Scientific Research Group in Egypt (SRGE) Swarm Intelligence (II) Ant Colony optimization Scientific Research Group in Egypt (SRGE) Dr. Ahmed Fouad Ali Suez Canal University, Dept. of Computer Science, Faculty of Computers and informatics Member of the Scientific Research Group in Egypt

Scientific Research Group in Egypt www.egyptscience.net

Meta-heuristics techniques

Outline 1. Ant colony optimization (ACO)(Main idea) 2. History of ACO 3. ACO parameters definitions 4. Ant colony optimization (ACO) 5. ACO Algorithm 6. Advantage / disadvantage 7. References

Swarm intelligence (Main Idea) Suppose you and a group of friends are on a treasure finding mission. Each one in the group has a metal detector and can communicate the signal and current position to the n nearest neighbors. Each person therefore knows whether one of his neighbors is nearer to the treasure than him. If this is the case, you can move closer to that neighbor. In doing so, your chances are improved to find the treasure. Also, the treasure may be found more quickly than if you were on your own.

Ant colony optimization (Main Idea) In a series of experiments on a colony of ants with a choice between two unequal length paths leading to a source of food, biologists have observed that ants tended to use the shortest route. A model explaining this behavior is as follows: An ant runs more or less at random around the colony. if it discovers a food source, it returns more or less directly to the nest, leaving in its path a trail of pheromone.

Ant colony optimization (Main Idea) These pheromones are attractive, nearby ants will be inclined to follow, more or less directly, the track. Returning to the colony, these ants will strengthen the route. If two routes are possible to reach the same food source, the shorter one will be, in the same time, traveled by more ants than the long route will. The short route will be increasingly enhanced, and the long route will eventually disappear, pheromones are volatile.

History of ACO First proposed by M. Dorigo, 1992. Heuristic optimization method inspired by biological systems. Population based algorithm for solving difficult combinatorial optimization problems. Traveling Salesman, vehicle routing, sequential ordering, graph coloring, routing in communications networks Ant behavior is a kind of stochastic distributed optimization behavior

ACO parameters definitions Stigmergy a term coined by French biologist Pierre-Paul Grasse, is interaction through the environment. Two individuals interact indirectly when one of them modifies the environment and the other responds to the new environment at a later time.

ACO parameters definitions cont. Pheromone Trails Species lay pheromone trails traveling from nest, to nest or possibly in both directions. Pheromones evaporate. Pheromones accumulate with multiple ants using path.

Ant colony optimization TSP Initializing the pheromone amounts on each route to a positive, small random value. A simple transition rule for choosing the next city to visit, is where Ti j(t) is the pheromone intensity on edge (i, j) between cities i and j, the k-th ant is denoted by k, α is a constant, and Ci,k is the set of cities ant k still have to visit from city i.

Ant colony optimization TSP The transition rule above can be improved by including local information on the desirability of choosing city j when currently in city i, i.e.the next city to visit, is where α and ß are adjustable parameters that control the weight of pheromone intensity and

Ant colony optimization TSP with dij the Euclidean distance between cities i and j At the end of each route, Tk, constructed by ant k, the pheromone intensity Tij on the edges of that route is updated, using Where

Ant colony optimization TSP The parameter Q has a value of the same order of the length of the optimal route, Lk(t) is the length of the route traveled by ant k, and m is the total number of ants. The constant p ϵ [0,1], is referred to as the forgetting factor, which models the evaporation over time of pheromone deposits.

ACO Algorithm for TSP. Initialize the pheromone deposits on each edge (i, j) between cities i and j to small positive random values, i.e. Tij(0) ~ U(0, max). 2. Place all ants k ϵ 1,…, m on the originating city. 3. Let T+ be the shortest trip, and L+ the length of that trip. 4. For t = I to tmax do the following: For each ant, build the trip Tk (t) by choosing the next city n — 1 times (n is the number of cities), with probability Фij,k(t). Compute the length of the route, Lk(t), of each ant. If an improved route is found, update T+ and L+. Update the pheromone deposits on each edge. 5. Output the shortest route T+.

Advantage / disadvantage Retains memory of entire colony instead of previous generation only. Less affected by poor initial solutions (due to combination of random path selection and colony memory). Has been applied to a wide variety of applications.

Advantage / disadvantage Theoretical analysis is difficult: Due to sequences of random decisions (not independent). Probability distribution changes by iteration. Convergence is guaranteed, but time to convergence uncertain. Coding is somewhat complicated, not straightforward Pheromone “trail” additions/deletions, global updates and local updates.

References Computational Intelligence An Introduction Andries P. Engelbrecht, University of Pretoria South Africa Some slides adapted from a presentation “Ant Colony Optimization. A metaheuristic approach to hard network optimization problems”. Particle Swarm Optimization http://www.particleswarm.info/ http://www.swarmintelligence.org

Thank you Ahmed_fouad@ci.suez.edu.eg http://www.egyptscience.net