Solving fuzzy multi-objective optimization using non-dominated sorting genetic algorithm II

Abstract

This paper presents the stages for solving fuzzy multi-objective optimization problems using genetic algorithm approach. Before applying non-dominated sorting genetic algorithm II (NSGA II) techniques to obtain optimal solution, first multi-objective possibilistic (fuzzy) programming was converted into an equivalent auxiliary crisp model to form deterministic programming model. To determine the best solution from Pareto set, we implied feasibility degree of decision variable and satisfaction degree of decision maker. The best optimal solution is the intersection between α-feasibility degree and satisfaction degree of the decision makers that has the highest fuzzy membership degree. For numerical experiment, we used simple formulation in multi-objective fuzzy linear programming model with three maximum objective functions, three decision variables, and six constraints. The comparison of the results shows that our results are better for two objectives than that of compromising programming.