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An evolutionary algorithm based on rank-1 approximation for sparse large-scale multi-objective problems

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Abstract

Most existing evolutionary algorithms encounter difficulties in dealing with multi-objective problems (MOPs) whose Pareto optimal solutions are sparse, especially when the decision space of the MOP is large. Most existing sparse evolutionary algorithms (EAs) lack the tricks specially for large-scale problems, and the existing tricks need some grouping/variable analysis methods to divide the large-scale variables, which severely affects the effect of optimization. To fill this gap, an evolutionary algorithm based on rank-1 approximation, suitable to reduce the dimensionality of sparse higher-order datasets, is proposed. First, canonical polyadic decomposition is introduced to divide the higher-dimensional set of decision variables into several lower-dimensional sub-sets. These sub-populations are alternatively optimized by a sparse evolution algorithm with special genetic strategies, to search for improved solutions in their respective lower-dimensional decision sub-space. Finally, the whole population is asymptotically optimized by all the sub-populations. The proposed algorithm first introduces the rank-1 approximation into the dimensionality reduction in sparse large-scale variables, combines it with the sparse EA, and proposes efficient alternative optimization strategy to solve the non-convex problem resulted from the multiple sub-problems. It is compared with other state-of-the-art algorithms for large-scale and sparse problems. The experimental results indicate that it outperforms other algorithms in terms of optimization performance and convergence rate.

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References

  • A Knee-Guided Evolutionary Algorithm for Compressing Deep Neural Network. IEEE Transactions on Cybernetics. 2021, 51(3):1626–1638

  • Abdel-Basset M, Mohamed R, Mirjalili S (2021) A Novel Whale Optimization Algorithm Integrated with Nelder-Mead Simplex for Multi-objective Optimization Problems. Knowl-Based Syst 212:1–28

    Article  Google Scholar 

  • Antonio LM, Coello CA (2018) Coevolutionary Multiobjective Evolutionary Algorithm: Survey of the State-of-the-art. IEEE Trans Evol Comput 22(6):851–865

    Article  Google Scholar 

  • Antonio L. M. and Coello Coello C. A.. Use of Cooperative Coevolution for Solving Large Scale Multiobjective Optimization Problems. In Proc. IEEE Congr. Evol. Comput., Cancun, Mexico, 2013: 2758–2765

  • Cao B, Zhao J, Lv Z et al (2017) A Distributed Parallel Cooperative Coevolutionary Multiobjective Evolutionary algorithm for Large-scale Optimization. IEEE Trans Ind Informat 13(4):2030–2038

    Article  Google Scholar 

  • Chen HK, Cheng R, Wen JM et al (2020a) Solving Large-scale Many-objective Optimization Problems by Covariance Matrix Adaptation Evolution Strategy with Scalable Small Subpopulations. Information Science 509:457–469

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Z, Huang CP, Lin SF (2020b) A New Sparse Representation Framework for Compressed Sensing MRI. Knowl-Based Syst 188:1–10

    Article  Google Scholar 

  • Cheng H., Ran C., and Danial Y.. Adaptive Offspring Generation for Evolutionary Large-Scale Multiobjective Optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2020, In Press.

  • Duan CX, Pan J, Li R (2020) Thick Cloud Removal of Remote Sensing Image Using Temporal Smoothness and Sparsity Regularized Tensor Optimization. Remote Sensing 12(20):1–26

    Article  Google Scholar 

  • Faramondi L.. Network Structure Vulnerability: A Multiobjective Attacker Perspective. IEEE Trans. Syst., Man., Cybern., Syst. In Press.

  • Feng J, Yang LT, Zhang R et al (2020) A Tensor-based Optimization Model for Secure Sustainable Cyber-Physical-Social Big Data Computations. IEEE Transactions on Sustainable Computing 5(2):223–234

    Article  Google Scholar 

  • Guo D., Wang X. L., Gao K. L., et al.. Evolutionary Optimization of High-Dimensional Multiobjective and Many-Objective Expensive Problems Assisted by a Dropout Neural Network. IEEE Transactions on Systems, Man, and Cybernetics: Systems. In Press

  • He C, Li LH, Tian Y et al (2019) Accelerating Large-Scale Multiobjective Optimization via Problem Reformulation. IEEE Trans Evol Comput 23(6):949–961

    Article  Google Scholar 

  • Hong D, Kolda TG, Duersch JA (2020) Generalized Canonical Polyadic Tensor Decomposition. SIAM Rev 62(1):133–163

