A multiobjective genetic algorithm based on NSGA II for deriving final ranking from a medium-sized fuzzy outranking relation

Exploitation of a Medium-Sized Fuzzy Outranking Relation Based on Multi-objective Evolutionary Algorithms to Derive a Ranking

“…Based on the objective functions defined previously, the multi-objective combinatorial optimization problem is formulated as follows: (17) where is the set of partial orders of classes of alternatives of A , p is a partial order of classes of alternatives of a given set of alternatives A and 0 is a minimum level of credibility. Because there are not constraints with respect to how the alternatives have to be grouped together, which would in some way reduce the complexity of this problem, the only clear way of finding the true Pareto front, with respect to a particular fitness measure, is to consider the entire polytope of potential solutions.…”

“…Several techniques to derive a ranking from a fuzzy outranking relation have been proposed in the literature of MCDA [3][4][5][6][7][8][9][10] .…”

“…17 and to present an empirical study to demonstrate its performance, a performance comparison with other MOEAs, and a new case study. The MOEA is a ranking procedure based on the hybridization of the reference point method with the non-dominated sorting genetic algorithm (NSGA-II); we call it RP 2 -NSGA-II, a MOEA procedure for grouping alternatives that are indifferent while also separating the classes that are strictly preferred to others…”