Skip to main content

A Differential Evolution Approach for Solving Integer Programming Problems

  • Conference paper
  • First Online:
Proceedings of Fourth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 336))

Abstract

Basic differential evolution (DE), a potential optimizer, is mainly used for dealing with problem having continuous variables. However, it is observed that many real-life problems occurring in different fields such as chemical engineering, computer science, and management science deal with integer variables. Such problems are known as integer programming problems (IPP) and require a suitable technique for their solution. In the present study, we propose some slight modifications in basic structure of DE and apply it for solving PP. The proposed algorithm is named differential evolution for IPP (DEIPP), and its performance is evaluated on a set of benchmark problems. It is observed that our suggested DEIPP is quite efficient for dealing with optimization problem having integer or discrete and binary variables.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Storn, K.: Price, differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, International Computer Science Institute, Berkeley, CA (1995)

    Google Scholar 

  2. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–354 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Wu, S.J., Chow, P.T.: Genetic algorithms for solving mixed-discrete optimization problems. J. Franklin Inst. 331(4), 381–401 (1994)

    Article  Google Scholar 

  4. Gantovnik, V.B., Anderson-Cook, C.M., Gürdal, Z., Watson, L.T.: A genetic algorithm with memory for mixed discrete–continuous design optimization. Comput. Struct. 81(20), 2003–2009 (2003)

    Article  Google Scholar 

  5. Wang, S.C., Yeh, M.F.: A modified particle swarm optimization for aggregate production planning. Expert Syst. Appl. 41(6), 3069–3077 (2014)

    Article  Google Scholar 

  6. Rein, P., Allen Silver, E.: Decision Systems for Inventory Management and Production Planning. Wiley, New York (1979)

    Google Scholar 

  7. Herrera Juan, F.R., et al.: Pareto optimality and robustness in bi-blending problems. Top 22(1), 254–273 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lopes Rui Borges et al: Location-arc routing problem: heuristic approaches and test instances. Comput. Oper. Res. 43, 309–317 (2014)

    Article  MathSciNet  Google Scholar 

  9. Wisittipanich, W., Kachitvichyanukul, V.: A pareto-archived differential evolution algorithm for multi-objective flexible job shop scheduling problems. In: Logistics Operations, Supply Chain Management and Sustainability, pp. 325–339. Springer International Publishing, Switzerland (2014)

    Google Scholar 

  10. Zhang, J., Li, X.: Research and design of flexible job shop scheduling system. In: Proceedings of the 2012 International Conference on Cybernetics and Informatics. Springer, New York (2014)

    Google Scholar 

  11. Sivasankaran, P., Shahabudeen, P.: Literature review of assembly line balancing problems. In: The International Journal of Advanced Manufacturing Technology, pp. 1–30 (2014)

    Google Scholar 

  12. Soumis, F.: Airline crew scheduling: models, algorithms, and data sets. In: Kasirzadeh, A., Saddoune, M. (2014)

    Google Scholar 

  13. Eva, Barrena, et al.: Exact formulations and algorithm for the train timetabling problem with dynamic demand. Comput. Oper. Res. 44, 66–74 (2014)

    Article  MathSciNet  Google Scholar 

  14. Soria-Alcaraz, Jorge A., et al.: Effective learning hyper-heuristics for the course timetabling problem. Eur. J. Oper. Res. 238(1), 77–86 (2014)

    Article  MathSciNet  Google Scholar 

  15. Chen, K., Ross, S.M.: An adaptive stochastic knapsack problem. Eur. J. Oper. Res. 239, 625–635 (2014)

    Google Scholar 

  16. Christofides, N.: Worst-case analysis of a new heuristic for the travelling salesman problem. No. RR-388. Carnegie-Mellon Univ Pittsburgh Pa Management Sciences Research Group (1976)

    Google Scholar 

  17. Beasley, John E., Chu, Paul C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 392–404 (1996)

    Article  MATH  Google Scholar 

  18. Dyckhoff, Harald: A typology of cutting and packing problems. Eur. J. Oper. Res. 44(2), 145–159 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  19. Dumas, Yvan, Desrosiers, Jacques, Soumis, Francois: The pickup and delivery problem with time windows. Eur. J. Oper. Res. 54(1), 7–22 (1991)

    Article  MATH  Google Scholar 

  20. Yang, W.H., Tarng, Y.S.: Design optimization of cutting parameters for turning operations based on the Taguchi method. J. Mater. Process. Technol. 84(1), 122–129 (1998)

    Article  Google Scholar 

  21. Krzysztof, Kuchcinski: Constraints-driven scheduling and resource assignment. ACM Trans. Des. Autom. Electron. Syst. (TODAES) 8(3), 355–383 (2003)

    Article  Google Scholar 

  22. Beamon Benita, M.: Supply chain design and analysis: models and methods. Int. J. Prod. Econ. 55(3), 281–294 (1998)

    Article  Google Scholar 

  23. Norkin, V.I., Pflug, G.C., Ruszczyński, A.: A branch and bound method for stochastic global optimization. Math. Program 83(1–3), 425–450 (1998)

    Google Scholar 

  24. Wu, S.J., Chow, P.T.: Genetic algorithms for solving mixed-discrete optimization problems. J. Franklin Inst. 331(4), 381–401 (1994)

    Article  Google Scholar 

  25. Gantovnik, V.B., Anderson-Cook, C.M., Gürdal, Z., Watson, L.T.: A genetic algorithm with memory for mixed discrete–continuous design optimization. Comput. Struct. 81(20), 2003–2009 (2003)

    Article  Google Scholar 

  26. Storn, R., Price, K.: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kennedy, J., Eberhart, R.: Particle swarm optimization. Proc. IEEE Int. Conf. Neural Netw. 4(2) 1942–1948 (1995)

    Google Scholar 

  28. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  29. Dervis, Karaboga, Basturk, Bahriye: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39(3), 459–471 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  30. Gao, J., Hong L., Yong-Chang J.: Modified differential evolution for the integer programming problems. In: International Conference on Artificial Intelligence and Computational Intelligence, AICI’09, vol. 1 (2009)

    Google Scholar 

  31. Angira, R., Babu, B.V.: Optimization of process synthesis and design problems: a modified differential evolution approach. Chem. Eng. Sci. 61, 4707–4721 (2006)

    Article  Google Scholar 

  32. Srinivas, M., Rangaiah, G.P.: Differential evolution with tabu list for solving nonlinear and mixed-integer nonlinear programming problems. Ind. Eng. Chem. Res. 46, 7126–7135 (2007)

    Article  Google Scholar 

  33. Changshou, Deng, et al.: Structure-encoding differential evolution for integer programming. J. Softw. 6(1), 140–147 (2011)

    Google Scholar 

  34. Li, H., Zhang, L.: A discrete hybrid differential evolution algorithm for solving integer programming problems. Eng. Optim. ISSN, 1029–0273 (2013)

    Google Scholar 

  35. Tantawy, S.F.: A new procedure for solving integer linear programming problems. Arab. J. Sci. Eng. (2014). doi: 10.1007/s13369-014-1079-6

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hira Zaheer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Zaheer, H., Pant, M. (2015). A Differential Evolution Approach for Solving Integer Programming Problems. In: Das, K., Deep, K., Pant, M., Bansal, J., Nagar, A. (eds) Proceedings of Fourth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 336. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2220-0_33

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-2220-0_33

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2219-4

  • Online ISBN: 978-81-322-2220-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics