Combining (Integer) linear programming techniques and metaheuristics for combinatorial optimization

Studies in Computational Intelligence

Volumn 114, Issue , 2008, Pages 31-62

  Raidl, Günther R ^a   Puchinger, Jakob ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46949084856     PISSN: 1860949X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-78295-7_2     Document Type: Article

References (89)

1. C Aggarwal, J. Orlin, and R. Tai. Optimized crossover for the independent set problem. Operations Research, 45:226-234, 1997.
2. R. Ahuja, J. Orlin, and A. Tiwari. A greedy genetic algorithm for the quadratic assignment problem. Computers & Operations Research, 27:917-934, 2000.
3. R. K. Ahuja, Ö Ergun, J. B. Orlin, and A. P. Punnen. A survey of very large-scale neighborhood search techniques. Discrete Applied Mathematics, 123(1-3): 75-102, 2002.
4. E. Alba, F. Almeida, M. Blesa, C. Cotta, M. Díaz, I. Dorta, J. Gabarró, J. González, C. León, L. Moreno, J. Petit, J. Roda, A. Rojas, and F. Xhafa. MALLBA: Towards a combinatorial optimization library for geographically distributed systems. In Proceedings of the XII Jornadas de Paralelismo, pages 105-110. Editorial U.P.V., 2001.
5. E. Alba, F. Almeida, M. Blesa, C. Cotta, M. Díaz, I. Dorta, J. Gabarró, J. González C., León, L. Moreno, J. Petit, J. Roda, A. Rojas, and F. Xhafa. MALLBA: A library of skeletons for combinatorial optimisation. In B. Monien and R. Feldman, editors, Euro-Par 2002 Parallel Processing, volume 2400 of Lecture Notes in Computer Science, pages 927-932. Springer-Verlag, Berlin, Germany, 2002.
6. F. Almeida, M. Blesa, C. Blum, J. M. Moreno, M. Pérez, A. Roli, and M. Sampels, editors. Hybrid Metaheuristics - Third International Workshop, HM 2006, volume 4030 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 2006.
7. D. Applegate, R. Bixby, V. Chvátal, and W. Cook. On the solution of the traveling salesman problem. Documenta Mathematica, Extra Volume ICM III:645-656, 1998.
8. P. Augerat, J. M. Belenguer, E. Benavent, A. Corberan, and D. Naddef. Separating capacity constraints in the CVRP using tabu search. European Journal of Operational Research, 106(2):546-557, 1999.
9. E. Balas and E. Zemel. An algorithm for large zero-one knapsack problems. Operations Research, 28:1130-1154, 1980.
10. F. Barahona and R. Anbil. The volume algorithm: Producing primal solutions with a subgradient method. Mathematical Programming, Series A, 87(3):385-399, 2000.
11. D. Bertsimas and J. N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific, 1997.
12. M. Blesa, C. Blum, A. Roli, and M. Sampels, editors. Hybrid Metaheuristics - Second International Workshop, HM 2005, volume 3636 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 2005.
13. C. Blum, A. Roli, and M. Sampels, editors. Hybrid Metaheuristics - First International Workshop, HM 2004. Proceedings, Valencia, Spain, 2004.
14. K. Büdenbender, T. Grünert, and H.-J. Sebastian. A hybrid tabu search/branchand- bound algorithm for the direct flight network design problem. Transportation Science, 34(4):364-380, 2000.
15. P. C. Chu and J. E. Beasley. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics, 4:63-86, 1998.
16. D. Clements, J. Crawford, D. Joslin, G. Nemhauser, M. Puttlitz, and M. Savelsbergh. Heuristic optimization: A hybrid AI/OR approach. In A. Davenport and C. Beck, editors, Proceedings of the Workshop on Industrial Constraint-Directed Scheduling, 1997. Held in conjunction with the Third International Conference on Principles and Practice of Constraint Programming (CP97).
17. R. K. Congram. Polynomially Searchable Exponential Neighbourhoods for Sequencing Problems in Combinatorial Optimisation. PhD thesis, University of Southampton, Faculty of Mathematical Studies, UK, 2000.
18. R. K. Congram, C. N. Potts, and S. L. van de Velde. An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS Journal on Computing, 14(1):52-67, 2002.
19. C. Cotta. A study of hybridisation techniques and their application to the design of evolutionary algorithms. AI Communications, 11(3-4):223-224, 1998.
20. C. Cotta and J. M. Troya. Embedding branch and bound within evolutionary algorithms. Applied Intelligence, 18:137-153, 2003.
21. E. Danna and C. Le Pape. Two generic schemes for efficient and robust cooperative algorithms. In Michela Milano, editor, Constraint and Integer Programming, pages 33-57. Kluwer Academic Publishers, 2003.
