1. Ant colony optimization algorithms Mykulska Eugenia yuginia.m@gmail.com

2. 1. Summary 2. Detailed 3. Common extensions 4. Convergence 5. Pheromone update 6. Applications 7. Some problem 8. Definition difficulty 9. Stigmergy algorithms 10. Related methods

3. ant colony optimization algorithm In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.

4. This algorithm is a member of ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations..

5. Initially proposed by Marco Dorigo in 1992 in his PhD thesis, the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food.

7. A little from biology A little from biology The original idea comes from observing the exploitation of food resources among ants, in which ants individually limited cognitive abilities have collectively been able to find the shortest path between a food source and the nest.

9. An ant (called "blitz") 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; 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 there are two routes to reach the same food source then, in a given amount of time, the shorter one will be traveled by more ants than the long route; The short route will be increasingly enhanced, and therefore become more attractive; The long route will eventually disappear because pheromones are volatile; Eventually, all the ants have determined and therefore "chosen" the shortest route.

10. The basic philosophy of the algorithm involves the movement of a colony of ants through the different states of the problem influenced by two local decision policies, viz., trails and attractiveness.

11. Thereby, each such ant incrementally constructs a solution to the problem. When an ant completes a solution, or during the construction phase, the ant evaluates the solution and modifies the trail value on the components used in its solution. This pheromone information will direct the search of the future ants

12. Furthermore, the algorithm also includes two more mechanisms, viz., trailevaporation and daemon actions. Trail evaporation reduces all trail values over time thereby avoiding any possibilities of getting stuck in local optima. The daemon actions are used to bias the search process from a non-local perspective.

13. Elitist ant system Max-Min ant system (MMAS) Ant Colony System Rank-based ant system (ASrank) Continuous orthogonal ant colony (COAC)

14. Example pseudo-code and formulae procedure ACO_MetaHeuristic while(not_termination) generateSolutions() daemonActions() pheromoneUpdate() end while end procedure

15. In general, the kth ant moves from state x to state y with probability where τ xy is the amount of pheromone deposited for transition from state x to y, 0 ≤ α is a parameter to control the influence of τ xy, η xy is the desirability of state transition xy (a priori knowledge, typically1 / d xy, where d is the distance) and β ≥ 1 is a parameter to control the influence of η xy.

16. Pheromone update When all the ants have completed a solution, the trails are updated by where is the amount of pheromone deposited for a state transition xy, ρ is the pheromone evaporation coefficient and is the amount of pheromone deposited, typically given for a TSP problem (with moves corresponding to arcs of the graph) by where L k is the cost of the kth ant's tour (typically length) and Q is a constant.

18. It must visit each city exactly once; A distant city has less chance of being chosen (the visibility); The more intense the pheromone trail laid out on an edge between two cities, the greater the probability that that edge will be chosen; Having completed its journey, the ant deposits more pheromones on all edges it traversed, if the journey is short; After each iteration, trails of pheromones evaporate.

20. Scheduling problem Vehicle routing problem Assignment problem Set problem Others

21. Initialization: chromosomes are randomly created. At this point, it is very important that the population is diverse. Otherwise, the algorithm may not produce good solutions. Evaluation: each chromosome is rated on how well the chromosome solves the problem at hand. A fitness value is assigned to each chromosome. Selection: the fittest chromosomes are selected for propagation into the future generation based on how fit they are. Recombination: individual chromosomes and pairs of chromosomes are recombined, modified and then put back into the population.

23. References Buckland, M., 2002, AI Techniques for Game Developers, Premier Press, United States of America. Dorigo,M., & Gambardella, L. M (1997) Ant colonies for the traveling salesman problem. BioSystems, 43,73-81 Jearakul, C.,1999 2D and 3D Watefall Chart Control, [Online], Available: http:/www.codeguru.com.controls/Waterfall.shtml [Accessed 3/9/2003] Jones, M., 2003, AI Application Programming, Publisher: David Pallali. Lodos, J, 1999 Replacing a view in a doc-view application, [Online], Available: http:/www.codeguru.com/doc_view/ReplacingView.shtml [Accessed 2/9/2003] Nordmeyer, J., Automatic Font Handling Class, [Online], Available: http://www.codeproject.com/gdi/autofont.asp [Accessed 28/10/2003] Prosise, J, 1999,Programming Windows with MFC, 2 nd Edition, Microsoft Press, Redmond Washington Rule,K..1999 Flicker Free Drawing in MFC, [Online], Available: http:/www.codeproject.com/gdi/flickerfree.asp [Accessed 24/9/2003] Wyant,D., 2002, CPerfTimer timer class, [Online], Available: http:/www.codeproject.com/datetime/perftimer.asp [Accessed 24/9/2003]

24. Mykulska Eugenia yuginia.m@gmail.com