MILP method for objective reduction in multi-objective optimization

A procedure for reducing objectives in a multi-objective optimization problem given a set of Pareto solutions is presented. Three different models are detailed, which achieve three different degrees of objective reduction. These models are based on maintaining the dominance structure of the problem. To compare the performance of the proposed models, these are tested with pure mathematical cases and with actual data from previous works in the field of multi-objective optimization. The first model provides the reduced subset of objectives that do not alter the dominance structure of the problem at all. The second model determines the minimum subset of objectives that alters the dominance structure with an upper predefined limit for the error. The last model provides the subset of objectives with a previously defined cardinality, which achieves the minimum error. The possibility of different inputs introduces flexibility into the models, which accounts for the preferences of the decision-maker.