bare_conf.tex

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\begin{document}
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\title{The most awesome paper on how to solve the PCST problem with dAG }


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\begin{abstract}
The abstract goes here. DO NOT USE SPECIAL CHARACTERS, SYMBOLS, OR MATH IN YOUR TITLE OR ABSTRACT. This stuff is goooooood, you should read it.

\end{abstract}

\begin{IEEEkeywords}
PCST; metaheuristics, genetic algorithms;

\end{IEEEkeywords}


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\section{Introduction}
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\section{Genetic Algorithms}

In this section it's described the proposed solution to solve the PCST problem using AG and dAG 


\begin{algorithm}
  \begin{algorithmic}
\STATE
\STATE 
\STATE $t \gets 0$;
\STATE Init(P(0));
\STATE Eval(P(0));
\REPEAT 
\REPEAT
\STATE  $I_1$, $I_2 = Select(P(t));$
\IF{ random $>$ $p_{\text{cross}}$ } 
\STATE $I \gets $ Crossover($I_1$, $I_2$);
\ENDIF
\IF{ random $>$ $p_{\text{mut}}$ } 
\STATE $I \gets $ Mutation($I$);
\ENDIF
\IF{ $I \notin P(t) $}
\STATE Eval($I$);
\STATE Replace($I$, $P(t)$);
\ENDIF
\UNTIL{there's $k$ new individuals in the interation}
\STATE  $t \gets t + 1$;  
\UNTIL{there isn't a better solution after the $\Omega$ iterations;}
\STATE
\end{algorithmic}
\caption{Pseudo code of the AG used to resolve the PCST}
  \label{alg:pseudoAG}
\end{algorithm}


First The initial population is created. Each individual of this population encode a tentative solution. A fitness function associate a value to every individual which represent the cost of this solution for the PCST. Then evolution process start where the different stochastic operators, such as selection, crossover, mutation  are applied on the popultion in order to generate a new population. The selection operator choose 2 solution from the current population as parents of the new individual. The probability of seleccion is proportional to his {\em fitness}, so the indiviual with the biggest fitness has more probabilities of survive.

Once the parents are selected, crossover and muration are applied with a probability of $p_{\text{cross}}$ and $p_{\text{mut}}$ respectively, where $0 \leq p_{\text{cross}} \leq 1 $ and $0 \leq p_{\text{mut}} \leq 1$. Finaly the new prpoosed individuals will be included in the new population only if in the population there's not a identical solution, in order to give a minimal diversity to the population~\cite{raidl99}. \\


\subsubsection{Evaluation}
The fitness function is given for the cost function of the PCST, definded in ...


\subsubsection{Enconding}
The first step to design a GA is define a convinient representation model. In the PCST problem all the possible solution are set of trees, which are composed by edges and vertices. If the vertices of the solution are know, the three could be rebuilded using the minimum spanning tree algorithm. That's way the binary encoding $\sigma = (\sigma_1, \sigma_2, \ldots, \sigma_n)$ of size $|V|$ will be used, where each $\sigma_k$ with value of 1 represent that the vertex is presented in th solution, otherwise will be 0.

Once we have the set of vertices enconded in the chromosome $\sigma$ we can build the solution using the Algorithm~\ref{alg:mprim} which is based on the algorithm of Prim~\cite{580470}. In fact this algorithm has the same cyclomatic complexity of the Prim's algorithm, it mean $O(|V||E|)$ or $O(|E| + |V| \log(|V |))$ if the Binary Heap~\cite{580470} implementation is used.

It's possible that  the algorithm~\ref{alg:mprim}, give as result a disjoin graph. This could be produced in a non-complete graph in which there's not the necessary edges to conecte all the vertices of a factible solution without visit the intermediate vertex. In this cases the subtree with better fitness will be choosen. In that way the best tree is selected.

\begin{algorithm}
  \begin{algorithmic}
\STATE
\REQUIRE A graph $G = (V,E)$. 
\REQUIRE Set of vertices $V_T \subseteq V$ in the solution.
\STATE $V_{new} = \{x\}$, where $x \in V_T$ a randomly selected vertex.
\STATE $E_{new} = \{\}$
\REPEAT 
\STATE Choose a edge $(u,v)$ with less weight $u \in V_{new}\, \wedge \, v \notin V_{new} \, \wedge \, v \in V_T $. 
\COMMENT{if there's si hay multiple edges with the same weight, we choose one randomly.}
\STATE $V_{new} = V_{new}  + v$
\STATE $E_{new} = E_{new} + (u,v)$
\UNTIL{$V_{new} = V_T$}
\STATE
\RETURN $G = (V_{new}, E_{new})$
\end{algorithmic}
\caption{Modified Prim Algorithm, used to create a feasible solution for PCST}
  \label{alg:mprim}
  
\end{algorithm}

\subsubsection{Initialization}
\label{sec:init}
Typically the generation of the initial population of a AG must created randomly. However, is posible create a initial population in a {\em clever} way, trying to produce better quality solution, which allow to the GA find solutions faster or even better solutions. So two mechanism to create new initial polulation will be used. The first, came up with the inituitive strategy of create random solutions, applying postprocessing algorithm to improve theirs quality. 

