SpringerLink
Log in

Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms

混合算法改善品位不确定露天矿生产调度问题的性能

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

One of the surface mining methods is open-pit mining, by which a pit is dug to extract ore or waste downwards from the earth’s surface. In the mining industry, one of the most significant difficulties is long-term production scheduling (LTPS) of the open-pit mines. Deterministic and uncertainty-based approaches are identified as the main strategies, which have been widely used to cope with this problem. Within the last few years, many researchers have highly considered a new computational type, which is less costly, i.e., meta-heuristic methods, so as to solve the mine design and production scheduling problem. Although the optimality of the final solution cannot be guaranteed, they are able to produce sufficiently good solutions with relatively less computational costs. In the present paper, two hybrid models between augmented Lagrangian relaxation (ALR) and a particle swarm optimization (PSO) and ALR and bat algorithm (BA) are suggested so that the LTPS problem is solved under the condition of grade uncertainty. It is suggested to carry out the ALR method on the LTPS problem to improve its performance and accelerate the convergence. Moreover, the Lagrangian coefficients are updated by using PSO and BA. The presented models have been compared with the outcomes of the ALR-genetic algorithm, the ALR-traditional sub-gradient method, and the conventional method without using the Lagrangian approach. The results indicated that the ALR is considered a more efficient approach which can solve a large-scale problem and make a valid solution. Hence, it is more effectual than the conventional method. Furthermore, the time and cost of computation are diminished by the proposed hybrid strategies. The CPU time using the ALR-BA method is about 7.4% higher than the ALR-PSO approach.

摘要

露天采矿工艺是地表采矿的一种方法, 通过开挖坑洞从地表向下开采矿石或废物。工业生产过 程中, 露天矿的长期生产调度(LTPS)问题是最大的生产难题之一, 而基于确定性方法和不确定性的方 法被认为是解决此类问题的主要策略。在过去几年中, 许多研究人员充分探究了一种成本较低的新型 计算法, 即元启发式方法, 用以解决矿山设计和生产调度问题。该方法尽管无法保证最终方案的最优 性, 但能够以相对较低的计算成本推算出足够优秀的解决方案。本文提出了增**拉格朗日松弛(ALR) 与粒子群优化(PSO), 以及ALR 和蝙蝠算法(BA)的两种混合算法模型, 以解决不确定品位条件下的露 天矿生产调度问题。该混合模型采用ALR 方法解决露天矿生产调度问题, 以提高其计算性能并加快 收敛速度, 并通过PSO 或BA 更新拉格朗日系数。所提出的计算模型与ALR 遗传算法、ALR 传统次 梯度法和常规方法(未使用拉格朗日方法)的计算结果进行了比较, 结果表明:相比于常规方法, ALR 法可以更加有效地解决大规模问题, 并提出合理的解决方案。此外, 混合算法可以降低计算时间和成 本, ALR-BA 方法的CPU 运算时间比ALR-PSO 方法大约高7.4%。

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. JOHNSON T B. Optimum production scheduling [C]// Proceedings of 8th International Symposium on Computers and Operations research. Salt Lake City, 1969: 539–562.

  2. WILLIAMS C E. Computerized year-by-year open pit mine scheduling [J]. Society of Mining Engineers, AIME, Transactions, 1974, 256: 45–52.

    Google Scholar 

  3. GERSHON M E. Optimal mine production scheduling: evaluation of large scale mathematical programming approaches [J]. International Journal of Mining Engineering, 1983, 1(4): 315–329.

    Article  Google Scholar 

  4. DAGDELEN K, JOHNSON T B. Optimum open pit mine production scheduling by Lagrangian parametrization [C]// Proceeding of the 19th International Symposium on the Application of Computers and Operations Research in the Mineral Industry. Pennsylvania, University Park: Pennsylvania State University, 1986, 13: 127–142.

    Google Scholar 

  5. RAVENSCROFT P J. Risk analysis for mine planning by conditional simulation [J]. Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 1992, 101: 82–88.

    Google Scholar 

  6. DOWD P A. Risk assessment in reserve estimation and open-pit planning [J]. Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 1994, 103: 148–154.

    Google Scholar 

  7. ELEVLI B. Open pit mine design and extraction sequencing by use of OR and AI concept [J]. International Journal of Surface Mining, Reclamation and Environmental, 1995, 9: 149–153.

