We propose a Decomposition-based Multi-objective Evolutionary Algorithm (MOEA/D) that incorporates a linkage identification technique to enhance the ability to solve difficult multi-objective optimization problems that have complex interactions among genes. Ensuring tight linkages is essential for genetic recombination operators to work effectively by preserving building blocks. For problems which are difficult to ensure tight linkages in encoding, the dependencies among loci have to be analyzed to identify the linkages for each building block. The proposed MOEA/D employs Linkage Identification with non-Monotonicity Detection (LIMD) to identify the linkages among pairs of loci by checking the non-monotonicity of fitness differences caused by pairwise perturbations for each scalar function in the MOEA/D. The results of numerical experiments conducted using a difficult multi-objective test function in which each building block is loosely encoded over the strings indicate that the proposed MOEA/D-LIMD outperforms the original MOEA/D and MOEA/D with tree-based graphical model (MOEA/D- GM).
