Ant colony algorithm

Ant colony algorithm • Ant colony algorithmmimics the behavior of insect colonies completing their activities Ant colony looking for food < == > Solving a problem N Individual ants < == > N Solutions Each time the colony goes to < == > Population of N solutions look for food and returns to the nest

Ant colony algorithm • Ant colony algorithmmimics the behavior of insect colonies completing their activities • Collective process: Some kind of invisible agent (having a global memory of the process) is coordinating and having an impact on the behavior of each individual The solutions of the current population (associated with the individual insects) are used to update this global memory (trace of pheromone) Indeed the traces of pheromone is evaporating during the process It is reinforced according to the new solutions generated

Ant colony algorithm • Antcolonyalgorithmmimics the behavior of insect colonies completingtheiractivities • Individualprocess: A new feasible solution (corresponding to an antgoing out to look for food) isgenerated by means of a constructive method (the antmovingforward) that uses the information in the global memory of the invisible agent

Ant colony algorithm • Ant colony algorithm for solving the graph coloring problem Contructing a new solution (corresponding to an ant): - In traditional construction procedure (Greedy, GRASP, for instance), at each iteration we select an activity and a resource to assigned to it according to the best desirability of the pair ( for instance, to optimize the objective function given the values of the variables already fixed) - In ant colony algorithm, at each iteration the selection of the pair activity & resource is made according to the desirability of the pair and also according to past history included in the global memory

Ant colony algorithm • Ant colony algorithm for solving the graph coloring problem • Contructing a new solution (corresponding to an ant): - In traditional construction procedure (Greedy, GRASP, for instance), at each iteration we select an activity and a resource to assigned to it according to the best desirability of the pair ( for instance, to optimize the objective function given the values of the variables already fixed) - In ant colony algorithm, at each iteration the selection of the pair activity & resource is made according to the desirability of the pair and also according to past history included in the global memory

Ant colony algorithm • Ant colony algorithm for solving the graph coloring problem • Contructing a new solution (corresponding to an ant): - In traditional construction procedure (Greedy, GRASP, for instance), at each iteration we select a vertex and a color to assigned to it according to the best desirability of the pair ( for instance, to optimize the objective function given the values of the variables already fixed) - In ant colony algorithm, at each iteration the selection of the pair activity & resource is made according to the desirability of the pair and also according to past history included in the global memory

Graph coloring problem: Vertices are ordered in decreasing order of their degree Vertices selected in that order For each vertex, select a color in order to reduce the number of pairs of adjacent vertices already colored with the same color Graph coloring problem: Vertices are ordered in decreasing order of their degree Vertices selected in that order For each vertex, select a color in order to reduce the number of pairs of adjacent vertices already colored with the same color and accounting for the quality of solutions where the vertex has the color. Impact of a given solution decreases with the number of iterations since it was generated Graph coloring problemGreedy vs Ant Colony

Ant colony algorithm • Ant colony algorithm for solving the graph coloring problem • Contructing a new solution (corresponding to an ant): - In traditional construction procedure (Greedy, GRASP, for instance), at each iteration we select vertex and a color to assigned to it according to the best desirability of the pair ( for instance, to optimize the objective function given the values of the variables already fixed) - In ant colony algorithm, at each iteration the selection of the pair vertex & color is made according to the desirability of the pair and also according to past history included in the global memory

Graph coloring problem: Vertices are ordered in decreasing order of their degree Vertices selected in that order For each vertex, select a color in order to reduce the number of pairs of adjacent vertices already colored with the same color Graph coloring problem: Vertices are ordered in decreasing order of their degree Vertices selected in that order For each vertex, select a color in order to reduce the number of pairs of adjacent vertices already colored with the same color and accounting for the quality of solutions where the vertex has the color. Impact of a given solution decreases with the number of iterations since it was generated (evaporation) Graph coloring problemGreedy vs Ant Colony

Graph coloring: Selecting vertex

Graph coloring: Selecting color

Graph coloring: Updating Traces

Ant colony algorithm