Exact solution methodologies for linear and (mixed) integer bilevel programming

Studies in Computational Intelligence

Volumn 482, Issue , 2013, Pages 221-245

  Saharidis, Georgios K D ^a   Conejo, Antonio J ^b   Kozanidis, George ^a  

^a UNIVERSITY OF THESSALY   (Greece)

^b UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84893112383     PISSN: 1860949X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-37838-6_8     Document Type: Article

References (92)

1. Al-Khayyal, F.A.: An implicit enumeration procedure for the general linear complementarity problem. Mathematical Programming Studies 31, 1-20 (1987).
2. Amouzegar, M.A., Moshirvaziri, K.: Determining optimal pollution control policies: An application of bilevel programming. European Journal of Operational Research 119, 100-120 (1999). (Pubitemid 30510472)
3. Anandalingam, G., Apprey, V.: Multi-level programming and conflict resolution. European Journal of Operational Research 51, 233-247 (1991). (Pubitemid 21700346)
4. Anandalingam, G., White, D.J.: A solution method for the linear static stackelberg problem using penalty functions. IEEE Transactions on Automatic Control 35(10), 1170- 1173 (1990).
5. Audet, C., Hansen, P., Jaumard, B., Savard, G.: Links between linear bilevel and mixed 0-1 programming problems. Journal of Optimization Theory and Applications 93(2), 273-300 (1997).
6. Audet, C., Haddad, J., Savard, G.: A note on the definition of a linear bilevel programming solution. Applied Mathematics and Computation 181, 351-355 (2006). (Pubitemid 44528023)
7. Audet, C., Savard, G., Zghal, W.: New branch and cut algorithm for bilevel linear programming. Journal of Optimization Theory and Applications 134(2), 353-370 (2007).
8. Bard, J.F.: An efficient point algorithm for a linear two-stage optimization problem. Operations Research 31(4), 670-684 (1983).
9. Bard, J.F.: An investigation of the linear three level programming problem. IEEE Transactions on Systems, Man, and Cybernetics 14(5), 711-717 (1984).
10. Bard, J.F.: Practical bilevel optimization. Kluwer Academic Publishers, Dordrecht (1998).
11. Bard, J.F., Falk, J.E.: An explicit solution to the multilevel programming problem. Computers and Operations Research 9(1), 77-100 (1982).
12. Bard, J.F., Moore, J.T.: A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing 11, 281-292 (1990).
13. Bard, J.F., Moore, J.T.: An algorithm for the discrete bilevel programming problem. Naval Research Logistics 39(3), 419-435 (1992).
14. Baringo, L., Conejo, A.J.:Wind power investment within a market environment. Applied Energy 88(9), 3239-3247 (2011a).
15. Baringo, L., Conejo, A.J.: Transmission and wind power investment. IEEE Transactions on Power Systems (2011b) (accepted).
16. BenAyed, O.: Bilevel linear programming. Computers and Operations Research 20(5), 485-501 (1993).
17. BenAyed, O., Blair, C.E.: Computational difficulties of bilevel linear programming. Operations Research 38(3), 556-560 (1990).
18. BenAyed, O., Boyce, D.E., Blair, C.E.:A general bilevel linear programming formulation of the network design problem. Transportation Research - Part B 22B(4), 311-318 (1988).
19. BenAyed, O., Blair, C.E., Boyce, D.E., LeBlanc, L.J.: Construction of a real-world bilevel linear programming model of the highway network design problem. Annals of Operations Research 34, 219-254 (1992).
20. Bialas, W.F., Karwan, M.H.: Multilevel linear programming. Research Report No. 78-1, Operation Research Program, Department of Industrial Engineering, State University of New York at Buffalo (1978).
21. Bialas, W.F., Karwan, M.H.: On two-level optimization. IEEE Transactions on Automatic Control 27(1), 211-214 (1982).
22. Bialas, W.F., Karwan, M.H.: Two-level linear programming. Management Science 30(8), 1004-1020 (1984).
23. Bracken, J., McGill, J.T.: Defense applications of mathematical programs with optimization problems in the constraints. Operations Research 22(5), 1086-1096 (1974).
