previous position and the best position obtained from the particles of its neighborhood. The feed-back process of the whole system over the entities is modelled by the storage of this two best positions as the result of communications between the system entities.\\

Other swarm optimization methods have been developped like Artificial Immune Systems \cite{castro02} which is based on the metaphor of immune system as a collective intelligence process. F. Schweitzer proposes also a generic method based on distributed agents, using approaches of statistical many-particle physics \cite{schweitzer2003}.\\

The method proposed in this paper is based on Ant Clustering and Ant Nest Building, allowing to deal with self-organization processes emerging from spatial constraints and attractives area. 

%\subsection{Distributed Computation}


%\subsection{Swarm Intelligence and Self-organization Support}

%\section{Multi-center Multi-criteria Problem}
%\label{sec: problem}

% \subsection{Spatial organization emergence}
% \label{subsec: spatialOrganizationEmergence}
% 
% \subsection{Emergent spatial organization regulation}
% \label{subsec: regulation}
% 
% \subsection{Urban dynamics}
% \label{subsec: urbanDynamics}
% 
% \subsubsection{cultural dynamics}
% 
% \subsubsection{gentrification}

\begin{figure*} [ht]
 \begin{center}
 \includegraphics[width=0.65\textwidth]{CaptureAntClustering1.png}\\
(a) initial step\\
 \includegraphics[width=0.65\textwidth]{CaptureAntClustering2.png}\\
(b) intermediate step
 \caption{Ant Clustering Simulation using Repast on OpenMap}
 \label{antClustering}
 \end{center}
 \end{figure*}


\begin{figure*} [ht]
 \begin{center}
 \includegraphics[width=0.45\textwidth]{anneau.png}~~~~~~
\includegraphics[width=0.45\textwidth]{mqt2.png}\\~\\
 \includegraphics[width=0.5\textwidth]{CaptureOneQueen1.png}~~~~~~
\includegraphics[width=0.5\textwidth]{CaptureMultiQueen.png}
 \caption{Templates and associated Ant Nest Building Simulation. On the left, with one queen. On the right with two queen }
 \label{antNestBuilding}
 \end{center}
 \end{figure*}


\begin{figure*}[ht]
\begin{center}
\includegraphics[width=\textwidth]{culturalMultiQueenModel.png}
\caption{Cultural Equipment Dynamics Modelling}
\label{culturalModelling}
\end{center}
\end{figure*}


 \begin{figure*} [ht]
 \begin{center}
 \includegraphics[width=0.7\textwidth]{CaptureOneQueen1.png}\\
(a) after few step\\
 \includegraphics[width=0.7\textwidth]{CaptureOneQueen2.png}\\
(b) after queen adaptive development
 \caption{Adaptive queen behavior modelling: according to its surround material spatial perception, the queen evolves}
 \label{adaptiveQueen}
 \end{center}
 \end{figure*}



\section{Emergent Spatial Organizations over Complex Behavioral Clustering}
\label{sec:emergentSpatialOrganization}
%\section{Multi-queen ant nest building}
%\label{multiqueen}

%\subsection{From self-organized clustering to spatially constrained emergent building}
%\label{subsec: clustering2spatial}

We will describe in the section, the general algorithm which is proposed to model emergent spatial organizations. This algorithm is based on the ant clustering. We introduce pheromon template to spatially control the clustering from local attraction. This method is a decentralized approach which allow to combinate multi-center and multi-criteria problem and we will show how we can apply it to modelling cultural dynamics in urban area. We conclude this section with the description of a adaptive process which lead to model the feedback of the emergent system on its own mecanisms. 

\subsection{Ant clustering}

Ant clustering algorithm is inspirated by the corposes or larvea classification and aggregation that the ants colony are able to do in the real life. The ants are moving inside a closed area and are able to move some material which are randomly put on this area. After a while, and without any kind of centralized coordonation, the ants success to create some material clusters.\\

