Abstract Multiobjective evolutionary algorithm (MOEA) is a nature-inspired population based algorithm, it has attracted much attention from the researches and made a great progress since MOEA can generate a set of nondominated solutions in a single run. However, there are some challenges for practical application in the aspect of constraint handing, encoding scheme, the evolutionary operators design and Pareto solution selection. Hence, in order to overcome the above bottle-neck problems, this chapter will present three algorithms to discuss the application of MOEA on constrained multiobjective optimization problems, clustering learning, classification learning and sparse clustering.