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Weighted mean of vectors algorithm with neighborhood information interaction and vertical and horizontal crossover mechanism for feature selection

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Abstract

The Weighted Mean of Vectors Algorithm (INFO) is an enhanced weighted average method that optimizes vector positions using three strategies: updating rule, vector combination, and local search. This algorithm exhibits notable optimization capabilities and high convergence accuracy. However, it is not without limitations; specifically, it tends to become trapped in local optima when addressing multi-peaked functions, suffers from a lack of population diversity, and is prone to premature convergence. To address these issues, this paper presents an improved version of the algorithm, WCINFO, which integrates a weighted voting (WV) strategy and a horizontal and vertical crossover (CC) strategy. The WV strategy facilitates early-stage information exchange among search agents and neighboring individuals, while the CC strategy effectively prevents the algorithm from becoming trapped in local optima. This study evaluates WCINFO’s performance using the IEEE CEC 2017 test set, comparing it against the original INFO algorithm, seven mainstream meta-heuristic algorithms (MAs), and eleven enhanced MAs. The Wilcoxon signed-rank test is employed to assess WCINFO’s performance. The results indicate that WCINFO surpasses the other algorithms in convergence accuracy, speed, and robustness. Furthermore, to ascertain WCINFO’s efficacy in feature selection (FS), its binary variant, BWCINFO, is compared against eight other binary classifiers across 16 publicly available datasets. WCINFO achieved the lowest classification error rates compared to other algorithms and selected the fewest features across all 16 datasets. Additionally, it attained 100% accuracy on six of these datasets, with the size of the feature subsets being less than 35.2% of the original number of features.

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Data Availability

The experimental datasets used for feature selection in this study are primarily sourced from publicly available datasets, such as those from the UCI repository (https://archive.ics.uci.edu/dataset/33/dermatology).

References

  1. Gollou AR, Ghadimi N (2017) A new feature selection and hybrid forecast engine for day-ahead price forecasting of electricity markets. J Intell Fuzzy 32(6):4031–4045

    MATH  Google Scholar 

  2. Gu S, Cheng R, Jin Y (2018) Feature selection for high-dimensional classification using a competitive swarm optimizer. Soft Comput 22:811–822

    MATH  Google Scholar 

  3. Dahiya T, Vashishth N, Garg D et al (2023) Novel heuristic algorithm & its application for reliability optimization. In: International Journal of Mathematical Engineering and Management Sciences 8(4):755–768

  4. Iemets OA, Yemets OA, Parfonova TA (2013) Branch and bound method for optimization problems on fuzzy sets. J Autom Inf Sci 45(4)

  5. Krishnan K, Mitchell JE (2006) A unifying framework for several cutting plane methods for semidefinite programming. Optim Methods Softw 21(1):57–74

    MathSciNet  MATH  Google Scholar 

  6. Lazarev AA, Werner F (2009) A graphical realization of the dynamic programming method for solving NP-hard combinatorial problems. Comput Math Appl 58(4):619–631

    MathSciNet  MATH  Google Scholar 

  7. Li Y, Luo Y, Wu X et al (2024) Variational bayesian learning based localization and channel reconstruction in RIS-aided systems. IEEE Trans Wirel Commun

  8. Sun G et al (2019) Low-latency and resource-efficient service function chaining orchestration in network function virtualization. IEEE Internet Things J 7(7):5760–5772

    MATH  Google Scholar 

  9. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    MathSciNet  MATH  Google Scholar 

  10. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95-international conference on neural networks. IEEE 4:1942–1948

  11. Bo Sun JS, Wei M (2024) 3D trajectory planning model of unmanned aerial vehicles (UAVs) in a dynamic complex environment based on an improved ant colony optimization algorithm. J Nonlinear Convex Anal 25(4):737–746

    MATH  Google Scholar 

  12. Qi A et al (2024) FATA: an efficient optimization method based on geophysics. Neurocomputing 128289. https://doi.org/10.1016/j.neucom.2024.128289

  13. Heidari AA et al (2019) Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems 97:849–872

    MATH  Google Scholar 

  14. Li S et al (2020) Slime mould algorithm: A new method for stochastic optimization. Future Gener Comput Syst 111:300–323

