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, [Formula: see text]-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.
The modular structure of a network is closely related to the dynamics toward clustering. In this paper, a method for community detection is proposed via the clustering dynamics of a network. The initial phases of the nodes in the network are given randomly, and then they evolve according to a set of dedicatedly designed differential equations. The phases of the nodes are naturally separated into several clusters after a period of evolution, and each cluster corresponds to a community in the network. For the networks with overlapping communities, the phases of the overlapping nodes will evolve to the interspace of the two communities. The proposed method is illustrated with applications to both synthetically generated and real-world complex networks.
The link prediction algorithm which based on node similarity is the research hotspot in recent years. In addition, there are some methods which based on the network community structure information to predict the missing links, however, these studies only concerned about the obvious information between different communities such as direct links. We found that it is hard to predict the missing links if the two communities have little direct connections. In fact, there is similarity between communities such as the similarity between nodes and this similarity is significant for prediction. So, we define a community similarity feature which named community relevance by using not only the obvious information but also the latent information between different communities in this paper. Then a novel algorithm which based on the community relevance and ruler inference is proposed to predict missing links. In this method, we extract the community structure by using the local information of the network first. Next, calculate the relevance of each pair of communities by using the new community relevance indices. Finally, a simple prediction model which based on ruler inference is applied to estimate the probability of the missing links. It is shown that the proposed method has more effective prediction accuracy and the community relevance features improve the predictor with low time complexity, with experiments on benchmark networks and real-world networks in different scales, and compared with other ten sate of the art approaches.
Related to the safety of public lives and property in the lower area of reservoirs, flood control is a priority for most large reservoirs. Considering both dam safety and downstream flood control, reservoir flood control is a multi-objective problem (MOP). To meet the needs of irriCommunicated by V. Loia. B Fang Liu gation and generating electricity after the flood, the decision maker usually has his/her preferred final scheduling water level. To deal with this kind of MOP with user-preference information, we incorporate user-preference information into the framework of MOEA/D (multi-objective evolutionary algorithm-based decomposition). The widely used preference information is mainly composed of reference points and preference directions. Compared with the Pareto dominancebased multi-objective evolutionary algorithms (MOEAs), MOEA/D can naturally include two kinds of preference information since MOEA/D is directly based on the reference point and the preference direction. The weight vector of a subproblem in MOEA/D is just its preference. Aiming to obtain uniformly distributed solutions on the objective space, one of innovation points in this paper is using modified Tchebycheff decomposition instead of Tchebycheff decomposition as the decomposition method. To focus the search on the interesting regions of decision maker, the other innovation point in this paper is to integrate biased subproblem (weight vector) adjustment into the framework of MOEA/D. The distribution of subproblems (weight vectors) are adjusted periodically so that the subproblems are re-distributed adaptively to search the interesting regions. Some subproblems, which are far away from the preference regions, are deleted. And then some new subproblems, which are expected to search the preference regions, are added into the current evolutionary population. The efficiency and the effectiveness of the proposed algorithm are assessed through multi-objective reservoir flood control problem and two-to ten-objective test problems.Keywords Multi-objective optimization · Evolutionary algorithm · Decomposition · Preference · Biased weight vector adjustment · Reservoir flood control 123 X. Ma et al.
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