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The performance of the most existing classical evolutionary multiobjective optimization (EMO) algorithms, especially for Pareto-based EMO algorithms, generally deteriorates over the number of objectives in solving many-objective optimization problems (MaOPs), in which the number of objectives is greater than three. Objective reduction methods that transform an MaOP into the one with few objectives, are a promising way for solving MaOPs. The dominance-based objective reduction methods, e.g. k-EMOSS and \(\delta \)-MOSS, omitting an objective while preserving the dominant structure of the individuals as much as possible, can achieve good performance. However, these algorithms have higher computational complexity. Therefore, this paper presents a novel measure for measuring the capacity of preserving the dominance structure of an objective set, i.e., the redundancy of an objective to an objective set. Subsequently, we propose a fast algorithm to find a minimum set of objectives preserving the dominance structure as much as possible. We compare the proposed algorithm with its counterparts on eleven test instances. Numerical studies show the effectiveness of the proposed algorithm.

In this paper, we present a new method to fast approximate the hypervolume measurement by improving the classical Monte Carlo sampling method. Hypervolume value can be used as a quality indicator or selection indicator for multiobjective evolutionary algorithms (MOEAs), and thus the efficiency of calculating this measurement is of crucial importance especially in the case of large sets or many dimensional objective spaces. To fast calculate hypervolume, we develop a new Monte Carlo sampling method by decreasing the amount of Monte Carlo sample points using a novel decomposition strategy in this paper. We first analyze the complexity of the proposed algorithm in theory, and then execute a series experiments to further test its efficiency. Both simulation experiments and theoretical analysis verify the effectiveness and efficiency of the proposed method.

The evolutionary multiobjective algorithms have been demonstrated the effectiveness in dealing with multiobjective optimization problems. However, when solving the problems with many objectives, i.e., the number of objectives is greater than three, it needs a large population size to maintain population diversity and provide a good approximation to the Pareto front. The dilemma between limited computational resources and the exponentially increasing population size is a big challenge. Thus, we suggest a hierarchical decomposition-based evolutionary algorithm for solving many-objective optimization problems in this paper. Specifically, it constructs a binary tree on a set of large-scale uniform weight vectors. We only compare a candidate solutions with the solutions on the path from root to a leaf node of the tree to assign it into an appropriate node. The proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of the proposed algorithm is \(\mathcal {O}(Mlog(\mathbb {N}))\) for dealing with a new candidate solution. Empirical results fully demonstrate the effectiveness and competitiveness of the proposed algorithm.

Green communication has become a hot topic in the field of wireless communication. This paper aims to improve the Quality of Service (QoS) of the system and minimizes the energy consumption by the spectrum-energy cooperation between adjacent base stations. We formulate the proposed spectrum-energy cooperation model as a hybrid constrained many-objective optimization problem (MaOP). To improve the efficiency of optimization algorithm, an alternate optimization algorithm is presented to address the proposed complex MaOP. The evolutionary multiobjective algorithm is employed for spectrum cooperation optimization which is discrete optimization problem, meanwhile classical optimization method is employed for energy consumption optimization and energy cooperation optimization that are continuous optimization problems. Simulation results show the effectiveness of the algorithm.

The excellent performance of evolutionary multi-objective algorithms based on S metric selection (SMS) has been identified by many researchers. However, huge computational effort of S metric calculation has limited the full application of those algorithms. This paper proposes a novel S metric selection evolutionary algorithm (SMS-M2M) based on the population decomposition strategy MOEA/D-M2M. In SMS-M2M, SMS is conducted in each subpopulation instead of the whole population, which can avoid the S metric calculation of the total population. The purpose of population decomposition is to directly reduce the huge computational effort of calculating S metric and thus to give a simple but effective method to improve the effectiveness of SMS based algorithm. SMS-M2M utilizes the same SMS with a popular SMS based evolutionary algorithm SMS-EMOA. Numerical studies of SMS-M2M and SMS-EMOA have shown that the M2M population decomposition can effectively reduce the computational effort of SMS, meanwhile the theoretic analysis identifies the efficiency and effectiveness of SMS-M2M.

In Time Division Long Term EvolutionTD-LTE system, decreasing the cross time slot interference is very important to improve the system throughput. Accordingly, we will propose a multi-cells Orthogonal Frequency Division MultiplexingOFDM resource allocation model for TD-LTE system in this paper, which considers the cross time slot interference and the fairness. Subsequently, a TD-LTE resource allocation evolutionary algorithm based on adaptive fairness threshold is proposed to solve this model through introducing adaptive fairness threshold. Empirical studies show that the proposed model and algorithm can effectively decrease the cross time slot interference and improve the transmit rate of OFDM system under the same fairness.