Piecewise lexicographic programming: A new model for practical decision problems

A new model for practical decision problems is presented. It allows one to consider lexicographic preference structures by introducing the new class of piecewise lexicographic functions which impose a total order in the objective-and-constraint space. In this way, the concepts of objective and constraints are merged into a new unified notion of co-objective. Moreover, the lexicographic preference structure may be applied not only among different coobjectives, but also among different ranges of the same decision variable. The main merits of this model appear to be its versatility (it is able to deal with different types of multiobjective optimization situations without requiring user interaction) and its compactness (it does not require one to increase the original number of decision variables and constraints). A linear version of the model is investigated in more detail.