Brunel University, School of Information Systems, Computing and Mathematics
Abstract
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis we consider two research problems, namely, (i) language constructs
for modelling stochastic programming (SP) problems and (ii) solution methods
for processing instances of different classes of SP problems. We first describe a
new design of an SP modelling system which provides greater extensibility and
reuse. We implement this enhanced system and develop solver connections. We
also investigate in detail the following important classes of SP problems: singlestage
SP with risk constraints, two-stage linear and stochastic integer programming
problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing
decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several
solution methods for stochastic integer programming and report a computational
study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.Financial support was obtained from OptiRisk Systems