22. E. Danna, E. Rothberg, and C. Le Pape. Exploring relaxation induced neighborhoods to improve MIP solutions. Mathematical Programming, Series A, 102:71-90, 2005.
23. G. B. Dantzig, D. R. Fulkerson, and S. M. Johnson. Solution of a large scale traveling salesman problem. Operations Research, 2:393-410, 1954.
24. J. Denzinger and T. Offermann. On cooperation between evolutionary algorithms and other search paradigms. In William Porto et al., editors, Proceedings of the 1999 Congress on Evolutionary Computation (CEC) volume 3, pages 2317-2324. IEEE Press, 1999.
25. I. Dumitrescu and T. Stützle. Combinations of local search and exact algorithms. In Günther R. Raidl et al., editors, Applications of Evolutionary Computation, volume 2611 of Lecture Notes in Computer Science, pages 211-223. Springer-Verlag, Berlin, Germany, 2003.
26. M. El-Abd and M. Kamel. A taxonomy of cooperative search algorithms. In Blesa Aguilera et al. [12], pages 32-41.
27. A. Eremeev. On complexity of optimized crossover for binary representations. In Dirk V. Arnold, Thomas Jansen, Michael D. Vose, and Jonathan E. Rowe, editors, Theory of Evolutionary Algorithms, number 06061 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany, 2006. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany.
28. Ö. Ergun and J. B. Orlin. A dynamic programming methodology in very large scale neighborhood search applied to the traveling salesman problem. Discrete Optimization, 3(1):78-85, 2006.
29. G. Ribeiro Filho and L. A. Nogueira Lorena. Constructive genetic algorithm and column generation: An application to graph coloring. In Lui Pao Chuen, editor, Proceedings of APORS 2000, the Fifth Conference of the Association of Asian-Pacific Operations Research Societies within IFORS, 2000.
30. M. Fischetti, F. Glover, and A. Lodi. The feasibility pump. Mathematical Programming, 104(1):91-104, 2005.
31. M. Fischetti, C. Polo, and M. Scantamburlo. Local branching heuristic for mixed-integer programs with 2-level variables, with an application to a telecommunication network design problem. Networks, 44(2):61-72, 2004.
32. M. Fischetti and A. Lodi. Local Branching. Mathematical Programming, Series B, 98:23-47, 2003.
33. M. L. Fisher. The Lagrangian Relaxation Method for Solving Integer Programming Problems. Management Science, 27(1):1-18, 1981.
34. A. Frangioni. About Lagrangian methods in integer optimization. Annals of Operations Research, 139(1):163-193, 2005.
35. A. P. French, A. C. Robinson, and J. M. Wilson. Using a hybrid genetic algorithm/branch and bound approach to solve feasibility and optimization integer programming problems. Journal of Heuristics, 7:551-564, 2001.
36. J. E. Gallardo, C. Cotta, and A. J. Fernández. Solving the multidimensional knapsack problem using an evolutionary algorithm hybridized with branch and bound. In Mira and Álvarez [57], pages 21-30.
37. J. E. Gallardo, C. Cotta, and A. J. Fernández. On the hybridization of memetic algorithms with branch-and-bound techniques. IEEE Transactions on Systems, Man and Cybernetics, Part B, 37(1 :77-83, 2007.
38. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, 1979.
39. P. C. Gilmore and R. E. Gomory. A linear programming approach to the cutting stock problem. Operations Research, 9:849-859, 1961.
40. F. Glover. Parametric tabu-search for mixed integer programming. Computers & Operations Research, 33(9):2449-2494, 2006.
41. F. Glover and G. Kochenberger, editors. Handbook of Metaheuristics volume 57 of International Series in Operations Research & Management Science. Kluwer Academic Publishers, 2003.
42. F. Glover, M. Laguna, and R. Martí. Fundamentals of scatter search and path relinking. Control and Cybernetics, 39(3):653-684, 2000.
43. F. Glover. Surrogate constraints. Operations Research, 16(4):741-749, 1968.
44. P. Hansen, J. Brimberg, N. Mladenović, and D. Urosević. Primal-dual variable neighborhood search for the simple plant location problem. INFORMS Journal on Computing, to appear.
45. P. Hansen and N. Mladenović. An introduction to variable neighborhood search. In S. Voß, S. Martello, I. Osman, and C. Roucairol, editors, Meta-heuristics: Advances and trends in local search paradigms for optimization, pages 433-438. Kluwer Academic Publishers, 1999.
46. P. Hansen, N. Mladenović, and D. Urosević. Variable neighborhood search and local branching. Computers & Operations Research, 33(10):3034-3045, 2006.
