A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) MATING SELECTION AND REPLACEMENT MECHANISM <s> We implement a cellular genetic algorithm with two neighborhood structures following the concept of structured demes: One is for interaction among individuals and the other is for mating. The effect of using these two neighborhood structures on the search ability of cellular genetic algorithms is examined through computational experiments on function optimization problems. Experimental results show that good results are obtained from the combination of a small interaction neighborhood and a large mating neighborhood. This relation in the size of the two neighborhood structures coincides with many cases of biological evolution in nature such as plants and territorial animals. It is also shown that the search ability of cellular genetic algorithms is deteriorated by the opposite combination of the two neighborhood structures. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) MATING SELECTION AND REPLACEMENT 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
Different from just improving either mating selection or replacement, it makes sense to conduct both in one algorithm to further raise algorithm performance. The neighborhood structure should be independent when choosing mating parents and replacing old solutions. Also, different MOPs or a specific problem may need different neighborhood sizes, and thus, adaptive neighborhood sizes firmly contribute to the performance improvement of an algorithm. Ishibuchi et al. BIB001 introduced two neighborhood structures, i.e., the mating neighborhood for parent selection and the replacement neighborhood for interaction among individuals. The effect of neighborhood size on the algorithm performance was also studied, and a better result could be obtained by combining a small permutation neighborhood with a large matching neighborhood. The mating neighborhood is the entire population, while the replacement neighborhood size should be set to be much smaller than that of the original neighborhood in  . To overcome the shortcomings of the fixed neighborhood size in MOEA/D, Zhao et al. BIB002 suggested an ensemble of different neighborhood sizes in MOEA/D and adaptively adjusted their selection probabilities based on their historical information. During an evolution, each subproblem selects one candidate from the pool containing K fixed-size neighborhoods based on the candidates' previous performance of generating improved solutions. Experimental results demonstrated that the mechanism combining adaptation and optimization is effective for improving the performance of multiobjective optimization algorithms.