Skip to main content
SpringerLink
Log in

A novel x-shaped binary particle swarm optimization

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Definitive optimization algorithms are not able to solve high-dimensional optimization problems because the search space grows exponentially with the problem size and an exhaustive search will be impractical. Therefore, approximate algorithms are applied to solve them. A category of approximate algorithms are meta-heuristic algorithms. They have shown an acceptable efficiency to solve these problems. Among them, particle swarm optimization (PSO) is one of the well-known swarm intelligence algorithms to optimize continuous problems. A transfer function is applied in this algorithm to convert the continuous search space to the binary one. The role of the transfer function in binary PSO (BPSO) is very important to enhance its performance. Several transfer functions have been proposed for BPSO such as S-shaped, V-shaped, linear and other transfer functions. However, BPSO algorithm can sometimes find local optima or show slow convergence speed in some problems because of using the velocity of PSO and these transfer functions. In this study, a novel transfer function called x-shaped BPSO (XBPSO) is proposed to increase exploration and exploitation of BPSO in the binary search space. The transfer function uses two functions and improved rules to generate a new binary solution. The proposed method has been run on 33 benchmark instances of the 0–1 multidimensional knapsack problem (MKP), two discrete maximization functions and 23 minimization functions. The results have been compared with some well-known BPSO and discrete meta-heuristic algorithms. The results showed that x-shaped transfer function considerably increased the solution accuracy and convergence speed in BPSO algorithm. The average error of compared algorithms on all 0–1 MKP benchmark instances indicated that XBPSO has the minimum error of 8.9%. Also, the mean absolute error (MAE) obtained by XBPSO on two discrete maximization functions is 0.45. Moreover, the proposed transfer function provides superior solutions in 18 functions from 23 minimization functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Bansal JC, Deep K (2012) A modified binary particle swarm optimization for knapsack problems. Appl Math Comput 218(22):11042–11061

    MathSciNet  MATH  Google Scholar 

  • Beasley JE (1990) OR-library: distributing test problems by electronic mail. J Oper Res Soc 41(11):1069–1072

    Article  Google Scholar 

  • Beheshti Z (2018) BMNABC: binary multi-neighborhood artificial bee colony for high-dimensional discrete optimization problems. Cybernet Syst 49(7–8):452–474

    Article  Google Scholar 

  • Beheshti Z (2020) A time-varying mirrored S-shaped transfer function for binary particle swarm optimization. Inf Sci 512:1503–1542

    Article  MathSciNet  Google Scholar 

  • Beheshti Z, Shamsuddin SM (2015) Non-parametric particle swarm optimization for global optimization. Appl Soft Comput J 28:345–359

    Article  Google Scholar 

  • Beheshti Z, Shamsuddin SM, Yuhaniz SS (2013) Binary accelerated particle swarm algorithm (BAPSA) for discrete optimization problems. J Glob Optim 57(2):549–573

    Article  MathSciNet  MATH  Google Scholar 

  • Beheshti Z, Shamsuddin SM, Hasan S (2015) Memetic binary particle swarm optimization for discrete optimization problems. Inf Sci 299:58–84

    Article  Google Scholar 

  • Beheshti Z, Shamsuddin SM, Hasan S, Wong NE (2016) Improved centripetal accelerated particle swarm optimization. Int J Adv Soft Comput Appl 8(2):1–26

    Google Scholar 

  • Chegini N, Saeed AB, Najafi F (2020) A new intelligent fault diagnosis method for bearing in different speeds based on the FDAF-score algorithm, binary particle swarm optimization, and support vector machine. Soft Comput 24(13):10005–10023

    Article  Google Scholar 

  • Costa MFP, Rocha AC, Francisco RB, Fernandes EMGP (2014) Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization. Adv Oper Res

  • Derrac J, Salvador G, Daniel M, Francisco H (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  • Eberhart RC, Shi Y (2001) Particle swarm optimization: developments, applications and resources. In: Proceedings of the 2001 congress on evolutionary computation, pp 81–86

  • Emary E, Zawbaa HM, Hassanien AE (2016a) Binary ant lion approaches for feature selection. Neurocomputing 213:54–65

    Article  Google Scholar 

  • Emary E, Zawbaa HM, Hassanien AE (2016b) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Article  Google Scholar 

