Adaptive decomposition-based evolutionary approach for multiobjective sparse reconstruction

Abstract

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 scenarios of high-dimensional reconstruction. Furthermore, these algorithms focus on estimating the whole Pareto front rather than the knee region, thus leading to solutions with limited diversity in the knee region and causing a 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 the diversity of solutions in the whole objective space. Then, we propose a two-stage iterative soft-thresholding (IST)-based local search operator for improving 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 makes it possible to focus the selection effort on the knee region, hence involving low computational complexity. Experimental results on images, and simulated and benchmark signals demonstrate the superiority of ADEA in terms of reconstruction accuracy and computational efficiency, compared to five stateof-the-art algorithms.

Multi-Objective Sparse Reconstruction With Transfer Learning and Localized Regularization

“…A twophase evolutionary approach was proposed in [16], where the statistical feature of the non-dominated solutions was extracted, and non-zero entries were located. Later, an adaptive decomposition-based evolutionary approach (ADEA) [10] was provided. It not only searches the whole PF with the guidance of reference vectors, but also devotes additional search effort to the knee region.…”

“…Using the two-stage iterative soft-thresholding (IST) based local search strategy in ADEA [10] as a baseline, we elaborate the proposed localized regularization-based local search, as shown in Algorithm 4. The population firstly undergoes normalization and solution association (refer to Section III-A) as a preparatory process.…”

“…where p ∈ (0, 1] is the norm, and λ is a predefined regularization parameter to balance the regularization term x p and the measurement error b − Ax 2 2 . The reconstruction performance is highly sensitive to λ [10], since it balances the feasibility and the sparsity of x. Nowadays, several heuristic methods have been proposed for selecting λ, e.g., the projected generalized Stein unbiased risk estimator-based method [11], the method based on projection onto Epigraph Sets [12], Homotopy continuation methods [13], and the crossvalidation approach [14].…”

“…The second challenge exists in local search operators. Conventional iterative thresholding methods [8] [20] [9], are generally integrated into MOSR solvers as local search operators [15] [21] [10]. Therefore, the local search process requires setting the regularization parameters.…”

Convergence Acceleration for Multiobjective Sparse Reconstruction via Knowledge Transfer

“…The knee region was exploited with preference. In [14], we proposed an adaptive decomposition-based evolutionary approach (ADEA). With the guidance of reference vectors, more search effort on the approximating knee region was executed by adaptively adding the reference vectors.…”