    Article  Google Scholar 

  8. DENBY B, SCHOFIELD D. Inclusion of risk assessment in open-pit design and planning [J]. Transactions of the Institution of Mining and Metallurgy, Section A: Mining Technology, 1995, 104: 67–71.

    Google Scholar 

  9. TOLWINSKI B. Scheduling production for open-pit mines [C]// Proceedings of APCOM’98. 1994: 19–23.

  10. AKAIKE A, DAGDELEN K. A strategic production scheduling method for an open-pit mine [C]// Proceedings of the 28th Application of Computers and Operation Research in the Mineral Industry. 1999: 729–738.

  11. WHITTLE D. Proteus environment: Sensitivity analysis made easy [C]// Whittle North American Strategic Mine Planning Conference. Colorado, 2000.

  12. JOHNSON T B, DAGDELEN K, RAMAZAN S. Open pit mine scheduling based on fundamental tree algorithm [C]// Proceeding of the 30th International Symposium on the Application of Computers and Operations Research in the Mineral Industry SME: Littleton. 2002: 147–159.

  13. DIMITRAKOPOULOS R, FARRELLY C T, GODOY M. Moving forward from traditional optimization: Grade uncertainty and risk effects in open pit design [J]. Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology, 2002, 111: 82–88.

    Google Scholar 

  14. GODOY M, DIMITRAKOPOULOS R. Managing risk and waste mining in long-term production scheduling of open-pit mines [J]. SME Transactions, 2004, 316: 43–50.

    Google Scholar 

  15. DIMITRAKOPOULOS R, RAMAZAN S. Uncertainty based production scheduling in open pit mining [J]. SME Transactions, 2004, 316: 106–112.

    Google Scholar 

  16. RAMAZAN S, DIMITRAKOPOULOS R. Recent application of operations research in open pit mining [J]. SME Transactions, 2004, 316: 73–78.

    Google Scholar 

  17. RAMAZAN S, DIMITRAKOPOULOS R. Traditional and new MIP models for production planning with in-situ grade variability [J]. International Journal of Surface Mining, Reclamation and Environment, 2004, 18(2): 85–98.

    Article  Google Scholar 

  18. GHOLAMNEJAD J, OSANLOO M, KARIMI B. A chance-constrained programming approach for open pit long-term production scheduling in stochastic environments [J]. The Journal of the South African Institute of Mining and Metallurgy, 2006, 106: 105–114.

    Google Scholar 

  19. GHOLAMNEJAD J, OSANLOO M. A chance constrained integer programming model for open pit long-term production planning [C]// Proceedings of the Sixteenth International Symposium on Mine Planning and Equipment Selection (MPES). 2007: 359–372.

  20. RAMAZAN S, DIMITRAKOPOULOS R. Stochastic optimization of long-term production scheduling for open pit mines with a new integer programming formulation, orebody modelling and strategic mine planning [C]// The Australasian Institute of Mining and Metallurgy, Spectrum Series. 2007, 14(2): 385–392.

    Google Scholar 

  21. BOLAND N, DUMITRESCU I, FROYLAND G, GLEIXNER A M. LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity [J]. Computers & Operations Research, 2009, 36(4): 1064–1089.

    Article  MATH  Google Scholar 

  22. BLEY A, BOLAND N, FRICKE C, FROYLAND G. A strengthened formulation and cutting planes for the open pit mine production scheduling problem [J]. Computers & Operations Research, 2010, 37(9): 1641–1647.

    Article  MATH  Google Scholar 

  23. KUMRAL M. Robust stochastic mine production scheduling [J]. Engineering Optimization, 2010, 42(6): 567–579.

    Article  MathSciNet  Google Scholar 

  24. LAMGHARI A, DIMITRAKOPOULOS R. A diversified Tabu search approach for the open-pit mine production scheduling problem with metal uncertainty [J]. European Journal of Operational Research, 2012, 222(3): 642–652.

    Article  MATH  Google Scholar 

  25. GHOLAMNEJAD J, MOOSAVI E. A new mathematical programming model for long-term production scheduling considering geological uncertainty [J]. The Journal of the Southern African Institute of Mining and Metallurgy, 2012, 112(2): 77–81.

    Google Scholar 

  26. NANJARI E L, GOLOSINSKI T S. Optimising open pit mine scheduling taking into consideration time value of money and mining restrictions [J]. International Journal of Mining, Reclamation and Environment, 2013, 27(3): 156–165.

