Handling Priority Levels in Mixed Pareto-Lexicographic Many-Objective Optimization Problems

This paper studies a class of mixed Pareto-Lexicographic multi-objective optimization problems where the preference among the objectives is available in different priority levels (PLs) before the start of the optimization process – akin to many practical problems involving domain experts. Each priority level (PL) is a group of objectives having an identical importance in terms of optimization, so that they must be optimized in the standard Pareto sense. However, between two PLs, a lexicographic preference structure exists. Clearly, finding the entire set of Pareto optimal solutions first and then choosing the lexicographic solutions using the given PL structure is not computationally efficient. A new efficient algorithm is presented here using a recent mathematical breakthrough in handling infinite and infinitesimal quantities: the Grossone methodology. The proposal has been implemented within a popular multi-objective optimization algorithm (NSGA-II), thereby obtaining its generalized version named PL-NSGA-II, although other EMO or EMaO algorithms could have also been used instead. A quantitative comparison of PL-NSGA-II performance against existing algorithms is made. Results clearly show the advantage of the proposed Grossone-based methodology in solving such priority-level many-objective problems.