    Article  MathSciNet  MATH  Google Scholar 

  • Ji JZ, Liu JD, Zou A (2019) ACOEC-FD: Ant Colony Optimization for Learning Brain Effective Connectivity Networks from Functional MRI and Diffusion Tensor Imaging. Front Neurosci 13:1–15

    Article  Google Scholar 

  • Lalou M, Tahraoui MA, Kheddouci H (2018) The Critical Node Detection Problem in Networks: A Survey. Comput Sci Rev 28:92–117

    Article  MathSciNet  MATH  Google Scholar 

  • Lathauwer LE, Moor BD, Vandewalle J et al (2000) A Multilinear Singular Value Decomposition. SIAM J Matrix Anal Appl 21(4):1253–1278

    Article  MathSciNet  MATH  Google Scholar 

  • Liu R, Liu J, Li Y et al (2020) A Random Dynamic Grouping Based Weight Optimization Framework for Large-scale Multi-objective Optimization Problems. Swarm Evol Comput 55:1–10

    Article  Google Scholar 

  • Lu ZC, Whalen I, Dhebar Y et al (2021) Multiobjective Evolutionary Design of Deep Convolutional Neural Networks for Image Classification. IEEE Trans Evol Comput 25(2):277–291

    Article  Google Scholar 

  • Ma XL, Liu F, Qi YT et al (2016) A Multiobjective Evolutionary Algorithm based on Decision Variable Analyses for Multiobjective Optimization Problems with Large-Scale Variables. IEEE Trans Evol Comput 20(2):275–298

    Article  Google Scholar 

  • Nazih M, Minaoui K, Comon P (2020) Using the Proximal Gradient and the Accelerated Proximal Gradient as A Canonical Polyadic Tensor Decomposition Algorithms in Difficult Situations. Signal Process 171:1–9

    Article  Google Scholar 

  • Nebro AJ, Durillo JJ, Nieto G et al (2009) SMPSO: A New PSO-based Metaheuristic for Multi-objective Optimization. IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making 2009:66–73

    Google Scholar 

  • Pistolesi F, Lazzerini B (2019) TeMA: A Tensorial Memetic Algorithm for Many-Objective Parallel Disassembly Sequence Planning in Product Refurbishment. IEEE Trans Industr Inf 15(6):3743–3753

    Article  Google Scholar 

  • Taguchi YH, Turki T (2021) Mathematical Formulation and Application of Kernel Tensor Decomposition based Unsupervised Feature Extraction. Knowl-Based Syst 217:1–10

    Article  Google Scholar 

  • Tan Z,Wang H, Liu S, Multi-stage dimension reduction for expensive sparse multiobjective optimization problems. Neurocomputing, 2021:159–174

  • Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: A Matlab Platform for Evolutionary Multi-objective Optimization. IEEE Comput Intell Mag 12(4):73–87

    Article  Google Scholar 

  • Tian Y, Lu C, Zhang X et al (2020b) Solving large-scale multiobjective optimization problems with sparse optimal solutions via unsupervised neural networks. IEEE Trans Cybern 51(6):3115–3128

    Article  Google Scholar 

  • Tian Y, Zhang XY, Wang C et al (2020a) An Evolutionary Algorithm for Large-Scale Sparse Multi-objective Optimization Problems. IEEE Trans Evol Comput 24(2):380–393

    Article  Google Scholar 

  • Tian Y, Lu C, Zhang X, et al., A pattern mining based evolutionary algorithm for large-scale sparse multi-objective optimization problems. IEEE Trans Cybern., https://doi.org/10.1109/TCYB.2020.3041325

  • Tian Y, Liu R, Zhang X et al., A multi-population evolutionary algorithm for solving large-scale multi-model multi-objective optimization problems. IEEE Trans Evol Comput

  • Tian Y., Liu R. C., Zhang X. Y., et al.. A Multi-Population Evolutionary Algorithm for Solving Large-Scale Multi-Modal Multi-Objective Optimization Problems. IEEE Transactions on Evolutionary Computation. 2020c. In Press.

