Implementation of cellular genetic algorithms with two neighborhood structures for single-objective and multi-objective optimization

In cellular algorithms, a single neighborhood structure for local selection is usually assumed to specify a set of neighbors for each cell. There exist, however, a number of examples with two neighborhood structures in nature. One is for local selection for mating, and the other is for local competition such as the fight for water and sunlight among neighboring plants. The aim of this paper is to show several implementations of cellular algorithms with two neighborhood structures for single-objective and multi-objective optimization problems. Since local selection has already been utilized in cellular algorithms in the literature, the main issue of this paper is how to implement the concept of local competition. We show three ideas about its utilization: Local elitism, local ranking, and local replacement. Local elitism and local ranking are used for single-objective optimization to increase the diversity of solutions. On the other hand, local replacement is used for multi-objective optimization to improve the convergence of solutions to the Pareto frontier. The main characteristic feature of our approach is that the two neighborhood structures can be specified independently of each other. Thus, we can separately examine the effect of each neighborhood structure on the behavior of cellular algorithms.

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