Multiobjective decomposition-based Mallows Models estimation of distribution algorithm. A case of study for permutation flowshop scheduling problem

Estimation of distribution algorithms (EDAs) have become a reliable alternative to solve a broad range of single and multi-objective optimization problems. Recently, distance-based exponential models, such as Mallows Model (MM) and Generalized Mallows Model (GMM), have demonstrated their validity in the context of EDAs to deal with permutation-based optimization problems. The aim of this paper is two-fold. First, we introduce a novel general multi-objective decomposition-based EDA using Kernels of Mallows models (MEDA/D-MK framework) for solving multi-objective permutation-based optimization problems. Second, in order to demonstrate the validity of the MEDA/D-MK, we have applied it to solve the multi-objective permutation flowshop scheduling problem (MoPFSP) minimizing the total flow time and the makespan. The permutation flowshop scheduling problem is one of the most studied problems of this kind due to its fields of application and algorithmic challenge. The results of our experiments show that MEDA/D-MK outperforms an improved MOEA/D variant specific tailored for minimizing makespan and total flowtime. Furthermore, our approach achieves competitive results compared to the best-known approximated Pareto fronts reported in the literature for the benchmark considered.