A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> D. USER PREFERENCES <s> Evolutionary algorithms that rely on dominance ranking often suffer from a low selection pressure problem when dealing with many-objective problems. Decomposition and user-preference based methods can help to alleviate this problem to a great extent. In this paper, a user-preference based evolutionary multi-objective algorithm is proposed that uses decomposition methods for solving many-objective problems. Decomposition techniques that are widely used in multi-objective evolutionary optimization require a set of evenly distributed weight vectors to generate a diverse set of solutions on the Pareto-optimal front. The newly proposed algorithm, R-MEAD2, improves the scalability of its previous version, R-MEAD, which uses a simplexlattice design method for generating weight vectors. This makes the population size is dependent on the dimension size of the objective space. R-MEAD2 uses a uniform random number generator to remove the coupling between dimension and the population size. This paper shows that a uniform random number generator is simple and able to generate evenly distributed points in a high dimensional space. Our comparative study shows that R-MEAD2 outperforms the dominance-based method R-NSGA-II on many-objective problems. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> D. USER PREFERENCES <s> In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems. <s> BIB002 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> D. USER PREFERENCES <s> User preference is of great importance when dealing with many objective optimization. Using the preference information to obtain preferred parts of the Pareto set has become prevalent in the research domain of Evolutionary Multiobjective Optimization (EMO). In this paper, a target region provided by the decision maker (DM), defined by the preferred range of every objective, is utilized to articulate the preference in-formation. This information is integrated with two well-known multiobjective evolutionary algorithms based on decomposition: MOEA/D and NSGA-III. The newly proposed preference-based algorithms, called T-MOEA/D and T-NSGA-III, can be used both a-priori and interactively. Experiments have demonstrated the benefit of applying them interactively. The DM can easily and quickly adjust the preferences according to the current results, and the proposed algorithms can successfully find non-dominated solutions complying with the preferences. Comparative experiments show that the proposed algorithms outperform the dominance-based algorithm T-NSGA-II on many-objective benchmark problems. <s> BIB003
EAs usually take a long time to solve problems, which is considered as a defect of these algorithms. Embedding user preferences in MOEA/D a priori or interactively can avoid unnecessary space searches and thus effectively shortens the operating time of an algorithm, where user preferences could be represented by reference points BIB001 , reference vectors BIB002 or target region BIB003 . 