Skip to main content
Log in

Embedding Advanced Harmony Search in Ordinal Optimization to Maximize Throughput Rate of Flow Line

  • Research Article - Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Flow line systems are production systems in which successive operations are performed on a product in a manner so that it moves through the factory in a certain direction. This work firstly formulates a flow line system as an integer-ordered inequality-constrained simulation–optimization problem and present a stochastic simulation procedure to estimate the throughput rate. The mathematical formulation and simulated procedure can be used for any distribution of processing rate and can be applied to high-dimensional problems. An approach that embeds advanced harmony search (AHS) in ordinal optimization (OO), abbreviated as AHSOO, is developed to find a near-optimal design of the flow line system to maximize the throughput rate. The proposed approach comprises three levels, which are meta-modeling, diversification and intensification. A radial basis function network is a meta-model to approximate the performance of a design. The proposed approach integrates the AHS approach for diversification with improved optimal computing budget allocation (IOCBA) for intensification. AHS favorably explores the solution space initially and moves toward exploiting good solutions close to the end. The IOCBA maximized the overall simulation efficiency for finding an optimal solution. The proposed AHSOO is tested on three examples. In the moderately sized example, simulation results reveal that the average best-so-far performances that were determined using PSO, GA and ES were 6.12, 9.65 and 8.53% less than that obtained using AHSOO—even after the former took more than 50 times the CPU time that was consumed by AHSOO upon completion. Analytical results reveal that the proposed method yields designs of much higher quality with a much higher computing efficiency than the seven competing methods.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

\(\mathbf{x}={[}b_{2},\cdots , b_{n}, r_{1},\ldots ,r_{n}{]}^\mathrm{{T}}\) :

A feasible design

\(\Omega \) :

Solution space

\(b_{i}\) :

Buffer allocation of Station i

\(r_{i}\) :

Processing rate of Station i

B :

Upper bound of total buffer space

R :

Upper bound of total processing rate

\(E{[}\mathrm{TH}(\mathbf{x}){]}\) :

Expected throughput rate of \(\mathbf{x}\)

\(\hbox {TH}_l (\mathbf{x})\) :

Throughput rate of the \(l\hbox {th}\) replication

\(\overline{\hbox {TH}} (\mathbf{x})\) :

Sample mean of replications

\(L_\mathrm{{e}}\) :

Replications of accurate evaluation

\(\overline{\hbox {TH}} _\mathrm{e} (\mathbf{x})\) :

Throughput rate obtained by accurate evaluation

\(f(\mathbf{x})\) :

Output performance

\(\mathrm{PE}(\mathbf{x})\) :

Penalty function

\(f_\mathrm{{e}} (\mathbf{x})\) :

Performance obtained using accurate evaluation

L :

Number of replications

M :

Sample size of RBFN

\(F(\mathbf{x}|{\varvec{\upomega }})\) :

Output of RBFN

H :

Number of hidden nodes in RBFN

\({\varvec{\upmu }}_{h}\) :

Centers of RBFN

\(\varphi (\cdot )\) :

Set of RBF

\({\varvec{\upomega }}={[}\omega _{1}, \ldots , \omega _{H}{]}\) :

Weight vector of RBFN

\(\rho \) :

Standard deviation of Gaussian function

\(\hbox {PAR}_{\mathrm{min}}\) :

Minimum pitch adjustment rate

\(\hbox {PAR}_{\mathrm{max}}\) :

Maximum pitch adjustment rate

\(\hbox {BW}_{\mathrm{min}}\) :

Minimum distance bandwidth

\(\hbox {BW}_{\mathrm{max}}\) :

Maximum distance bandwidth

\(t_{\max }\) :

Maximum number of iterations

\(\mathbf{x}_{\mathrm{{best}}}^{t}\) :

Best harmony at iteration t

\(\mathbf{x}_{\mathrm{{worst}}}^{t}\) :

Worst harmony at iteration t

N :

Number of selected excellent designs for IOCBA

\(C_\mathrm{{b}}\) :

Allowable computational budget

\(n_{i}\) :

Amount of replications allocated to the \(i\hbox {th}\) design

\(n_{0}\) :

Initial amount of replications

\(\Delta \) :

Incremental computational budget

s :

Factor of computational time reduction

\(\mathbf{x}^{*}\) :

Near-optimal design obtained by solution method

\(f_{e} (\mathbf{x}^{*})\) :

Throughput rate of near-optimal design

\(\Theta \) :

Representative subset

rk :

Rank of near-optimal design

r :

Processing rate of the Erlang distribution

\(\eta \) :

Shape parameter of the Erlang distribution

\(\alpha _\mathrm{{G}}\) :

Confidence parameter in global stage

\(\delta _{\mathrm{G}}\) :

Indifference zone parameter in global stage

\(\alpha _\mathrm{{L}}\) :

Confidence parameter in local stage

\(\delta _\mathrm{{L}}\) :

Indifference zone parameter in local stage

\(\alpha _\mathrm{{C}}\) :

Confidence parameter in cleanup stage

\(\delta _\mathrm{{C}}\) :