  • Engelbrecht AP, Pampara G (2007) Binary differential evolution strategies. In: 2007 IEEE congress on evolutionary computation, pp 1942–47

  • Fan K, Zhang R, Xia G (2007) Solving a class of job-shop scheduling problem based on improved BPSO algorithm. Syst Eng Theory Pract 27(11):111–117

    Article  Google Scholar 

  • Faris H, Mafarja MM, Heidari AA, Aljarah I, Al-Zoubi AM, Mirjalili S, Fujita H (2018) An efficient binary SALP swarm algorithm with crossover scheme for feature selection problems. Knowl-Based Syst 154:43–67

    Article  Google Scholar 

  • Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305

    MathSciNet  MATH  Google Scholar 

  • Garg H, Sharma SP (2013) Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput Ind Eng 64(1):247–255

    Article  Google Scholar 

  • Hariharan M, Sindhu R, Vijean V, Yazid H, Nadarajaw T, Yaacob S, Polat K (2018) Improved binary dragonfly optimization algorithm and wavelet packet based non-linear features for infant cry classification. Comput Methods Progr Biomed 155:39–51

    Article  Google Scholar 

  • Harrison KR, Ombuki-Berman BM, Engelbrecht AP (2019) A parameter-free particle swarm optimization algorithm using performance classifiers. Inf Sci 503:381–400

    Article  MathSciNet  Google Scholar 

  • Islam M, Jakirul XL, Mei Y (2017) A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO. Appl Soft Comput 59:182–196

    Article  Google Scholar 

  • Jia D, Duan X, Khan MK (2014) Binary artificial bee colony optimization using bitwise operation. Comput Ind Eng 76:360–365

    Article  Google Scholar 

  • Kennedy J (1999) Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the 1999 congress on evolutionary computation, 1999, CEC 99, vol 3, pp 1931–38

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks, IEEE Service Center, Piscataway, NJ, vol 4, pp 1942–1948

  • Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: Proceedings of the IEEE international conference on systems, man, and cybernetics. IEEE Computer Society, Washington, DC, USA, vol 5, pp 4104–8

  • Kiran MS (2015) The continuous artificial bee colony algorithm for binary optimization. Appl Soft Comput 33:15–23

    Article  Google Scholar 

  • Lai Daphne T C, Miyakawa M, Sato Y (2020) Semi-supervised data clustering using particle swarm optimisation. Soft Comput 24(5):3499–3510

    Article  Google Scholar 

  • Lee S, Soak S, Sanghoun O, Pedrycz W, Jeon M (2008) Modified binary particle swarm optimization. Progr Nat Sci 18(9):1161–1166

    Article  MathSciNet  Google Scholar 

  • Lin G, Guan J (2018a) A hybrid binary particle swarm optimization for the obnoxious p-median problem. Inf Sci 425:1–17

    Article  MathSciNet  Google Scholar 

  • Lin G, Guan J (2018b) Solving maximum set K-covering problem by an adaptive binary particle swarm optimization method. Knowl Based Syst 142:95–107

    Article  Google Scholar 

  • Liu J, Mei Y, Li X (2016) An analysis of the inertia weight parameter for binary particle swarm optimization. IEEE Trans Evol Comput 20(5):666–681

    Article  Google Scholar 

  • Liu L, Junji W, Meng S (2019) Analysis and improvement of neighborhood topology of particle swarm optimization. J Comput Methods Sci Eng 19:955–968

    Google Scholar 

  • Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312

    Article  Google Scholar 

  • Mafarja M, Aljarah I, Heidari AA, Faris H, Fournier-Viger P, Li X, Mirjalili S (2018) Binary dragonfly optimization for feature selection using time-varying transfer functions. Knowl Based Syst 161:185–204

    Article  Google Scholar 

  • Mapetu JP, Buanga ZC, Kong L (2019) Low-time complexity and low-cost binary particle swarm optimization algorithm for task scheduling and load balancing in cloud computing. Appl Intell 49(9):3308–3330

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mirjalili S, Mirjalili SM, Yang X-S (2014) Binary Bat algorithm. Neural Comput Appl 25(3):663–681

    Article  Google Scholar 

  • Nezamabadi-Pour H, Maghfoori-Farsangi M (2008) Binary particle swarm optimization: challenges and new solutions. J Comput Soc Iran (CSI) Comput Sci Eng 6:21–32

