A Parallel Interior Point Method and Its Application to Facility Location Problems

Authors:
Amal De Silva;David Abramson
Affiliations:
School of Computing and Information Technology, Griffith University, Nathan, QLD 4111, Australia. E-mail: amal@cit.gu.edu.au, davida@cit.gu.edu.au;School of Computing and Information Technology, Griffith University, Nathan, QLD 4111, Australia. E-mail: amal@cit.gu.edu.au, davida@cit.gu.edu.au
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

We present a parallel interior point algorithm to solve block structured linear programs. This algorithm can solve block diagonal linear programs with both side constraints (common rows) and side variables (common columns). The performance of the algorithmis investigated on uncapacitated, capacitated and stochastic facility location problems. The facility location problems are formulated as mixed integer linear programs. Each subproblem of the branch and bound phase of the MIP is solved using the parallel interior point method. We compare the total time taken by the parallel interior point method with the simplex method to solve the complete problems, as well as the various costs of reoptimisation of the non-root nodes of the branch and bound. Computationalresults on two parallel computers (Fujitsu AP1000 and IBM SP2) are also presented in this paper.