Combinatorial Optimization of Stochastic Multi-objective Problems: An Application to the Flow-Shop Scheduling Problem

The importance of multi-objective optimization is globably established nowadays. Furthermore, a great part of real-world problems are subject to uncertainties due to, e.g., noisy or approximated fitness function(s), varying parameters or dynamic environments. Moreover, although evolutionary algorithms are commonly used to solve multiobjective problems on the one hand and to solve stochastic problems on the other hand, very few approaches combine simultaneously these two aspects. Thus, flow-shop scheduling problems are generally studied in a single-objective deterministic way whereas they are, by nature, multiobjective and are subjected to a wide range of uncertainties. However, these two features have never been investigated at the same time. In this paper, we present and adopt a proactive stochastic approach where processing times are represented by random variables. Then, we propose several multi-objective methods that are able to handle any type of probability distribution. Finally, we experiment these methods on a stochastic bi-objective flow-shop problem.