A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> C. MOEA/D APPLICATION RESEARCH 1) LARGE-SCALE OR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS <s> A considerable amount of research has been devoted to multiobjective optimization problems. However, few studies have aimed at multiobjective large-scale optimization problems (MOLSOPs). To address MOLSOPs, which may involve big data, this paper proposes a message passing interface MPI -based distributed parallel cooperative coevolutionary multiobjective evolutionary algorithm (DPCCMOEA). DPCCMOEA tackles MOLSOPs based on decomposition. First, based on a modified variable analysis method, we separate decision variables into several groups, each of which is optimized by a subpopulation (species). Then, the individuals in each subpopulation are further separated to several sets. DPCCMOEA is implemented with MPI distributed parallelism and a two-layer parallel structure is constructed. We examine the proposed algorithm using the multiobjective test suites Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group. In comparison with cooperative coevolutionary generalized differential evolution 3 and multiobjective evolutionary algorithm based on decision variable analyses, which are state-of-the-art cooperative coevolutionary multiobjective evolutionary algorithms, experimental results show that the novel algorithm has better performance in both optimization results and time consumption. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> C. MOEA/D APPLICATION RESEARCH 1) LARGE-SCALE OR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS <s> The current literature of evolutionary many-objective optimization is merely focused on the scalability to the number of objectives, while little work has considered the scalability to the number of decision variables. Nevertheless, many real-world problems can involve both many objectives and large-scale decision variables. To tackle such large-scale many-objective optimization problems (MaOPs), this paper proposes a specially tailored evolutionary algorithm based on a decision variable clustering method. To begin with, the decision variable clustering method divides the decision variables into two types: 1) convergence-related variables and 2) diversity-related variables. Afterward, to optimize the two types of decision variables, a convergence optimization strategy and a diversity optimization strategy are adopted. In addition, a fast nondominated sorting approach is developed to further improve the computational efficiency of the proposed algorithm. To assess the performance of the proposed algorithm, empirical experiments have been conducted on a variety of large-scale MaOPs with up to ten objectives and 5000 decision variables. Our experimental results demonstrate that the proposed algorithm has significant advantages over several state-of-the-art evolutionary algorithms in terms of the scalability to decision variables on MaOPs. <s> BIB002 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> C. MOEA/D APPLICATION RESEARCH 1) LARGE-SCALE OR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS <s> For large scale global optimization (LSGO) problems, many algorithms have been proposed in recent years. However, there are still some issues to be further handled since the search space grows exponentially and the problem solving becomes more and more difficult as the problem scale becomes larger and larger. In this paper, we propose a new hybrid algorithm for solving large-scale global optimization problems. First, we adopt an existing group algorithm to divide the large-scale problem into several small-scale problems. Second, a modified self-adaptive discrete scan method is designed to roughly scan the whole search space and then focus the search on the promising regions. Third, a hybrid search strategy is proposed, which adaptively chooses the one-dimensional search scheme or the covariance matrix adaptation evolutionary strategy to solve the subproblems of separable, partially (additively) separable problems or non-separable problems, respectively. To demonstrate the performance of the proposed algorithm, we conduct the experiments on 15 difficult LSGO problems in CEC’2013 benchmark suite and compare the performance of the proposed algorithm with that of the several state-of-the-art algorithms. The results show that the proposed algorithm is more effective than the compared algorithms in terms of solution accuracy. <s> BIB003 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> C. MOEA/D APPLICATION RESEARCH 1) LARGE-SCALE OR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS <s> In this paper, we propose a framework to accelerate the computational efficiency of evolutionary algorithms on large-scale multiobjective optimization. The main idea is to track the Pareto optimal set (PS) directly via problem reformulation. To begin with, the algorithm obtains a set of reference directions in the decision space and associates them with a set of weight variables for locating the PS. Afterwards, the original large-scale multiobjective optimization problem is reformulated into a low-dimensional single-objective optimization problem. In the reformulated problem, the decision space is reconstructed by the weight variables and the objective space is reduced by an indicator function. Thanks to the low dimensionality of the weight variables and reduced objective space, a set of quasi-optimal solutions can be obtained efficiently. Finally, a multiobjective evolutionary algorithm is used to spread the quasi-optimal solutions over the approximate Pareto optimal front evenly. Experiments have been conducted on a variety of large-scale multiobjective problems with up to 5000 decision variables. Four different types of representative algorithms are embedded into the proposed framework and compared with their original versions, respectively. Furthermore, the proposed framework has been compared with two state-of-the-art algorithms for large-scale multiobjective optimization. The experimental results have demonstrated the significant improvement benefited from the framework in terms of its performance and computational efficiency in large-scale multiobjective optimization. <s> BIB004 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> C. MOEA/D APPLICATION RESEARCH 1) LARGE-SCALE OR COMPUTATIONALLY EXPENSIVE OPTIMIZATION PROBLEMS <s> Distributed cooperative co-evolution (DCC) is an effective way to solve large-scale optimization problems. The cooperative co-evolution methodology can reduce the optimizing complexity by dividing a large-scale problem into small subcomponents, and distributed computation can accelerate the optimizing speed. However, existing DCC algorithms often encounter deficiency in overlapping problems that cannot be ideally divided due to unavoidable overlaps between subcomponents. To address this issue, this paper proposes an algorithm called distributed cooperative co-evolutionary covariance matrix adaptation evolution strategy (DCCMAES) to solve large-scale overlapping optimization problems. First, a new grouping scheme is introduced, where a variable, if needed, can be assigned into multiple subcomponents. Second, to address the conflicts caused by optimizing multiple copies of shared variables, a random orthogonal experiment method is proposed to generate global solutions. Moreover, three cooperation schemes are proposed to coordinate the optimizers in DCCMAES during evolution. The experiments on benchmark functions and a real-world application show that DCCMAES is promising for global optimization of large-scale overlapping problems. <s> BIB005
MOEA/D has been widely used in the fields of engineering, industry, and science. However, it still faces challenges in solving large-scale or computationally expensive optimization problems. These problems involve both many objectives and large-scale decision variables, which leads to a rapid decline in EAs' performance when solving them. In recent years, some researchers have proposed various algorithms for overcoming this challenge. Zhang et al. BIB002 proposed an evolutionary algorithm based on a decision variable clustering method that divides the decision variables into convergence-and diversity-related ones. These two types of decision variables were optimized with a convergence and diversity optimization strategy, respectively. It is still possible to improve the diversity of decision variable classification and the computational efficiency of the clustering method. Wu et al. BIB003 presented a new hybrid algorithm including two phases of decomposition and optimization. The algorithm divides a large-scale problem into several small-scale ones. A modified self-adaptive discrete scan method and a hybrid search strategy were designed to solve the subproblems on the promising regions. Designing some effective decomposition methods for solving large-scale problems is valuable and challenging in the future. Another challenge with such problems is that they require a large number of individual evaluations, resulting in a slow convergence speed of algorithms to solve them. Some research directions may be promising such as: a) using deep learning algorithms to acquire the features of largescale problems, and then discarding redundant information to reconstruct the problem model BIB004 , thus reducing its scale greatly; b) training the historical solution data to preselect the better solutions to reduce the number of individuals for evaluation; and c) combining the high-efficiency parallelism of parallel computers with the natural parallelism of MOEA/D to accelerate the optimization process, such as the cooperatively distributed co-evolutionary process mentioned in BIB001 , BIB005 .