Joao Paulo Papa edited Introduction.tex  over 8 years ago

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The work proposed by Papa et al.~\cite{Papa_2015} goes beyond that point by combining different solutions obtained through distinct meta-heuristic techniques. Since each technique has its own weaknesses, the idea is to explore a higher level of optimization in order to improve each individual solution by means of the combination of all obtained solutions so far. Although such step can be performed by any optimization technique, we opted to employ Genetic Programming (GP) for two main reasons: (i) we did not use any meta-heuristic technique that has been employed during the first step of optimization in order to avoid biases, and (ii) GP provides a more powerful combination process as a hyper-heuristic technique, since it can apply a number of arithmetic operations for that purpose, instead of using movement-based equations to place agents from one position to another.  Genetic Programming~\cite{Koza_1992} is an evolutionary-based optimization algorithm that models each solution as an individual, which is usually represented as a tree composed of ``function"\ and ``terminal"\ nodes. The function nodes encode the arithmetic operators used over the terminal nodes in order to evaluate the trees (Figure~\ref{f.gp_tree}). At each iteration, specific operations over the current population are performed to design the next generation of individuals, being the most used ones: (i) mutation, (ii) crossover and (iii) reproduction.  will be used to perform operations over the individuals  \section{Methodology}  \label{s.material}