A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 1) PF VISUALIZATION <s> Many-objective optimization problems bring great difficulties to the existing multiobjective evolutionary algorithms, in terms of selection operators, computational cost, visualization of the high-dimensional tradeoff front, and so on. Objective reduction can alleviate such difficulties by removing the redundant objectives in the original objective set, which has become one of the most important techniques in many-objective optimization. In this paper, we suggest to view objective reduction as a multiobjective search problem and introduce three multiobjective formulations of the problem, where the first two formulations are both based on preservation of the dominance structure and the third one utilizes the correlation between objectives. For each multiobjective formulation, a multiobjective objective reduction algorithm is proposed by employing the nondominated sorting genetic algorithm II to generate a Pareto front of nondominated objective subsets that can offer decision support to the user. Moreover, we conduct a comprehensive analysis of two major categories of objective reduction approaches based on several theorems, with the aim of revealing their strengths and limitations. Lastly, the performance of the proposed multiobjective algorithms is studied extensively on various benchmark problems and two real-world problems. Numerical results and comparisons are then shown to highlight the effectiveness and superiority of the proposed multiobjective algorithms over existing state-of-the-art approaches in the related field. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 1) PF VISUALIZATION <s> Many-objective optimization problems (MaOPs) bring great hardship to most of the existing classical evolutionary multi-objective optimization algorithms, respecting selection operators, computational cost, visualization of the high-dimensional Pareto front, and so on. Objective reduction can help mitigate such hardship by removing the redundant objectives in the original objective set to some extent. Objective reduction problem is inherently a multiobjective optimization problem because we aim to preserve the dominance structure by using as little objectives as possible. In this paper, we propose an objective reduction algorithm based on constrained evolutionary multiobjective algorithm. A novel local search is presented for finding the Pareto-front by searching the neighbor. We compared the proposed algorithm with three algorithms on eleven test instances. The experimental results show the proposed algorithm can obtain a stable performance without any parameter need to fine tune. <s> BIB002
For the visualization of a PF in a high-dimensional space, most of the existing work shows that the indicator function value only varies along with the increase of the objective value, instead of displaying the location and distribution of the obtained solution vectors in a scatter plot, where each axis represents one objective. Facing this challenge, one of the future research directions is to apply some intelligent algorithms, such as big data and deep learning, to reduce the number of objectives while keeping the original objectives features unchanged. Then, one MaOP can be simplified to an MOP for considerable visualization, allowing DMs to easily select their preferred solutions. The idea of treating objective reduction as a multiobjective search problem in BIB002 and BIB001 is worth learning. For the MaOPs whose objectives could not be further reduced, the mapping transformation technique can be used to map solution vectors from the high-dimensional objective space to the two-dimensional or three-dimensional objective space, while preserving the dominance relationship among the solution vectors.