A Modified Flower Pollination Algorithm for Fractional Programming Problems

Abstract

Flower pollination algorithm is a new nature-inspired algorithm, based on the characteristics of flowering plants. In this paper, a new method is developed chaos-based Flower Pollination Algorithm (CFPA) to solve Fractional Programming Problems (FPPs). The proposed algorithm is tested using several ROP benchmarks. The test aims to prove the capability of the CFPA to solve any type of FPPs. The solution results employing the CFPA algorithm are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using CFPA indicated the superiority of the proposed technique among others in computational time.

Keywords

• Flower Pollination Algorithm; Nature-Inspired Algorithm; Optimization; Chaos; Fractional Programming Problems.

Kaynakça

1. [1] M. Jaberipour and E. Khorram, “Solving the sum-ofratios problems by a harmony search algorithm,” Journal of computational and applied mathematics, vol. 234, pp. 733–742, 2010.
2. [2] H. Wolf, “A parametric method for solving the linear fractional programming problem,” Operations Research, vol. 33, pp. 835–841, 1985.
3. [3] A. Charnes and W. Cooper, “An explicit general solution in linear fractional programming,” Naval Research Logistics Quarterly, vol. 20, pp. 449–467, 1973.
4. [4] M. Hosseinalifam, “A Fractional Programming Approach for Choice-Based Network Revenue Management,” UNIVERSITE DE MONTREAL, 2009.
5. [5] I. Stancu-Minasian, Fractional programming: theory, methods and applications, vol. 409. Kluwer academic publishers Dordrecht, 1997.
6. [6] H. Jiao, Z. Wang, and Y. Chen, “Global optimization algorithm for sum of generalized polynomial ratios problem,” Applied Mathematical Modelling, vol. 37, pp. 187–197, 2013.
7. [7] P. Shen, Y. Chen, and Y. Ma, “Solving sum of quadratic ratios fractional programs via monotonic function,” Applied Mathematics and Computation, vol. 212, pp. 234–244, 2009.
8. [8] A. Sameeullah, S. D. Devi, and B. Palaniappan, “Genetic algorithm based method to solve linear fractional programming problem,” Asian Journal of Information Technology, vol. 7, pp. 83–86, 2008.

