The gateway placement optimization (GPO) is a critical issue in satellite network that aims to obtain an optimal scheme to deploy different gateways in a network to achieve high-performed satellite-ground communication. Existing studies usually treat the GPO as a single-objective optimization problem, which significantly deviates from real-world scenarios and limits practical applicability. However, numerous performances like the gateway traffic load balancing, the distance between gateways, the traffic load of satellites, and the number of gateways within the satellite’s management range should be considered in the GPO problem, indicating that it is inherently a many-objective optimization problem (MaOP). Therefore, in this paper, a new mathematical model is designed which constructs the GPO as an MaOP. To address it, this paper further proposes a bi-velocity coevolutionary multiswarm particle swarm optimization (BCMPSO) algorithm. The BCMPSO follows the multiple populations for multiple objectives framework, running different populations in parallel, each optimizing a specific objective to search different parts of the Pareto front sufficiently. Meanwhile, a binary PSO with a bi-velocity update mechanism and a discrete position update mechanism is proposed as the optimizer in each population. Comparison experiments with several state-of-the-art methods confirm the effectiveness and competitiveness of the BCMPSO for many-objective GPO.

Feature selection (FS) is a significant research topic in machine learning and artificial intelligence, but it becomes complicated in the high dimensional search space due to the vast number of features. Evolutionary computation (EC) has been widely used in solving FS by modeling it as an expensive wrapper-form optimization task, where a classifier is used to obtain classification accuracy for fitness evaluation (FE). In this article, we propose that the FS problem can be also modeled as a cheap filter-form optimization task, where the FE is based on the relevance and redundancy of the selected features. The wrapper-form optimization task is beneficial for classification accuracy while the filter-form optimization task has the strength of a lighter computational cost. Therefore, different from existing multitask-based FS that uses various wrapper-form optimization tasks, this article uses a multiform optimization technique to model the FS problem as a wrapper-form optimization task and a filter-form optimization task simultaneously. An evolutionary multitask FS (EMTFS) algorithm for parallel tacking these two tasks is proposed followed by, in which a two-channel knowledge transfer strategy is proposed to transfer positive knowledge across the two tasks. Experiments on widely used public datasets show that EMTFS can select as few features as possible on the premise of superior classification accuracy than the compared state-of-the-art FS algorithms.

The Kriging model has been widely used in regression-based surrogate-assisted evolutionary algorithms (SAEAs) for expensive multiobjective optimization by using one model to approximate one objective, and the fusion of all the models forms the fitness surrogate. However, when tackling expensive many-objective optimization problems, too many models are required to construct such a fitness surrogate, which incurs cumulative prediction uncertainty and higher computational cost. Considering that the fitness surrogate works to predict different objective values to help select promising solutions with good convergence and diversity, this article proposes a novel model reduction idea to change the many-models-based fitness surrogate to a two-models-based indicator surrogate (TIS) that directly approximates convergence and diversity indicators. Based on TIS, a hierarchical and ensemble SAEA (HES-EA) is proposed with three stages. First, the HES-EA transforms the many objectives of the real-evaluated solutions into two indicators (i.e., the convergence and diversity indicators) and divides these solutions into different clusters. Second, an HES consisting of a cluster surrogate and different TISs is trained through these clustered solutions and their indicators. Third, during the optimization process, the HES can predict the candidate solutions’ cluster information via the cluster surrogate and indicator information via the TISs. Promising solutions can thus be selected based on the predicted information via a clustering-based sequential selection strategy without real fitness evaluation consumption. Compared with state-of-the-art SAEAs on three widely used benchmark suites up to 184 instances and one real-world application, HES-EA shows its superiority in both optimization performance and computational cost.

Feature selection (FS), which aims to minimize the classification error and the number of selected features, can essentially be modeled as a multiobjective optimization problem. To deal with such multiobjective FS (MOFS) problems, many multiobjective evolutionary algorithms (MOEAs) have been proposed. These MOEAs can find multiple optimal solutions, whereas substantial computational resources are required for fitness evaluations (FEs). More seriously, due to the high dimensionality and sparsity of FS problems, many FEs will be spent on unpromising solutions, resulting in a meaningless loss of computational resources. In this paper, two innovations are made so as to improve the performance of MOEAs for MOFS. First, we propose a surrogate-assisted flip (SF) strategy for MOEAs to reduce the FE waste on potentially unpromising solutions and improve search efficiency. This SF strategy is free of FE consumption and theoretically can be embedded in any MOEA to deal with MOFS problems. The experimental results show that this SF can improve the performance of different MOEAs, especially in reducing the number of selected features. Second, based on SF, we propose a more efficient SF -assisted MOEA for dealing with high-dimensional MOFS problems. The proposed algorithm divides the whole search space into different subspaces based on redundant feature subsets clustering to achieve parallel search, so as to reduce the search difficulty. The experimental results show that this algorithm is even more competitive than other SF -assisted MOEAs.

