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

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

26 2

26 2 Optimization with ant colonies and 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 randomly generated population. Individuals of the population are updated with the use of crossover and mutation operators. 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 cases the NN is a distributed learning technique that changes its structure based on external or internal information that flows through the network. All these nature-inspired algorithms share many common features with ACO. Random techniques are present in the update mechanism of ACO, SA, and GA. Interaction and self-organization are present in ACO and GA. Emergence capabilities are present in ACO and NN [20]. As a final note, in the recent past it has been shown that under certain conditions, some versions of ACO (e.g., Graph-based Ant System [45]) can 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 many ant-based algorithms that use only one colony of ants. In the next chapter we present an algorithm that, in contrast to these algorithms, applies multiple colonies.

3 The multiple ant-colonies approach: the mesh-partitioning problem Combinatorial optimization problems, which appears in data-mining and text-mining, belong to the wider class of so-called clustering problems, which are concerned with the grouping of objects into homogeneous subgroups. For these problems, ant-based algorithms have also been proposed [48]. However, ant-based clustering differs from ACO in several fundamental respects: • It draws its inspiration from the clustering behavior observed in real ants (not the foraging behavior, as in the case of ACO). • In contrast to ACO, it is not a metaheuristic; it tackles only the specific task of clustering. • Unlike ACO, it does not make use of artificial pheromone. • It shows no synergetic effect, i.e., its performance is mostly independent of population size. Rather than the ant-based clustering approach to combinatorial optimization, we discuss three approaches that are based on ACO metaheuristics. Informally, each of these approaches uses multiple ant colonies instead of only one (as is the case 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 Many of the problems that arise in mechanical, civil, automobile, and aerospace engineering can be expressed in terms of partial differential equations and 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 into the discrete form of a set of geometrical elements consisting of

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