Optimization algorithms for multi-objective problems with fuzzy data

This paper addresses multi-objective problems with fuzzy data which are expressed by means of triangular fuzzy numbers. In our previous work, we have proposed a fuzzy Pareto approach for ranking the generated triangular-valued functions. Then, since the classical multi-objective optimization methods can only use crisp values, we have applied a defuzzification process. In this paper, we propose a fuzzy extension of two well-known multi-objective evolutionary algorithms: SPEA2 and NSGAII by integrating the fuzzy Pareto approach and by adapting their classical techniques of diversity preservation to the triangular fuzzy context. An application on multi-objective Vehicle Routing Problem (VRP) with uncertain demands is finally proposed and evaluated using some experimental tests.