Neural Processing Letters

, Volume 50, Issue 3, pp 2305–2322 | Cite as

Short-Term Traffic Flow Prediction Based on Least Square Support Vector Machine with Hybrid Optimization Algorithm

  • Chuan Luo
  • Chi HuangEmail author
  • Jinde Cao
  • Jianquan Lu
  • Wei Huang
  • Jianhua Guo
  • Yun Wei


Accurate short-term traffic flow prediction plays an indispensable role for solving traffic congestion. However, the structure of traffic data is nonlinear and complicated. It is a challenge to get high precision. The least square support vector machine (LSSVM) has powerful capabilities for time series and nonlinear regression prediction problems if it can select appropriate parameters. To search the optimal parameters of LSSVM, this paper proposes a hybrid optimization algorithm which combines particle swarm optimization (PSO) with genetic algorithm. The main contributions are twofold: (1) A hybrid optimization method is proposed, which can skip the local optimal pitfall with less learning time by introducing a selection strategy, crossover and mutation operators into PSO; (2) the crossover and mutation operators are controlled by adaptive probability functions. The crossover and mutation probabilities increase when the population fitness is concentrated, and decrease when the fitness is dispersed. It can effectively improve the precision and speed of convergence. The proposed model is verified based on the measured data. The experimental results show that our new model yields better prediction ability and relatively high computational efficiency compared with other related models.


Least square support vector machine Traffic flow prediction Particle swarm optimization Genetic algorithm 



This work was jointly supported by the National Science Foundation of China under Grants 61603268, 61272530, 61573096 and 61573102, the Shanxi province plan project on Science and Technology of Social Development under Grant 201703D321032.


