MOEA/D with Iterative Thresholding Algorithm for Sparse Optimization Problems

Hui Li¹, Xiaolei Su¹, Zongben Xu¹, and Qingfu Zhang²

¹Institute for Information and System Sciences & Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi,710049, China
lihui10@mail.xjtu.edu.cn
suxl062641@stu.xjtu.edu.cn
zbxu@mail.xjtu.edu.cn

²School of Computer Science & Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK
qzhang@essex.ac.uk

Abstract. Currently, a majority of existing algorithms for sparse optimization problems are based on regularization framework. The main goal of these algorithms is to recover a sparse solution with k non-zero components(called k-sparse). In fact, the sparse optimization problem can also be regarded as a multi-objective optimization problem, which considers the minimization of two objectives (i.e., loss term and penalty term). In this paper, we proposed a revised version of MOEA/D based on iterative thresholding algorithm for sparse optimization. It only aims at finding a local part of trade-off solutions, which should include the k-sparse solution. Some experiments were conducted to verify the effectiveness of MOEA/D for sparse signal recovery in compressive sensing. Our experimental results showed that MOEA/D is capable of identifying the sparsity degree without prior sparsity information.

Keywords: sparse optimization, multi-objective optimization, hard/ half thresholding algorithm, evolutionary algorithm

LNCS 7492, p. 93 ff.

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