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Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

16 2

16 2 Optimization with ant colonies constraints, Ω, are built into the ants’ constructive procedure in such a way that in every step of the construction process only feasible solution components can be added to the current partial solution. Algorithm 2.1 Ant-Colony Optimization 1: while termination condition not satisfied do 2: ScheduleActivities 3: AntsActivity 4: PheromoneEvaporation 5: DaemonActions 6: end ScheduleActivities 7: end while The Algorithm 2.1 consists of three major activities: AntActivity: In the construction phase an ant incrementally builds a solution by adding solution components to the partial solution constructed so far. The probabilistic choice of the next solution component to be added is done by means of transition probabilities. More specifically, ant n in step t moves from vertex i ∈ C to vertex j ∈ C with a probability given by: ⎧ τij ⎪⎨ α(t)ηβ ij ∑ j ∈ N l∈N τ α i,k prob ij,k (t) = i,k il (t)ηβ il , (2.1) ⎪⎩ 0 j ∉ N i,k where η ij is a priori available heuristic information, α and β are two parameters that determine the relative influence of the pheromone trail τ ij and heuristic information, respectively, and N i,n is the feasible neighborhood of vertex i. If α = 0, then only heuristic information is considered. Similarly, if β = 0, then only pheromone information is at work. Once an ant builds a solution, or while a solution is being built, the pheromone is being deposited (in vertices or on connections) according to the evaluation of a (partial) solution. This pheromone information will direct the search of the ants in the following iterations. The solution construction ends when an ant comes to the ending vertex (where the food is located).

2.3 Organizing principles 17 PheromoneEvaporation: Pheromone-trail evaporation is a procedure that simulates the reduction of pheromone intensity. It is needed in order to avoid a too quick convergence of the algorithm to a sub-optimal solution. More specifically, pheromone evaporation is given by: τ NEW ij = (1 − ρ)τ OLD ij , (2.2) where ρ ∈ (0, 1] is an evaporation factor. DaemonActions: Daemon actions can be used to implement centralized actions that cannot be performed by single ants. Examples are the use of a local search procedure applied to the solutions built by the ants, or the collection of global information that can be used to decide whether or not it is useful to deposit additional pheromone to bias the search process from a non-local perspective. As we can see from the pseudo code in Algorithm 2.1, the ScheduleActivities construct does not specify how the three activities should be scheduled or synchronized, which also applies to the ants itself. This means it is up to the programmer to specify how these procedures will interact (in parallel or independently). This kind of approach leads to a lot of different organizing and design principles in ant colony optimization. 2.3 Organizing principles A study of the swarm intelligence approach [7] revealed a useful set of organizing principles that can guide the design of efficient distributed applications for different kinds of problems. ACO inherits the following notable features: Autonomy: The system does not require outside management or maintenance. Ants are autonomous, controlling their own behavior in a self-organized way. Adaptability: Interactions between ants can arise through indirect communication via the local environment; two individuals interact indirectly when one of them modifies the environment and the other responds to the new environment at a later time. In this way ants are able to dynamically detect changes in the environment

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