24. Brown, G., Carlyle, M., Salmerón, J., Wood, K.: Defending critical infrastructure. Interfaces 36, 530-544 (2006). (Pubitemid 44905062)
25. Burton, R.M., Obel, B.: The multilevel approach to organizational issues of the firm - A critical review. OMEGA The International Journal of Management Science 5(4), 395- 414 (1977).
26. Campelo, M., Scheimberg, S.: A note on a modified simplex approach for solving bilevel linear programming problems. European Journal of Operations Research 126(2), 454- 458 (2000).
27. Campelo, M., Dantas, S., Scheimberg, S.: A note on a penalty function approach for solving bilevel linear programs. Journal of Global Optimization 16, 245-255 (2000).
28. Candler, W.: A linear bilevel programming algorithm: A comment. Computers and Operations Research 15(3), 297-298 (1988). (Pubitemid 18616924)
29. Candler, W., Norton, R.:Multi-level programming and development policy.World Bank, Bank Staff Working Paper No. 258 (1977).
30. Candler, W., Townsley, R.: A linear two-level programming problem. Computers and Operations Research 9, 59-76 (1982).
31. Cao, D., Chen, M.: Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach. European Journal of Operational Research 169, 97-110 (2006). (Pubitemid 41336616)
32. Cassidy, R.G., Kirby, M.J.L., Raike, W.M.: Efficient distribution of resources through three levels of government. Management Science 17(8), 462-473 (1971).
33. Chinchuluun, A., Pardalos, P.M., Huang, H.-X.: Multilevel (hierarchical) optimization: Complexity issues, optimality conditions, algorithms. In: Advances in Applied Mathematics and Global Optimization -Advances in Mechanics and Mathematics, vol. 17, ch. 6, pp. 197-221 (2009).
34. Clark, P.A., Westerberg, A.W.: Optimization for design problems having more than one objective. Computers and Chemical Engineering 7(4), 259-278 (1983).
35. Colson, B., Marcotte, P., Savard, G.: Bilevel programming: A survey. 4OR 3, 87-107 (2005). (Pubitemid 41603224)
36. Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Annals of Operations Research 153, 235-256 (2007).
37. Constantin, I., Florian, M.: Optimizing frequencies in a transit network: A non-linear bilevel programming approach. International Transactions in Operational Research 2(2), 149-164 (1995).
38. Cote, J.-P., Marcotte, P., Savard, G.: A bilevel modelling approach to pricing and fare optimisation in the airline industry. Journal of Revenue and Pricing Management 2(1), 23-36 (2003).
39. Dempe, S.: A simple algorithm for the linear bilevel programming problem. Optimization 18(3), 373-385 (1987).
40. Dempe, S.: Foundations of bilevel programming. Kluwer Academic Publishers, Dordrecht (2002).
41. Dempe, S.: Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3), 333-359 (2003). (Pubitemid 36995924)
42. Dempe, S.: Bilevel programming. In: Audet, C., Hansen, P., Savard, G. (eds.) Essays and Surveys in Global Optimization, ch. 6, pp. 165-194 (2005).
43. DeNegre, S.T., Ralphs, T.K.: A branch and cut algorithm for integer bilevel linear programs. Operations research and cyber-infrastructure, Operations Research/Computer Science Interfaces Series 47(2), Part 1, 65-78 (2009).
44. Erkut, E., Gzara, F.: Solving the hazmat transport network design problem. Computers and Operations Research 35, 2234-2247 (2008). (Pubitemid 350161136)
45. Falk, J.E., Soland, R.M.: An algorithm for separable nonconvex programming problems. Management Science 15, 550-569 (1969).
46. Fortuny-Amat, J., McCarl, B.: A representation and economic interpretation of a twolevel programming problem. Journal of the Operational Research Society 32(9), 783-792 (1981). (Pubitemid 12521956)
47. Garcés, L.P., Conejo, A.J., Garćia-Bertrand, R., Romero, R.: A bi-level approach to transmission expansion planning within a market environment. IEEE Transactions on Power Systems 24(3), 1513-1522 (2009).
