Enhanced Correlation Matrix Based Visualization for Multi- and Many-objective optimization

Visualization of an approximate solution set in multi- and many-objective optimization is a crucial component of the optimization process. To date, the focus of many of the visualization techniques is illustration of the distribution and convergence of solutions set without making any visual connection between the decision variables and solutions set. This paper proposes simple correlation-based visualization scheme called Enhanced Correlation Matrix plot (ECM) capable of showing the relationship among decision variables and objective values. The ECM plot can provide visual correlation information between each decision variable and objective functions as well as objective-wise relationship for different regions of the approximated solution set. Moreover, it can provide visual distribution of solutions along each objective. The efficiency of the proposed method is demonstrated on three widely used two-to eight objective-benchmark problems and two real-world problems with 6 and 17 decision variables. The experimental results show that the proposed ECM plot can provide essential information pertaining to relationships among objective functions and objective-to-decision variables.