  1. 1.
    Rong Y, Zhang X, Feng X, Tk H, Wei W, Xu D (2015) Comparative analysis for traffic flow forecasting models with real-life data in Beijing. Adv Mech Eng 7(12):1312–1325Google Scholar
  2. 2.
    Hu W, Yan L, Wang H, Du B, Tao D (2017) Real-time traffic jams prediction inspired by biham, middleton and levine (bml) model. Inf Sci 381(C):209–228Google Scholar
  3. 3.
    Meng Q, Peng Y (2007) A new local linear prediction model for chaotic time series. Phys Lett A 370(5–6):465–470zbMATHGoogle Scholar
  4. 4.
    Ojeda L, Kibangou A, Wit C (2013) Adaptive Kalman filtering for multi-step ahead traffic flow prediction. In: American control conferenceGoogle Scholar
  5. 5.
    Wang Y, Papageorgiou M (2005) Real-time freeway traffic state estimation based on extended kalman filter: a general approach. Transp Res Part B 39(2):141–167Google Scholar
  6. 6.
    Lorek K, Willinger G (1996) A multivariate time-series prediction model for cash-flow data. Account Rev 71(1):81–102Google Scholar
  7. 7.
    Ahmed M, Cook A (1979) Analysis of freeway traffic time series data by using Box–Jenkins techniques. Transp Res Rec 722:1–9Google Scholar
  8. 8.
    Sun H, Liu H, Xiao H, He R, Ran B (2003) Use of local linear regression model for short-term traffic forecasting. Transp Res Rec 1836:143–150Google Scholar
  9. 9.
    Clark S (2003) Traffic prediction using multivariate nonparametric regression. J Transp Eng 129(2):161–168Google Scholar
  10. 10.
    Li Q, Lan S, Zhang J (2013) Short-term traffic forecasting based on nonparametric regression and floating car data. Comput Eng Des 34(9):3298–3332Google Scholar
  11. 11.
    Jiang X, Adeli H (2005) Dynamic wavelet neural network model for traffic flow forecasting. J Transp Eng 131(10):771–779Google Scholar
  12. 12.
    Egrioglu E, Yolcu U, Aladag H, Bas E (2014) Recurrent multiplicative neuron model artificial neural network for non-linear time series forecasting. Neural Process Lett 41(2):249–258Google Scholar
  13. 13.
    Shao H, Xu D, Zheng G (2011) Convergence of a batch gradient algorithm with adaptive momentum for neural networks. Neural Process Lett 34(3):221–228Google Scholar
  14. 14.
    Zhang H, Xu D, Zhang Y (2014) Boundedness and convergence of split-complex back-propagation algorithm with momentum and penalty. Neural Process Lett 39(3):297–307Google Scholar
  15. 15.
    Li Y (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46:59–69Google Scholar
  16. 16.
    Li Y, Lou J, Wang Z, Alsaadi F (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Frankl Inst 355:6520–6530zbMATHGoogle Scholar
  17. 17.
    Hu W, Liang H, Peng C (2013) A hybrid chaos-particle swarm optimization algorithm for the vehicle routing problem with time window. Entropy 15(4):1247–1270MathSciNetzbMATHGoogle Scholar
  18. 18.
    Habtemichael F, Cetin M (2016) Short-term traffic flow rate forecasting based on identifying similar traffic patterns. Transp Res Part C 66:61–78Google Scholar
  19. 19.
    Zheng Z, Su D (2014) Short-term traffic volume forecasting: a k-nearest neighbor approach enhanced by constrained linearly sewing principle component algorithm. Transp Res Part C Emerg Technol 43:143–157MathSciNetGoogle Scholar
  20. 20.
    Hong W, Dong Y, Zheng F, Wei S (2011) Hybrid evolutionary algorithms in a svr traffic flow forecasting model. Appl Math Comput 217(15):6733–6747MathSciNetzbMATHGoogle Scholar
  21. 21.
    Wu C, Wei C, Su D, Chang M, Ho J (2003) Travel-time prediction with support vector regression. In: Proceedings of the 2003 IEEE international conference on intelligent transportation systems, vol 5(4), pp 276–281Google Scholar
  22. 22.
    Zhang Y, Xie Y (2007) Forecasting of short-term freeway volume with v-support vector machines. Transp Res Rec J Transp Res Board 2024(1):92–99Google Scholar
  23. 23.
    Hu W, Yan L, Liu K, Wang H (2015) A short-term traffic flow forecasting method based on the hybrid pso-svr. Neural Process Lett 43(1):155–172Google Scholar
  24. 24.
    Jia Y, Wu J, Du Y (2016) Traffic speed prediction using deep learning method. In: 2016 IEEE 19th international conference on intelligent transportation systemsGoogle Scholar
  25. 25.
    Huang W, Song G, Hong H, Xie K (2014) Deep architecture for traffic flow prediction: deep belief networks with multitask learning. IEEE Trans Intell Transp Syst 15(5):2191–2201Google Scholar
  26. 26.
    Lv Y, Duan Y, Kang W (2014) Traffic flow prediction with big data: a deep learning approach. IEEE Trans Intell Transp Syst 16(2):1–9Google Scholar
  27. 27.
    Chen X, Wei Z, Liu X, Cai Y, Li Z, Zhao F (2017) Spatiotemporal variable and parameter selection using sparse hybrid genetic algorithm for traffic flow forecasting. Int J Distrib Sens Netw 13(6):1–14Google Scholar
