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Research Article Open access CC BY 4.0

Combining a Continuous Search Algorithm with a Discrete Search Algorithm for Solving Non-linear Bi-level Programming Problem

Eghbal Hosseini, Isa Nakhai Kamalabadi

Journal of Scientific Research and Reports · pp. 549–559 · Published 10 Apr 2015

10.9734/JSRR/2015/15831

Abstract

The multi-level programming problems, have received much interest from researchers because of their application in several areas such as economic, traffic, finance, management, transportation and so on. Among these, the bi-level programming problem (BLPP) is an appropriate tool to model these real problems. It has been proven that the general BLPP is an NP-hard problem, so it is a practical and complicated problem therefore solving this problem would be significant. However the literature shows several algorithms to solve different forms of the bi-level programming problems (BLPP), but there is no any hybrid approach of combining of two meta-heuristic algorithms. In this paper, the authors combine particle swarm optimization (PSO), which is a continuous approach, with a proposed modified genetic algorithm (MGA), which is a discrete algorithm, using a heuristic function and constructing an effective hybrid approaches (PSOMGA). Using the Karush-Kuhn-Tucker conditions the BLPP is converted to a non-smooth single level problem, and then it is smoothed by a new heuristic method for using PSOMGA. The smoothed problem is solved using PSOMGA which is a fast approximate method for solving the non-linear BLPP. The presented approach achieves an efficient and feasible solution in an appropriate time, as justified by comparison with test problems.

Particle swarm optimization genetic algorithm non-linear bi-level programming problem karush-kuhn-tucker conditions

References (24)

  1. 1 Numerical optimization [DOI]
  2. 2 Descent approaches for quadratic bilevel programming [DOI]
  3. 3 Genetic algorithm based approach to bi-level linear programming [DOI]
  4. 4 Linear bilevel programming solution by genetic algorithm [DOI]
  5. 5 Fuzzy goal programming approach to multilevel programming problems [DOI]
  6. 6 An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions [DOI]
  7. 7 Interactive fuzzy goal programming approach for bilevel programming problem [DOI]
  8. 8 A hybrid intelligent algorithm by combining particle swarm optimization with chaos searching technique for solving nonlinear bilevel programming problems [DOI]
  9. 9 Neural network for solving convex quadratic bilevel programming problems [DOI]
  10. 10 Fuzzy programming approach to multi-level programming problems [DOI]
  11. 11 Interactive fuzzy programming for multilevel linear programming problems [DOI]
  12. 12 A penalty function method based on Kuhn–Tucker condition for solving linear bilevel programming [DOI]
  13. 13 Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem [DOI]
  14. 14 Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem [DOI]
  15. 15 Estimation of distribution algorithm for a class of nonlinear bilevel programming problems [DOI]
  16. 16 Model, solution concept, and Kth-best algorithm for linear trilevel programming [DOI]
  17. 17 Interactive fuzzy decision making method for solving bilevel programming problem [DOI]
  18. 18 A neural network approach for solving linear bilevel programming problem [DOI]
  19. 19 An augmented Lagrangian multiplier method based on a CHKS smoothing function for solving nonlinear bilevel programming problems [DOI]
  20. 20 Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method [DOI]
  21. 21 Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints [DOI]
  22. 22 A genetic algorithm approach to fuzzy quadratic bilevel programming [DOI]
  23. 23 A Genetic Approach for Solving Bi-Level Programming Problems
  24. 24 Two Approaches for Solving Non-linear Bi-level Programming Problem [DOI]

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