Evolutionary multitasking (EMT), as a very popular research topic in the evolutionary computation community, has been used to solve high-dimensional FS problems and has shown good performance recently. However, most of the existing EMT-based methods still have two drawbacks. First, they only consider using filter-based task generation strategies to retain highly relevant features for generating the additional tasks, whereas the redundancy between features is ignored. Second, they always consider a complete variable vector (e.g., global optimum or mean positional information of a population at current generation) as positive knowledge and transfer it, which greatly weakens the variety of transferred knowledge and increases the possibility of falling into local optimality. To deal with these two drawbacks, we propose a new EMT-assisted multitask particle swarm optimization (MPSO) algorithm with two innovations for high-dimensional FS. First, we propose a dual clustering-based task generation strategy to generate tasks by considering both feature relevance and redundancy. Second, we propose a fine-grain knowledge transfer strategy to realize explicit transfer of knowledge between different tasks. Experimental results on 15 public datasets show the effectiveness and competitiveness of our proposed MPSO algorithm over other state-of-the-art FS methods in dealing with high-dimensional FS problems.

Surrogate-assisted evolutionary algorithms (SAE-As), mainly including regression-based SAEAs and classification-based SAEAs, are promising for solving expensive multi-objective optimization problems (EMOPs). Regression-based SAEAs usually use complex regression models to approximate the fitness evaluation, which will suffer from high training costs to obtain a fine-accuracy surrogate. In contrast, classification-based SAEAs can achieve solution selection via coarse binary relations predicted by classifiers, thus avoiding high requirements in prediction accuracy and training costs. However, most of the binary relations in existing classification-based SAEAs mainly only involve convergence comparison whereas diversity maintenance is neglected. Considering the capacity of the grid technique in maintaining both convergence and diversity, we propose a new classification method called grid classification to discretize the objective space into grids and train a lightweight grid classification-based surrogate (GCS), for which low training costs are needed. The GCS can evaluate the solution performance in terms of both convergence and diversity simultaneously according to the predicted grid locations, which opens up a new field for follow-up research on classification-based SAEAs. Following this, a GCS-assisted particle swarm optimization algorithm is proposed for tackling EMOPs. Experimental results on widely-used benchmark problems (including high-dimensional EMOPs) and a 222-high-dimensional real-world application problem show its competitiveness in terms of both optimization performance and computational cost.

Feature selection, which aims to improve the classification accuracy and reduce the size of the selected feature subset, is an important but challenging optimization problem in data mining. Particle swarm optimization (PSO) has shown promising performance in tackling feature selection problems, but still faces challenges in dealing with large-scale feature selection in Big Data environment because of the large search space. Hence, this paper proposes a bi-directional feature fixation (BDFF) framework for PSO and provides a novel idea to reduce the search space in large-scale feature selection. BDFF uses two opposite search directions to guide particles to adequately search for feature subsets with different sizes. Based on the two different search directions, BDFF can fix the selection states of some features and then focus on the others when updating particles, thus narrowing the large search space. Besides, a self-adaptive strategy is designed to help the swarm concentrate on a more promising direction for search in different stages of evolution and achieve a balance between exploration and exploitation. Experimental results on 12 widely-used public datasets show that BDFF can improve the performance of PSO on large-scale feature selection and obtain smaller feature subsets with higher classification accuracy.

The convergence and diversity enhancement of multiobjective evolutionary algorithms (MOEAs) to efficiently solve many-objective optimization problems (MaOPs) is an active topic in evolutionary computation. By considering the advantages of the multiple populations for multiple objectives (MPMO) framework in solving multiobjective optimization problems and even MaOPs, this article proposes an MPMO-based algorithm with a bias sorting (BS) method (termed MPMO-BS) for solving MaOPs to achieve both good convergence and diversity performance. For convergence, the BS method is applied to each population of the MPMO framework to enhance the role of nondominated sorting by biasedly paying more attention to the objective optimized by the corresponding population. This way, all the populations in the MPMO framework evolve together to promote the convergence performance on all objectives of the MaOP. For diversity, an elite learning strategy is adopted to generate locally mutated solutions, and a reference vector-based maintenance method is adopted to preserve diverse solutions. The performance of the proposed MPMO-BS algorithm is assessed on 29 widely used MaOP test problems and two real-world application problems. The experimental results show its high effectiveness and competitiveness when compared with seven state-of-the-art MOEAs for many-objective optimization.

Data-driven evolutionary algorithms (DDEAs) have shown strong capacity in solving optimization problems with the help of surrogate models. However, current DDEAs often fall into the trap of inaccurate surrogates if no additional data can be obtained for the surrogates update during the optimization process. In addition, when dealing with multiobjective optimization problems, the surrogates in DDEAs will further suffer the difficulty of aggravating cumulative predicted fitness error. To overcome these difficulties, we propose a two-surrogate collaboration (TSC) management method, in which a Kriging surrogate and a radial basis function network (RBFN) surrogate are adopted to approximate the real fitness evaluation for the parent solutions and the newly generated offspring solutions, respectively. This TSC management method can effectively reduce the prediction uncertainty and improve the prediction performance of each surrogate without any other surrogate update process. During the optimization process, we use a modified social learning particle swarm optimization (SLPSO) as the basic search method and propose an offline DDEA. With the help of TSC, our resulting SLPSO-TSC algorithm can search for potential optimal solutions quickly and effectively without the help of any real fitness evaluation during the optimization process. The performance of the proposed SLPSO-TSC algorithm is verified on eleven widely used benchmark problems and compared with five different offline DDEAs. The experimental results show the high competitiveness of our proposed SLPSO-TSC for offline data-driven multiobjective optimization.