Visualization of high-dimensional data is counter-intuitive using conventional graphs. Parallel coordinates are proposed as an alternative to explore multivariate data more effectively. However, it is difficult to extract relevant information through the parallel coordinates when the data are high-dimensional with thousands of lines overlapping. The order of the axes determines the perception of information on parallel coordinates. Thus, the information between attributes remain hidden if coordinates are improperly ordered. Here we propose a general framework to reorder the coordinates. This framework is general to cover a large range of data visualization objective. It is also flexible to contain many conventional ordering measures. Consequently, we present the coordinate ordering binary optimization problem and enhance towards a computationally efficient greedy approach that suites high-dimensional data. Our approach is applied on wine data and on genetic data. The purpose of dimension reordering of wine data is highlighting attributes dependence. Genetic data are reordered to enhance cluster detection. The presented framework shows that it is able to adapt the measures and criteria tested.