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Fix typos <noupdate>
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@ -91,7 +91,7 @@ Can be seen as a search process over graphs:
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\end{subfigure}
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\end{subfigure}
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\end{figure}
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\end{figure}
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Meta heuristics finds a balance between:
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Meta heuristics aim to find a balance between:
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\begin{descriptionlist}
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\begin{descriptionlist}
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\item[Intensification] \marginnote{Intensification}
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\item[Intensification] \marginnote{Intensification}
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Look for moves near the neighborhood.
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Look for moves near the neighborhood.
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@ -335,7 +335,7 @@ The fringe is ordered according the estimated scores.
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\end{tabular}
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\end{tabular}
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\end{center}
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\end{center}
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In generally, it is better to use heuristics with large values (i.e. heuristics that don't underestimate too much).
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In general, it is better to use heuristics with large values (i.e. heuristics that don't underestimate too much).
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\begin{figure}[ht]
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\begin{figure}[ht]
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\centering
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\centering
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@ -74,8 +74,8 @@ They also tend to prefer paths marked with the highest pheromone concentration.
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\item[Pheromone update]
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\item[Pheromone update]
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After each step, the pheromone trail is updated depending on an evaporation factor $\rho \in [0, 1]$:
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After each step, the pheromone trail is updated depending on an evaporation factor $\rho \in [0, 1]$:
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\[ \tau_{ij} = (1 - \rho) \tau_{ij} + \sum_{k=1}^{n_\text{ants}} \Delta \tau_{ij}^{(k)} \]
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\[ \tau_{ij} = (1 - \rho) \tau_{ij} + \sum_{k=1}^{n_\text{ants}} \Delta \tau_{ij}^{(k)} \]
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$\tau_{ij}^{(k)}$ of the $k$-th ant is defined as:
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$\Delta \tau_{ij}^{(k)}$ of the $k$-th ant is defined as:
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\[ \tau_{ij}^{(k)} = \begin{cases}
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\[ \Delta \tau_{ij}^{(k)} = \begin{cases}
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\frac{1}{L_k} & \text{if ant } k \text{ used the arch } (i, j) \\
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\frac{1}{L_k} & \text{if ant } k \text{ used the arch } (i, j) \\
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0 & \text{otherwise}
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0 & \text{otherwise}
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\end{cases} \]
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\end{cases} \]
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@ -172,7 +172,7 @@ In a bird flock, the movement of the individuals tend to:
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\item Stay in the flock.
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\item Stay in the flock.
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\item Avoid collisions.
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\item Avoid collisions.
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\end{itemize}
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\end{itemize}
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However, a model based on the these rules does not have a common objective.
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However, a model based on these rules does not have a common objective.
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PSO introduces as common objective the search of food.
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PSO introduces as common objective the search of food.
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Each individual that finds food can:
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Each individual that finds food can:
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