    Article  Google Scholar 

  27. SATTARVAND J, NIEMANN-DELIUS C. A new metaheuristic algorithm for long-term open pit production planning [J]. Archives of Mining Sciences, 2013, 58(1): 107–118.

    Article  Google Scholar 

  28. GOODFELLOW R, DIMITRAKOPOULOS R. Algorithmic integration of geological uncertainty in push back designs for complex multi-process open pit mines [J]. Mining Technology, 2013, 122(2): 67–77.

    Article  Google Scholar 

  29. DIMITRAKOPOULOS R, JEWBALI A. Joint stochastic optimization of short and long term mine production planning: Method and application in a large operating gold mine [J]. IMM Transactions, Mining Technology, 2013, 122(2): 110–123.

    Article  Google Scholar 

  30. LEITE A, DIMITRAKOPOULOS R. Stochastic optimization of mine production scheduling with uncertain ore/metal/waste supply [J]. International Journal of Mining Science and Technology, 2014, 24(6): 755–762.

    Article  Google Scholar 

  31. MOOSAVI E, GHOLAMNEJAD J, ATAEE-POUR M, KHORRAM E. Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem [J]. Journal of Central South University, 2014, 21: 2848–2856.

    Article  Google Scholar 

  32. MOOSAVI E, GHOLAMNEJAD J, ATAEE-POUR M, KHORRAM E. A hybrid augmented Lagrangian multiplier method for the open pit mines long-term production scheduling problem optimization [J]. Journal of Mining Science, 2014, 50: 1047–1060.

    Article  Google Scholar 

  33. KOUSHAVAND B, ASKARI-NASAB H, DEUTSCH C V. A linear programming model for long-term mine planning in the presence of grade uncertainty and a stockpile [J]. International Journal of Mining Science and Technology, 2014, 24: 451–459.

    Article  Google Scholar 

  34. ASAD M W A, DIMITRAKOPOULOS R, ELDERT J V. Stochastic production phase design for an open pit mining complex with multiple processing streams [J]. Engineering Optimization, 2014, 46(8): 1139–1152.

    Article  Google Scholar 

  35. LAMGHARI A, DIMITRAKOPOULOS R, FERLAND A J. A variable neighbourhood descent algorithm for the open-pit mine production scheduling problem with metal uncertainty [J]. Journal of the Operational Research Society, 2014, 65: 1305–1314.

    Article  Google Scholar 

  36. SHISHVAN M S, SATTARVAND J. Long term production planning of open pit mines by ant colony optimization [J]. European Journal of Operational Research, 2015, 240(3): 825–836.

    Article  MATH  Google Scholar 

  37. MOKHTARIAN M, SATTARVAND J. An imperialist competitive algorithm for solving the production scheduling problem in open pit mine [J]. International Journal of Mining and Geo-Engineering, 2016, 50(1): 131–143.

    Google Scholar 

  38. MOKHTARIAN M, SATTARVAND J. Commodity price uncertainty propagation in open-pit mine production planning by Latin hypercube sampling method [J]. Journal of Mining & Environment, 2016, 7(2): 215–227.

    Google Scholar 

  39. GOODFELLOW R, DIMITRAKOPOULOS R. Global optimization of open pit mining complexes with uncertainty [J]. Applied Soft Computing, 2016, 40: 292–304.

    Article  Google Scholar 

  40. LAMGHARI A, DIMITRAKOPOULOS R. Progressive hedging applied as a metaheuristic to schedule production in open-pit mines accounting for reserve uncertainty [J]. European Journal of Operational Research, 2016, 253(3): 843–855.

    Article  MathSciNet  MATH  Google Scholar 

  41. LAMGHARI A, DIMITRAKOPOULOS R. Network-flow based algorithms for scheduling production in multi-processor open-pit mines accounting for metal uncertainty [J]. European Journal of Operational Research, 2016, 250(1): 273–290.

    Article  MathSciNet  MATH  Google Scholar 

  42. BAKHTAVAR E, JAFARPOUR A, YOUSEFI S. Optimal production strategy of bimetallic deposits under technical and economic uncertainties using stochastic chance-constrained programming [J]. Journal of Mining & Environment, 2017, 8(3): 475–485.

