The article considers a decision-making problem for multi-criteria problems characterized by a large number of criteria and alternatives. As one of stages in making decisions in such situations, it is proposed to use a filtering of alternatives based on their visual images. For these purposes, the paper describes main aspects of this approach, as well as a statement of the algorithms for constructing the corresponding visual images based on radar and radial diagrams. A description of data preparation for operation of visualization algorithms for multi-criteria alternatives with an aim of their filtering is given. The paper describes software "Al-ternativesVisualizer" that implements the proposed algorithms, as well as providing interaction with an expert for visual filtering of multi-criteria alternatives. Additionally, the capabilities of the developed software are described. They include filtering alternatives based on threshold values, as well as the possibility of conducting a series of experiments in order to obtain the union or the intersection of filtered sets of alternatives. An experimental study of the developed algorithms and approaches effectiveness based on a synthetic test and an experiment on visual filtering of real alternatives describing the accuracy of calculating the inviscid flow around a cone using several OpenFoam solvers (rhoCentralFoam, pisoCentral-Foam, sonicFoam, rhoPimpleFoam, QGDFoam) is presented. Each solver is characterized by 288 criteria, and with the help of the developed algorithms during visual filtering, the clear predominance of two solvers over the others is established.