Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) is a multi-objective evolutionary algorithm that works by decomposing the multi-objective optimization problem into several single-objective subproblems. The subproblems are constructed by aggregating different optimization objectives in a single function that will act as objective function. A commonly used aggregation approach is the Tchebycheff method. The central idea in MOEA/D is that the optimal solutions to two neighboring subproblems should be similar. By relying on this idea, the algorithm can deliver state-of-the-art performance on difficult multi-objective optimization problems.

This chapter introduces the reader to MOEA/D, describing the algorithm and its underlying concepts, such as Tchebycheff scalarization. The chapter thus provides the background necessary for the user to successfully apply MOEA/D to practical optimization problems. The presentation is complemented with pseudocode and Python code.