Visualization of Pareto Front Points when Solving Multi-objective Optimization Problems

In this paper, a new strategy of visualizing Pareto front points is proposed when solving multi-objective optimization problems. A problem of graphical representation of the Pareto front points arises when the number of objectives is larger than 2 or 3, because, in this case, the Pareto front points are multidimensional. We face the problem of multidimensional data visualization. The visualization strategy proposed is based on a combination of clustering and dimensionality reduction. Moreover, in the obtained projection of the Pareto front points onto a plane, the points are marked according to the Euclidean distance of multidimensional points, corresponding to the points visualized, from the ideal point. In the experimental investigation of the paper, neural gas is used for data clustering, and multidimensional scaling is applied to dimensionality reduction, as well as to visualizing multidimensional data. The strategy can be implemented in a decision support system and it would be useful for a decision maker, who needs to review and evaluate many points of the Pareto fronts, for example, obtained by genetic algorithms.