A Solution-Cascading Approach to the Decomposition of Staircase Linear Programs

Abstract

A computationally efficient decomposition technique for large-scale linear programs with an underlying linked staircase structure is presented in this paper. The technique utilizes a solution-cascading approach with subproblem solutions. On a set of test problems, drawn from a variety of applications, the procedure has resulted in a reduction in computation time averaging about 68% of the undecomposed time. Similar tests on groups of randomly generated problems resulted in time savings as high as 95%. Three features of the approach make it particularly attractive. First, it is a meta-algorithm. That is, it can be embedded within any appropriate LP solver, implying even better time savings with more efficient solvers. Second, the procedure should become relatively less expensive as the problem size increases. Third, the procedure easily lends itself to parallel processing.

Keywords:

• Optimization
• Decomposition
• Solution Cascading
• Staircase Linear Programs