When the initial population is created randomly, the resultant three could have {\em leaves} wich doesn't increase the income. On the contrary, including this {\em leaves} on the solution increase the cost of the solution, because the cost of connect this leaf is grater than the income. That's way the prune described in the Algorithm~\ref{alg:poda} is applied to every solution of the initial population, with the propose of remove all the leaves which his prize is smaller than the cost of includ them. 

For the second mechanism the Dijstra Algorithm~\cite{2215313} is used in every vertice with prize greater than 0 giving as result a three which could be prune with the algorithm~\ref{alg:poda}.


\begin{algorithm}
{\bf procedure}$prune(v, \, T = (V,E))$
  \begin{algorithmic}
\FORALL{For all children $u$ of $v$}
\STATE prune($u$, $G$)
\IF{ $c(u,v) > p(u) $ and $isLeaf(u)$}
\STATE $V = V  - v$
\STATE $E = E - (u,v)$
\COMMENT{remove the edge $(u,v)$ and $u$ from $G$}
\ENDIF
\ENDFOR
\end{algorithmic}
\caption{Prune to remove leaf wich represent no value to the soltion.}
  \label{alg:poda}
\end{algorithm}

\subsubsection{Selection}
The {\em ranking selection} is used, which sort all the solution in asending way according to theirs {\em fitness}. Then you rank each solution from the best solution (rank 1) to the worst solution (rank $n \leq N$); the solutons with the same fitness are ranked with the same value. The best ranked solution have more probability to be choosen.


\subsubsection{Mutation}
The {\em two-point} and {\em bit-flop} mutation will be used.


\section{Parllel Genetic Algorithms}

\subsection{A distribued Genertic Algorithm for the PCST}

There's multiple parallel models of Evolutionary Algorithms, however this research is focus on the parallel model which not only reduce the running time but increase the quality of the solutions as well. That's way the {distributed Genetic Algorithms} (dGA) are used because they are proveen get better quality result in previeus works~\cite{94044, 658089, 590911, 543253}. 

The use of {\em dAG}, include a set of additional parameters. From which, the {\em Migration Gap} and the {\em Migration Rate} must be selected based on the result of theirs peformance. The main parameters of the migration policy include the followeing ones: 


\begin{itemize}
  \item {\em Selection of the Migrants}. A elite aproach is adopted, where only the best individuals of the {\em island} are selected to migrate. 

  \item {\em Replacement of the Migrants}.  The immigrant individuals will be incorporated to the population only if doesn't exist the same indiviual in the population, their fitness doesn't  matter. This is done to improve the diversity of the search.

  \item {\em Topology}. The unidireccional ring topology is used to direct the comunitaction between the islan, due his scalability~\cite{Cantu-Paz97predictingspeedups}. \\

  \item {\em Synchronous or asynchronous communication}. we adopt asynchronous comunication for the migrations because the reception of the individuals could happen anytime during the evolution of the island.
\end{itemize}



\section{Design of experiments}
\label{sec:designexp}

In this section the design of experiments used in the different stage of this reaseach is described . Ths allow analyse the behaivor of the peformance of the algorithms implemented trying to resolve the PCST. 


 \subsection{Data Collection}
\label{sec:instancias}
In this research 5 group of instance were used, which are described next.

\begin{itemize}
 \item Johnson tested their approximation algorithms on two sets of randomly generated instances~\cite{338637}. In the first set, called {\em Group P}, instances are unstructured and designed to have constant expected degree and profit to weight ration. The K group comprise random geometric instances designed to have a structure somewhat similar to street map~\cite{minkoff}. this instances has been used for other authors~\cite{1017391, Canuto01localsearch}.

 \item Canuto create sets of test derived from the Steiner problem instances of the well-know OR-Library2~\cite{Canuto01localsearch}. For each one of the instances of the groups 2 instance are generated by assigning zero profits to non-terminal vertices and randomly generated profits in the interval  $[1, maxprize]$ to terminal vertice. 

 \item Ivana use the same scheme of Canuto to generate an aditional set of 40 instances derivated from the E class from the {\em Steiner} Problem of OR-Library~\cite{ivana}. 
\end{itemize}


  \subsection{Design of experiments}
    In the last section show them 
  
  En la sección anterior se muestran las decisiones de diseño que se tomaron para implementar el AG para el PCST. Sin embargo, existen parámetros de los algoritmos genéticos que no pueden ser establecido previamente, sino que deben ajustarse en base a prueba y error. 

  Además, es de gran importancia que que la elección de estos parámetros no sea sesgada en favor de algunas instancias específicas, es decir, que los experimentos en base en prueba y error se realicen sobre múltiples instancias representativas. Además, tiene que haber un balance entre cantidad y representatividad, ya que si se eligen muchas instancias para los ajustes, se invertirá más tiempo del necesario en las pruebas. \\



  En la tabla~\ref{tab:muestra} se enumeran las instancias elegidas para realizar las pruebas, las que muestran ser representativa si se comparan con el conjunto total de instancias, que se pueden ver en el anexo~\ref{appx:infoinstancias}. Además, estas instancias mostraron ser las que presentan mayores desafíos de acuerdo a pruebas previas efectuadas.\\




\section{Computational Results}
\section{Conclusion and future work}






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\section{Conclusion}
The conclusion goes here. this is more of the conclusion

% conference papers do not normally have an appendix


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\section*{Acknowledgment}


The authors would like to thank...
more thanks here


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\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}




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