MILP models for objective reduction in multi-objective optimization: Error measurement considerations and non-redundancy ratio

A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb and Saxena's algorithm (Deb and Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.