دانلود رایگان مقاله انگلیسی یک رویکرد فازی عمومی برای بهینه سازی چند منظوره تحت عدم اطمینان - الزویر 2018

Abstract

Multi-objective optimization under uncertainty has gained considerable attention in recent years due to its practical applications in real-life. Many studies have been conducted on this topic, but almost all of them transformed the problem into a mono-objective one or just neglected the effects of uncertainty on the outcomes. This paper addresses specific uncertain multiobjective problems in which uncertainty is expressed by means of triangular fuzzy numbers. To handle these problems, we introduced a new approach able to solve them without any transformation by considering fuzziness propagation to the objective functions. The proposed approach is composed of two main contributions: First, a fuzzy Pareto dominance is defined for ranking the generated fuzzy solutions. Second, a generic fuzzy extension of wellknown evolutionary algorithms is suggested as resolution methods. An experimental study on multi-objective Vehicle Routing Problems (VRP) with uncertain demands is finally carried to evaluate our approach.

5. Conclusion

Through this work, we have contributed to the design of a generic approach for combinatorial multi-objective problems with fuzzy data, especially expressed by means of triangular fuzzy numbers and propagated to the objective functions. Our major contributions is two-fold: First, we have proposed a novel Pareto approach for ranking the fuzzy outcomes generated in our case. Second, we have introduced a fuzzy extension of three well-known multi-objective evolutionary algorithms. The usefulness of proposed algorithms was illustrated through the resolution of a practical VRP problem and their performance assessment was validated by means of some experimental tests. The computational results were straightforward and encouraging for multi-objective problems confronted with fuzziness. Notice that our implementation are added into the ParadisEO-MOEO platform under Git 2 .

As future work, we intend to make a robustness study to analyze in more detail the obtained solutions. We also intend to extend the well-known multiobjective performance indicators (i.e., Hypervolume indicator) to our fuzzy context. Finally, it would be interesting to validate the proposed approach for different fuzzy multi-objective routing problems, in which the fuzziness is expressed by other shapes like trapezoidal fuzzy numbers.