# An Improved MOEA/D with Optimal DE Schemes for Many-Objective Optimization Problems
## 1 Introduction
Although the dominance-based algorithms are prevailing, they also have their own limitations to overcome. One of the main drawbacks is that they are not very suitable for solving the many-objective optimization problems. Because in the face of the many-objective optimization problems, almost all of the solutions will become non-dominated with respect to each other in the population, this will reduce the selection pressure and hinder the process of evolution [16; 17]. With the continuous in-depth study of scholars around the world, the recent well-known MOEA, the multi-objective evolutionary algorithm based on decomposition, named MOEA/D [18], proposed by [PERSON] and [PERSON] in 2007, was dissimilar from the past algorithms. MOEA/D does not use the Pareto dominance, but uses the scalarization technique for fitness assignment to solve the multi-objective optimization problems. It uses scalarizing functions such as the weighted sum approach and the weighted Tchebycheff approach to decompose a MOP into a number of single subproblems and solves all of these subproblems in a single run (note that the description of the weighted sum approach and the weighted Tchebycheff will be shown in Section 2.2). Each subproblem is relevant to a weighted scalarizing function and neighborhood relationship, which should be considered between any two sub-problems. These algorithms based on MOEA/D in solving continuous and combinatorial MOPs have already achieved extremely promising results [19; 20; 21]. On the other hand, as an efficient and vigorous heuristic for the global optimization algorithm, differential evolution (DE) was proposed by [PERSON] and [PERSON] [22; 23]. As a prevalent EA, DE exhibits outstanding performance in solving a wide variety of problems in different fields. It employs crossover, mutation and selection operators to move its population toward the global optimum in each generation. DE as a successful EA is widely used to cope with many optimization problems, as well as it has good adaptability, so that it can be combined with other algorithms to solve MOPs at another level. In the course of [24], a simple DE scheme is combined with MOEA/D, called MOEA/D-DE, which solves a class of new MOPs that have complicated Pareto sets. In this version of MOEA/D, called MOEA/D-DE, mating parents are selected from the neighborhood and the whole population together. It also points out that the parameter setting in the DE scheme is very important for the performance of the MOEA/D-DE algorithm. The successful implementation of MOEA/D-DE not only shows the good performance of MOEA/D, but also shows the good adaptability of the DE algorithm. Therefore, we can make some effort following this means to attempt to solve more difficult MOPs. Moreover, it is undoubted that (1) is a multi-objective optimization problem and usually has two or three objectives. Nevertheless, in daily life, many real-world applications often involve four or more objectives for optimizing. Thus, we say that many-objective optimization problems are the class of MOPs that have four or more than four objectives. Because of its usefulness, it is not strange that the research on many-objective optimization problems has been one of the major research areas in the EMO community during recent years. To name only a few, in 2013, [PERSON] et al. [25] proposed an improved MOEA/D, named UMOEA/D (MOEA/D with uniform design). They used the uniform design method to set the weight vectors of MOEA/D for solving the many-objective problems and got some effective results. [PERSON] et al. [26] proposed an improved MOEA/D in the weight vector design method in 2014, called MOEA/D-AWA (MOEA/D with adaptive weight vector adjustment). They used a new weight vector initialization method and made the weight vectors adaptive. There were many experiments on MOPs and a small amount of experiments on the many-objective optimization problems, which certified how effective MOEA/D-AWA was.