    Google Scholar 

  43. KHAN A. Long-term production scheduling of open pit mines using particle swarm and bat algorithms under grade uncertainty [J]. Journal of the Southern African Institute of Mining and Metallurgy, 2018, 118: 361–368.

    Article  Google Scholar 

  44. RAHIMI E, MOOSAVI E, SHIRINABADI R, GHOLINEJAD M. Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit [J]. Journal of Central South University, 2018, 25(6): 1475–1488.

    Article  Google Scholar 

  45. TAHERNEJAD M M, ATAEI M, KHALOKAKAIE R. A practical approach to open-pit mine planning under price uncertainty using information gap decision theory [J]. Journal of Mining & Environment, 2018, 9(2): 527–537.

    Google Scholar 

  46. JELVEZ E, MORALES N, NANCEL-PENARD P. Open-pit mine production scheduling: Improvements to MineLib library problems [C]// Proceedings of the 27th International Symposium on Mine Planning and Equipment Selection (MPES). 2018: 223–232.

  47. KHAN A, ASAD M W A. A mathematical programming model for optimal cut-off grade policy in open pit mining operations with multiple processing streams [J]. International Journal of Mining, Reclamation and Environment, 2020, 34(3): 149–158.

    Article  Google Scholar 

  48. ALIPOUR A, KHODAIARI A A, JAFARI A, TAVAKKOLI-MOGHADDAM R. Uncertain production scheduling optimization in open-pit mines and its ellipsoidal robust counterpart [J]. International Journal of Management Science and Engineering Management, 2018, 13(3): 225.

    Google Scholar 

  49. CHATTERJEE S, DIMITRAKOPOULOS R. Production scheduling under uncertainty of an open-pit mine using Lagrangian relaxation and branch-and-cut algorithm [J]. International Journal of Mining, Reclamation and Environment, 2020, 34(5): 343–361.

    Article  Google Scholar 

  50. SENECAL R, DIMITRAKOPOULOS R. Long-term mine production scheduling with multiple processing destinations under mineral supply uncertainty, based on multi-neighbourhood Tabu search [J]. International Journal of Mining, Reclamation and Environment, 2020, 34(7): 459–475.

    Article  Google Scholar 

  51. DIEU V N, ONGSAKUL W. Augmented Lagrange hopfield network based Lagrangian relaxation for unit commitment [J]. Electrical Power and Energy Systems, 2011, 33: 522–530.

    Article  Google Scholar 

  52. TOSSERAMS S, ETMAN L F P, PAPALAMBROS P Y, ROODA J E. An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers [J]. Structural and Multidisciplinary Optimization, 2006, 31: 176–189.

    Article  MathSciNet  MATH  Google Scholar 

  53. RODRIGUES R N, da SILVA E L, FINARDI E C, TAKIGAWA F Y K T. Solving the short-term scheduling problem of hydrothermal systems via lagrangian relaxation and augmented Lagrangian [J]. Mathematical Problems in Engineering, 2012: 856178.

  54. XU H A, BAO Z R A, ZHANG T. Solving dual flexible job-shop scheduling problem using a Bat algorithm [J]. Advances in Production Engineering & Management, 2017, 12(1): 5–16.

    Article  MathSciNet  Google Scholar 

  55. SUNDARAM A, PAULO’S FORSIDO A, GERMAMO K M. Unit commitment using meta-heuristic search algorithm [J]. Imperial Journal of Interdisciplinary Research (IJIR), 2016, 2(12): 5–10.

    Google Scholar 

  56. ZHU B, ZHU W, LIU Z, DUAN Q, CAO L. A novel quantum-behaved bat algorithm with mean best position directed for numerical optimization [J]. Computational Intelligence and Neuroscience, 2016, Article ID 6097484.

  57. DIMITRAKOPOULOS R. Conditional simulation algorithms orebody uncertainty in open pit optimization [J]. International Journal of Surface Mining Reclamation and Environment, 1998, 12: 173–179.

    Article  Google Scholar 

  58. JOURNEL A G. Non-parametric estimation of spatial distributions [J]. Mathematical Geosciences, 1983, 15(3): 445–468.

    MathSciNet  Google Scholar 

  59. COHEN A I, WAN S H. A method for solving the fuel constrained unit commitment problem [J]. IEEE Transactions on Power Systems, 1987, 2: 608–614.

    Article  Google Scholar 

  60. VEMURI S, LEMONIDIS L. Fuel constrained unit commitment [J]. IEEE Transactions on Power Systems, 1992, 7(1): 410–415.

