Biplots in offline multiobjective reduction

Decision making process in multiobjective problems becomes more difficult in the presence of a large number of objectives and approximations to the Pareto optimal solutions. Consequently, the representation and visualization of the Pareto optimal frontier is not simple. Therefore, it is not clear for the decision maker the trade-off between the different alternative solutions. Thus, this creates enormous difficulties when choosing a solution from the Pareto-optimal set and constitutes a central question in the process of decision making. A methodology based on Principal Component Analysis and Biplot graphical representations is proposed to retrieve information from approximations to the Pareto optimal set and associations between objectives. Thus, taking into account biplot representations, offline objective reduction can be performed as well as the identification of proximities between solutions. Some examples and datasets with different number of objectives have been studied in order to evaluate the process of decision making through these methods. Results indicate that this statistical approach can be a valuable tool on decision making in multiobjective optimization.