Set Oriented Numerics
Generally, the multiobjective optimization problem involves finding a set with the best solutions among mathematically incomparable compromises, i.e., vectors whose image can not be improved by other vectors in all its components, but it could be improved in at least one of them. However, there are real-world problems in which a decision maker has knowledge about the problem or he/she wants to obtain optimal solutions with certain characteristics instead of all solutions. The reference point methods are useful for this scenario, the idea is to get the closest solution to a given vector, usually infeasible, which is a guess of the decision maker. Nevertheless, the scenario in which a reference point changes over time has been poorly treated. Recently, continuation methods have been used to solve the multiobjective optimization problem, these methods have the advantage that they move through the Pareto front as Hillermeier method and Pareto Tracer. The method proposed here, called Pareto Explorer, is a continuation method which takes into account preferences of the decision maker to calculate the predictor, which makes it also an interactive method. In addition, if we change the corrector by an achievement function, this method can be used to solve dynamic reference point problems. We present results on some benchmark models, as well as on a 14-objective problem that arises in the design of a laundry system.
- Oliver Cuate