In multi-criterion optimization, often decision makers (DMs) are not interested in the complete
Pareto-optimal front. Instead they have preferences favoring specific parts of the Pareto-optimal
front. Besides looking for a specific trade-off among objectives, DMs are also interested in certain
properties of solutions, such as, away from constraint surfaces, Paretoset boundaries, etc. Multicriterion decision-making (MCDM) literature provides a plethora of approaches for introducing
DM’s preference information in an interactive manner to solve multicriterion optimization problems. Often, interactions with DMs can be aided with a user-friendly visualization method or by
using special data analysis procedures. An earlier study has indicated the use of self-organizing
maps (SOM) as a tool for analyzing Pareto-optimal solutions. In this report, we demonstrate
how a specific MCDM method – NIMBUS – can be applied with the interpretable SOM (iSOM)
approach iteratively to arrive at one or more preferred solutions in a multi-criterion optimization
problem. The two-dimensional iSOM cells are marked with different colors and styles to clearly
indicate various properties of solutions – feasible and infeasible solutions, cluster boundaries, selected region for NIMBUS-based search, starting, alternate, intermediate, and final solutions. A
visual illustration of the entire high-dimensional search space into a reduced twodimensional space
allows DMs to have a better understanding of the interactions of the objectives and constraints
variablewise and to execute NIMBUS decision-making procedure in a well-informed manner. The
report demonstrates the proposed method to a number of multi- and many-objective numerical and
engineering problems. The approach is now ready to be applied to demonstrate working of other
popularly-used MCDM methods.
Index Terms—multi-criteria decision making, NIMBUS, SOM, Pareto optimal front, multicriterion optimization