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CACO: Colony-based Ant Colony Optimization

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Andrew Runka, MSc. CAS Group, Carleton University


¡ Meta-­‐heuristic search technique ¡ Inspired by foraging behaviour of real ants § Utilize collective information to make decisions ¡ Applicable to most graph problems 2


Set parameters, initialize pheromone trails LOOP Construct Solutions Optional Daemon Actions Update Pheromones END LOOP 3


pi,jα⎧⎧ τ ηi,j i⎪⎪= ⎨⎨∑ τc ∈ N i,jij⎪⎪⎩⎩ 0β, jαηi,βjif j ∈N otherwise ? ? 4


Δτij=m∑( 1−ρ)⋅τ+ Δτijk = 1kij⎧⎧ 1⎪⎪Δτ k= ij ⎨⎨ L⎪⎪⎩⎩ 0kif ant k uses edge i,j otherwise 5


¡ Independent, often conflicting goals ¡ Multiple optimal solutions § Trade-­‐off curve, Pareto Front, Non-­‐Dominated Set Objective 2 Objective 1 6


? ? 8


Initialization Final Output Construct Solutions Termination? Evaluate Solutions Adjust Attractions Apply Adjustment Rule False ∀ants: non-­dominated?True Pareto Front Update Pheromone 9


¡ Coverage § Ratio of dominated solutions 10


¡ Hypervolume 11


¡ Univariate Analysis § Mann-­‐Whitney-­‐Wilcoxon rank-­‐sum test 12


¡ Versus Alaya et al. (2007) § Coverage 13


¡ Versus Alaya et al. (2007) § Hypervolume (dominance ratios) 14


¡ Versus Zitzler & Thiele (1999) § Coverage 15


¡ Versus Zitzler & Thiele (1999) § Hypervolume 16


¡ Versus Zitzler & Thiele (1999) § Univariate analysis 17


¡ Versus Zitzler & Thiele (1999) § Trend (from hypervolume median) 18


¡ Non-­‐dominated Fronts § Knapsack.100.2 4000 3900 3800 3700 3600 <strong>CACO</strong> SPEA m-­‐ACO 3500 3400 3300 3000 3200 3400 3600 3800 4000 4200 4400 19


¡ Non-­‐dominated Fronts § Knapsack.250.2 10000 9800 9600 9400 9200 9000 <strong>CACO</strong> SPEA m-­‐ACO 8800 8600 8400 8200 8400 8600 8800 9000 9200 9400 9600 20


¡ Non-­‐dominated Fronts § Knapsack.500.2 19600 19400 19200 19000 18800 18600 18400 <strong>CACO</strong> SPEA m-­‐ACO 18200 18000 17800 17600 17800 18000 18200 18400 18600 18800 19000 19200 21


¡ Non-­‐dominated Fronts § Knapsack.750.2 28000 27800 27600 27400 27200 27000 26800 26600 <strong>CACO</strong> SPEA 26400 26200 26000 25800 26000 26500 27000 27500 28000 28500 22


Thank you! 23

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