The algorithm is based on the following and very simple behavioral rules that each ant implements~:

\begin{itemize}
 \item When a ant is moving without carrying yet material and find some material. The ant will take the material respecting the probability number~:
\begin{equation}
P_p=\left(\frac{k_1}{k_1+f}\right)^2
\label{eq:pp}
\end{equation}
where $f$ is the material density that the ant perceive locally around itself and $k_1$ is the treshold. It is easu=y to check that if $f<<k_1$ then $P_p$ is near the value $1$ and if $f>>k_1$ then $P_p$ is near the value $0$.
\item When a ant is moving with carrying some material, the probability to deposite it is compute by~:
\begin{equation}
P_d=\left(\frac{f}{k_2+f}\right)^2
\label{eq:pd}
\end{equation}
where $f$ is still the material density that the ant perceive locally around itself and $k_2$ is another treshold. It is easy to check that if $f<<k_2$ then $P_d$ is near the value $0$ and if $f>>k_2$ then $P_d$ is near the value $1$.
\end{itemize}

On the figure \ref{antClustering}, we show an implementation of this algorithm using the multi-agent platform called Repast \cite{repast2008}. The java version of this platform include some packages allowing to interface with geographical database and geographical information systems (GIS). On the figure \ref{antClustering}, the graphical output windows is made under OpenMap which is a GIS developped in Java. On this figure, we see the materials moved by the ants are the small grey circles, the ant moving without material are the green circles and the ant carrying material are the red circles. 

\subsection{Spatial constraints using template}

The ant clustering shows some spatial self-organizations but has the specificity to generate clusters at random places. According to the first random moves that the ants start to do in the beginning of the algorithm, some material will initiate aggregation and the clustering processus will complete them from these initial random first aggregations. To simulate some urban dynamics, we need to introduce specific location in respect of city center for exemple or cultural equipments. The clustering here will represent the people usage of theses centers or equipments and we need to introduce an attractive effect by using a pheromon template. This method follow the algorithm known as Ant Nest Building \cite{bonabeau99}. In ant colonies, the center corresponds to the position of the queen which needs to buid the nest and the ant colony move around it to protect the nest by various material taken on the ground. The queen emits a pheromon which allow to attract the ants during their building. The ant has to deposite the material carried only if the pheromon quantity perceived belongs to a specific range.  We use an attractive fonction called $P_t$, corresponding to a pheromon template and represented by the left top part of the figure \ref{antNestBuilding}.\\

Using this template function, we remplace in the clustering algorithm, the two provious probabilities defined in equation (\ref{eq:pp}) and equation (\ref{eq:pd}) by 

\begin{equation}
P_p'=P_p (1-P_t) 
\end{equation}

\begin{equation}
P_d'=P_d P_t
\end{equation}


\subsection{Multi-template modelling}
\label{subsec: multiTemplate}

The previous subsection describes one local attractive process characterized by the queen and its pheromon template emission. The advantage of this method is to be able to be combinated to solve multi-center and multi-criteria problem, using interactive processes, each one is represented by a queen and its pheromon template.\\

On the figure (\ref{antNestBuilding}), we can see on the left part, a single queen simulation and in the right part, a simulation with two queens and two pheromon templates. It is possible also for each queen to emits many different kinds of pheromons~: we called them colored pheromons. Each colored pheromon will attract only the ants associated to its color. 

\subsection{Application to cultural equipment dynamics}

The multi-template modelling can be used to model cultural equipment dynamics as described in the figure (\ref{culturalModelling}). On this figure, we associate to each cultural center (cinema, theatre, ...) a queen. Each queen will emit many pheromon templates, each template is assocoated to a specific criteria (according the the age, the sexe, ...). Initially, we put the material in the residential place. Each material has some characteristics, corresponding to the people living in this residential area. The simulation shows the self-organization processus as the result of the set of the attractive effect of all the center and all the templates.  

\subsection{Adaptive Spatial Organization Feedback Implementation}
\label{subsec: adaptiveFeedback}