    MATH  Google Scholar 

  15. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    MATH  Google Scholar 

  16. Yang XS, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483

    MATH  Google Scholar 

  17. Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Google Scholar 

  18. Yuan C et al (2024) Artemisinin optimization based on malaria therapy: algorithm and applications to medical image segmentation. Displays 102740. https://doi.org/10.1016/j.displa.2024.102740

  19. Lian J et al (2024) Parrot optimizer: Algorithm and applications to medical problems. Comput Biol Med 108064. https://doi.org/10.1016/j.compbiomed.2024.108064

  20. Tu J et al (2021) The Colony Predation Algorithm. J Bionic Eng 18(3):674–710

    MATH  Google Scholar 

  21. Houssein EH et al (2023) Liver Cancer Algorithm: A novel bio-inspired optimizer. Comput Biol Med 165:107389

    MATH  Google Scholar 

  22. Yang Y et al (2021) Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177:114864

    MATH  Google Scholar 

  23. Su H et al (2023) RIME: A physics-based optimization. Neurocomputing 532:183–214

    MATH  Google Scholar 

  24. Ahmadianfar I et al (2021) RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method. Expert Syst Appl 181:115079

    MATH  Google Scholar 

  25. Ahmadianfar I et al (2022) INFO: An efficient optimization algorithm based on weighted mean of vectors. Expert Syst Appl 195:116516

    MATH  Google Scholar 

  26. Jahandideh-Tehrani M, Bozorg-Haddad O, Loáiciga HA (2020) Application of particle swarm optimization to water management: an introduction and overview. Environ Monit Assess 192:1–18

    MATH  Google Scholar 

  27. Hakemi S et al (2022) A review of recent advances in quantum-inspired metaheuristics. Evol Intell 1-16. https://doi.org/10.1007/s12065-022-00783-2

  28. Agushaka JO et al (2023) Efficient initialization methods for population-based metaheuristic algorithms: a comparative study. Arch Comput Methods Eng 30(3):1727–1787

    MATH  Google Scholar 

  29. Zhang Q et al (2021) Gaussian barebone salp swarm algorithm with stochastic fractal search for medical image segmentation: A COVID-19 case study. Comput Biol Med 139:104941

    MATH  Google Scholar 

  30. Hu J et al (2022) Chaotic diffusion-limited aggregation enhanced grey wolf optimizer: insights, analysis, binarization, and feature selection. Int J Intell Syst 37(8):4864–4927

    MATH  Google Scholar 

  31. Li H et al (2022) A ranking-system-based switching particle swarm optimizer with dynamic learning strategies. Neurocomputing 494:356–367

    MATH  Google Scholar 

  32. Zhou X et al (2023) Random following ant colony optimization: continuous and binary variants for global optimization and feature selection. Appl Soft Comput 110513. https://doi.org/10.1016/j.asoc.2023.110513

  33. Hu J et al (2022) Dispersed foraging slime mould algorithm: Continuous and binary variants for global optimization and wrapper-based feature selection. Knowl-Based Syst 237:107761

    MATH  Google Scholar 

  34. Chen H et al (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45–59

    MathSciNet  MATH  Google Scholar 

  35. Zhao D et al (2021) Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy. Knowl-Based Syst 216:106510

    MATH  Google Scholar 

  36. Tan W-H, Mohamad-Saleh J (2023) A hybrid whale optimization algorithm based on equilibrium concept. Alex Eng J 68:763–786

    MATH  Google Scholar 

  37. Kumar A, Dhillon JS (2023) Enhanced Harris hawk optimizer for hydrothermal generation scheduling with cascaded reservoirs. Expert Syst Appl 226:120270

    MATH  Google Scholar 

  38. Tiwari P, Mishra VN, Parouha RP (2024) Developments and design of differential evolution algorithm for non-linear/non-convex engineering optimization. Arch Comput Methods Eng 31(4):2227–2263

    MATH  Google Scholar 

  39. Zhu N et al (2024) A hierarchical reinforcement learning-aware hyper-heuristic algorithm with fitness landscape analysis. Swarm Evol Comput 90:101669

