The solution of a variety of classes of global optimisation problems is required in the implementation of a framework for sensitivity analysis in multicriteria decision analysis. These problems have linear constraints, some of which have a particular structure, and a variety of objective functions, which may be smooth or non-smooth. The context in which they arise implies a need for a single, robust solution method. The literature contains few experimental results relevant to such a need. We report on our experience with the implementation of three stochastic algorithms for global optimisation: the multi-level single linkage algorithm, the topographical algorithm and the simulated annealing algorithm. Issues relating to their implementation and use to solve practical problems are discussed. Computational results suggest that, for the class of problems considered, simulated annealing performs well.