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Ta-Chun Lien

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Reference

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Objective Introduce principle of Ant System(AS) Inspiration for your research Algorithm term project

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Agenda Inspiration Biological Background Adapt to Computer System Ant System Travel Salesman Problem Model Definition Ant Cycle Algorithm Parameter Setting Basic Parameter setting from Model definition Synergistic Effects

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Agenda(contd) Properties Initialization Elitist Strategy Problem Size Experiment Travel Salesman Problem Asymmetric Travel Salesman Problem Conclusions and Extensions Contribution of this Paper Extension

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Inspiration Biological Background Adapt to Computer System

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Biological background One of the problems studied by ethologists was to understand how almost blind animals like ants could manage to establish shortest route paths from their colony to feeding sources and back The Answer is Pheromone Trails

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What is Pheromone(from wiki) A pheromone (from Greek phero "to bear" + hormone") is a chemical that triggers a natural behavioral response in another member of the same species. There are alarm pheromones, food trail pheromones, sex pheromones, and many others that affect behavior or physiology. Their use among insects has been particularly well documented, although many vertebrates and plants also communicate using pheromones.

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Trail Pheromones(from wiki) Trail pheromones are common in social insects. For example, ants mark their paths with these pheromones, which are non-volatile hydrocarbons. Certain ants lay down an initial trail of pheromones as they return to the nest with food. This trail attracts other ants and serves as a guide. As long as the food source remains, the pheromone trail will be continually renewed. The pheromone must be continually renewed because it evaporates quickly. When the supply begins to dwindle, the trailmaking ceases. In at least one species of ant, trails that no longer lead to food are also marked with a repellent pheromone.

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Biological background(contd)

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Adapt to computer system Artificial Ants will have some Memory They will not be completely Blind They will live an environment where time is discrete

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Adapt to computer system(contd)

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Ant System TSP problem (AS is designed to solve TSP Problem originally) Model Definition Ant Cycle Algorithm

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Travel Salesman Problem Given a graph G=(V,E), where: V:set of Cities E:set of edges between Cities and :Euclidean distance between i and j The problem is finding a minimal length closed tour that visits each town once

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Travel Salesman Problem(contd) TSP NPC, you can reduce HC to NPC For this problem, each simple agent have the following characteristics: (1)it choose the town to go with a function of the town distance and amount of trail (Pheromone Trails) (2)used a tabu list to make a legal tours (3)lays a substance called trail on each edge(i,j) visited, when it completes a tour (4)Each agent at time t chooses the next town, where it will be at time t+1

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Model Definition iteration and cycle tabu list Trail intensity update formula Transition probability formula(decide where to go)

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Iteration and Cycle (t)(i=1,,n) be the number of ants in town i at time t m=, total number of ants an iteration of the AS algorithm the m moves carried out by the m ants in the interval (t,t+1), and every n iteration of the algorithm called a cycle(completed a tour)

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Tabu list associate with each ant a data structure called the tabu list, that saves the town already visited and forbids the ant to visit them again before a cycle completed. when a cycle is completed, the tabu list is used to compute the ants travel distance

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Tabu Search(from wiki) Tabu search is a mathematical optimization method, belonging to the class of local search techniques. Tabu search enhances the performance of a local search method by using memory structures: once a potential solution has been determined, it is marked as "taboo" ("tabu" being a different spelling of the same word) so that the algorithm does not visit that possibility repeatedly. Tabu search is attributed to Fred Glover.

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Trail intensity update formula :intensity of trail on edge (i,j) at time t Trail intensity update formula: : is a coefficient such that(1 - )represents the evaporation of trail between time t and t+n(