48. Glackin, J., Ecker, J.G., Kupferschmid, M.: Solving bilevel linear programs using multiple objective linear programming. Journal of Optimization Theory and Applications 140(2), 197-212 (2009).
49. Golias, M.M., Saharidis, G.K.D., Boile, M., Theofanis, S.: Scheduling of inbound trucks at a cross-docking facility: Bi-objective vs bi-level modeling approaches. International Journal of Information Systems and Supply Chain Management 5(1) (2012) (in press).
50. Hansen, P., Jaumard, B., Savard, G.: New branch and bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical Computing 13(5), 1194-1217 (1992).
51. Haurie, A., Savard, G., White, D.J.: A note on: An efficient point algorithm for a linear two-stage optimization problem. Operations Research 38(3), 553-555 (1990). (Pubitemid 20720753)
52. Hobbs, B.F., Nelson, S.K.: A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Annals of Operations Research 34, 255-274 (1992).
53. J́udice, J.J., Faustino, A.M.: The solution of the linear bilevel programming problem by using the linear complementarity problem. Investigavio Operacional 8, 77-95 (1988).
54. J́udice, J.J., Faustino, A.M.: A sequential LCP method for bilevel linear programming. Annals of Operations Research 34(1), 89-106 (1992).
55. Kazempour, J., Conejo, A.J., Ruiz, C.: Strategic generation investment using a complementarity approach. IEEE Transactions on Power Systems 26(2), 940-948 (2011).
56. Koppe, M., Queyranne, M., Ryan, C.T.: Parametric integer programming algorithm for bilevel mixed integer programs. Journal of Optimization Theory and Applications 146(1), 137-150 (2010).
57. Labbe, M., Marcotte, P., Savard, G.: A bilevel model of taxation and its application to optimal highway pricing. Management Science 44(12), 1608-1622 (1998). (Pubitemid 128617774)
58. LeBlanc, L.J., Boyce, D.E.: A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transportation Research - Part B 20B(3), 259-265 (1986).
59. Liu, Y.H., Spencer, T.H.: Solving a bilevel linear program when the inner decision maker controls few variables. European Journal of Operational Research 81(3), 644-651 (1995).
60. Loridan, P., Morgan, J.: Weak via strong stackelberg problem: New results. Journal of Global Optimization 8, 263-287 (1996).
61. Maher, M.J., Zhang, X., Vliet, D.V.: A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows. Transportation Research - Part B 35, 23-40 (2001). (Pubitemid 32013368)
62. Marinakis, Y., Migdalas, A., Pardalos, P.M.: A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm. Journal of Global Optimization 38, 555-580 (2007). (Pubitemid 46976745)
63. Migdalas, A.: Bilevel programming in traffic planning: Models, methods and challenge. Journal of Global Optimization 7, 381-405 (1995).
64. Mitsos, A., Bollas, G.M., Barton, P.I.: Bilevel optimization formulation for parameter estimation in liquid-liquid phase equilibrium problems. Chemical Engineering Science 64, 548-559 (2009).
65. Moore, J.T., Bard, J.F.: The mixed integer linear bilevel programming problem. Operations Research 38(5), 911-921 (1990).
66. Motto, A.L., Arroyo, J.M., Galiana, F.D.: A mixed-integer LP procedure for the analysis of electric grid security under disruptive threat. IEEE Transactions on Power Systems 20(3), 1357-1365 (2005). (Pubitemid 41300948)
67. Onal, H.: Amodified simplex approach for solving bilevel linear programming problems. European Journal of Operations Research 67(1), 126-135 (1993).
68. Onal, H., Darmawan, D.H., Johnson, S.H.: A multilevel analysis of agricultural credit distribution in East Java, Indonesia. Computers and Operations Research 22(2), 227-236 (1995).
69. Pandzic, H., Conejo, A.J., Kuzle, I., Caro, E.: Yearly maintenance scheduling of transmission lines within a market environment. IEEE Transactions on Power Systems (2011) (in press).