    MATH  Google Scholar 

  40. Lee SJ, Kim BS (2023) Two-stage meta-heuristic for part-packing and build-scheduling problem in parallel additive manufacturing. Appl Soft Comput 136:110132

    MATH  Google Scholar 

  41. Gao Z, Zhao J, Li S (2020) The hybridized slime mould and particle swarm optimization algorithms. In: 2020 IEEE 3rd international conference on automation, electronics and electrical engineering (AUTEEE). IEEE, pp 304–308

  42. Gong X et al (2023) A hybrid algorithm based on state-adaptive slime mold model and fractional-order ant system for the travelling salesman problem. Complex Intell Syst 9(4):3951–3970

    MATH  Google Scholar 

  43. García S et al (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Inf Sci 180(10):2044–2064

    MATH  Google Scholar 

  44. Alcalá-Fdez J et al (2009) KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13:307–318

    MATH  Google Scholar 

  45. Peng Z et al (2020) A novel optimal bipartite consensus control scheme for unknown multi-agent systems via model-free reinforcement learning. Bull Comput Appl Math 369:124821

    MathSciNet  MATH  Google Scholar 

  46. Li X, Sun Y (2021) Application of RBF neural network optimal segmentation algorithm in credit rating. Neural Comput Appl 33:8227–8235

    MATH  Google Scholar 

  47. Lazar C et al (2012) A survey on filter techniques for feature selection in gene expression microarray analysis. IEEE/ACM Trans Comput Biol Bioinform 9(4):1106–1119

    MATH  Google Scholar 

  48. Kwak N, Choi C-H (2002) Input feature selection for classification problems. IEEE Trans Neural Netw 13(1):143–159

    MATH  Google Scholar 

  49. Chandrashekar G, Sahin F (2014) A survey on feature selection methods. Comput Electr Eng 40(1):16–28

    MATH  Google Scholar 

  50. Santana LEADS, de Paula Canuto AM (2014) Filter-based optimization techniques for selection of feature subsets in ensemble systems. Expert Syst Appl 41(4):1622–1631

    MATH  Google Scholar 

  51. Yang P, Liu W, Zhou BB et al (2013) Ensemble-based wrapper methods for feature selection and class imbalance learning. In: advances in knowledge discovery and data mining: 17th Pacific-Asia Conference, PAKDD 2013, Gold Coast, Australia, April 14-17, 2013, Proceedings, Part I 17. Springer Berlin Heidelberg, pp 544–555

  52. Li T et al (2022) A binary individual search strategy-based bi-objective evolutionary algorithm for high-dimensional feature selection. Inf Sci 610:651–673

    MATH  Google Scholar 

  53. Xue Y, Cai X, Neri F (2022) A multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale feature selection in classification. Appl Soft Comput 127:109420

    MATH  Google Scholar 

  54. Hu B et al (2016) Feature selection for optimized high-dimensional biomedical data using an improved shuffled frog leaping algorithm. IEEE/ACM Trans Comput Biol Bioinform 15(6):1765–1773

    MATH  Google Scholar 

  55. Hegazy AE, Makhlouf M, El-Tawel GS (2020) Improved salp swarm algorithm for feature selection. J King Saud Univ – Comput Inf Sci 32(3):335–344

    Google Scholar 

  56. Abdel-Basset M et al (2021) BSMA: A novel metaheuristic algorithm for multi-dimensional knapsack problems: Method and comprehensive analysis. Comput Ind Eng 159:107469

    MATH  Google Scholar 

  57. Jadhav S, He H, Jenkins K (2018) Information gain directed genetic algorithm wrapper feature selection for credit rating. Appl Soft Comput 69:541–553

    MATH  Google Scholar 

  58. Lai JCY, Leung FHF, Ling SH (2009) A new differential evolution with wavelet theory based mutation operation. In: 2009 IEEE Congress on Evolutionary Computation. IEEE, pp 1116–1122

  59. Yong X, Gao Y-L (2023) Improved firefly algorithm for feature selection with the ReliefF-based initialization and the weighted voting mechanism. Neural Comput Appl 35(1):275–301