  28. 28.
    Maglogiannis I, Zafiropoulos E, Anagnostopoulos I (2009) An intelligent system for automated breast cancer diagnosis and prognosis using svm based classifiers. Appl Intell 30(1):24–36Google Scholar
  29. 29.
    Chen X, Yang J, Ye Q (2011) Recursive projection twin support vector machine via within-class variance minimization. Pattern Recognit 44(10–11):2643–2655zbMATHGoogle Scholar
  30. 30.
    Cao L (2003) Support vector machines experts for time series forecasting. Neurocomputing 51:321–339Google Scholar
  31. 31.
    Vapnik V (1998) Statistical learning theory. Wiley, New YorkzbMATHGoogle Scholar
  32. 32.
    Huh M (2015) Kernel-trick regression and classification. Commun Stat Appl Methods 22(2):201–207Google Scholar
  33. 33.
    Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgezbMATHGoogle Scholar
  34. 34.
    Suykens J, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9(3):293–300Google Scholar
  35. 35.
    Stone H (1973) An efficient parallel algorithm for the solution of a tridiagonal linear system of equations. J ACM 20(1):27–38MathSciNetzbMATHGoogle Scholar
  36. 36.
    Sun X, Su B, Chen L, Yang Z, Chen J, Zhang W (2016) Nonlinear flux linkage modeling of a bearingless permanent magnet synchronous motor based on aw-lssvm regression algorithm. Int J Appl Electromagn Mech 51(2):151–159Google Scholar
  37. 37.
    Wang S, Yu L, Tang L, Wang S (2011) A novel seasonal decomposition based least squares support vector regression ensemble learning approach for hydropower consumption forecasting in china. Energy 36(11):6542–6554Google Scholar
  38. 38.
    Hemmati-Sarapardeh A, Alipour-Yeganeh-Marand R, Naseri A, Safiabadi A, Gharagheizi F, Ilani-Kashkouli P, Mohammadi A (2013) Asphaltene precipitation due to natural depletion of reservoir: determination using a sara fraction based intelligent model. Fluid Phase Equilibria 354:177–184Google Scholar
  39. 39.
    Liao R, Zheng H, Grzybowski S, Yang L (2011) Particle swarm optimization-least squares support vector regression based forecasting model on dissolved gases in oil-filled power transformers. Electr Power Syst Res 81(12):2074–2080Google Scholar
  40. 40.
    Cong Y, Wang J, Li X (2016) Traffic flow forecasting by a least squares support vector machine with a fruit fly optimization algorithm. Procedia Eng 137:59–68Google Scholar
  41. 41.
    Liu H, Jiang Z (2013) Research on failure prediction technology based on time series analysis and aco-lssvm. Comput Mod 1(5):219–222Google Scholar
  42. 42.
    Sulaiman M, Mustafa M, Shareef H, AbdKhalid S (2012) An application of artificial bee colony algorithm with least squares supports vector machine for real and reactive power tracing in deregulated power system. Int J Electr Power Energy Syst 37(1):67–77Google Scholar
  43. 43.
    Kennedy J (2011) Particle swarm optimization. Encyclopedia of machine learning. Springer, Berlin, pp 760–766Google Scholar
  44. 44.
    Hu W, Wang H, Qiu Z, Nie C, Yan L (2016a) A quantum particle swarm optimization driven urban traffic light scheduling model. Neural Comput Appl 29(3):901–911Google Scholar
  45. 45.
    Hu W, Wang H, Yan L, Du B (2016b) A swarm intelligent method for traffic light scheduling: application to real urban traffic networks. Appl Intell 44(1):208–231Google Scholar
  46. 46.
    Wu Q (2011) Hybrid model based on wavelet support vector machine and modified genetic algorithm penalizing gaussian noises for power load forecasts. Expert Syst Appl 38(1):379–385Google Scholar
  47. 47.
    Zhang H, Xiao Y, Bai X (2016) Ga-support vector regression based ship traffic flow prediction. Int J Control Autom 9(2):219–228Google Scholar
  48. 48.
    Tian Y, Hu W, Du B, Hu S, Cong N, Cheng Z (2018) Iqga: a route selection method based on quantum genetic algorithm- toward urban traffic management under big data environment. World Wide Web. Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Chuan Luo
    • 1
  • Chi Huang
    • 1
    • 2
    • 3
    Email author
  • Jinde Cao
    • 3
  • Jianquan Lu
    • 3
  • Wei Huang
    • 4
  • Jianhua Guo
    • 4
  • Yun Wei
    • 5
  1. 1.College of Data ScienceTaiyuan University of TechnologyTaiyuanChina
  2. 2.School of Economic Information EngineeringSouthwestern University of Finance and EconomicsChengduChina
  3. 3.School of MathematicsSoutheast UniversityNanjingChina
  4. 4.Intelligent Transportation System Research CenterSoutheast UniversityNanjingChina
  5. 5.National Engineering Laboratory for Green and Safe Construction Technology in Urban Rail TransitBeijingChina

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