For urban water systems, identification of proper policies under uncertainty for desired water supply planning targets is critical, complex and difficult. Traditionally, the urban water sector uses ad hoc trial-and-error approaches to search the solution space of operating rules and investment options in pursuit of “good” solutions. The number of potentially feasible solutions can be astronomic, and improved solutions are likely to be missed, resulting in sub-optimal decision-making and a large opportunity cost to the community. Multi-criterion optimization produces a set of Pareto-optimal solutions. The multi-criterion framework better reflects the decision-making environment and, moreover, can efficiently identify optimal solutions that hitherto have been missed during trial-and-error searches.

In the context of urban water, decisions must often be taken in the face of the unknown. Ensuring robustness of the solutions is therefore essential. The uncertainties in a problem have to be represented in such a manner that their effects on present decision-making can properly be taken into account. In this study, we propose the Minmax Regret (MMR) method which involves multi-criterion optimization using one or more criteria based on expected values across a range of uncertain scenarios and simultaneously minimizing the maximum regret for each criterion over the scenarios.

A case study based on the Canberra water supply system is used to demonstrate the hybrid optimization approach. The system is simulated using the WATHNET simulation model with monthly runoff data for the period 1871 to 2008. A range of scenarios were constructed representing uncertainty about the impact of climate change on future runoff. The hybrid optimization approach is used to generate Pareto trade-off curves between minimized expected present worth costs and minimized maximum cost regret. These curves are used to demonstrate how robust optimal decisions can be made in the face of deep uncertainty about climate change.