A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 2) ALGORITHM FOR SOLVING MAOPS <s> State-of-the-art multiobjective evolutionary algorithms (MOEAs) treat all the decision variables as a whole to optimize performance. Inspired by the cooperative coevolution and linkage learning methods in the field of single objective optimization, it is interesting to decompose a difficult high-dimensional problem into a set of simpler and low-dimensional subproblems that are easier to solve. However, with no prior knowledge about the objective function, it is not clear how to decompose the objective function. Moreover, it is difficult to use such a decomposition method to solve multiobjective optimization problems (MOPs) because their objective functions are commonly conflicting with one another. That is to say, changing decision variables will generate incomparable solutions. This paper introduces interdependence variable analysis and control variable analysis to deal with the above two difficulties. Thereby, an MOEA based on decision variable analyses (DVAs) is proposed in this paper. Control variable analysis is used to recognize the conflicts among objective functions. More specifically, which variables affect the diversity of generated solutions and which variables play an important role in the convergence of population. Based on learned variable linkages, interdependence variable analysis decomposes decision variables into a set of low-dimensional subcomponents. The empirical studies show that DVA can improve the solution quality on most difficult MOPs. The code and supplementary material of the proposed algorithm are available at http://web.xidian.edu.cn/fliu/paper.html . <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 2) ALGORITHM FOR SOLVING MAOPS <s> In the last three decades there have been a number of efficient multi-objective optimization algorithms capable of solving real-world problems. However, due to the complexity of most real-world problems (high-dimensionality of problems, computationally expensive, and unknown function properties) researchers and decision-makers are increasingly facing the challenge of selecting an optimization algorithm capable of solving their hard problems. In this paper, we propose a simple yet efficient hybridization of multi- and many-objective optimization algorithms framework called hybrid many-objective optimization algorithm using fusion of solutions obtained by several many-objective algorithms (fusion) to gain the combined benefits of several algorithms and reducing the challenge of choosing one optimization algorithm to solve complex problems. During the optimization process, the Fusion framework (1) executes all optimization algorithms in parallel, (2) it combines solutions of these algorithms and extracts well-distributed solutions using predefined structured reference points or user-defined reference points, and (3) adaptively selects best-performing algorithm to tackle the problem at different stages of the search process. A case study of the fusion framework by considering GDE3, SMPSO, and SPEA2 as multi-objective optimization algorithms is presented. Experimental results on five unconstrained and four constrained benchmark test problems with three to ten objectives show that the Fusion framework significantly outperforms all algorithms involved in the hybridization process as well as the NSGA-III algorithm in terms of diversity and convergence of obtained solutions. Furthermore, the proposed framework is consistently able to find accurate solutions for all test problems which can be interpreted as its high robustness characteristic. <s> BIB002
A great deal of research work has been conducted on manyobjective optimization, most of which aims at proposing mechanisms or methods for MaOPs with a large number of objectives, but little attention has been paid to MaOPs with many decision variables. Therefore, the algorithms for solving MaOPs in such a scenario need to be studied further. Ma et al. BIB001 proposed an MOEA based on decision variable analysis, which decomposes decision variables into several low-dimensional subcomponents, and thus a complicated MOP is decomposed into a set of simpler sub-MOPs. How to deal with mixed variables better is also an open problem. This literature inspires that we can use learning algorithms to analyze the characteristics of decision variables and the potential relationship between variables. Due to the complexity of MaOPs, such as highdimensionality, computational expense, and unknown function properties, designing or selecting an optimization algorithm for solving these hard problems is challenging. Ibrahim et al. BIB002 combined the benefits of several optimization algorithms and proposed a hybrid multi-and manyobjective optimization algorithms framework to obtain the fusion of solutions. Inspired by this idea, it is a promising future research direction to design a hybrid algorithm that adaptively selects a best-performing algorithm at different stages of the search process and executes all algorithms in parallel to reduce the computational cost. In addition, many multiobjective optimization algorithms have only been tested on MOPs, and their performance should be further evaluated on various test problems with many objectives.