Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

8.3 Computational Challenges Associated to Optimisation

The previous paragraphs have illustrated the various formulations of optimisation under uncertainty that are required to be solved in order to make a decision on a technico-economic basis. More will be said regarding the computational implications. Indeed, stochastic optimisation generates tough computational challenges (Beyer and Sendhoff, 2007) both regarding the computational cost and the difficulties in guaranteeing robustness through theoretical results for the existence and unicity of optima and the convergence of the algorithms.

8.3.1 Static Optimisation (Utility-Based)

An initial idea is to optimise the choice of d from the point of view of a given risk measure c_Z(dd), which may be:

• maximise expectation of net present value, that is minimise expected net present costs of a loss scheme such as flood control;
• maximise the expected utility of the net present value or more complex expressions in time: formally, this includes also the case of minimising probability of undesired event, such as insolvency;
• optimise other combinations between risk measures of the output such as expected utility penalised by variance, utility quantiles and so on.

In general, a computational difficulty arises with the subsequent optimisation programs:

(8.37)

as the distribution of the variable of interest z (total cost, utility, etc.) may depend ...