ABSTRACT
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.
KEYWORDS
Multi-Objective Optimization, Lexicographic Optimization, Evolutionary Computation, Grossone Methodology
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