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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Donoho, D.: Compressed sensing. IEEE Trans. on Information Theory 52, 1289–1306 (2006)
Natarajan, B.K.: Sparse Approximate Solutions to Linear Systems. SIAM Journal on Computing 24, 227–234 (1995)
Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. on Signal Processing 41, 3397–3415 (1993)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Annals of Statistics 23, 407–499 (2004)
Tropp, J., Gilbert, A.: Signal recovery from partial information via orthogonal matching pursuit. IEEE Trans. on Information Theory 53, 4655–4666 (2006)
Candés, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure Applied Mathematics 59, 1207–1223 (2006)
Xu, Z., Chang, X., Xu, F., Zhang, H.: L1/2 Regularization: A Thresholding Representation Theory and A Fast Solver. Technical report, Xi’an Jiaotong University (2010)
Bredies, K., Lorenz, D.: Iterated hard shrikage for minimization problems with sparsity constraints. SIAM Journal of Scientific Computing 30, 657–683 (2008)
Zhou, A., Qu, B.Y., Li, H., Zhao, S.Z., Suganthan, P.N., Zhang, Q.: Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation 1(1), 32–49 (2011)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002)
Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. Evolutionary Computation 11(6), 712–731 (2007)
Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Tibshirani, R.: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society 46, 431–439 (1996)
Blumensath, T., Davies, M.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27, 265–274 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, H., Su, X., Xu, Z., Zhang, Q. (2012). MOEA/D with Iterative Thresholding Algorithm for Sparse Optimization Problems. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32964-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-32964-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32963-0
Online ISBN: 978-3-642-32964-7
eBook Packages: Computer ScienceComputer Science (R0)