A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem

Published Online:https://doi.org/10.1287/ijoc.1030.0050

References

  • Aboudi R., Jörnsten K. Tabu search for general zero-one integer programs using the pivot and complement heuristic. ORSA J. Comput. (1994) 6:82–93LinkGoogle Scholar
  • Balas E. An additive algorithm for solving linear programs with 0–1 variables. Oper. Res. (1965) 13:517–546LinkGoogle Scholar
  • Balas E., Martin C. H. Pivot and complement—A heuristic for 0–1 programming. Management Sci. (1980) 26:86–96LinkGoogle Scholar
  • Beasley J.OR Library (1995) . Available from msemga.ms.ic.ac.uk, http://www.ms.ic.ac.uk/info.htmlGoogle Scholar
  • Beaujon G. J., Marin S. P., McDonald G. C. Balancing and optimizing a portfolio of R&D projects. Naval Res. Logist. (2001) 48:18–40CrossrefGoogle Scholar
  • Cabot A. V. An enumeration algorithm for knapsack problems. Oper. Res. (1970) 18:306–311LinkGoogle Scholar
  • Cappanera P.Discrete Facility Location and Routing of Obnoxious Activities (1999) . Ph.D. thesis, Department of Mathematics, Università degli Studi di Milano, Milan, Italy. Available at http://www.di.unipi.it/~cappanerGoogle Scholar
  • Cappanera P., Gallo G., Maffioli F. Discrete facility location and routing of obnoxious activities. Discrete Appl. Math. (2002) 133:3–28CrossrefGoogle Scholar
  • Chu P. C., Beasley J. E. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics (1998) 4:63–86CrossrefGoogle Scholar
  • Crama Y., Mazzola J. B. On the strength of relaxations of multidimensional knapsack problems. INFOR (1994) 32:219–225Google Scholar
  • Dantzig G. B. Discrete variable extremum problems. Oper. Res. (1957) 5:266–277LinkGoogle Scholar
  • Freville A. The multidimensional 0–1 knapsack problem: An overview. Eur. J. Oper. Res. (2004) 155:1–21CrossrefGoogle Scholar
  • Freville A., Plateau G. An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem. Discrete Appl. Math. (1994) 49:189–212CrossrefGoogle Scholar
  • Gavish B., Pirkul H. Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality. Math. Programming (1985) 31:78–105CrossrefGoogle Scholar
  • Gilmore P. C., Gomory R. E. The theory and computation of knapsack functions. Oper. Res. (1966) 14:1045–1074LinkGoogle Scholar
  • Glover F. Surrogate constraint duality in mathematical programming. Oper. Res. (1975) 23:434–453LinkGoogle Scholar
  • Glover F., Kochenberger G. A., Osman I. H., Kelly J. P. Critical event tabu search for multidimensional knapsack problems. Meta Heuristics: Theory and Applications (1996) (Kluwer Academic Publishers, Boston, MA) 407–427CrossrefGoogle Scholar
  • Glover F., Laguna M.Tabu Search (1997) (Kluwer Academic Publishers, Boston, MA) CrossrefGoogle Scholar
  • Hanafi S., Freville A. An efficient tabu search approach for the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. (1998) 106:659–675CrossrefGoogle Scholar
  • Haul C., Voss S., Woodruff D. L. Using surrogate constraints in genetic algorithms for solving multidimensional knapsack problems. Adv. Comput. Stochastic Optim., Logic Programming, Heuristic Search (1998) (Kluwer Academic Publishers, Boston, MA) 235–251CrossrefGoogle Scholar
  • Korte B., Schnader R., Mangasarian O. L., Meyer R. R., Robinson S. M. On the existence of fast approximation schemes. Nonlinear Programming 4 (1981) (Academic Press, New York) 415–437CrossrefGoogle Scholar
  • Løkketangen A., Glover F. Solving zero-one mixed integer programming problems using tabu search. Eur. J. Oper. Res. (1998) 106:624–658CrossrefGoogle Scholar
  • Magazine M. J., Chern M. S. A note on approximation schemes for multidimensional knapsack problems. Math. Oper. Res. (1984) 9:244–247LinkGoogle Scholar
  • Magazine M. J., Oguz O. A heuristic algorithm for the multidimensional zero-one knapsack problem. Eur. J. Oper. Res. (1984) 16:319–326CrossrefGoogle Scholar
  • Martello S., Toth P.Knapsack Problems: Algorithms and Computer Implementations (1990) (John Wiley and Sons, Chichester, U.K.) Google Scholar
  • Martello S., Pisinger D., Toth P. New trends in exact algorithms for the 0–1 knapsack problem. Eur. J. Oper. Res. (2000) 123:325–332CrossrefGoogle Scholar
  • Osorio M. A., Glover F., Hammer P. Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions. X Congreso Latino-Iberoamericano de Investigación de Operaciones y Sistemas, México, D.F., Mexico, September 2000 (2000) . http://optnet.itwm.fhg.de/opt-net/documents/v00w39n1Google Scholar
  • Pirkul H. A heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Res. Logist. (1987) 34:161–172CrossrefGoogle Scholar
  • Pisinger D. Core problems in knapsack algorithms. Oper. Res. (1999) 47:570–575LinkGoogle Scholar
  • Plastria F. Static competitive facility location: An overview of optimisation approaches. Eur. J. Oper. Res. (2001) 129:461–470CrossrefGoogle Scholar
  • Romero-Morales D., Carrizosa E., Conde E. Semi-obnoxious location models: A global optimization approach. Eur. J. Oper. Res. (1997) 102:295–301CrossrefGoogle Scholar
  • Selman B., Kautz H., Cohen B. Noise strategies for improving local search. Proc. AAAI-94 (1994) 1Seattle, WA:337–343Google Scholar
  • Shih W. A branch and bound method for the multiconstraint 0–1 knapsack problem. J. Oper. Res. Soc. (1979) 30:369–378CrossrefGoogle Scholar
  • Voss S., Du D. Z., Pardalos P. M. Tabu search: Applications and prospects. Network Optimization Problems: Algorithms, Applications and Complexity (1993) (World Scientific Publishing Co., Singapore) 333–353CrossrefGoogle Scholar
  • Walser J. P. Integer optimization by local search—A domain-independent approach. Lecture Notes in Artificial Intelligence, LNAI-1637 (1999) (Springer-Verlag, Heidelberg, Germany) . Chapter 3Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.