Pure and Mixed Lexicographic-Paretian Many-Objective Optimization: State of the Art

This work aims at reviewing the state of the art of the eld of lexicographic many-objective optimization. The discussion starts with a review of the literature, emphasizing the numerous application in the real life and the recent burst received by the advent of new computational frameworks which work well in such contexts, e.g., Grossone Methodology. Then the focus shifts on a new class of problems proposed and studied for the rst time only recently: the Priority-Levels Mixed-Pareto-Lexicographic Multi-Objective-Problems (PL-MPL-MOPs). This class of programs preserves the original pref- erence ordering of pure many-objective lexicographic optimization, but instantiates it over multi-objective problems rather than scalar ones. Interestingly, PL-MPL-MOPs seem to be very well qualied for modeling real world tasks, such as the design of either secure or fast vehicles. The work also describes the implementation of an evolutionary algorithm able to solve PL-MPL-MOPs, and reports its performance when compared against other popular optimizers.