Fuzzy Lorenz Ant Colony System to solve multiobjective reentrant hybride flowshop scheduling problem

This article deals with the multiobjective reentrant hybrid flowshop scheduling problem. In the latter several tasks has to be processed in a system and the special feature here is that they must be processed several times on each machines. The system is composed of multiple stages which contain parallel identical machines. Since the tasks must reenter the system at the end of the normal process they create conflict with the following tasks. This problem is NP-Hard and we have developed a metaheuristics to solve it. The latter is an Lorenz Multi-Objective Ant Colony System (L-Ant). In this paper this algorithm becomes a Fuzzy-Logic Controller to adapt parameters α and β at each generation t with respect to the structure of the population in previous generations (t - 1) and (t - 2). The two objectives are the makespan and the total tardiness minimization. In this works we compare the classic L-Ant and the latter improved by FLC (so called Fuzzy Lorenz Ant). These two algorithms are tested on multiple instances adapted from the literature. Finally the comparisons of the results obtained by the algorithms are done with two different multi-objectives measures.