An interactive descriptive graphical approach to data analysis for trade-off decisions in multi-objective programming

This paper reports the development of data analysis procedures for the purpose of aiding trade-off decisions in the case of optimizing many objectives. Very often, conflicts exist among objectives and prevent the attainment of optimal levels for all of them. In actual fact, trade-offs constitute the most important activity in such classes of problems, which has been termed multi-objective programming. Candidate solutions are generated and evaluated until one with a satisfactory compromise is found. The present work, employs multivariate data analysis on the standard data matrix assembled from rows of performance index values of the candidates. The matrix captures the raw information gained and the data analysis aims to discover its underlying structure, as the relationship among the objectives. The emphasis is on enhancing the user’s understanding and intuition through an interactive approach, which is both descriptive and graphical. The user understands the problem better by interactively searching for a suitable structure for the matrix, and obtains intuition on the trade-offs required by employing the structure together with the data matrix in an interactive algorithm. An example in computer-aided design serves to illustrate the various techniques developed.