  • Walker DJ, Craven MJ (2020) Identifying Good Algorithm Parameters in Evolutionary Multi- and Many-objective Optimization: A Visualisation Approach. Appl Soft Comput 88:1–11

    Article  Google Scholar 

  • Wang JH, Cen BZ, Gao SC et al (2020) Cooperative Evolutionary Framework with Focused Search for Many-Objective Optimization. IEEE Transactions on Emerging Topics in Computational Intelligence 4(3):398–412

    Article  Google Scholar 

  • Wang JJ, Wang DD, Huang TZ et al (2021a) Endmember Independence Constrained Hyperspectral Unmixing via Nonnegative Tensor Factorization. Knowl-Based Syst 216:1–13

    Article  Google Scholar 

  • Wang SQ, Chen YY, Jin Y et al (2021b) Error-robust Low-Rank Tensor Approximation for Multi-view Clustering. Knowl-Based Syst 215:1–9

    Article  Google Scholar 

  • Wang Q, Zhang Q, Meng F, Li B (2023) Objective-hierarchy based large-scale evolutionary algorithm for improving joint sparsity-compression of neural network. Inf Sci 640:1–32

    Article  Google Scholar 

  • Xue B, Zhang M, Browne WN (2013) Particle Swarm Optimization for Feature Selection in Classification: A Multi-objective Approach. IEEE Trans Cybern 43(6):1656–1671

    Article  Google Scholar 

  • Yang GA, Yang JJ, Lu ZZ et al (2020) A Convolutional Neural Network with Sparse Representation. Knowl-Based Syst 209:1–11

    Article  Google Scholar 

  • Yang S. S., Tian Y., He C., et al.. A Gradient-Guided Evolutionary Approach to Training Deep Neural Networks. IEEE Transaction on Neural Networks and Learning Systems. In Press.

  • Zhang X, Duan F, Zhang L et al (2017) Pattern Recommendation in Task-oriented Applications: A Multi-objective Perspective. IEEE Comput Intell Mag 12(3):43–53

    Article  Google Scholar 

  • Zhang Y, He CL, Song XF et al (2021a) A Multi-strategy Integrated Multi-objective Artificial Bee Colony for Unsupervised Band Selection of Hyperspectral Images. Swarm Evol Comput 60:1–15

    Google Scholar 

  • Zhang Q, Li H (2007) MOEA/D: A Multiobjective Evolutionary Algorithm based on Decomposition. IEEE Trans Evol Comput 11(6):712–731

    Article  Google Scholar 

  • Zhang X, Tian Y, Cheng R et al (2018) A Decision Variable Clustering-based Evolutionary Algorithm for Large-scale Many-objective Optimization. IEEE Trans Evol Comput 22(1):97–112

    Article  Google Scholar 

  • Zhang Y, Tian Y, Zhang X (2021b) Improved SparseEA for Sparse Large-scale Multi-objective Optimization Problems. Complex & Intelligent Systems 9:1–16

    Google Scholar 

  • Zhang JL, Wang W, Zhang ZP et al (2021c) TrustTF: A Tensor Factorization Model Using User Trust and Implicit Feedback for Context-aware Recommender Systems. Knowl-Based Syst 209:1–8

    Google Scholar 

  • Zhang YW, Yin CH, Liu ZH et al (2020) Recurrent Tensor Factorization for Time-Aware Service Recommendation. Appl Soft Comput 85:1–10

    Google Scholar 

  • Zille H, Ishibuchi H, Mostaghim S et al (2018) A Framework for Large-Scale Multiobjective Optimization Based on Problem Transformation. IEEE Trans Evol Comput 22(2):260–275

    Article  Google Scholar 

Download references

Acknowledgements

This work was found by Jilin Provincial Science and Technology Development Project (20200201165JC).

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. Students Affairs Department, Criminal Investigation Police, University of China, Shenyang, 110854, China

    Xiyue Chen

  2. Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, 100083, China

    Jing Pan

  3. School of Computer Science, Northeast Electric Power University, Jilin, 132012, China

    Bin Li & Qingzhu Wang

Authors
  1. Xiyue Chen
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  2. Jing Pan
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  3. Bin Li
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  4. Qingzhu Wang
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Contributions

XC was contributed to validation, writing, review and editing—revised draft. JP was contributed to writing—review and editing. BL was contributed to funding acquisition. QW was contributed to methodology, validation, writing—original draft.

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Correspondence to Xiyue Chen.

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Chen, X., Pan, J., Li, B. et al. An evolutionary algorithm based on rank-1 approximation for sparse large-scale multi-objective problems. Soft Comput 27, 15853–15871 (2023). https://doi.org/10.1007/s00500-023-08825-2

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