As explained in the section \ref{sec:modcomp}, complex systems deal not only with emergent organization processus from the interaction of its own entities, but also with the feedback processus of the organization over its own components. In the proposed model, we can take into account such feedback process and we present in the figure \ref{adaptiveQueen}, an adaptive processus which make the queen (which describe the organization itself) modify the environment and the clustering processus itself. Following the template function, the queen locally defines around it two zones. The first zone is near itself and it is expected to not find material there. The second zone corresponds to the template maximum and it is expected to find a great concentration of material there. In the simulation, we count in dynamical way the number of material in these two zones and when these numbers reach some tresholds, we make evolve the queen by increasing its own size and so increasing the 2 associated zones. Afetr this evolution, the ants have to move some material following the new template function attraction. The low part of the figure shows the evolution of the queen which has evolve 6 times since the simulation beginning. On this figuer, we can see the red curves counting the zones density. Each gap in these density curves correspond to an evolution of the queen. 
% The community swarm optimization method is based on a genetic algorithm over a population of spatial automata-based agents. The formation of the community is the result of the population evolution, crossing by a selection process computed with the fitness function defined in the following.\\
% 
% For this computation, we deal with two distances defined on agent sets. The first is the spatial distance associated with the agent spatial location and the second is the behavioral semi-distance defined in the definition \ref{behavioralDistance}.\\
% 
% %%% definition of the fitness %%%%%%
% \begin{definition}
% {\bf Community clustering and detection fitness}\\
% Let ${\cal{V}}_x$ a
% neighbourhood of the agent $x$, relative to its spatial location.  
% We define $f(x)$ the agent fitness of the agent $x$ as~:
% $$
% f(x) = 
% \left\lbrace
% \begin{array}{ll}
% \frac{ {\displaystyle card({\cal{V}}_x) } }
%      { {\displaystyle \sum\limits_{y_i \in {\cal{V}}_{x}} d(x, y_i)^2} } 
%      \ \ \ \ &\mbox{if} \sum\limits_{y_i \in {\cal{V}}_{x}} d(x,
% y_i)^2 \neq 0 \\
% \infty &\mbox{otherwise}
% \end{array}
% \right.
% $$
% where $d(x,y)$ is the behavioral distance between the two agents $x$ and $y$.\\
% \end{definition}
% 
% This fitness allows to implement a co-evolution process which generates an emergent set of community swarms. These community swarm formation is the result of both the emergence of the spatial location of the generated communities and the adaptive behavior of the communities as the result of the homogeneisation of the behavioral automata of all agents which compose these emergent communities. 
% 
% %\subsection{General CSO algorithm}
% %\label{subsec:algorithm}
% 
% % \textcolor{red}{Description of the whole algorithm based on (1) Initial description of the representation based on spatial behavior, described by transition rules (2) building of the initial spatial behavioral automata population describing the previous representation (3) Genetic evolution process}
% 
% CSO algorithm needs a initial step description which is the major step of the modelling process. The way of going from the problem formulation to the initial spatial automata-based agents must be realized in accuracity. The formal description of the methodology to use, for this initial step, is described in Algorithm \ref{iniAlgo}.
% 
% \begin{algorithm}[h]
% 1. Problem formulation by the definition of a set of transition rules \;
% 2. Building of the behavioral automata based on the previous set of transition rules, describing the sequences and the context of their applications \;
% 3. Discretization of the spatial domain, according to its topological properties (Cellular automaton, network or graph, Geographical Information System) with the spatial location of the initial virtual population of spatial automata-based agents\;
% \caption{Methodology to model the initial step of CSO}
% \label{iniAlgo}  
% \end{algorithm}
% 
% The core of the CSO algorithm is described by the iterative scheme defined in the Algorithm \ref{coreAlgo}. \\
% 
% \begin{algorithm}[h]
% Building the initial virtual population of the spatial automata-based agents (following the methodology of Algorithm (\ref{iniAlgo})) \;
% \Repeat{(the sum of the fitness values of the whole population reachs a threshold) $or$ (the maximum iteration number is reached) }
% {
% \For{Each couple of individuals in the population}
% 	{Reproduction step generating 2 new children as described in the section (\ref{subsec:geneticOp}) \;
% 	Mutation step as described in the section (\ref{subsec:geneticOp}) \;
% 	}
% Selection of the half population of the individuals corresponding to the highest values of the agent fitness described in section (\ref{subsec:adaptiveObjective}) \;} 
% \caption{Iteratice scheme of CSO}
% \label{coreAlgo}
% \end{algorithm}
% 
% An example of fitness function computation output is illustrated by the figure \ref{communitySamples} where we show, on the same population, an high level fitness individual which will be probably kept inside the population at the next iteration and a low level fitness individual which be probably removed from the population at the next iteration. The colors used describe graphically the chromosome composition, allows to appreciate the similarity of the individuals. 
% 
% \begin{figure*} [ht]
% \begin{center}
% \includegraphics[scale=0.2]{community1.png}
% \includegraphics[scale=0.2]{community2.png}
% \caption{Two examples of the result of selection operators within the CSO algorithm}
% \label{communitySamples}
% \end{center}
% \end{figure*}


\section{Conclusion and Perspectives}
\label{sec: conclusion}

\begin{thebibliography}{1}

\bibitem{alaoui2006a} M.A. Aziz-Alaoui, C. Bertelle (eds),{\em Emergent properties in Natural and Artificial Dynamical Systems}, ``Understanding Complex Systems'' serie, Springer, 2006.

