Ant Colony Optimization

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Ant Colony Optimization

• Ryan Ward

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Overview

• Ant Colony Optimization (ACO) uses ants finding
  food as inspiration for algorithms to find near
  optimal solutions to computationally intensive
  problems
• Has been applied to multiple NP-hard problems
  such as the Traveling Salesman Problem, Job-Shop
  Scheduling Problem, and the Quadratic Assignment
  Problem

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Traveling Salesman Problem

• Given n nodes on a graph, find the circuit that
  visits all the nodes with the lowest cost
• 2D Euclidean Symmetric

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Natural Ant System

• Initially, ants explore randomly
• Leave behind pheromone when they travel back to
  colony from food
• Pheromone evaporates over time
• Ants follow strong pheromone left behind by other
  ants
• Short routes to food have more pheromone (less
  distance less evaporation)

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Consequences of Natural System

• Independent agents communicating to each other by
  effecting the environment
• Agents act independently by exploring solution
  space early, then together by converging on good
  solutions
• Continuously updating and changing solution
  (partial on-line algorithm)

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• Create n agents, initialize cost and pheromone
  matrices
• While end conditions are not met
• agents create circuits, deciding where to go at
  each step depending on cost and pheromone
• update pheromone

• Pheromone updating can be done in multiple ways
• All ants add pheromone to their best route
• The ant(s) with the best route adds pheromone

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Exploration vs. Exploitation

• Pheromone vs. known cost
• Evaporation
• Pheromone added by ants is a function of distance
• Pheromone subtracted after move
• How ants add pheromone

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Best Route Found per Iteration