Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation

To illustrate the ability of a midsized water utility to use a multiobjective evolutionary algorithm (MOEA) in an active water supply planning process, I will describe some recent work at Colorado Springs Utilities (CSU). Any views or opinions expressed here are strictly those of the author and do not necessarily reflect those of CSU. For the purposes of this discussion, MOEAs are considered as a class of algorithms that mimic natural selection in order to search for and find a solution to a multiobjective problem (generally a minimization or maximization problem). MOEAs solve optimization problems by using techniques such as inheritance, selection, crossover, and mutation. Some algorithms may incorporate additional search methods such as particle swarm. In multiobjective analysis, the Pareto optimal set concept, also known as a noninferior set of solutions, is used. Qualitatively, a Pareto solution of a multiobjective problem does not, in general, have a unique solution. For example, it is not usually possible to find a single point at which all the criteria have their minima. Instead, it is common to have a set of solutions, in which moving from one solution to another results in the improvement of one criterion while causing deterioration in another. Using MOEA techniques can enable practitioners to evaluate tradeoffs amongst different projects, programs, and policies. There seems to be little use by those in the water supply community, presumably due to the complexity of the task, the computing power requirements, and the ability to manage and analyze large amounts of data. For the last decade or so, researchers have been making great progress in the area of MOEA development. Today MOEAs exist that require minimal parameterization in order to find good approximations to a Pareto set, where in the past these parameterizations may have been problem-specific. Additionally, the parameterization requirements likely vary between algorithms and may include population sizes, the number of complexes, and mutation and crossover rates. This seemingly simple improvement is a large step forward in enabling water resources engineers to trust and use these advanced tools without the added complexity of MOEA parameterization. CSU provides potable water to nearly 450,000 residents of Colorado Springs. Located along the Front Range of Colorado, CSU is heavily reliant on Colorado River transbasin water. CSU is in the midst of a long-term planning process in which analytic tool development includes the use of MOEAs. During the course of this planning project, consecutive droughts developed in local watersheds and in the Colorado River Basin immediately following near-record snow pack in water year 2011. The drought persisted into the spring of 2013 and the forecast remained bleak. As a result, CSU enacted outdoor watering restrictions effective April 1, 2013, as did most other Front Range water providers. During the last half of April and into early May, the central Rocky Mountains in Colorado experienced a series of heavy and wet snow storms leading to dramatic increases in Colorado River Basin snow pack. While some residents questioned the need for watering restrictions in light of the storms, total seasonal snowpack remained below normal, resulting in the need for continued restrictions. This example of short-term uncertainty exemplifies the need for robust and flexible operational policies, along with analytical methods capable of supporting the necessary complexity. While more traditional Monte Carlo–type analyses may still play a role in risk assessments and operational policy evaluation, CSU decided to use MOEAs as well. Why MOEAs for drought policy analysis? To hedge against the risk of future droughts. As part of CSU’s drought study, we analyzed the historical, naturalized flows of the Colorado River at the Glenwood Springs flow gauge (Colorado River Basin headwater). From that analysis, we developed a drought index suitable for CSU planning. The drought index was applied to annual stochastic inflow time series that were developed using historical observed and paleoflow data for the Glenwood gauge that were derived by David Yates from the National Center for Atmospheric Research. Using the drought index, we identified 2,328 total 10-year sequences out of 20,650 possible 10-year sequences for further drought policy evaluation. CSU’s longstanding MODSIM based Operations and Yield model (O&Y model) was then used for all system simulations. Out of 2,328 baseline drought simulations, 425 produced a storage shortage (i.e., less than one year demand in system storage). This one year of demand storage value represents the current CSU emergency storage policy, and was adopted as a preliminary value for risk tolerance. From those 425 sequences, further screening was conducted to identify a small subset for the MOEA analysis that would provide varying temporal distributions of low system inflows. In other words, we tested the system performance against several different types of 10-year drought sequences. How does a water provider manage current droughts and hedge against future droughts given the uncertainty of future hydrologic conditions, customer demands, and other risk factors? At the most basic level, the responsibility of a water provider is to deliver potable water at a reliability and cost agreed to by its policy makers. However, there is conflict between the management objectives of delivering water for the current year (demand reliability) and storing water to hedge against future drought (storage reliability). For our multiobjective optimization problem, these two reliabilities were used as objective functions along with two additional objective functions: demand vulnerability (the magnitude of the shortage) and storage resilience (how quickly storage recovers from a deficit). While cost is an extremely important consideration for water utilities, we decided not to use it as an objective function in this early analysis. However, cost and a selection from 20 other system state variables, such as system spills and incursion into restricted reservoir pools, are being evaluated with a group of CSU staff, experts in their individual disciplines, to assess additional aspects of system performance for the Pareto approximate solutions. Those additional experts range from water rights administrators to field operators. We are still early in the process, and there is a need to continually engage our internal experts to help safeguard against unrealistic assumptions, results, and conclusions. It is imperative to keep the subject matter experts in the analysis and decision process