\bibitem{geosimulation} Benenson, I., Torrens, P.M. (2004) {\it Geosimulation - Automata-based modeling of urban phenomena}, Wiley.

\bibitem{bertelle2008a} C. Bertelle, G.H.E. Duchamp, H. Kadri-Dahmani (eds), {\em Complex Systems and Self-Organization Modelling}, ``Understanding Complex Systems'' serie, Springer, 2008 (in press).

\bibitem{BFJOP2} Bertelle, C., Flouret, M., Jay, V., Olivier, D., Ponty, J.-L. (2001) 
{\it Genetic algorithms on automata with 
multiplicities for adaptive agent behaviour in emergent organizations} In {\em 
SCI'2001}, Orlando, Florida, USA, 
22-25th July 2001.

\bibitem{bonabeau99} Bonabeau, E., Dorigo, M., Theraulaz, G. (1999) {\it Swam Intelligence, from natural to artificial systems}, a volume in the Santa Fe Institute Studies in the Sciences of Complexity, Oxford University Press.

\bibitem{castro02} De Castro, L.N., Timmis, J. (2002) {\it Artificial immune system: a new computational approach}, Springer-Verlag, London, U.K.

\bibitem{ghnemat05} Ghnemat, R., Oqeili, S., Bertelle, C., Duchamp, G.H.E. (2006) {\it Automata-Based Adaptive Behavior for Economic Modelling Using Game Theory}, in Aziz-Alaoui, M.A., Bertelle, C., {\it Emergent Properties in Natural and Artificial Dynamical Systems}, Springer.

\bibitem{ghnemat07} Ghnemat, R., Bertelle, C., Duchamp, G.H.E. (2007) {\it Adaptive Automata Community Detection and Clustering, a generic methodology}, in {\em Proceedings of World Congress on Engineering 2007, International Conference of Computational Intelligence and Intelligent Systems}, pp 25-30, London, U.K., 2-4th July 2007.

\bibitem{Gol} Goldberg, D.E. (1989) {\em Genetic Algorithms}, Addison-Wesley.   
%
\bibitem{kennedy95} Kennedy, J., Eberhart, R.C. (1995) {\it Particle Swarm Optimization} In {\em Proceedings of IEEE International Conference on Neural Networks (Perth, Australia)}, IEEE Service Center, Piscataway, NJ, 5(3), pp 1942-1948.

\bibitem{Mo} Le Moigne, J.-L. (1999) {\it La mod\'elisation des syst\`emes 
complexes}, Dunod. 

\bibitem{repast2008}
Repast web site (2008) \\{\tt http://repast.sourceforge.net}.

\bibitem{reynolds87} Reynolds, C.W. (1987) {\it Flocks, Herds and Schools: a distributed behavioral model} In {\em Computer Graphics}, 21(4) (SIGGRAPH'87 Conference Proceedings), pp 25-34.

\bibitem{schweitzer2003} Schweitzer, F. (2003) {\it Brownian Agents and Active Particles}, Springer.
%

\bibitem{weiss} Weiss, G. (ed.) (1999) {\em Multiagent Systems}, MIT Press.

\bibitem{xiao05} Xiao, N. (2005) {\it Geographic optimization using evolutionary algorithms} In {\em 8th International Conference on GeoComputation}, University of Michigan, USA.


\end{thebibliography}

\end{document}

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\section{Formatting your paper}
\label{sec:format}


\section{MAJOR HEADINGS}
\label{sec:majhead}

\subsection{Subheadings}
\label{ssec:subhead}

\subsubsection{Sub-subheadings}
\label{sssec:subsubhead}


\section{ILLUSTRATIONS, GRAPHS, AND PHOTOGRAPHS}
\label{sec:illust}
Illustrations must appear within the designated margins.  They may span the two
columns.  If possible, position illustrations at the top of columns, rather
than in the middle or at the bottom.

