Complutense University Library

Model, solution concept, and Kth-best algorithm for linear trilevel programming

Zhang, Guangquan and Lu, Jie and Montero de Juan, Francisco Javier and Zeng, Yi (2010) Model, solution concept, and Kth-best algorithm for linear trilevel programming. Information Sciences, 180 (4). pp. 481-492. ISSN 0020-0255

[img] PDF
Restricted to Repository staff only until 2020.

515kB

Official URL: http://www.sciencedirect.com/science/article/pii/S0020025509004496

View download statistics for this eprint

==>>> Export to other formats

Abstract

Trilevel programming refers to hierarchical optimization problems in which the top-level,
middle-level, and bottom-level decision entities all attempt to optimize their individual
objectives, but are impacted by the actions and partial control exercised by decision entities located at other levels. To solve this complex problem, in this study first we propose the use of a general linear trilevel programming (LTLP) subsequently, we develop a trilevel Kth-best algorithm to solve LTLP problems. A user-friendly trilevel decision support tool is also developed. A case study further illustrates the effectiveness of the proposed method.


Item Type:Article
Uncontrolled Keywords:Trilevel programming; Bilevel programming; Hierarchical decision-making; Kth-best algorithm; Optimization; Decision support systems
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16010
References:

M.A. Abo-Sinna, I.A. Baky, Interactive balanced space approach for solving multi-level multi-objective programming problems, Information Sciences 177 (16) (2007) 3397–3410.

J. Amat, B. McCarl, A representation and economic interpretation of a two-level programming problem, Journal of the Operational Research Society 32 (1981) 783–792.

G. Anandalingam, T. Friesz, Hierarchical optimization: an introduction, Annals of Operations Research 34 (1992) 1–11.

J. Bard, Optimality conditions for the bilevel programming problem, Naval Research Logistics Quarterly 31 (1984) 13–26.

J. Bard, Practical Bilevel Optimization, Kluwer, Dordrecht, 1998.

J. Bard, J. Falk, An explicit solution to the multi-level programming problem, Computer and Operations Research 9 (1982) 77–100.

J. Bard, J. Falk, Necessary conditions for the linear three-level programming problem, in: Proceedings of the 21st IEEE Conference on Decision and Control, vol. 21, 1982, pp. 642–646.

J. Bard, J.T. Moore, A branch-and-bound algorithm for the bilevel programming problem, SIAM Journal on Scientific and Statistical Computing 11 (1990) 281–292.

O. Ben-Ayed, Bilevel linear programming, Computers and Operations Research 20 (1993) 485–501.

W. Bialas, M. Karwan, Two-level linear programming, Management Science 30 (1984) 1004–1020.

C. Blair, The computational complexity of multi-level linear programs, Annals of Operations Research 34 (1992) 13–19.

H.I. Calvete, C. Gale, P.M. Mateo, A new approach for solving linear bilevel problems using

D. Cao, L.C. Leung, A partial cooperation model for non-unique linear two-level decision problems, European Journal of Operational Research 140 (2002) 134–141.

D. Cao, M. Chen, Capacitated plant selection in a decentralized manufacturing environment: a bilevel optimization approach, European Journal of Operational Research 169 (2006) 97–110.

S.-W. Chiou, A bi-level programming for logistics network design with system-optimized flows, Information Sciences 179 (14) (2009) 2434–2441.

V. Cutello, J. Montero, Hierarchies of aggregation operators, International Journal of Intelligent Systems 9 (1994) 1025–1045.

S. Dempe, Foundations of Bilevel Programming, Kluwer, Dordrecht, 2002.

C. Feng, C. Wen, Bi-level and multi-objective model to control traffic flow into the disaster area post-earthquake, Journal of the Eastern Asia Society for Transportation Studies 6 (2005) 4253–4268.

P. Hansen, B. Jaumard, G. Savard, New branch-and-bound rules for linear bilevel programming, SIAM Journal on Scientific and Statistical Computing 13 (1992) 1194–1217.

B.F. Hobbs, B. Metzler, J.S. Pang, Strategic gaming analysis for electric power systems: an MPEC approach, IEEE Transactions on Power Systems 15 (2000) 637–645.

M. Labbé, P. Marcotte, G. Savard, A bilevel model of taxation and its application to optimal highway pricing, Management Science 44 (1999) 1608–1822.

Y.J. Lai, Hierarchical optimization: a satisfactory solution, Fuzzy Sets and Systems 77 (1996) 321–335

B. Liu, Stackelberg–Nash equilibrium for multilevel programming with multiple followers using genetic algorithms, Computers and Mathematics with Applications 36 (1998) 79–89.

J. Lu, C. Shi, G. Zhang, On bilevel multi-follower decision-making: general framework and solutions, Information Sciences 176 (2006) 1607–1627.

J. Lu, C. Shi, G. Zhang, T. Dillon, Model and extended Kuhn–Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation, International Journal of Global Optimization 38 (2007) 597–608.

J. Lu, C. Shi, G. Zhang, D. Ruan, An extended branch-and-bound algorithm for bilevel multi-follower decision making in a referential-uncooperative situation, International Journal of Information Technology and Decision Making 6 (2007) 371–388.

Z. Lukac, K. Soric, V.V. Rosenzweig, Production planning problem with sequence dependent setups as a bilevel programming problem, European Journal of Operational Research 187 (2008) 1504–1512.

J. Montero, D. Gomez, H. Bustince, On the relevance of some families of fuzzy sets, Fuzzy Sets and Systems 158 (2007) 2429–2442.

M. Sakawa, I. Nishizaki, Y. Uemura, Interactive fuzzy programming for multilevel linear programming problems with fuzzy parameters, Fuzzy Sets and Systems 109 (2000) 3–19.

X. Shi, H. Xia, Interactive bilevel multi-objective decision making, Journal of the Operational Research Society 48 (1997) 943–949.

H.S. Shih, Y.J. Lai, E.S. Lee, Fuzzy approach for multi-level programming problems, Computers and Operations Research 23 (1996) 73–91.

S. Sinha, S.B. Sinha, KKT transformation approach for multi-objective multi-level linear programming problems, European Journal of Operational Research 143 (2002) 19–31.

H.A. Taha, Operations Research: An Introduction, eighth ed., Prentice-Hall, 2007.

H.V. Stackelberg, Theory of the Market Economy, Oxford University Press, New York, 1952.

U.P. Wen, S.T. Hsu, Linear bilevel programming problems – a review, Journal of the Operational Research Society 42 (1991) 123–133.

Deposited On:19 Jul 2012 11:06
Last Modified:06 Feb 2014 10:36

Repository Staff Only: item control page