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.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-32964-7_10
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