Multivariate Analysis to Assist Decision-Making in Many-objective Engineering Optimization Problems

Abstract

Data processing (or the transformation of data into knowledge and/or information) has become an indispensable tool for decision-making in many areas of engineering. Engineering optimization problems with many objectives are common. However, the decision-making process for these problems is complicated since there are many trade-offs that are difficult to identify. Thus, in this work, multivariate statistical methods, Principal Component Analysis (PCA) and Cluster Analysis (CA), have been studied and applied to analyze the results of many objective engineering optimization problems. PCA reduces the number of objectives to a very small number, CA through the similarities and dissimilarities, creates groups of solutions, i.e., bringing together in the same group solutions with the same characteristics and behaviors. Two engineering optimization problems with many objectives are solved: a mechanical problem consisting in the optimal design of laminated plates, with four objectives and a problem of optimization of the radar waveform, with nine objectives. For the problem of the design of laminated plates through PCA allowed to reduce to two objectives and through CA it was possible to create three distinct groups of solutions. For the problem of optimization of the radar waveform, it was possible to reduce the objectives from nine to two objectives representing the greatest variability of the data, and CA defined three distinct groups of solutions. These results demonstrate that these tools are effective to assist the decision-making processes in the presence of a large number of solutions and/or objectives.