Ant Colony Optimization - Carleton University

Ant Colony Optimization

Ant Colony Optimization

• Collective foraging behaviour of ants• Use Travelling Salesman Problem (TSP) as

example problem• Other problems too:

– Quadratic Assignment Problem– Graph Colouring – Job-shop scheduling– Sequential ordering– Vehicle routing

General Observations

• Although general in nature, ACO performance rival problem-specific heuristics

• Coupling ACO to local optimizers can generate “world class” results

• ACO can easily deal with changing environments (stochastic time-varying): does not have to be static (cf GA/GP)

• AntNet (routing) provides extremely good performance in building routing tables adaptively

Foraging Strategies in Ants

• Many ant species have trail-following behavior when foraging:– Individual ants deposit pheromones from

source to nest– Foragers follow trails

• Process of influencing one ant by another by use of a chemical trail is recruitment– Mass recruitment if this is the only mechanism

Binary Bridge• Deneubourg: Linepithema humile ant chooses path

to food source based upon self-organization• Food source separated from nest by bridge with

two branches of equal length• No pheromone initially• Paths have equal probability of selection initially• Random fluctuations cause a few more ants to

choose one branch over another• Depositing pheromone while walking causes more

ants to select one branch over other

Variation of Ant Branch Choice

Swarm Intelligence: Bonabeau et al

Model

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• Ai = # ants using path A, Bi = # ants using path B.•Value of n determines degree of non-linearity in system• Value of k measures degree of attraction of branch• Best match to experiments:

• n ~ 2, k ~ 20• If Ai >> Bi, Ai >> 20, Pa ~ 1• If Ai >> Bi, Ai < 20, Pa ~ 0.5

Choice Dynamics

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Experimental Results vs. Model

Excellent agreement with model


Model

Another experiment …

• One branch longer than the other• Fluctuations again amplified

– Ratio varies as the length ratio of branches• “Bad” initial fluctuations could cause this

mechanism to fail– Too simple to explain, other effects exist

Lasius Niger Ants

• Force selection of long trail, add short trail later

• Introduce ants after stabilization occurs; i.e. non-optimal solution!

• Lasius Niger ant detects that it’s moving away from source: does U turn

Recovers from sub-optimal solution


Short branch laterTwo branches initially

Other effects …• Pheromone evaporation

– Short time scale allows ants to avoid being trapped in sub-optimal solutions

– Also prevents long trails from developing• However:

– Pheromone evaporation rates vary tremendously … up to timescales of months

– So, biology and engineering may differ • So, what’s optimal …it depends

– Sensitivity to pheromone and rate of evaporation are two factors in search– More sensitive to pheromone => more cooperation– High evaporation rate => rapid reaction to changing environment

• Ant colony optimization– It uses evaporation … departure from biology

Minimum Spanning Tree

• Aron et al– Multiple nests and bridges– Linepithema humile can solve minimum

spanning tree problem – Not NP hard, but Steiner problem is

Figure 2.6 Redundant bridges not usedMinimum spanning tree created!

Swarm Intelligence: Bonabeau et al.

Figure 2.7Redundant bridges not usedMinimum spanning tree created!


Figure 2.8

Doesn’t have to be small network!


Raid Patterns of Army Ants• Large, cohesive society• High degree of coordination:

– 100’s of thousands of individuals for foraging– 1000’s of sq kms covered in a day

• Eciton burchelli swarms:– > 200,000 ants– search column > 15m wide

• Dynamic, but same basic structure– Loops of different dimension: small at front, bigger at

rear

Figure 2.9


Army Ant Model• Environment represented as a 2D grid

– Discrete simulation• Ants lay pheromone trails on way out to front and when

returning to nest– Deposit 1 pheromone unit per unit area on way to raid site– Threshold of 1000 units per site– Returning ants drop 10 units per site if < 300 units at site– Fixed fraction (1/30th) evaporates per time unit

• Ants return on finding prey• At each time step:

– Ant decides to advance or stay– More pheromone, higher chance of moving

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lr pp ��1 Very similar to foraging equation

Figure 2.10


Rules

• 10 ants leave/unit time• 20 ants max. per site• If site full, ant moves to other site or stays

put• Food distribution

– Probability of finding a food source/site– When found, an ant returns to the nest with 1

unit of food

Figure 2.11


Army ants …

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Ant Colony Optimization - Carleton University