A novel data-driven visualization of n-dimensional feasible region using interpretable self-organizing maps (iSOM).

Abstract

Graphical optimization allows solving one or two dimensional optimization problems visually by merely plotting the objective function and constraint function contours. In addition to the discovery of optima, such a visualization-based approach enables understanding and interpretation of design variable and objective behavior with respect to feasibility and optimality, permitting intuitive decision making for designers. However, visualization of optimization problems in higher dimensions is challenging, though it is desirable. Interpretable self-organizing map (iSOM) is an artificial neural network that enables visualization of many dimensions via two-dimensional representations. We introduce iSOM to solve multidimensional optimization problems graphically. In the current work, a novel graphical representation of the n-dimensional feasible region, called B-matrix is constructed using iSOM. B-matrix is used to represent feasible range of design variables and objective function on separate plots. Consequently, dimension-wise shrinkage in the search space is also obtained. The proposed approach is demonstrated on various benchmark analytical examples and engineering examples with dimensions ranging from 2 to 30.