Visualization-aided multi-criteria decision-making using interpretable self-organizing maps

In multi-criterion optimization, decision-makers (DMs) are not often interested in the complete Pareto-optimal front. Instead, they have preferences favoring specific parts of the front. Multi-criterion decision-making (MCDM) literature provides a plethora of approaches for introducing DM’s preference information in an interactive manner to solve multi-criterion optimization problems. 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 paper, we demonstrate how a specific MCDM method – NIMBUS – can be executed with the interpretable SOM (iSOM) approach iteratively to arrive at one or more preferred solutions. A visual illustration of the entire high-dimensional search space into multiple reduced two-dimensional spaces allows DMs to have a better understanding of the interactions of the objectives and constraints independently, and execute the NIMBUS decision-making procedure with a more wholistic approach. The paper demonstrates the proposed method on a number of multi- and many-objective numerical and engineering problems. The approach is now ready to be integrated with other popular MCDM methods.