Ant Colony Optimization

Problem Domain

• TSP planar problem

Ant Trails

• See Figure 1 in the paper
• A real-life ant trail

Some AI Themes in ACO

• Emergent Properties
• Reinforcement Learning
• Exploration vs. Exploitation
• Parallel and Distributed

Artificial Ant Abilities

• Can detect distance
• Have a working memory to avoid repeating cities
• Probabilistically prefer close cities with high pheromone levels

Notation

• m - the number of ants
• n - the number of cities
• L_n,n - length of TSP created using the nearest neighbor heuristic
• r, u, s - specific cities
• τ(r,u) - amount of pheromone between cities r and u
• τ ₀ - the initial amount of pheromone on each trail, in the paper it is equal to (n * L_n,n)^-1.
• η(r,u) - inverse of distance between cities r and u
• α - pheromone decay rate
• β - relative importance of distance to pheromone level
• q - a random variable, [0, 1]
• q ₀ - used to decide how an ant should choose which trail to follow
• φ(r,s) = (length of shortest tour found)^-1

Trail Selection

• See Equations 1 and 2 in the paper

Pheromone Updating

• Local: τ(r,s) = (1 - α) * τ(r,s) + α * τ ₀
• Global: τ(r,s) = (1 - α) * τ(r,s) + α * &phi(r,s)