Computational Experience with a Parallel Implementation of an Interior-Point Algorithm for Multicommodity Network Flows

A parallel implementation of the specialized interior-point algorithm for multicommodity network flows introduced in [6] is presented. In this algorithm, the positive definite systems of each iteration are solved through a scheme that combines direct factorizations and a preconditioned conjugate gradient (PCG) method. Although this numerical procedure works well in practice, it requires the solution of at least k systems of equations at each iteration of the PCG, k being the number of commodities to be routed through the network.

[1]  Bob Francis,et al.  Silicon Graphics Inc. , 1993 .

[2]  Jacek Gondzio,et al.  Parallel Implementation of a Central Decomposition Method for Solving Large-Scale Planning Problems , 2001, Comput. Optim. Appl..

[3]  Barry W. Peyton,et al.  Block Sparse Cholesky Algorithms on Advanced Uniprocessor Computers , 1991, SIAM J. Sci. Comput..

[4]  Irvin J. Lustig,et al.  Gigaflops in linear programming , 1996, Oper. Res. Lett..

[5]  Mustafa Ç. Pinar,et al.  Parallel Decomposition of Multicommodity Network Flows Using a Linear-Quadratic Penalty Algorithm , 1992, INFORMS J. Comput..

[6]  Hans Werner Meuer,et al.  Top500 Supercomputer Sites , 1997 .

[7]  Stephen J. Wright,et al.  pPCx: Parallel Software for Linear Programming , 1997, PPSC.

[8]  Erling D. Andersen,et al.  A parallel interior-point algorithm for linear programming on a shared memory machine , 1998 .

[9]  Mauricio G. C. Resende,et al.  An implementation of Karmarkar's algorithm for linear programming , 1989, Math. Program..

[10]  D. Medhi.  Parallel bundle-based decomposition for large-scale structured mathematical programming problems , 1990 .

[11]  Jordi Castro,et al.  A Specialized Interior-Point Algorithm for Multicommodity Network Flows , 1999, SIAM J. Optim..

[12]  Jacek Gondzio,et al.  Solving nonlinear multicommodity flow problems by the analytic center cutting plane method , 1997, Math. Program..

[13]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[14]  Giorgio Gallo,et al.  A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems , 1999, INFORMS J. Comput..

[15]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[16]  R. V. Helgason,et al.  Algorithms for network programming , 1980 .