99
Views
0
CrossRef citations to date
0
Altmetric
Articles

Distance confined path problem and separable integer programming

, &
Pages 447-462 | Received 04 Jul 2011, Accepted 19 Jan 2012, Published online: 16 Mar 2012

References

  • Androutsopoulos , KN and Zografos , KG . 2008 . Solving the K-shortest path problem with time windows in a time varying network . Oper. Res. Lett. , 36 : 692 – 695 .
  • Bell , DE and Shapiro , JF . 1977 . A convergent duality theory for integer programming . Oper. Res. , 25 : 419 – 434 .
  • Bretthauer , KM and Shetty , B . 1995 . The non-linear resource allocation problem . Oper. Res. , 43 : 670 – 683 .
  • Byers , TH and Waterman , MS . 1984 . Determining all optimal and near-optimal solutions when solving shortest path problems by dynamic programming . Oper. Res. , 32 : 1381 – 1384 .
  • Cormen , TH , Leiserson , CE , Rivest , RL and Stein , C . 2002 . Introduction to Algorithms , Cambridge , MA : The MIT Press .
  • Dai , Y , Imai , H , Iwano , K and Katoh , N . 1993 . “ How to treat deleted requests in semi-online problems ” . In Proceedings of the 4th International Symposium on Algorithm and Computation, Lecture Notes in Computer Science , Vol. 762 , 48 – 57 . New York : Spring-Verlag .
  • Eppstein , D . 1999 . Finding the k shortest paths . SIAM J. Comput. , 28 : 652 – 673 .
  • Fisher , ML . 1981 . The Lagrangian relaxation method for solving integer programming problems . Manage. Sci. , 27 : 1 – 18 .
  • Fisher , ML and Sharpiro , JF . 1974 . Constructive duality in integer programming . SIAM J. Appl. Math. , 27 : 31 – 52 .
  • Gavish , B , Glover , F and Pirkul , H . 1991 . Surrogate constraints in integer programming . J. Inform. Optimi. Sci. , 12 : 219 – 228 .
  • Geoffrion , AM . 1974 . Lagrangian relaxation for integer programming problems . Math. Program. Study , 2 : 82 – 114 .
  • Hadjiconstantinous , E and Christofides , N . 1999 . An efficient implementation of an algorithm for finding k shortest simple paths . Network , 34 : 88 – 101 .
  • Hochbaum , DS . 1995 . A non-linear knapsack problem . Oper. Res. Lett. , 17 : 103 – 110 .
  • Ibaraki , T and Katoh , N . 1988 . Resource Allocation Problems: Algorithmic Approaches , Cambrige , , MA : MIT Press .
  • Karwan , MH and Rardin , RL . 1980 . Searchability of the composite and multiple surrogate dual functions . Oper. Res. , 28 : 1251 – 1257 .
  • Karwan , MH and Rardin , RL . 1984 . Surrogate dual multiplier search procedures in integer programming . Oper. Res. , 32 : 52 – 69 .
  • Katoh , N , Ibaraki , T and Mine , H . 1982 . Efficient algorithm for k-shortest simple paths . Network , 12 : 411 – 427 .
  • Lawler , EL . 1972 . A procedure for computing the k best solutions to discrete optimizations and its application to the shortest path problem . Manage. Sci. , 18 : 401 – 405 .
  • Li , D . 1999 . Zero duality gap in integer programming: P-norm surrogate constraint method . Oper. Res. Lett. , 25 : 89 – 96 .
  • Li , D and Sun , XL . 2000 . Success guarantee of dual search in integer programming: p-th power Lagrangian method . J. Global Optim. , 18 : 235 – 254 .
  • Li , D and Sun , XL . 2006 . Nonlinear Integer Programming , New York : Springer Press .
  • Li , D , Sun , XL and Wang , FL . 2006 . A convergent Lagrangian and contour-cut method for non-linear integer programming with a quadratic objective function . SIAM J. Optim. , 17 : 372 – 400 .
  • Li , D , Sun , XL , Wang , J and McKinnon , K . 2009 . Convergent Lagrangian and domain cut method for non-linear knapsack problems . Comput. Optim. Appl. , 42 : 67 – 104 .
  • Li , D , Wang , J and Sun , XL . 2007 . Computing exact solution to non-linear integer programming: Convergent Lagrangian and objective level cut method . J. Global Optim. , 39 : 127 – 154 .
  • Li , D , Wang , Q , Wang , J and Yao , YR . July 6–11 2008 . “ Mitigation of curse of dimensionality in dynamic programming ” . In Proceedings of The 17th IFAC World Congress 7778 – 7783 . Seoul , , Korea
  • Li , D and White , DJ . 2000 . P-th power Lagrangian method for integer programming . Ann. Oper. Res. , 98 : 151 – 170 .
  • Nemhauser , GP and Wolsey , LA . 1998 . Integer and Combinational Optimization , New York : Wiley .
  • Shapiro , JF . 1979 . A survey of Lagrangian techniques for discrete optimization . Ann. Discr. Math. , 5 : 113 – 138 .
  • Sun , XL and Li , D . 2000 . Asymptotic strong duality for bounded integer programming: a logarithmic-exponential dual formulation . Math. Oper. Res. , 25 : 625 – 644 .
  • Wang , CY . 2009 . “ Surrogate dual search in nonlinear integer programming ” . In M.Phil Thesis , Shatin, N.T. , , Hong Kong : Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong .
  • Yen , JY . 1971 . Finding the K shortest loopless paths in a network . Manage. Sci. , 17 : 712 – 716 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.