70. Ruiz, C., Conejo, A.J.: Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Transactions on Power Systems 24(4), 1855-1866 (2009) 8 Exact Solution Methodologies for Linear and Integer Bilevel Programming 245.
71. Ryu, J.-H., Dua, V., Pistikopoulos, E.N.: A bilevel programming framework for enterprise-wide process networks under uncertainty. Computers and Chemical Engineering 28, 1121-1129 (2004). (Pubitemid 38520963)
72. Saharidis, G.K.D., Ierapetritou, M.G.: Resolution method for mixed integer bilevel linear problems based on decomposition technique. Journal of Global Optimization 44(1), 29- 51 (2009).
73. Saharidis, G.K.D., Golias, M.M., Boile, M., Theofanis, S., Ierapetritou, M.G.: The berth scheduling problem with customer differentiation: A new methodological approach based on hierarchical optimization. International Journal of Advanced Manufacturing Technology 46, 377-393 (2010).
74. Saharidis, G.K.D., Androulakis, I.P., Ierapetritou, M.G.: Model building using bi-level optimization. Journal of Global Optimization 49, 49-67 (2011).
75. Salmerón, J., Wood, K., Baldick, R.: Analysis of electric grid security under terrorist threat. IEEE Transactions on Power Systems 19(2), 905-912 (2004).
76. Salmerón, J., Wood, K., Baldick, R.:Worst-case interdiction analysis of large-scale electric power grids. IEEE Transactions on Power Systems 24, 96-104 (2009).
77. Shi, C., Zhang, G., Lu, J.: On the definition of linear bilevel programming solution. Applied Mathematics and Computation 160(1), 169-176 (2005a).
78. Shi, C., Lu, J., Zhang, G.: An extended Kuhn-Tucker approach for linear bilevel programming. Applied Mathematics and Computation 162, 51-63 (2005b).
79. Shi, C., Lu, J., Zhang, G.: An extended Kth best approach for linear bilevel programming. Applied Mathematics and Computation 164, 843-855 (2005c). (Pubitemid 40467226)
80. Shi, C., Lu, J., Zhang, G., Zhou, H.: An extended branch and bound algorithm for linear bilevel programming. Applied Mathematics and Computation 180, 529-537 (2006). (Pubitemid 44441538)
81. Suh, S., Kim, T.J.: Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review. Annals of Operations Research 34, 203- 218 (1992).
82. Tuy, H., Migdalas, A., Varbrand, P.: A global optimization approach for the linear twolevel program. Journal of Global Optimization 3, 1-23 (1993).
83. Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: A bibliography review. Journal of Global Optimization 5(3), 291-306 (1994).
84. Wen, U.P., Hsu, S.T.: A note on a linear bilevel programming algorithm based on bicriteria programming. Computers and Operations Research 16(1), 79-83 (1989).
85. Wen, U.P., Hsu, S.T.: Linear bi-level programming problems - A review. Journal of the Operational Research Society 42(2), 125-133 (1991).
86. Wen, U.P., Yang, Y.H.: Algorithms for solving the mixed integer two-level linear programming problem. Computers and Operations Research 17(2), 133-142 (1990). (Pubitemid 20648615)
87. White, D.J.: Solving bi-level linear programmes. Journal of Mathematical Analysis and Applications 200(1), 254-258 (1996). (Pubitemid 126160629)
88. White, D.J., Anandalingam, G.: A penalty function approach for solving bilevel linear programs. Journal of Global Optimization 3(4), 397-419 (1993).
89. Yin, Y.: Multiobjective bilevel optimization for transportation planning and management problems. Journal of Advanced Transportation 36(1), 93-105 (2002). (Pubitemid 34515076)
90. Clark, P.A., Westerberg, A.W.: Bilevel programming for steady state chemical process design - I. Fundamentals and algorithms. Computers and Chemical Engineering 14(1), 87-97 (1990).
91. Nicholls, M.G.: Aluminum production modeling - A nonlinear bilevel programming approach. Operations Research 43(2), 208-218 (1995).
92. Unlu, G.: A linear bilevel programming algorithm based on bicriteria programming. Computers and Operations Research 14(2), 173-179 (1987). (Pubitemid 17556069)