The Lake Problem

The Lake Problem is a stylized decision problem regarding pollution control often used to demonstrate approaches for supporting decision making under uncertainty.

The population of a city has to decide on the amount of annual pollution it will put into a lake. If the pollution in the lake passes a threshold, it will suffer irreversible eutrophication. Allowing increased pollution reduces costs. Making large changes to allowed pollution between years is also difficult.

Approaches

The lake problem has the ability to represent tipping points, nonlinearity, and deep uncertainties. It has been used to demonstrate new methods and software, including the EMA Workbench and OpenMORDM.

Methods applied include:

Variants of the problem include:
  • Known and uncertain model parameters and thresholds
  • Representation of decision alternatives through "direct policy search", which optimises a state-aware control rule rather than the pollution releases themselves

Selected case studies

  • Original formulation, demonstrating impact of uncertainty and lags

    Carpenter SR, Ludwig D, Brock WA (1999) Management of eutrophication of lakes subject to potentially irreversible change. Ecological Applications, 9 (751), p. 771. doi: 10.1890/1051-0761(1999)009[0751:MOEFLS]2.0.CO;2

  • Shows that stakeholders maximizing their expected utility can cause periodic collapses of the lake ecosystem if there is uncertainty about the lake’s eutrophication thresholds

    Peterson GD, Carpenter SR, Brock WA (2003) Uncertainty and the management of multistate ecosystems: an apparently rational route to collapse. Ecology 84:1403-1411. doi:10.1890/0012-9658(2003)084[1403:UATMOM]2.0.CO;2

  • Identifies robust solutions that compromise optimality for acceptable performance under a broader envelope of uncertainty assumptions (Efficiency-Robustness trade-offs)

    R.J. Lempert, M. Collins (2007) Managing the risk of uncertain threshold response: comparison of robust, optimum, and precautionary approaches. Risk Anal., 24 (4) (2007), pp. 1009-1026. doi:10.1111/j.1539-6924.2007.00940.x

  • Demonstration of many-objective robust decision making

    Singh R, Reed PM, Keller K (2015) Many-objective robust decision making for managing an ecosystem with a deeply uncertain threshold response. Ecology and Society 20(3): 12. doi:10.5751/ES-07687-200312

  • Demonstration of the EMA Workbench

    Kwakkel JH (2017) The Exploratory Modeling Workbench: An open source toolkit for exploratory modeling, scenario discovery, and (multi-objective) robust decision making. Environmental Modelling & Software 96, 239–250. doi:10.1016/j.envsoft.2017.06.054

  • Demonstration of the OpenMORDM R package

    Hadka D, Herman JD, Reed PM, Keller K (2015) OpenMORDM: an open source framework for many objective robust decision making. Environ. Model. Softw., 74, pp. 114-129. doi:10.1016/j.envsoft.2015.07.014

  • Presents a version of the lake problem as a threshold problem for benchmarking of optimisation algorithms

    Ward VL, Singh R, Reed PM, Keller K (2015) Confronting tipping points: can multi-objective evolutionary algorithms discover pollution control tradeoffs given environmental thresholds? Environ. Model. Softw., 73 (1) (2015), pp. 27-43. doi:10.1016/j.envsoft.2015.07.020

  • Demonstration of "direct policy search" with many-objective robust decision making

    Quinn JD, Reed PM, Keller K (2017) Direct policy search for robust multi-objective management of deeply uncertain socio-ecological tipping points. Environmental Modelling & Software. 92: 125–141. doi:10.1016/j.envsoft.2017.02.017