Indifference zone parameter in cleanup stage

cp:

Number of ISC iterations between constraint prunings

OvS:

Optimization-via-simulation

ISC:

Industrial Strength COMPASS

IICSOP:

Integer-ordered inequality-constrained simulation–optimization problem

AHS:

Advanced harmony search

OO:

Ordinal optimization

RBFN:

Radial basis function network

IOCBA:

Improved optimal computing budget allocation

IHS:

Improved harmony search

MHS:

Modified harmony search

NDHS:

Novel derivative harmony search

GHS:

Global-best harmony search

NGHS:

Novel global harmony search

SFLSP:

Stochastic flow line simulation procedure

GA:

Genetic algorithm

ES:

Evolution strategy

PSO:

Particle swarm optimization

ABC:

Artificial bee colony

ACO:

Ant colony optimization

HS:

Harmony search

SOM:

Self-organizing feature map

MSE:

Mean squared error

HMS:

Harmony memory size

HMCR:

Harmony memory consideration rate

PAR:

Pitch adjustment rate

HM:

Harmony memory

BW:

Distance bandwidth

OCBA:

Optimal computing budget allocation

ABSFP:

Average best-so-far performances at termination

References

  1. Shaaban, S.; McNamara, T.; Hudson, S.: Mean time imbalance effects on unreliable unpaced serial flow lines. J. Manuf. Syst. 33(3), 357–365 (2014)

    Article  Google Scholar 

  2. Wang, G.; Shin, Y.W.; Moon, D.H.: Comparison of three flow line layouts with unreliable machines and profit maximization. Flex. Serv. Manuf. J. 28(4), 669–693 (2016)

    Article  Google Scholar 

  3. Konishi, K.: A tuning strategy to avoid blocking and starving in a buffered production line. Eur. J. Oper. Res. 200(2), 616–620 (2010)

    Article  MATH  Google Scholar 

  4. Bierbooms, R.; Adan, I.J.B.; van Vuuren, M.: Approximate performance analysis of production lines with continuous material flows and finite buffers. Stoch. Models 29(1), 1–30 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aziz, A.; Jarrahi, F.; Abdul-Kader, W.: Modeling and performance evaluation of a series-parallel flow line system with finite buffers. INFOR 48(2), 103–120 (2010)

    MathSciNet  Google Scholar 

  6. Robinson, S.: Simulation: The Practice of Model Development and Use. Wiley, Chichester (2004)

    Google Scholar 

  7. ExtendSim User Guide. Release 9, Imagine That, Incorporated (2013)

  8. Wang, Y.R.; Chen, A.N.: Production logistics simulation and optimization of industrial enterprise based on Flexsim. Int. J. Simul. Model 15(4), 732–741 (2016)

    Article  Google Scholar 

  9. Jarrahi, F.; Abdul-Kader, W.: Performance evaluation of a multi-product production line: an approximation method. Appl. Math. Model. 39(13), 3619–3636 (2015)

    Article  MathSciNet  Google Scholar 

  10. Takemoto, Y.; Arizono, I.: Production allocation optimization by combining distribution free approach with open queueing network theory. Int. J. Adv. Manuf. Technol. 63(1–4), 349–358 (2012)

    Article  Google Scholar 

  11. Sörensena, K.; Janssensb, G.K.: A Petri net model of a continuous flow transfer line with unreliable machine. Eur. J. Oper. Res. 152(1), 248–262 (2004)

    Article  MathSciNet  Google Scholar 

  12. Gao, S.Y.; Chen, W.W.: A partition-based random search for stochastic constrained optimization via simulation. IEEE Trans. Autom. Control 62(2), 740–752 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xu, J.; Hong, L.J.; Nelson, B.L.: Industrial strength COMPASS: a comprehensive algorithm and software for optimization via simulation. ACM Trans. Model. Comput. Simul 20(1), 3:1–3:29 (2010)

    Article  Google Scholar 

  14. Helber, S.; Schimmelpfeng, K.; Stolletz, R.; Lagershausen, S.: Using linear programming to analyze and optimize stochastic flow lines. Ann. Oper. Res 182(1), 193–211 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  15. Weiss, S.; Stolletz, R.: Buffer allocation in stochastic flow lines via sample-based optimization with initial bounds. OR Spectrum 37(4), 869–902 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  16. Costa, A.; Alfieri, A.; Matta, A.; Ficheraa, S.: A parallel Tabu search for solving the primal buffer allocation problem in serial production systems. Comput. Oper. Res. 64, 97–112 (2015)

    Article  MATH  Google Scholar 

  17. Jones, J.C.P.; Frey, J.; Shayestehmanesh, S.: Stochastic simulation and performance analysis of classical knock control algorithms. IEEE Trans. Control Syst. Technol. 25(4), 1307–1317 (2017)

    Article  Google Scholar 

  18. Ho, Y.C.; Zhao, Q.C.; Jia, Q.S.: Ordinal Optimization: Soft Optimization for Hard Problems. Springer, New York (2007)