All halftone illustrations must be clear in black and white. Color illustrations will appear in the CD-ROM version of the proceedings, but the printed version will be produced in black and white. Therefore, make sure that your illustrations are acceptable when printed in black and white. If you would like to produce a separate black and white version of your paper for use in the printed proceedings, please contact the conference secretariat.

Caption and number every illustration. Figures and tables should be numbered consecutively and  separately from each other. The illustration number should be a bold Arabic number followed by a period. The caption itself should not be in bold and should be centred below the figure or above the table.

Below is an example of how to include a figure with sub-figures.
% An example of how to insert images. Delete the ``\vspace'' line,
% uncomment the preceding line ``\centerline...'' and replace ``imageX.ps''
% with a suitable PostScript file name.
% -------------------------------------------------------------------------
\begin{figure}[htb]

\begin{minipage}[b]{1.0\linewidth}
  \centering
% \centerline{\epsfig{figure=image1.ps,width=8.5cm}}
  \vspace{1.5cm}
  \centerline{(a) Result 1}\medskip
\end{minipage}
%
\begin{minipage}[b]{.48\linewidth}
  \centering
% \centerline{\epsfig{figure=image3.ps,width=4.0cm}}
  \vspace{1.5cm}
  \centerline{(b) Results 2}\medskip
\end{minipage}
\hfill
\begin{minipage}[b]{0.48\linewidth}
  \centering
% \centerline{\epsfig{figure=image4.ps,width=4.0cm}}
  \vspace{1.5cm}
  \centerline{(c) Result 3}\medskip
\end{minipage}
%
\caption{Example of placing a figure with experimental results in sub-figures.}
\label{fig:res}
%
\end{figure}

An example of including tables is illustrated below. Note that the caption here is on top of the illustration.
\begin{table}[htb]
\caption{Example of placing a table.}
\label{tab:res}
\begin{center}
\begin{tabular}{|c||c|c|c|}
\hline
Result &  Result & Result & Result \\ \hline \hline
1 & 2 & 3 & 4 \\ \hline
\end{tabular}
\end{center}
\end{table}

% To start a new column (but not a new page) and help balance the last-page
% column length use \vfill\pagebreak.
% -------------------------------------------------------------------------
\vfill
\pagebreak


\section{EQUATIONS}
\label{sec:equations}
Number equations consecutively with Arabic numbers in parentheses placed at the right hand margin of each column. Following is an example
\begin{equation}
a = b + c.
\end{equation}


\section{FOOTNOTES}
\label{sec:foot}
Use footnotes sparingly (or not at all!) and place them at the bottom of the column on the page on which they are referenced. Use 9-point type, single-spaced. To help your readers, avoid using footnotes altogether and include necessary peripheral observations in the text (within parentheses, if you prefer, as in this sentence).

\section{COPYRIGHT FORMS}
\label{sec:copyright}
You must submit your fully completed, signed IEEE copyright release form when you submit your final paper for publication. We {\bf must} have this form before your paper can be published in the proceedings. The copyright form is available as a Word file and a PDF file.

\section{REFERENCE FORMATTING}
\label{sec:ref}
List and number all bibliographical references at the end of the paper. The references can be numbered in alphabetical order or in order of appearance in the document.  When referring to them in the text, type the corresponding reference number in square brackets as shown at the end of this sentence \cite{smith}.


% References can be produced using the bibtex program from suitable
% BiBTeX files (here: strings, refs, manuals). The IEEEbib.bst bibliography
% style file from IEEE produces unsorted bibliography list.
% -------------------------------------------------------------------------
%\bibliographystyle{IEEEbib}
%\bibliography{strings,refs,manuals}
%----------------------------------------------
% Alternatively, you can use the \thebibliography environment directly, as
% illustrated below.

\begin{thebibliography}{1}

\bibitem{smith} A.B. Smith, C.D. Jones, and E.F. Roberts, ``Journal article title,'' {\em
Journal Name,} vol. 1, no. 3, pp. 1--10, Mar. 2000.

\bibitem{jones} C.D. Jones, A.B. Smith, and E.F. Roberts, {\em Book Title},
Publisher, Location, 2000.

\bibitem{smith2} A.B. Smith, C.D. Jones, and E.F. Roberts, ``Conference paper title,''
in {\em Proc. Conference Name}, Location, Dates, vol. I, pp. 11--14.

\end{thebibliography}

\end{document}
