A parallel forward network simplex algorithm and implementation
We describe a parallel forward network simplex algorithm for solving dynamic (multiperiod) network flow problems. The serial algorithm solves a single period network flow problem and progresses by considering longer and longer time horizons until the last time period is reached. The method is efficient because of a natural problem decomposition (causing computational decision horizons), which limits pricing and pivoting effort to the last few time periods following augmentation. With the proper data structures, an Forward Network implementation can typically solve T period problems in solution CPU times and pivot counts that are a linear in T. Most pure network codes have solution CPU times that are quadratic in T. We implemented a parallel forward network code, called PFORNET, on a dedicated, 8 processor, Intel iPSC/2 Hypercube. We partition the problem data by consecutive time period chunks. Each processor executes a forward network primal simplex algorithm concurrently. Processor 1 then performs the final linking with negligible effort. The method is remarkably robust when solving problems with a small number of time periods. For problems having a large number of periods, almost perfectly parallelizable performance is obtained. The forward network simplex method performs true concurrent parallel pricing and pivoting on a decomposed basis tree in a distributed memory environment.
- OSTI ID:
- 35780
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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