moGrams: A Network-Based Methodology for Visualizing the Set of Nondominated Solutions in Multiobjective Optimization

An appropriate visualization of multiobjective nondominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their relationship. In this paper, we propose a novel methodology that allows the visualization of the nondominated solutions in the design space and their relationships by means of a network. The nodes represent the solutions in the objective space while the edges show the relationships among the solutions in the design space. Our proposal (called moGrams) thus provides a joint visualization of both objective and design spaces. It aims at helping the decision maker to get more understanding of the problem so that (s)he can choose the most appropriate and flexible final solution. moGrams can be applied to any multicriteria problem in which the solutions are related by a similarity metric. Besides, the decision maker interaction is facilitated by modifying the network based on the current preferences to obtain a clearer view. An exhaustive experimental study is performed using four multiobjective problems with a variable number of objectives to show both usefulness and versatility of moGrams. The results exhibit interesting characteristics of our methodology for visualizing and analyzing solutions of multiobjective problems.