Linear Programming on the Cell/BE

Abstract

Linear programming is a form of mathematical optimisation in which one seeks to optimise a linear function subject to linear constraints on the variables. It is a very versatile tool that has many important applications, one of them being modelling of production and trade in the petroleum industry. The Cell Broadband Engine, developed by IBM, Sony and Toshiba, is an innovative multicore architecture that has already been proven to have a great potential for high performance computing. However, developing applications for the Cell/BE is challenging, particularily due to the low-level memory management that is mandated by the architecture, and because careful optimisation by hand is often required to get the most out of the hardware. In this thesis, we investigate the opportunities for implementing a parallel solver for sparse linear programs on the Cell/BE. A parallel version of the standard simplex method is developed, and the ASYNPLEX algorithm by Hall and McKinnon is partially implemented on the Cell/BE. We have met substantial challenges when it comes to numerical stability, and this has prevented us from spending sufficient time on Cell/BE-specific optimisation and support for large data sets. Our implementations can therefore only be regarded as proofs of concept, but we provide analyses and discussions of several aspects of the implementations, which may guide the future work on this topic.