Optimisation of stochastic programming by hidden Markov modelling based scenario generation

Optimisation of stochastic programming by hidden Markov modelling based scenario generation

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are represented by a discrete scenario tree and the quality of the solutions obtained is governed by the quality of the scenarios generated. We propose a new techni...

Scenario generation in stochastic programming

Stability-based methods for scenario generation in stochastic programming are reviewed. In particular, we briefly discuss Monte Carlo sampling, Quasi-Monte Carlo methods, quadrature rules based on sparse grids and optimal quantization. In addition, we provide some convergence results based on recent developments in multivariate integration. The method of optimal scenario reduction and technique...

Scenario-based Stochastic Constraint Programming

To model combinatorial decision problems involving uncertainty and probability, we extend the stochastic constraint programming framework proposed in [Walsh, 2002] along a number of important dimensions (e.g. to multiple chance constraints and to a range of new objectives). We also provide a new (but equivalent) semantics based on scenarios. Using this semantics, we can compile stochastic const...

A framework for modelling stochastic optimisation algorithms with Markov chains

Evaluation of scenario-generation methods for stochastic programming

In this paper, we discuss the evaluation of quality/suitability of scenario-generation methods for a given stochastic programming model. We formulate minimal requirements that should be imposed on a scenario-generation method before it can be used for solving the stochastic programming model. We also show how the requirements can be tested. The procedure of testing a scenario-generation method ...