A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) REPAIR ALGORITHMS <s> Multiobjective evolutionary algorithm based on decomposition (MOEA/D) has attracted a great deal of attention and has obtained enormous success in the field of evolutionary multiobjective optimization. It converts a multiobjective optimization problem (MOP) into a set of scalar optimization subproblems and then uses the evolutionary algorithm (EA) to optimize these subproblems simultaneously. However, there is a great deal of randomness in MOEA/D. Researchers in the field of evolutionary algorithm, reinforcement learning and neural network have reported that the simultaneous consideration of randomness and opposition has an advantage over pure randomness. A new scheme, called opposition-based learning (OBL), has been proposed in the machine learning field. In this paper, OBL has been integrated into the framework of MOEA/D to accelerate its convergence speed. Hence, our proposed approach is called opposition-based learning MOEA/D (MOEA/D-OBL). Compared with MOEA/D, MOEA/D-OBL uses an opposition-based initial population and opposition-based learning strategy to generate offspring during the evolutionary process. It is compared with its parent algorithm MOEA/D on four representative kinds of MOPs and many-objective optimization problems. Experimental results indicate that MOEA/D-OBL outperforms or performs similar to MOEA/D. Moreover, the parameter sensitivity of generalization opposite point and the probable to use OBL is experimentally investigated. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) REPAIR ALGORITHMS <s> Dynamic constrained optimization problems have received increasing attention in recent years. We study differential evolution which is one of the high performing class of algorithms for constrained continuous optimization in the context of dynamic constrained optimization. The focus of our investigations are repair methods which are crucial when dealing with dynamic constrained problems. Examining recently introduced benchmarks for dynamic constrained continuous optimization, we analyze different repair methods with respect to the obtained offline error and the success rate in dependence of the severity of the dynamic change. Our analysis points out the benefits and drawbacks of the different repair methods and gives guidance to its applicability in dependence on the dynamic changes of the objective function and constraints. <s> BIB002
An algorithm of this kind converts an infeasible solution to a feasible one by using repair operators. Fan et al.  proposed a new opposition-based repair operator to fix the infeasible solutions and then integrated it into two classical multiobjective EAs, MOEA/D and NSGA-II. This repair operator employs a reversed correction strategy that is inspired by the concept of opposition-based learning (OBL) BIB001 . The OBL method considers not only an estimate but also its corresponding opposite estimate, which can effectively avoid the search falling into local optimum. Finally, for the benchmark problems of CTPs and CMOPs, the algorithm with the proposed operator outperforms that with the two other kinds of repair operators used commonly in terms of convergence and diversity. Repair methods are crucial to dealing with dynamic constrained problems since they help to move the infeasible solutions toward a feasible region. Ameca-Alducin et al. BIB002 investigated four repair methods with DE for dynamic constrained optimization, including reference-based repair, offspring-repair, mutant-repair, and gradient-based repair. Also, three different measures were proposed to compare the performance of these repair methods, and then their advantages and disadvantages were analyzed in terms of the experimental results. Although the literature studied the performance of various repair operators in the processing of the dynamic CMOP under the DE algorithm, these operators can still be applied to the MOEA/D, and the performances of resulting algorithms are compared as well.