Adaptive decomposition-based evolutionary approach for multiobjective sparse reconstruction

© 2018 Elsevier Inc. This paper aims at solving the sparse reconstruction (SR) problem via a multiobjective evolutionary algorithm. Existing multiobjective evolutionary algorithms for the SR problem have high computational complexity, especially in high-dimensional reconstruction scenarios. Furthermore, these algorithms focus on estimating the whole Pareto front rather than the knee region, thus leading to limited diversity of solutions in knee region and waste of computational effort. To tackle these issues, this paper proposes an adaptive decomposition-based evolutionary approach (ADEA) for the SR problem. Firstly, we employ the decomposition-based evolutionary paradigm to guarantee a high computational efficiency and diversity of solutions in the whole objective space. Then, we propose a two-stage iterative soft-thresholding (IST)-based local search operator to improve the convergence. Finally, we develop an adaptive decomposition-based environmental selection strategy, by which the decomposition in the knee region can be adjusted dynamically. This strategy enables to focus the selection effort on the knee region and achieves low computational complexity. Experimental results on simulated signals, benchmark signals and images demonstrate the superiority of ADEA in terms of reconstruction accuracy and computational efficiency, compared to five state-of-the-art algorithms

An adaptation reference-point-based multiobjective evolutionary algorithm

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones. This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics

Convergence acceleration for multiobjective sparse reconstruction via knowledge transfer

© Springer Nature Switzerland AG 2019. Multiobjective sparse reconstruction (MOSR) methods can potentially obtain superior reconstruction performance. However, they suffer from high computational cost, especially in high-dimensional reconstruction. Furthermore, they are generally implemented independently without reusing prior knowledge from past experiences, leading to unnecessary computational consumption due to the re-exploration of similar search spaces. To address these problems, we propose a sparse-constraint knowledge transfer operator to accelerate the convergence of MOSR solvers by reusing the knowledge from past problem-solving experiences. Firstly, we introduce the deep nonlinear feature coding method to extract the feature mapping between the search of the current problem and a previously solved MOSR problem. Through this mapping, we learn a set of knowledge-induced solutions which contain the search experience of the past problem. Thereafter, we develop and apply a sparse-constraint strategy to refine these learned solutions to guarantee their sparse characteristics. Finally, we inject the refined solutions into the iteration of the current problem to facilitate the convergence. To validate the efficiency of the proposed operator, comprehensive studies on extensive simulated signal reconstruction are conducted

Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Multiobjective Sparse Ensemble Learning by Means of Evolutionary Algorithms

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Ensemble learning can improve the performance of individual classifiers by combining their decisions. The sparseness of ensemble learning has attracted much attention in recent years. In this paper, a novel multiobjective sparse ensemble learning (MOSEL) model is proposed. Firstly, to describe the ensemble classifiers more precisely the detection error trade-off (DET) curve is taken into consideration. The sparsity ratio (sr) is treated as the third objective to be minimized, in addition to false positive rate (fpr) and false negative rate (fnr) minimization. The MOSEL turns out to be augmented DET (ADET) convex hull maximization problem. Secondly, several evolutionary multiobjective algorithms are exploited to find sparse ensemble classifiers with strong performance. The relationship between the sparsity and the performance of ensemble classifiers on the ADET space is explained. Thirdly, an adaptive MOSEL classifiers selection method is designed to select the most suitable ensemble classifiers for a given dataset. The proposed MOSEL method is applied to well-known MNIST datasets and a real-world remote sensing image change detection problem, and several datasets are used to test the performance of the method on this problem. Experimental results based on both MNIST datasets and remote sensing image change detection show that MOSEL performs significantly better than conventional ensemble learning methods

Channel Estimation of IRS-Aided Communication Systems with Hybrid Multiobjective Optimization

In this paper, we propose a compressive channel estimation technique for IRS-assisted mmWave multi-input and multi-output (MIMO) system. To reduce the training overhead, the inherent sparsity in mmWave channels is exploited. By utilizing the properties of Kronecker products, IRS-assisted mmWave channel estimation are converted into a sparse signal recovery problem, which involves two competing cost function terms (measurement error and a sparsity term). Existing sparse recovery algorithms solve the combined contradictory objectives function using a regularization parameter, which leads to a suboptimal solution. To address this concern, a hybrid multi-objective evolutionary paradigm is developed to solve the sparse recovery problem, which can overcome the difficulty in the choice of regularization parameter value. Simulation results show that under a wide range of simulation settings, the proposed algorithm achieves competitive error performance compared to existing channel estimation algorithms

Hybrid Evolutionary-based Sparse Channel Estimation for IRS-assisted mmWave MIMO Systems

The intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) communication system has emerged as a promising technology for coverage extension and capacity enhancement. Prior works on IRS have mostly assumed perfect channel state information (CSI), which facilitates in deriving the upper-bound performance but is difficult to realize in practice due to passive elements of IRS without signal processing capabilities. In this paper, we propose a compressive channel estimation techniques for IRS-assisted mmWave multi-input and multi-output (MIMO) system. To reduce the training overhead, the inherent sparsity of mmWave channels is exploited. By utilizing the properties of Kronecker products, IRS-assisted mmWave channel is converted into a sparse signal recovery problem, which involves two competing cost function terms (measurement error and sparsity term). Existing sparse recovery algorithms solve the combined contradictory objectives function using a regularization parameter, which leads to a suboptimal solution. To address this concern, a hybrid multiobjective evolutionary paradigm is developed to solve the sparse recovery problem, which can overcome the difficulty in the choice of regularization parameter value. Simulation results show that under a wide range of simulation settings, the proposed method achieves competitive error performance compared to existing channel estimation methods

Gridless Evolutionary Approach for Line Spectral Estimation with Unknown Model Order

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this problem is NP-hard to compute, relaxations of atomic $l_0$ norm, such as nuclear norm and reweighted atomic norm, have been employed for promoting sparsity. However, the relaxations give rise to a resolution limit, subsequently leading to biased model order and convergence error. To overcome the above shortcomings of relaxation, we propose a novel idea of simultaneously estimating the frequencies and model order by means of the atomic $l_0$ norm. To accomplish this idea, we build a multiobjective optimization model. The measurment error and the atomic $l_0$ norm are taken as the two optimization objectives. The proposed model directly exploits the model order via the atomic $l_0$ norm, thus breaking the resolution limit. We further design a variable-length evolutionary algorithm to solve the proposed model, which includes two innovations. One is a variable-length coding and search strategy. It flexibly codes and interactively searches diverse solutions with different model orders. These solutions act as steppingstones that help fully exploring the variable and open-ended frequency search space and provide extensive potentials towards the optima. Another innovation is a model order pruning mechanism, which heuristically prunes less contributive frequencies within the solutions, thus significantly enhancing convergence and diversity. Simulation results confirm the superiority of our approach in both frequency estimation and model order selection.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl