A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> A. ADAPTIVE MECHANISM <s> It is well-known that multiobjective problems with many objectives are difficult for Pareto dominance-based algorithms such as NSGA-II and SPEA. This is because almost all individuals in a population are non-dominated with each other in the presence of many objectives. In such a population, the Pareto dominance relation can generate no strong selection pressure toward the Pareto front. This leads to poor search ability of Pareto dominance-based algorithms for many-objective problems. Recently it has been reported that better results can be obtained for many-objective problems by the use of scalarizing functions. The weighted sum usually works well in scalarizing function-based algorithms when the Pareto front is convex. However, we need other functions such as the weighted Tchebycheff when the Pareto front is non-convex. In this paper, we propose an idea of automatically choosing between the weighted sum and the weighted Tchebycheff for each individual in each generation. The characteristic feature of the proposed idea is to use the weighted Tchebycheff only when it is needed for individuals along non-convex regions of the Pareto front. The weighted sum is used for the other individuals in each generation. The proposed idea is combined with a high-performance scalarizing function-based algorithm called MOEA/D (multiobjective evolutionary algorithm based on decomposition) of Zhang and Li (2007). Effectiveness of the proposed idea is demonstrated through computational experiments on modified multiobjective knapsack problems with non-convex Pareto fronts. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> A. ADAPTIVE MECHANISM <s> The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has demonstrated superior performance by winning the multiobjective optimization algorithm competition at the CEC 2009. For effective performance of MOEA/D, neighborhood size (NS) parameter has to be tuned. In this letter, an ensemble of different NSs with online self-adaptation is proposed (ENS-MOEA/D) to overcome this shortcoming. Our experimental results on the CEC 2009 competition test instances show that an ensemble of different NSs with online self-adaptation yields superior performance over implementations with only one fixed NS. <s> BIB002 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> A. ADAPTIVE MECHANISM <s> Recently, MOEA/D multi-objective evolutionary algorithm based on decomposition has achieved great success in the field of evolutionary multi-objective optimization and has attracted a lot of attention. It decomposes a multi-objective optimization problem MOP into a set of scalar subproblems using uniformly distributed aggregation weight vectors and provides an excellent general algorithmic framework of evolutionary multi-objective optimization. Generally, the uniformity of weight vectors in MOEA/D can ensure the diversity of the Pareto optimal solutions, however, it cannot work as well when the target MOP has a complex Pareto front PF; i.e., discontinuous PF or PF with sharp peak or low tail. To remedy this, we propose an improved MOEA/D with adaptive weight vector adjustment MOEA/D-AWA. According to the analysis of the geometric relationship between the weight vectors and the optimal solutions under the Chebyshev decomposition scheme, a new weight vector initialization method and an adaptive weight vector adjustment strategy are introduced in MOEA/D-AWA. The weights are adjusted periodically so that the weights of subproblems can be redistributed adaptively to obtain better uniformity of solutions. Meanwhile, computing efforts devoted to subproblems with duplicate optimal solution can be saved. Moreover, an external elite population is introduced to help adding new subproblems into real sparse regions rather than pseudo sparse regions of the complex PF, that is, discontinuous regions of the PF. MOEA/D-AWA has been compared with four state of the art MOEAs, namely the original MOEA/D, Adaptive-MOEA/D, -MOEA/D, and NSGA-II on 10 widely used test problems, two newly constructed complex problems, and two many-objective problems. Experimental results indicate that MOEA/D-AWA outperforms the benchmark algorithms in terms of the IGD metric, particularly when the PF of the MOP is complex. <s> BIB003 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> A. ADAPTIVE MECHANISM <s> Adaptive operator selection (AOS) is used to determine the application rates of different operators in an online manner based on their recent performances within an optimization process. This paper proposes a bandit-based AOS method, fitness-rate-rank-based multiarmed bandit (FRRMAB). In order to track the dynamics of the search process, it uses a sliding window to record the recent fitness improvement rates achieved by the operators, while employing a decaying mechanism to increase the selection probability of the best operator. Not much work has been done on AOS in multiobjective evolutionary computation since it is very difficult to measure the fitness improvements quantitatively in most Pareto-dominance-based multiobjective evolutionary algorithms. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Thus, it is natural and feasible to use AOS in MOEA/D. We investigate several important issues in using FRRMAB in MOEA/D. Our experimental results demonstrate that FRRMAB is robust and its operator selection is reasonable. Comparison experiments also indicate that FRRMAB can significantly improve the performance of MOEA/D. <s> BIB004
The adaptive mechanism that is suitable for complex MOPs can realize the dynamic adjustment of MOEA/D components, such as the decomposition method BIB001 , weight vector BIB003 , neighborhood size BIB002 , and reproduction operator BIB004 . With the increasing focus on artificial intelligence (AI), algorithm automation will be a hotspot in the optimization community.