The paper is devoted to the problem of multidimensional data visualization, when an overflow of the image with graphic objects makes it difficult to understand the trends and patterns existing in the data. One of the emerging problems is the visual clutter problem and the aim of the paper is to analyse the criteria which can quantitatively assess the quality of the clutter reduction methods for data visualization in parallel coordinates. An overview of clutter reduction methods, and the aesthetic criteria used to evaluate parallel coordinate plots and chartings, is presented. The study explored the dimension reordering and algorithms based on the clustering. The quality of the results was assessed by the aesthetic criteria. The evaluation criteria system could potentially make it possible to select the best clutter reduction technique automatically.