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A New Steady-State MOEA/D for Sparse Optimization

  • Hui LiEmail author
  • Jianyong Sun
  • Yuanyuan Fan
  • Mingyang Wang
  • Qingfu Zhang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 650)

Abstract

The classical algorithms based on regularization usually solve sparse optimization problems under the framework of single objective optimization, which combines the sparse term with the loss term. The majority of these algorithms suffer from the setting of regularization parameter or its estimation. To overcome this weakness, the extension of multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been studied for sparse optimization. The major advantages of MOEA/D lie in two aspects: (1) free setting of regularization parameter and (2) detection of true sparsity. Due to the generational mode of MOEA/D, its efficiency for searching the knee region of the Pareto front is not very satisfactory. In this paper, we proposed a new steady-state MOEA/D with the preference to search the region of Pareto front near the true sparse solution. Within each iteration of our proposed algorithm, a local search step is performed to examine a number of solutions with similar sparsity levels in a neighborhood. Our experimental results have shown that the new MOEA/D clearly performs better than its previous version on reconstructing artificial sparse signals.

Keywords

Sparse optimization Multiobjective optimization Evolutionary algorithm MOEA/D 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers for their constructive comments and suggestions on the original manuscript. This work was supported by the National Science Foundation of China under Grant 61573279, Grant 61175063, and Grant 61473241, Grant 11626252, Grant 11690011, the National Basic Research Program of China under Grant 2017CB329404.

References

  1. 1.
    Donoho, D.: Compressed sensing. IEEE Trans. Image Process. 52(4), 1289–1306 (2006)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Natraajan, B.: Sparse approximation to linear systems. SIAM J. Comput. 24(2), 227–234 (1995)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Davis, G., Mallat, S., Avellaneda, M.: Adaptive greedy approximations. Constr. Approx. 13(1), 57–98 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Temlyakov, V.: The best m-term approximation and greedy algorithms. Adv. Comput. Math 8(3), 249–265 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  6. 6.
    Blumensath, T., Davies, M.: Normalized iterative hard thresholding: guaranteed stability and performance. IEEE J. Sel. Top. Sign. Process. 4(2), 298–309 (2010)CrossRefGoogle Scholar
  7. 7.
    Donoho, D.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Xu, Z., Chang, X.Y., Xu, F., Zhang, H.: L1/2 regularization: a thresholding representation theory and a fast solver. IEEE Trans. Neural Netw. Learn. Syst. 23(7), 1013–1027 (2012)CrossRefGoogle Scholar
  9. 9.
    Zeng, J., Lin, S., Wang, Y., Xu, Z.: L1/2 regularization: convergence of iterative half thresholding algorithm. IEEE Trans. Sig. Process. 62(9), 2317–2329 (2014)CrossRefGoogle Scholar
  10. 10.
    Li, L., Yao, X., Stolkin, R., Gong, M., He, S.: An evolutionary multiobjective approach to sparse reconstruction. IEEE Trans. Evol. Comput. 18(6), 827–845 (2014)CrossRefGoogle Scholar
  11. 11.
    Li, H., Su, X., Xu, Z., Zhang, Q.: MOEA/D with iterative thresholding algorithm to sparse optimization problems. In: Proceedings of 12th International Conference on Parallel Problem Solving from Nature (PPSN), pp. 93–101 (2012)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Hui Li
    • 1
    Email author
  • Jianyong Sun
    • 1
  • Yuanyuan Fan
    • 1
  • Mingyang Wang
    • 1
  • Qingfu Zhang
    • 2
  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of Computer ScienceCity University of Hong KongKowloonHong Kong

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