Ant Colony Optimization The Metaheuristic ACO Variants Analysis Outline Application Examples DM812 METAHEURISTICS 1. Ant Colony Optimization Context Lecture 8 Inspiration from Nature Ant Colony Optimization 2. The Metaheuristic http://www.aco-metaheuristic.org/ 3. ACO Variants Marco Chiarandini 4. Analysis Theoretical Department of Mathematics and Computer Science Experimental University of Southern Denmark, Odense, Denmark <marco@imada.sdu.dk> 5. Application Examples Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis Outline Swarm Intelligence Application Examples Application Examples Definition: Swarm Intelligence 1. Ant Colony Optimization Swarm intelligence deals with systems composed of many individuals that Context coordinate using decentralized control and self-organization. Inspiration from Nature In particular, it focuses on the collective behaviors that emerges from the local interactions of the individuals with each other and with their 2. The Metaheuristic environment and without the presence of a coordinator 3. ACO Variants Examples: Artificial swarm intelligence 4. Analysis Natural swarm intelligence Theoretical artificial life (boids) colonies of ants and termites Experimental robotic systems schools of fish computer programs for flocks of birds 5. Application Examples tackling optimization and data herds of land animals analysis problems.
Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis Swarm Intelligence The Biological Inspiration Application Examples Application Examples Double-bridge experiment [Goss, Aron, Deneubourg, Pasteels, 1989] Research goals in Swarm Intelligence: scientific modelling swarm intelligence systems to understand the mechanisms that allow coordination to arise from local individual-individual and individual-environment interactions engineering exploiting the understanding developed by the scientific stream in order to design systems that are able to solve problems of practical relevance If the experiment is repeated a number of times, it is observed that each of the two bridges is used in about 50% of the cases. About 100% the ants select the shorter bridge Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis Self-organization Stigmergy Application Examples Application Examples Four basic ingredients: 1 Multiple interactions "The coordination of tasks and the regulation of constructions does 2 Randomness not depend directly on the workers, but on the constructions themselves. The worker does not direct his work, but is guided by it. 3 Positive feedback (reinforcement) It is to this special form of stimulation that we give the name 4 Negative feedback (evaporating, forgetting) STIGMERGY (stigma, sting; ergon, work, product of labour = stimulating product of labour)." Grassé P. P., 1959 Communication is necessary Two types of communication: Stigmergy Direct : antennation, trophallaxis (food or liquid exchange), Stimulation of workers mandibular contact, visual contact, chemical contact, etc. by the performance Indirect : two individuals interact indirectly when one of them they have achieved modifies the environment and the other responds to the new Grassé P. P., 1959 environment at a later time. This is called stigmergy and it happens through pheromone.
Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis Mathematical Model Why Does it Work? Application Examples Application Examples [Goss et al. (1989)] developed a model of the observed behavior: Three important components: Assuming that at a given moment in time, TIME: a shorter path receives pheromone m 1 ants have used the first bridge quicker (this is often called: "differential length effect") m 2 ants have used the second bridge, QUALITY: a shorter path receives more The probability Pr[ X = 1] for an ant to choose the first bridge is: pheromone COMBINATORICS: a shorter path receives ( m 1 + k ) h pheromone more frequently because it is likely Pr[ X = 1] = ( m 1 + k ) h + ( m 2 + k ) h to have a lower number of decision points (parameters k and h are to be fitted to the experimental data) Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis From Real to Artificial Ants From Real to Artificial Ants Application Examples Application Examples Our Basic Design Choices Ants are given a memory of Using Pheromone and Memory to Choose the Next Node visited nodes Ants build solutions probabilistically (without updating pheromone trails) For ant k : Ants deterministically retrace p k � � backward the forward path to ijd ( t ) = f τ ijd ( t ) update pheromone Ants deposit a quantity of pheromone function of the quality of the solution they generated
Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis From Real to Artificial Ants From Real to Artificial Ants Application Examples Application Examples Ants’ Pheromone Trail: Deposition and Evaporation Evaporation: Ants’ Probabilistic Transition Rule τ ijd ( t + 1) ← (1 − ρ ) · τ ijd ( t ) For ant k : Deposition � τ ijd ( t )] α p k ijd ( t ) = τ ijd ( t + 1) ← τ ijd ( t + 1) + ∆ k � α ijd ( t ) � � τ ihd ( t ) h ∈ J k i ( i, j ) ’s are the links visited by ant k , and ijd ( t ) ∼ quality k τ ijd is the amount of pheromone trail on edge ( i, j, d ) ∆ k J k i is the set of feasible nodes ant k positioned on node i can move eg: quality k proportional to the inverse of to the time it took ant k to build the path from i to d via j . Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Inspiration from Nature Analysis Analysis From Real to Artificial Ants From Real to Artificial Ants Application Examples Application Examples Ants’ Probabilistic Transition Rule (Revised) Using Pheromones and Heuristic to Choose the Next Node τ ijd ( t )] α · � � η ijd ( t )] β For ant k p k ijd ( t ) = � α · � η ijd ( t )] β � � τ ihd ( t ) p k ijd ( t ) = f ( τ ijd ( t ) , η ijd ( t )) h ∈ J k i τ ijd is the amount of pheromone trail on edge ( i, j, d ) τ ijd is a value stored in a pheromone table η ijd is the heuristic evaluation of link ( i, j, d ) η ijd is a heuristic evaluation of link ( i, j, d ) which introduces J k i is the set of feasible nodes ant k positioned on node i can move problem specific information to
Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic Context Context ACO Variants ACO Variants Inspiration from Nature Artificial versus Real Ants: Inspiration from Nature Analysis Analysis From Real to Artificial Ants Application Examples Application Examples Main Differences Simple Ant Colony Optimization Algorithm Artificial ants: 1. Ants are launched at regular instants from each node to randomly chosen destinations Live in a discrete world 2. Ants build their paths probabilistically with a probability function of: Deposit pheromone in a problem dependent way artificial pheromone values Can have extra capabilities: heuristic values local search, lookahead, backtracking 3. Ants memorize visited nodes and costs incurred Exploit an internal state (memory) 4. Once reached their destination nodes, ants retrace their paths Deposit an amount of pheromone function of the solution quality backwards, and update the pheromone trails Can use heuristics 5. Repeat from 1. The pheromone trail is the stigmergic variable Ant Colony Optimization Ant Colony Optimization The Metaheuristic The Metaheuristic ACO Variants ACO Variants Ant Colony Optimization Analysis Analysis Outline Application Examples Application Examples The Metaheuristic The optimization problem is transformed into the problem of finding 1. Ant Colony Optimization the best path on a weighted graph G ( V, E ) called construction graph Context Inspiration from Nature The artificial ants incrementally build solutions by moving on the construction graph. 2. The Metaheuristic The solution construction process is stochastic 3. ACO Variants biased by a pheromone model, that is, a set of parameters associated with graph components (either nodes or edges) whose values are 4. Analysis modified at runtime by the ants. Theoretical All pheromone trails are initialized to the same value, τ 0 . Experimental At each iteration, pheromone trails are updated by decreasing 5. Application Examples ( evaporation ) or increasing ( reinforcement ) some trail levels on the basis of the solutions produced by the ants
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