Hybrid particle swarm optimization and differential evolution algorithm for bi-level programming problem and its application to pricing and lot-sizing decisions

Journal of Intelligent Manufacturing

Volumn 26, Issue 3, 2015, Pages 471-483

  Ma, Weimin ^a   Wang, Miaomiao ^a   Zhu, Xiaoxi ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

Bi level programming problem; Differential evolution; Hierarchical; Particle swarm optimization; Pricing and lot sizing

Indexed keywords

ALGORITHMS; COSTS; OPTIMIZATION; PARTICLE SWARM OPTIMIZATION (PSO); WATER CRAFT;

BI-LEVEL PROGRAMMING; DIFFERENTIAL EVOLUTION; DIFFERENTIAL EVOLUTION ALGORITHMS; HIERARCHICAL; HYBRID PARTICLE SWARM OPTIMIZATION; INTERACTIVE ITERATION; LOT SIZING; RESTRICTIVE CONDITIONS;

EVOLUTIONARY ALGORITHMS;

EID: 84929523238     PISSN: 09565515     EISSN: 15728145     Source Type: Journal    
DOI: 10.1007/s10845-013-0803-5     Document Type: Article

References (41)

1. Abad, P. L. (2003). Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale. European Journal of Operational Research, 144, 677–685.
2. Belmecheri, F., Prins, C., Yalaoui, F., & Amodeo, L. (2012). Particle swarm optimization algorithm for a vehicle routing problem with heterogeneous fleet, mixed backhauls, and time windows. Journal of Intelligent Manufacturing,. doi:10.1007/s10845-012-0627-8.
3. Bingül, Z., & Karahan, O. (2011). A Fuzzy Logic Controller tuned with PSO for 2 DOF robot trajectory control. Expert Systems with Applications, 38(1), 1017–1031.
4. Cai, Y. Q., Wang, J. H., & Yin, J. (2012). Learning-enhanced differential evolution for numerical optimization. Soft Computing, 16, 303–330.
5. Calvete, H. I., & Galé, C. (2011). On linear bi-level problems with multiple objectives at the lower level. Omega, 39, 33–40.
6. Calvete, H. I., Galé, C., & Mateo, P. M. (2008). A new approach for solving linear bi-level problems using genetic algorithms. European Journal of Operational Research, 188, 14–28.
7. Chan, F. T. S., & Tiwari, M. K. (2007). Swarm intelligence, focus on ant and particle swarm optimization. Vienna, Austria: I-Tech Education and Publishing.
8. Chu, C. H., & Hsieh, H. T. (2012). Generation of reciprocating tool motion in 5-axis flank milling based on particle swarm optimization. Journal of Intelligent Manufacturing, 23(5), 1501–1509.
9. Dewez, S., Labbé, M., Marcotte, P., & Savard, G. (2008). New formulations and valid inequalities for a bi-level pricing problem. Operations Research Letters, 36(2), 141–149.
10. Gaitonde, V. N., & Karnik, S. R. (2012). Minimizing burr size in drilling using artificial neural network (ANN)-particle swarm optimization (PSO) approach. Journal of Intelligent Manufacturing, 23(5), 1783–1793.
11. Gao, Y., Zhang, G. Q., Lu, J., & Wee, H. M. (2011). Particle swarm optimization for bi-level pricing problems in supply chains. Journal of Glob Optimization, 51, 245–254.
12. García-Nieto, J., & Alba, E. (2011). Restart particle swarm optimization with velocity modulation: A scalability test. Soft Computing, 15, 2221–2232.
13. Guan, Y. P., & Liu, T. M. (2010). Stochastic lot-sizing problem with inventory-bounds and constant order-capacities. European Journal of Operational Research, 207, 1398–1409.
14. Hejazia, S. R., Memariani, A., Jahanshahloo, G., & Sepehri, M. M. (2002). Linear bi-level programming solution by genetic algorithm. Computers & Operations Research, 29, 1913–1925.
15. Ilonen, J., Kamarainen, J., & Lampinen, J. (2003). Differential evolution training algorithm for feed-forward neural networks. Neural Processing Letters, 17(1), 93–105.
16. Janson, S., & Middendorf, M. (2005). A hierarchical particle swarm optimizer and its adaptive variant. IEEE Transactions on System, Man, and Cybernetics B, 35(6), 1272–1282.
17. Jeroslow, R. G. (1985). The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming, 32, 146–164.
18. Kébé, S., Sbihi, N., & Penz, B. (2012). A Lagrangean heuristic for a two-echelon storage capacitated lot-sizing problem. Journal of Intelligent Manufacturing, 23(6), 2477–2483.
19. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of the IEEE interational conference on neural networks, (pp. 1942–1948). Perth, Wa, Australia.
20. Kuo, R. J., & Huang, C. C. (2009). Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Computers & Mathematics with Applications, 58, 678–685.
21. Lan, K. M., Wen, U. P., Shih, H. S., & Lee, E. S. (2007). A hybrid neural network approach to bi-level programming problems. Applied Mathematics Letters, 20, 880–884.
22. Li, H. Y., & Meissner, J. (2011). Competition under capacitated dynamic lot-sizing with capacity acquisition. International Journal of Production Economics, 131, 535–544.
23. Li, M. Q., Lin, D., & Wang, S. Y. (2010). Solving a type of biobjective bi-level programming problem using NSGA-II. Computers & Mathematics with Applications, 59, 706–715.
24. Li, X. Y., Tian, P., & Min, X. P. (2006). A hierarchical particle swarm optimization for solving bi-level programming problems. Lecture Notes in Computer Science, Artificial Intelligence and Soft Computing- ICAISC, 2006(4029), 1169–1178.
25. Lu, L., & Qi, X. T. (2011). Dynamic lot-sizing for multiple products with a new joint replenishment model. European Journal of Operational Research, 212, 74–80.
26. Lukač, Z., Šorić, K., & Rosenzweig, V. V. (2008). Production planning problem with sequence dependent setups as a bi-level programming problem. European Journal of Operational Research, 187, 1504–1512.
27. Marcotte, P., Savard, G., & Zhu, D. L. (2009). Mathematical structure of a bi-level strategic pricing model. European Journal of Operational Research, 193, 552–566.
28. Plagianakos, V., Tasoulis, D., & Vrahatis, M. (2008). A review of major application areas of differential evolution. In Advances in differential evolution, Vol. 143, (pp. 197–238). Springer, Berlin.
29. Price, K. V., Storn, R. M., & Lampinen, J. A. (2005). Differential evolution: A practical approach to global optimization. Berlin: Springer.
30. Raa, B., & Aghezzaf, E. H. (2005). A robust dynamic planning strategy for lot-sizing problems with stochastic demands. Journal of Intelligent Manufacturing, 16(2), 207–213.
31. Rajesh, J., Gupta, K., Kusumakar, H. S., Jayaraman, V. K., & Kulkarni, B. D. (2003). A Tabu search based approach for solving a class of bi-level programming problems in chemical engineering. Journal of Heuristics, 9, 307–319.
32. Sadeghierad, M., Darabi, A., Lesani, H., & Monsef, H. (2010). Optimal design of the generator of micro turbine using genetic algorithm and PSO. Electrical Power and Energy Systems, 32, 804–808.
33. Sahin, H. K., & Ciric, R. A. (1998). A dual temperature simulated annealing approach for solving bi-level programming problem. Computers & Chemical Engineering, 23, 11–25.
34. Shih, H. S., Wen, U. P., Lee, E. S., Lan, K. M., & Hsiao, H. C. (2004). A neural network approach to multi-objective and multilevel programming problems. Computers & Mathematics with Applications, 48, 95–108.
35. Shi, Y., & Eberhart, R. (1999). Empirical study of particle swarm optimization. In International conference on evolutionary computation, (pp. 1945–1950). IEEE press, Washington, USA.
36. Storn, R. (1999). System design by constraint adaptation and differential evolution. IEEE Transactions on Evolutionary Computation, 3(1), 22–34.
37. Storn, R., & Price, K. (1997). Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.
38. Vincent, L. W. H., Ponnambalam, S. G., & Kanagaraj, G. (2012). Differential evolution variants to schedule flexible assembly lines. Journal of Intelligent Manufacturing, doi:10.1007/s10845-012-0716-8.
39. Wen, U. P., & Huang, A. D. (1996). A simple Tabu Search method to solve the mixed-integer problem bi-level programming problem. European Journal of Operational Research, 88, 563–571.
40. Yıldırmaz, C., Karabatı, S., & Sayın, S. (2009). Pricing and lot-sizing decisions in a two-echelon system with transportation costs. OR Spectrum, 31, 629–650.
41. Zhao, S. Z., Suganthan, P. N., & Das, S. (2011). Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Computing, 15, 2175–2185.