47. M. Haouaria and J. C. Siala. A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem. Computers & Operations Research, 33(5):1274-1288, 2006.
48. H. Hoos and T. Stützle. Stochastic Local Search - Foundations and Applications. Morgan Kaufmann, 2004.
49. B. Hu, M. Leitner, and G. R. Raidl. Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem. Journal of Heuristics, to appear.
50. G. W. Klau, I. Ljubić, A. Moser, P. Mutzel, P. Neuner, U. Pferschy, G. R. Raidl, and R. Weiskircher. Combining a memetic algorithm with integer programming to solve the prize-collecting Steiner tree problem. In K. Deb et al., editors, Genetic and Evolutionary Computation - GECCO 2004, volume 3102 of Lecture Notes in Computer Science, pages 1304-1315. Springer-Verlag, Berlin, Germany, 2004.
51. K. Kostikas and C. Fragakis. Genetic programming applied to mixed integer programming. In Maarten Keijzer et al., editors, Genetic Programming - EuroGP 2004, volume 3003 of Lecture Notes in Computer Science, pages 113-124. Springer-Verlag, Berlin, Germany, 2004.
52. E. L. Lawler and D. E. Wood. Branch and bounds methods: A survey. Operations Research, 4(4):669-719, 1966.
53. D. Lichtenberger. An extended local branching framework and its application to the multidimensional knapsack problem. Masterś thesis, Vienna University of Technology, Institute of Computer Graphics and Algorithms, Vienna, Austria, March 2005.
54. A. Z.-Z. Lin, J. Bean, and C. C. White. A hybrid genetic/optimization algorithm for finite horizon partially observed Markov decision processes. Journal on Computing, 16(1):27-38, 2004.
55. M. E. Lübbecke and J. Desrosiers. Selected topics in column generation. Operations Research, 53(6):1007-1023, 2005.
56. A. Marino, A. Prügel-Bennett, and C. A. Glass. Improving graph colouring with linear programming and genetic algorithms. In K. Miettinen, M. M. Makela, and J. Toivanen, editors, Proceedings of EUROGEN 99, pages 113-118, Jyväskyiä, Finland, 1999.
57. J. Mira and J. R. Álvarez, editors. Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach, volume 3562 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 2005.
58. A. Nagar, S. S. Heragu, and J. Haddock. A meta-heuristic algorithm for a bicriteria scheduling problem. Annals of Operations Research, 63:397-414, 1995.
59. G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, 1988.
60. T. Neto and J. P. Pedroso. GRASP for linear integer programming. In J. P. Sousa and M. G. C. Resende, editors, Metaheuristics: Computer Decision Making, Combinatorial Optimization Book Series, pages 545-574. Kluwer Academic Publishers, 2003.
61. J. P. Pedroso. Tabu search for mixed integer programming. In C. Rego and B. Alidaee, editors, Metaheuristic Optimization via Memory and Evolution, volume 30 of Operations Research/Computer Science Interfaces Series, pages 247-261. Springer-Verlag, Berlin, Germany, 2005.
62. S. Pirkwieser, G. R. Raidl, and J. Puchinger. Combining Lagrangian decomposition with an evolutionary algorithm for the knapsack constrained maximum spanning tree problem. In Carlos Cotta and Jano van Hemert, editors, Evolutionary Computation in Combinatorial Optimization - EvoCOP 2007, volume 4446 of Lecture Notes in Computer Science, pages 176-187. Springer-Verlag, Berlin, Germany, 2007.
63. D. Pisinger. An expanding-core algorithm for the exact 0-1 knapsack problem. European Journal of Operational Research, 87:175-187, 1995.
64. A. Plateau, D. Tachat, and P. Tolla. A hybrid search combining interior point methods and metaheuristics for 0-1 programming. International Transactions in Operational Research, 9:731-746, 2002.
65. M. Prandtstetter and G. R. Raidl. A variable neighborhood search approach for solving the car sequencing problem. In Pierre Hansen et al., editors, Proceedings of the 18th Mini Euro Conference on Variable Neighborhood Search, Tenerife, Spain, 2005.
66. J. Puchinger and G. R. Raidl. An evolutionary algorithm for column generation in integer programming: An effective approach for 2D bin packing. In X. Yao et al., editors, Parallel Problem Solving from Nature - PPSN VIII, volume 3242 of Lecture Notes in Computer Science, pages 642-651. Springer-Verlag, Berlin, Germany, 2004.
67. J. Puchinger and G. R. Raidl. Combining metaheuristics and exact algorithms in combinatorial optimization: A survey and classification. In Proceedings of the First International Work-Conference on the Interplay Between Natural and Artificial Computation, Part II, volume 3562 of Lecture Notes in Computer Science, pages 41-53. Springer-Verlag, Berlin, Germany, 2005.