    Article  Google Scholar 

  61. ABDUL-RAHMAN K H, SHAHIDEHPOUR S M, AGANAGIC M, MOKHTARI S. A practical resource scheduling with OPF constraints [J]. IEEE Transactions on Power Systems, 1996, 11(1): 254–259.

    Article  Google Scholar 

  62. PANG **. A novel Lagrangian relaxation level approach for scheduling steelmaking-refining-continuous casting production [J]. Journal of Central South University, 2017, 24(2): 467–477.

    Article  Google Scholar 

  63. FISHER M L. The Lagrangian relaxation method for solving integer programming problems [J]. Management Science Journal, 1981, 27(1): 1–18.

    MathSciNet  MATH  Google Scholar 

  64. ANDREANI R, BIRGIN E G, MARTINEZ J M, SCHUVERDT M L. On augmented Lagrangian methods with general lower-level constraints [J]. SIAM Journal on Optimization, 2008, 18(4): 1286–1309.

    Article  MathSciNet  MATH  Google Scholar 

  65. EBERHART R, KENNEDY J. A new optimizer using particle swarm theory [C]// Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE Service Center, 1995: 39–43.

  66. KENNEDY J, EBERHART R. Particle swarm optimization [C]// IEEE International Conference on Neural Networks 1995 (ICANN’95). Perth, Australia, 1995, 5: 1942–1948.

    Google Scholar 

  67. van DEN BERGH F, ENGELBRECHT A P. A new locally convergent particle swarm optimizer [C]// IEEE Conferences on Systems, 2002.

  68. CHUNMING Y, SIMON D. A new particle swarm optimization technique [C]// 18th International Conferences System Engineering (ICSEng). 2005, 2: 164–169.

    Article  Google Scholar 

  69. KENNEDY J, EBERHART R. A discrete binary version of the particle swarm algorithm [C]// IEEE International Conference on Computational Cybernetics and Simulation. 1997, 5: 4104–4108.

    Google Scholar 

  70. YANG X S. A new metaheuristic bat-inspired algorithm [C]// Proceedings of Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Studies in Computational Intelligence Series. Springer, Berlin/Heidelberg, 2010, 284: 65–74.

    MATH  Google Scholar 

  71. MIRJALILI S A, MIRJALILI S M, YANG X S. Binary bat algorithm [J]. Neural Computing and Applications, 2014, 25(3,4): 663–681.

    Article  Google Scholar 

  72. YANG X S, HE X. Bat algorithm: Literature review and applications [J]. International Journal of Bio-Inspired Computation, 2013, 5(3): 141–149.

    Article  Google Scholar 

  73. YANG X S. Bat algorithm for multi-objective optimization [J]. International Journal of Bio-Inspired Computation, 2011, 3(5): 267–274.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Petroleum and Mining Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

    Kamyar Tolouei, Ehsan Moosavi, Amir Hossein Bangian Tabrizi & Peyman Afzal

  2. Department of Mining Engineering, University of Kashan, Kashan, Iran

    Abbas Aghajani Bazzazi

Authors
  1. Kamyar Tolouei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ehsan Moosavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amir Hossein Bangian Tabrizi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peyman Afzal
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Abbas Aghajani Bazzazi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ehsan Moosavi.

Additional information

Contributors

The main research targets were expanded by Ehsan MOOSAVI and Kamyar TOLOUEI. Kamyar TOLOUEI and Ehsan MOOSAVI conducted the literature review and wrote the first draft of the manuscript. Ehsan MOOSAVi and Kamyar TOLOUEI established the models and calculated the results. Amir Hossein BANGIAN TABRIZI, Peyman AFZAL and Abbas AGHAJANI BAZZAZI analyzed the calculated results and edited the draft of manuscript. All authors replied to reviewers & apos; comments and revised the final version.

Conflict of interest

Kamyar TOLOUEI, Ehsan MOOSAVI, Amir Hossein BANGIAN TABRIZI, Peyman AFZAL, Abbas AGHAJANI BAZZAZI declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tolouei, K., Moosavi, E., Bangian Tabrizi, A.H. et al. Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms. J. Cent. South Univ. 27, 2479–2493 (2020). https://doi.org/10.1007/s11771-020-4474-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-020-4474-z

Key words

关键词

Search

Navigation