9. [9] H. I. Calvete, C. Galé, and P. M. Mateo, “A genetic algorithm for solving linear fractional bilevel problems,” Annals of Operations Research, vol. 166, pp. 39–56, 2009.
10. [10] S. Bisoi, G. Devi, and A. Rath, “Neural Networks for Nonlinear Fractional Programming,” International Journal of Scientific & Engineering Research, Volume 2, Issue 12, December-2011, vol. 2, 12, pp. 1–5, 2011.
11. [11] L. Xiao, “Neural Network Method for Solving Linear Fractional Programming,” in Computational Intelligence and Security (CIS), 2010 International Conference on, 2010, pp. 37– 41.
12. [12] A. Pal, S. Singh, and K. Deep, “Solution of fractional programming problems using PSO algorithm,” in Advance Computing Conference (IACC), 2013 IEEE 3rd International, 2013, pp. 1060–1064.
13. [13] I. M. Hezam and O. A. Raouf, “Employing Three Swarm Intelligent Algorithms for Solving Integer Fractional Programming Problems,” International Journal of Scientific and Engineering Research (IJSER), vol. 4, pp. 191–198, 2013.
14. [14] M. Abdel-Baset and I.M. Hezam, “An Effective Hybrid Flower Pollination and Genetic Algorithm for Constrained Optimization Problems,” Advanced Engineering Technology and Application An International Journal, vol. 4, 2015, pp. 27 – 27– 34.
15. [15] M. Abdel-Baset and I. Hezam “An Improved Flower Pollination Algorithm for Ratios optimization Problems,” Applied Mathematics & Information Sciences Letters An International Journal, vol. 3, No. 2, pp. 83–91,2015
16. [16]O. Raouf, I. El-henawy, and M. Abdel-Baset. "A novel hybrid flower pollination algorithm with chaotic harmony search for solving Sudoku puzzles." International Journal of Modern Education and Computer Science vol. 3, pp. 38-44, 2014.
17. [17] O. Raouf, M. A. Baset, I. Elhenawy, “A New Hybrid Flower Pollination Algorithm for Solving Constrained Global Optimization Problems”, International Journal of Applied Operational Research Vol. 4, No. 2, pp. 1-13, 2014. [18]O.Raouf, M.A. Baset, I. Elhenawy, “chaotic Harmony Search Algorithm with Different Chaotic Maps for Solving Assignment Problems”, International Journal of Computational Engineering & Management,Vol. 17, pp. 10-15, 2014.
18. [19] L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical review letters, vol. 64, p. 821, 1990. [20] O. Abdel-Raouf, M. Abdel-Baset, and I. El-henawy, “Improved Harmony Search with Chaos for Solving Linear Assignment Problems”, International Journal of Intelligent Systems and Applications, vol. 6,pp. 55-61 ,2014.
19. [21] A. Gandomi, X.-S. Yang, S. Talatahari, and A. Alavi, “Firefly algorithm with chaos,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, pp. 89–98, 2013. [22] J. Mingjun and T. Huanwen, “Application of chaos in simulated annealing,” Chaos, Solitons & Fractals, vol. 21, pp. 933–941, 2004.
20. [23] O. Abdel-Raouf, M. Abdel-Baset, and I. El-Henawy, “An Improved Chaotic Bat Algorithm for Solving Integer Programming Problems,” International Journal of Modern Education and Computer Science (IJMECS), vol. 6, p. 18, 2014.
21. [24] O. Abdel-Raouf, M. Abdel-Baset, and I. El-henawy, “An Improved Flower Pollination Algorithm with Chaos,” I.J. Education and Management Engineering, vol. 2, pp. 1–8, 2014.
22. [25] O. Abdel-Raouf, M. Abdel-Baset, and I. El-henawy, “Chaotic firefly algorithm for solving definite integral”, International Journal of Information Technology and Computer Science, vol. 6,pp. 19-24,2014. [26] O. A. Raouf, M. A. Baset, I. M. Elhenawy, “Improved
23. harmony search algorithm with chaos for solving definite integral”, International Journal of Operational Research,Vol. 21, No. 2, pp. 252-261, 2014. [27] I. M. Hezam, O. A. Raouf, and M. M. Hadhoud, “A
24. New Compound Swarm Intelligence Algorithms for Solving Global Optimization Problems,” INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY, vol. 10, pp. 2010–2020, 2013.
25. [28] Q.-J. Zhang and X. Q. Lu, “A Recurrent Neural Network for Nonlinear Fractional Programming,” Mathematical Problems in Engineering, vol. 2012, 2012.
26. [29] Y. Z. Mehrjerdi, “Solving fractional programming problem through fuzzy goal setting and approximation,” Applied Soft Computing, vol. 11, pp. 1735–1742, 2011.
27. [30] P. Shen, Y. Ma, and Y. Chen, “Global optimization for the generalized polynomial sum of ratios problem,” Journal of Global Optimization, vol. 50, pp. 439–455, 2011.
28. [31] C.-F. Wang and P.-P. Shen, “A global optimization algorithm for linear fractional programming,” Applied Mathematics and Computation, vol. 204, pp. 281–287, 2008.
29. [32] I. M. H. MOHAMED ABDEL-BASET, “AN IMPROVED FLOWER POLLINATION ALGORITHM BASED ON SIMULATED ANNEALING FOR SOLVING ENGINEERING OPTIMIZATION PROBLEMS,” Asian Journal of Mathematics and Computer Research, vol. 3, pp. 149–170, 2015.
30. [33] I. M. Hezam, M. Abd-ElBaset and I. Selem, “Cuckoo Search Algorithm for Stellar Population Analysis of Galaxies”, International Journal of Information Technology and Computer Science, vol. 7, pp.29-33,2015.