Pareto-optimality approach based on uniform design and fuzzy evolutionary algorithms for flexible job-shop scheduling problems (FJSPs)

摘要

In most combinatorial optimization problems, we have to simultaneously optimize a set of conflicting objective functions. The literature presents many possible considerations and techniques that can be useful to evaluate solutions [1, 2]. Mainly, we can distinguish two classes: the Pareto-optimality approaches and the non Pareto-optimality approaches. In a previous work, we have proposed a Pareto-optimality approach for solving Multi-objective Optimization Problems (MOPs) based on the hybridization of Fuzzy Logic (FL) and Evolutionary Algorithms (EAs) [3]. Such an approach makes it possible to construct a set of satisfactory solutions in order to provide flexibility to the decision-maker. In this work, we aim to enhance the suggested approach and we propose a new variant of such a hybridization. Thereafter, we show how Uniform Design (UD) can be used for finding a set of Pareto-optimality solutions uniformly scattered. This paper is organized as follows: in the second section, we shortly describe the Pareto-optimality concepts used for solving MOPs and those especially applied in EAs. Then, the mathematical formulation of FJSP is presented in the third section. The proposed hybrid approach will be described in the fourth section. The fifth section focuses on the illustration of the suggested approach by applying it to solve FJSP and highlights some practical aspects of the application of such an approach for solving hard combinatorial problems. Finally, the last part deals with concluding remarks and introduces some future research directions.