68. J. Puchinger and G. R. Raidl. Bringing order into the neighborhoods: Relaxation guided variable neighborhood search. Journal of Heuristics to appear.
69. J. Puchinger and G. R. Raidl. Models and algorithms for three-stage twodimensional bin packing. European Journal of Operational Research to appear.
70. J. Puchinger, G. R. Raidl, and M. Gruber. Cooperating memetic and branchand-cut algorithms for solving the multidimensional knapsack problem. In Proceedings of MIC 2005, the 6th Metaheuristics International Conference, pages 775-780, Vienna, Austria, 2005.
71. J. Puchinger, G. R. Raidl, and G. Koller. Solving a real-world glass cutting problem. In J. Gottlieb and G. R. Raidl, editors, Evolutionary Computation in Combinatorial Optimization - EvoCOP 2004, volume 3004 of Lecture Notes in Computer Science, pages 162-173. Springer-Verlag, Berlin, Germany, 2004.
72. J. Puchinger, G. R. Raidl, and U. Pferschy. The core concept for the multidimensional knapsack problem. In J. Gottlieb and G. R. Raidl, editors, Evolutionary Computation in Combinatorial Optimization - EvoCOP 2006, volume 3906 of Lecture Notes in Computer Science, pages 195-208. Springer-Verlag, Berlin, Germany, 2006.
73. G. R. Raidl and H. Feltl. An improved hybrid genetic algorithm for the generalized assignment problem. In H. M. Haddadd et al., editors, Proceedings of the 2003 ACM Symposium on Applied Computing, pages 990-995. ACM Press, 2004.
74. G. R. Raidl. An improved genetic algorithm for the multiconstrained 0-1 knapsack problem. In D. B. Fogel et al., editors, Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, pages 207-211. IEEE Press, 1998.
75. G. R. Raidl. A unified view on hybrid metaheuristics. In Almeida et al. [6], pages 1-12.
76. G. R. Raidl and J. Gottlieb. Empirical analysis of locality, heritability and heuristic bias in evolutionary algorithms: A case study for the multidimensional knapsack problem. Evolutionary Computation Journal, 13(4):441-475, 2005.
77. C. Rego. RAMP: A new metaheuristic framework for combinatorial optimization. In C. Rego and B. Alidaee, editors, Metaheuristic Optimization via Memory and Evolution, pages 441-460. Kluwer Academic Publishers, 2005.
78. W. Rei, J.-F. Cordeau, M. Gendreau, and P. Soriano. Accelerating Benders decomposition by local branching. Technical Report C7PQMR PO2006-02-X, HEC Montréal, Canada, 2006.
79. E. Rothberg. An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS Journal on Computing, 19(4):534-541, 2007.
80. A. Toniolo Staggemeier, A. R. Clark, U. Aickelin, and J. Smith. A hybrid genetic algorithm to solve a lot-sizing and scheduling problem. In B. Lev, editor, Proceedings of the 16th triannual Conference of the International Federation of Operational Research Societies, Edinburgh, U.K., 2002.
81. E. D. Taillard, L.-M. Gambardella, M. Gendreau, and J.-Y. Potvin. Adaptive memory programming: A unified view of meta-heuristics. European Journal of Operational Research, 135:1-16, 2001.
82. E. Talbi. A taxonomy of hybrid metaheuristics. Journal of Heuristics 8(5):541-565, 2002.
83. H. Tamura, A. Hirahara, I. Hatono, and M. Umano. An approximate solution method for combinatorial optimisation. Transactions of the Society of Instrument and Control Engineers, 130:329-336, 1994.
84. P. M. Thompson and J. B. Orlin. The theory of cycle transfers. Technical Report OR-200-89, MIT Operations Research Center, Boston, MA, 1989.
85. P. M. Thompson and H. N. Psaraftis. Cycle transfer algorithm for multivehicle routing and scheduling problems. Operations Research, 41:935-946, 1993.
86. M. Vasquez and J.-K. Hao. A hybrid approach for the 0-1 multidimensional knapsack problem. In B. Nebel, editor, Proceedings of the 17th International Joint Conference on Artificial Intelligence, IJCAI 2001 pages 328-333, Seattle, Washington, 2001. Morgan Kaufman.
87. M. Vasquez and Y. Vimont. Improved results on the 0-1 multidimensional knapsack problem. European Journal of Operational Research, 165:70-81, 2005.
88. L. A. Wolsey. Integer Programming. Wiley-Interscience, 1998.
89. D. L. Woodruff. A chunking based selection strategy for integrating metaheuristics with branch and bound. In S. Voß et al., editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 499-511. Kluwer Academic Publishers, 1999.