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

16 2 **Optimization** with **an**t colonies constraints, Ω, are built in**to** the **an**ts’ constructive procedure in such a way that in every step of the construction process only fe**as**ible solution components c**an** 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 ph**as**e **an** **an**t 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 me**an**s of tr**an**sition probabilities. More specifically, **an**t 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 **an**d β are two parameters that determine the relative influence of the pheromone trail τ ij **an**d heuristic information, respectively, **an**d N i,n is the fe**as**ible 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** **an**t 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 **an**ts in the following iterations. The solution construction ends when **an** **an**t comes **to** the ending vertex (where the food is located).

2.3 Org**an**izing principles 17 PheromoneEvaporation: Pheromone-trail evaporation is a procedure that simulates the reduction of pheromone intensity. It is needed in order **to** avoid a **to**o 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 fac**to**r. DaemonActions: Daemon actions c**an** be used **to** implement centralized actions that c**an**not be performed by single **an**ts. Examples are the use of a local search procedure applied **to** the solutions built by the **an**ts, or the collection of global information that c**an** be used **to** decide whether or not it is useful **to** deposit additional pheromone **to** bi**as** the search process from a non-local perspective. As we c**an** 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 **an**ts itself. This me**an**s 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 org**an**izing **an**d design principles in **an**t colony optimization. 2.3 Org**an**izing principles A study of the swarm intelligence approach [7] revealed a useful set of org**an**izing principles that c**an** guide the design of efficient distributed applications for different kinds of problems. ACO inherits the following notable features: Au**to**nomy: The system does not require outside m**an**agement or mainten**an**ce. Ants are au**to**nomous, controlling their own behavior in a self-org**an**ized way. Adaptability: Interactions between **an**ts c**an** arise through indirect communication via the local environment; two individuals interact indirectly when one of them modifies the environment **an**d the other responds **to** the new environment at a later time. In this way **an**ts are able **to** dynamically detect ch**an**ges in the environment

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140 Index Covariance Matrix Adaptat

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144 List of Algorithms

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160 Selected publications Izbrane o