M.A. Roseman, J.S. Gero, Reducing the Pareto Optimal Set in Multicriteria Optimization, Eng. Optim., 8, pp. 189-206 (1985).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....54 are non dominated or not. Pareto frontier reduction together with a multiobjective optimisation algorithm will be very useful, since it provides a clearer separation of the individuals. Pareto set reduction [ROS 85] based on the clustering of solutions, can be incorporated in two steps of a GA multiobjective optimisation: during the selection of individuals for reproduction and recombination and at the end, for the choice of the preferential solution from the Pareto set obtained. The method proposed by ....

....clustering of solutions, can be incorporated in two steps of a GA multiobjective optimisation: during the selection of individuals for reproduction and recombination and at the end, for the choice of the preferential solution from the Pareto set obtained. The method proposed by Roseman and Gero [ROS 85] produces the clustering of solutions that can be considered similar between themselves, in all or in some criteria. Then, inside the groups, the solutions that show to have preferential characteristics are selected. The technique consists in comparing the proximity of solutions on the ....

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M.A. Roseman, J.S. Gero, Reducing the Pareto Optimal Set in Multicriteria Optimization, Eng. Optim., 8, pp. 189-206 (1985).

....case of using a genetic algorithm, depends on the size of the population, it may be desirable in some cases to devise ways of reducing the number of elements in such set, in order to facilitate the analysis for the decision maker. Kunha, Oliveira and Covas [1997] proposed the incorporation of Roseman and Gero s algorithm [1985] into the GA to cluster together points that are within a certain distance (defined by the user) of each other in the Pareto front. Probably one of the most difficult problems in multiobjective optimization is to determine how to measure the quality of a solution. So far, practically visual ....

Roseman, M. A. and Gero, J. S. 1985. Reducing the Pareto optimal set in multicriteria optimization. Engineering Optimization 8, 189--206.

....to an unbalanced distribution in the population. Thus, pruning the external nondominated set while maintaining its characteristics might be necessary or even mandatory. A method that has been applied to this problem successfully and studied extensively in the same context is cluster analysis [42][43]. In general, cluster analysis partitions a collection of m elements into n groups of relatively homogeneous elements, where n m. The average linkage method [42] a clustering approach that has proven to perform well on this problem (cf. 42] has been chosen in this paper. Step 1: Initialize ....

....average distance to all other points in the cluster) as representative solution. Cunha et al. 20] also combined a multiobjective EA with a clustering approach in order to achieve reasonably sized Pareto sets. This algorithm, however, uses a different clustering method which has been proposed in [43]; thereby, for each objective, a tolerance value has to be specified. Moreover, it differs from SPEA with regard to the following two aspects: a) The nondominated solutions are not stored externally, and (b) fitness sharing is incorporated to preserve diversity in the population. B. A Simple ....

M. A. Rosenman and J. S. Gero, "Reducing the pareto optimal set in multicriteria optimization," Engineering Optimization, vol. 8, pp. 189--206, 1985.

....size. However, the goal is not only to prune a given set, but rather to generate a representative subset which maintains the characteristics of the original set. Cluster analysis demonstrably fits these requirements and has been successfully applied to this problem (see, e.g. Morse, 1980 ] Rosenman and Gero, 1985 ] In general, cluster analysis partitions a collection of p elements into q groups of relatively homogeneous elements, where q p. Dependent on the working mechanism of the algorithm two forms of clustering are distinguished: direct clustering and hierarchical clustering [ Morse, 1980 ] ....

....in Figure 3.4. Cunha, Oliviera, and Covas [ Cunha et al. 1997 ] also combined a multiobjective EA with a form of hierarchical clustering in order to achieve reasonably sized Pareto sets. Their algorithm, though, uses a different clustering method which has been proposed by Roseman and Gero [ Rosenman and Gero, 1985 ] thereby, for each objective a tolerance value has to be specified. Moreover, it differs from SPEA with regard to the following two aspects: a) the nondominated solutions are not stored externally, and b) fitness sharing is incorporated to preserve diversity in the population. Chapter 4 ....

M. A. Rosenman and J. S. Gero. Reducing the pareto optimal set in multicriteria optimization. Engineering Optimization, 8:189--206, 1985.

....algorithm, depends on the size of the population, it may be desirable in some cases to devise ways of reducing the number of elements in such set, in order to facilitate the analysis for the decision maker. Kunha, Oliveira and Covas [46] proposed the incorporation of Roseman and Gero s algorithm [79] into the GA to cluster together points that are within a certain distance (defined by the user) of each other in the Pareto front. Probably one of the most difficult problems in multiobjective optimization is to determine how to measure the quality of a solution. So far, practically visual ....

M. A. Roseman and J. S. Gero. Reducing the Pareto optimal set in multicriteria optimization. Engineering Optimization, 8:189--206, 1985.

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