    Book  MATH  Google Scholar 

  19. Horng, S.C.; Lin, S.Y.: Evolutionary algorithm assisted by meta-model in the framework of ordinal optimization and optimal computing budget allocation. Inf. Sci. 233, 214–229 (2013)

    Article  Google Scholar 

  20. Horng, S.C.: Combining artificial bee colony with ordinal optimization for stochastic economic lot scheduling problem. IEEE Trans. Syst. Man Cybern. Syst. 45(3), 373–384 (2015)

    Article  Google Scholar 

  21. Horng, S.C.; Lin, S.Y.: Ordinal optimization based metaheuristic algorithm for optimal inventory policy of assemble-to-order systems. Appl. Math. Model. 42, 43–57 (2017)

    Article  MathSciNet  Google Scholar 

  22. Dey, B.; Hossain, A.; Bhattacharjee, A.; Dey, R.; Bera, R.: Function approximation based energy detection in cognitive radio using radial basis function network. Intell. Autom. Soft Comput. 23(3), 393–403 (2017)

    Article  Google Scholar 

  23. Mahdavi, M.; Fesanghary, M.; Damangir, E.: An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput. 188, 1567–1579 (2007)

    MathSciNet  MATH  Google Scholar 

  24. Mohamed, A.O.; Rajeswari, M.: The variants of the harmony search algorithm: an overview. Artif. Intell. Rev. 36(1), 49–68 (2011)

    Article  Google Scholar 

  25. Shivaiea, M.; Kazemib, M.G.; Amelia, M.T.: A modified harmony search algorithm for solving load-frequency control of non-linear interconnected hydrothermal power systems. Sustain. Energy Technol. Assess. 10, 53–62 (2015)

    Google Scholar 

  26. Tsadiras, A.K.; Papadopoulos, C.T.; O’Kelly, M.E.J.: An artificial neural network based decision support system for solving the buffer allocation problem in reliable production lines. Comput. Ind. Eng. 66(4), 1150–1162 (2013)

    Article  Google Scholar 

  27. Munoz, M.A.; Sun, Y.; Kirley, M.; Halgamuge, S.K.: Algorithm selection for black-box continuous optimization problems: a survey on methods and challenges. Inf. Sci. 317, 224–245 (2015)

    Article  Google Scholar 

  28. Yang, X.S.: Nature-Inspired Optimization Algorithms. Elsevier, Boston (2014)

    MATH  Google Scholar 

  29. Kumar, R.; Srivastava, S.; Gupta, J.R.P.: Modeling and adaptive control of nonlinear dynamical systems using radial basis function network. Soft Comput. 21(15), 4447–4463 (2017)

    Article  Google Scholar 

  30. Ryan, T.P.: Sample Size Determination and Power. Wiley, New Jersey (2013)

    Book  MATH  Google Scholar 

  31. Wang, X.L.; Gao, X.Z.; Zenger, K.: An Introduction to Harmony Search Optimization Method. Springer, Berlin, Heidelberg (2014)

    Google Scholar 

  32. Chen, C.H.; Lee, L.H.: Stochastic Simulation-optimization: An Optimal Computing Budget Allocation. World Scientific, New Jersey (2010)

    Book  Google Scholar 

  33. SimOpt.org, Problem name: Throughput maximization. (2012). http://simopt.org/wiki/index.php?title=Throughput_Maximization

  34. Aote, S.S.; Raghuwanshi, M.M.; Malik, L.G.: Improved particle swarm optimization based on natural flocking behavior. Arab. J. Sci. Eng. 41(3), 1067–1076 (2016)

    Article  Google Scholar 

  35. Kardan, N.; Hassanzadeh, Y.; Bonab, B.S.: Shape optimization of trapezoidal labyrinth weirs using genetic algorithm. Arab. J. Sci. Eng. 42(3), 1219–1229 (2017)

    Article  Google Scholar 

  36. Beyer, H.G.; Sendhoff, B.: Toward a steady-state analysis of an evolution strategy on a robust optimization problem with noise-induced multimodality. IEEE Trans. Evol. Comput. 21(4), 629–643 (2017)

    Article  Google Scholar 

  37. Saidane, S.; Babai, M.Z.; Aguir, M.S.; Korbaa, O.: On the performance of the base-stock inventory system under a compound Erlang demand distribution. Comput. Ind. Eng. 66(3), 548–554 (2013)

    Article  Google Scholar 

  38. Hong, L.J.; Nelson, B.L.; Xu, J.: Industrial Strength COMPASS, [Online] (2011). http://www.iscompass.net/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shih-Cheng Horng.

Additional information

This research work is supported in part by the Ministry of Science and Technology in Taiwan, R.O.C., under Grant MOST 106-2221-E-324-002 and MOST 106-2221-E-129-007.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Horng, SC., Lin, SS. Embedding Advanced Harmony Search in Ordinal Optimization to Maximize Throughput Rate of Flow Line. Arab J Sci Eng 43, 1015–1031 (2018). https://doi.org/10.1007/s13369-017-2864-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-017-2864-9

Keywords

Navigation