    Google Scholar 

  • Pampara G, Franken N, Engelbrecht AP (2005) Combining particle swarm optimisation with angle modulation to solve binary problems. In: 2005 IEEE Congress on Evolutionary Computation, vol 1, pp 89–96

  • Patwal RS, Narang N, Garg H (2018) A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units. Energy 142:822–837

    Article  Google Scholar 

  • Rashedi E, Nezamabadi-Pour H, Saryazdi S (2010) BGSA: binary gravitational search algorithm. Nat Comput 9(3):727–745

    Article  MathSciNet  MATH  Google Scholar 

  • Sameer FO, Abu Bakar MR, Zaidan AA, Zaidan BB (2019) A new algorithm of modified binary particle swarm optimization based on the Gustafson-Kessel for credit risk assessment. Neural Comput Appl 31(2):337–346

    Article  Google Scholar 

  • Sevkli M, Guner AR (2006) A continuous particle swarm optimization algorithm for uncapacitated facility location problem. In: Dorigo M, Gambardella LM, Birattari M, Martinoli A, Poli R, Stützle T (eds) Ant colony optimization and swarm intelligence. Springer, Berlin, pp 316–323

    Chapter  Google Scholar 

  • Sharif M, Amin J, Raza M, Yasmin M, Satapathy SC (2020) An integrated design of particle swarm optimization (PSO) with fusion of features for detection of brain tumor. Pattern Recognit Lett 129:150–157

    Article  Google Scholar 

  • Shen Q, Jiang J-H, Jiao C-X, Shen G-l, Ru-Qin Yu (2004) Modified particle swarm optimization algorithm for variable selection in MLR and PLS Modeling: QSAR studies of antagonism of angiotensin II antagonists. Eur J Pharm Sci 22(2–3):145–152

    Article  Google Scholar 

  • Shi Y, Eberhart RC (1998) Parameter selection in particle swarm optimization. In: Porto VW, Saravanan N, Waagen D, Eiben AE (eds) Evolutionary programming VII. Springer, Berlin, pp 591–600

    Chapter  Google Scholar 

  • Singh S, Chauhan P, Singh N (2020) Capacity optimization of grid connected solar/fuel cell energy system using hybrid ABC-PSO algorithm. Int J Hydrogen Energy 45(16):10070–10088

    Article  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL Report 2005005:2005

    Google Scholar 

  • Veerasamy V, Wahab NIA, Ramachandran R, Othman ML, Hizam H, Irudayaraj AXR, Guerrero JM, Kumar JS (2020) A Hankel matrix based reduced order model for stability analysis of hybrid power system using PSO-GSA optimized cascade PI-PD controller for automatic load frequency control. IEEE Access 8:71422–71446

    Article  Google Scholar 

  • Wang L, Wang X, Jingqi F, Zhen L (2008) A novel probability binary particle swarm optimization algorithm and its application. J Softw 3(9):28–35

    Article  Google Scholar 

  • Wu H, Qian S, Liu Y, Wang D, Guo B (2020) An immune-based response particle swarm optimizer for knapsack problems in dynamic environments. Soft Comput 24:15409–15425

    Article  Google Scholar 

  • Xia X, Gui L, He G, Wei B, Zhang Y, Fei Yu, Hongrun W, Zhan Z-H (2020) An expanded particle swarm optimization based on multi-exemplar and forgetting ability. Inf Sci 508:105–120

    Article  MathSciNet  Google Scholar 

  • Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. Trans Evol Comput 3(2):82–102

    Article  Google Scholar 

  • Yuan X, Nie H, Anjun S, Wang L, Yuan Y (2009) An improved binary particle swarm optimization for unit commitment problem. Exp Syst Appl 36(4):8049–8055

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Zahra Beheshti

  2. Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Zahra Beheshti

Authors
  1. Zahra Beheshti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zahra Beheshti.

Ethics declarations

Conflict of interest

The author declares that she has no conflict of interest.

Human or animals participants

This article does not contain any studies with human participants or animals performed by the author.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Communicated by V. Loia.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Beheshti, Z. A novel x-shaped binary particle swarm optimization. Soft Comput 25, 3013–3042 (2021). https://doi.org/10.1007/s00500-020-05360-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05360-2

Keywords

Search

Navigation