    MATH  Google Scholar 

  60. Su H et al (2022) Multilevel threshold image segmentation for COVID-19 chest radiography: a framework using horizontal and vertical multiverse optimization. Comput Biol Med 146:105618

    MATH  Google Scholar 

  61. Su H et al (2023) A horizontal and vertical crossover cuckoo search: Optimizing performance for the engineering problems. J Comput Des Eng 10(1):36–64

    MathSciNet  MATH  Google Scholar 

  62. Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14

    MATH  Google Scholar 

  63. Wang Z et al (2024) Hunger games search algorithm based on stochastic individual information for engineering design optimization problems. J Comput Des Eng 11(3):280–307

    MATH  Google Scholar 

  64. Huang J et al (2024) Enhancing slime mould algorithm for engineering optimization: leveraging covariance matrix adaptation and best position management. J Comput Des Eng qwae054. https://doi.org/10.1093/jcde/qwae054

  65. Mirjalili S (2015) Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    MATH  Google Scholar 

  66. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    MATH  Google Scholar 

  67. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    MATH  Google Scholar 

  68. AbdElaziz M, Oliva D, Xiong S (2017) An improved Opposition-Based Sine Cosine Algorithm for global optimization. Expert Syst Appl 90:484–500

    MATH  Google Scholar 

  69. Cao Y et al (2018) Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Trans Evol Comput 23(4):718–731

    MATH  Google Scholar 

  70. Chen W-N et al (2012) Particle swarm optimization with an aging leader and challengers. IEEE Trans Evol Comput 17(2):241–258

    MATH  Google Scholar 

  71. Qiu F et al (2022) Boosting slime mould algorithm for high-dimensional gene data mining: diversity analysis and feature selection. Comput Math Methods Med 2022. https://doi.org/10.1155/2022/8011003

  72. Örnek BN et al (2022) A novel version of slime mould algorithm for global optimization and real world engineering problems: Enhanced slime mould algorithm. Math Comput Simulat 198:253–288

    MathSciNet  MATH  Google Scholar 

  73. Wei Y et al (2020) Predicting entrepreneurial intention of students: An extreme learning machine with Gaussian barebone Harris hawks optimizer. IEEE Access 8:76841–76855

    Google Scholar 

  74. Deep K (2022) A random walk Grey wolf optimizer based on dispersion factor for feature selection on chronic disease prediction. Expert Syst Appl 206:117864

    MATH  Google Scholar 

  75. Yong J, He F, Li H et al (2018) A novel bat algorithm based on collaborative and dynamic learning of opposite population. In: 2018 IEEE 22nd international conference on computer supported cooperative work in design ((CSCWD)). IEEE, pp 541–546

  76. Hao S et al (2023) Performance optimization of water cycle algorithm for multilevel lupus nephritis image segmentation. Biomed Signal Process Control 80:104139

    MATH  Google Scholar 

  77. Awad NH, Ali MZ, Suganthan PN (2017) Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 372–379

  78. Tanabe R, Fukunaga AS (2014) Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE congress on evolutionary computation (CEC). IEEE, pp 1658–1665

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Acknowledgments

This work was supported in part by the Natural Science Foundation of Zhejiang Province (LZ22F020005), National Natural Science Foundation of China (62076185, 62301367).

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Correspondence to Yi Chen or Huiling Chen.

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Appendix A

Appendix A

Table 12 Comparison results for WCINFO, WVINFO, CCINFO and INFO on 30 benchmark functions
Table 13 Comparison results between WCINFO and other MAs
Table 14 Comparison of WCINFO and enhanced MAs variants
Table 15 Comparison results of the fitness values obtained by BWCINFO and the other eight classification methods on the dataset
Table 16 Comparison results of the average error values obtained by BWCINFO and the other eight classification methods on the dataset
Table 17 Comparison results of the average value of the selected features obtained by BWCINFO and the other eight classification methods on the dataset
Table 18 Comparison results of the average running time obtained by BWCINFO and the other eight classification methods on the dataset

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Wang, Z., Chen, Y., Cai, Z. et al. Weighted mean of vectors algorithm with neighborhood information interaction and vertical and horizontal crossover mechanism for feature selection. Appl Intell 55, 85 (2025). https://doi.org/10.1007/s10489-024-05889-x

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