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

26 2 **Optimization** with **an**t colonies **an**d the interested reader is referred **to** [11, 18, 111] for additional surveys. 2.8 A comparison with other nature-inspired algorithms Nature inspired a number of modern optimization techniques [7]. The SA is modeled from the thermodynamic behavior of solids. The GA starts with a r**an**domly generated population. Individuals of the population are updated with the use of crossover **an**d mutation opera**to**rs. Each individual is evaluated using a fitness function. The Neural Network (NN) is a computing paradigm that is loosely modeled after cortical structures of the brain. In most c**as**es the NN is a distributed learning technique that ch**an**ges its structure b**as**ed on external or internal information that flows through the network. All these nature-inspired algorithms share m**an**y common features with ACO. R**an**dom techniques are present in the update mech**an**ism of ACO, SA, **an**d GA. Interaction **an**d self-org**an**ization are present in ACO **an**d GA. Emergence capabilities are present in ACO **an**d NN [20]. As a final note, in the recent p**as**t it h**as** been shown that under certain conditions, some versions of ACO (e.g., Graph-b**as**ed Ant System [45]) c**an** find the optimal solution with a probability arbitrarily close **to** one [46, 112]. But in general, the problem of convergence **to** the optimal solution of a generic ACO algorithm will most probably remain open due **to** generality of the ACO metaheuristic. Nevertheless, this results put ACO **to** the same level **as** the SA or GAs in terms of a solution-finding capability. As seen in Section 2.5, there are m**an**y **an**t-b**as**ed algorithms that use only one colony of **an**ts. In the next chapter we present **an** algorithm that, in contr**as**t **to** these algorithms, applies multiple colonies.

3 The multiple **an**t-colonies approach: the mesh-partitioning problem Combina**to**rial optimization problems, which appears in data-mining **an**d text-mining, belong **to** the wider cl**as**s of so-called clustering problems, which are concerned with the grouping of objects in**to** homogeneous subgroups. For these problems, **an**t-b**as**ed algorithms have also been proposed [48]. However, **an**t-b**as**ed clustering differs from ACO in several fundamental respects: • It draws its inspiration from the clustering behavior observed in real **an**ts (not the foraging behavior, **as** in the c**as**e of ACO). • In contr**as**t **to** ACO, it is not a metaheuristic; it tackles only the specific t**as**k of clustering. • Unlike ACO, it does not make use of artificial pheromone. • It shows no synergetic effect, i.e., its perform**an**ce is mostly independent of population size. Rather th**an** the **an**t-b**as**ed clustering approach **to** combina**to**rial optimization, we discuss three approaches that are b**as**ed on ACO metaheuristics. Informally, each of these approaches uses multiple **an**t colonies instead of only one (**as** is the c**as**e in ACO). We decided **to** evaluate these algorithms on a well-known NP-hard clustering problem called the mesh-partitioning problem [71, 99]. 3.1 The mesh-partitioning problem M**an**y of the problems that arise in mech**an**ical, civil, au**to**mobile, **an**d aerospace engineering c**an** be expressed in terms of partial differential equations **an**d solved with the finite-element method. If a partial differential equation involves a function, f, then the purpose of the finite-element method is **to** determine **an** approximation **to** f. To do this the domain is put in**to** the discrete form of a set of geometrical elements consisting of

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128 Acknowledgements

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