51,986 research outputs found
Generalized partition crossover for the traveling salesman problem
2011 Spring.Includes bibliographical references.The Traveling Salesman Problem (TSP) is a well-studied combinatorial optimization problem with a wide spectrum of applications and theoretical value. We have designed a new recombination operator known as Generalized Partition Crossover (GPX) for the TSP. GPX is unique among other recombination operators for the TSP in that recombining two local optima produces new local optima with a high probability. Thus the operator can 'tunnel' between local optima without the need for intermediary solutions. The operator is respectful, meaning that any edges common between the two parent solutions are present in the offspring, and transmits alleles, meaning that offspring are comprised only of edges found in the parent solutions. We design a hybrid genetic algorithm, which uses local search in addition to recombination and selection, specifically for GPX. We show that this algorithm outperforms Chained Lin-Kernighan, a state-of-the-art approximation algorithm for the TSP. We next analyze these algorithms to determine why the algorithms are not capable of consistently finding a globally optimal solution. Our results reveal a search space structure which we call 'funnels' because they are analogous to the funnels found in continuous optimization. Funnels are clusters of tours in the search space that are separated from one another by a non-trivial distance. We find that funnels can trap Chained Lin-Kernighan, preventing the search from finding an optimal solution. Our data indicate that, under certain conditions, GPX can tunnel between funnels, explaining the higher frequency of optimal solutions produced by our hybrid genetic algorithm using GPX
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A niching memetic algorithm for simultaneous clustering and feature selection
Clustering is inherently a difficult task, and is made even more difficult when the selection of relevant features is also an issue. In this paper we propose an approach for simultaneous clustering and feature selection using a niching memetic algorithm. Our approach (which we call NMA_CFS) makes feature selection an integral part of the global clustering search procedure and attempts to overcome the problem of identifying less promising locally optimal solutions in both clustering and feature selection, without making any a priori assumption about the number of clusters. Within the NMA_CFS procedure, a variable composite representation is devised to encode both feature selection and cluster centers with different numbers of clusters. Further, local search operations are introduced to refine feature selection and cluster centers encoded in the chromosomes. Finally, a niching method is integrated to preserve the population diversity and prevent premature convergence. In an experimental evaluation we demonstrate the effectiveness of the proposed approach and compare it with other related approaches, using both synthetic and real data
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