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

Keywords Multiple criteria analysis; Evolutionary multi-criterion optimization; Multi-criteria decision making; NIMBUS; Self-organizing maps Highlights * Utilizes trade-off and other information visually through iSOM within the NIMBUS method for an informed decision-making. * Assists decision-makers to comprehend better about various properties of preferred solutions. * Visually assists decision-makers to avoid infeasible or least preferred solutions and aids in choosing the most preferred solutions. * Illustrates iSOM-NIMBUS integrated approach on multi-objective optimization problems with 3 to 10 objectives. * Enables extension of the proposed method to the other popular MCDM methods. Abstract 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. Author Affiliation: (a) Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600 036, India (b) Department of Electrical and Computer Engineering, Michigan State University, East Lansing, USA * Corresponding author. Article History: Received 26 July 2022; Accepted 31 January 2023 Byline: Deepanshu Yadav [deepanshu.yadav380@gmail.com] (*,a), Deepak Nagar (a), Palaniappan Ramu [https://ed.iitm.ac.in/~palramu/] (a), Kalyanmoy Deb [https://www.egr.msu.edu/~kdeb/] (b)