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 and not to rely on the objective functions alone, as there are many aspects of a water supply system that are important to consider in addition to the objective functions. The objective functions should be considered powerful screening criteria or metrics and not the final answer. A metric matrix showing all possible tradeoffs of objective functions, in two dimensions, was developed and has proved to be a valuable visualization tool for discussion. By using sophisticated data visualization tools, additional information can be displayed using sizes and color for more powerful, albeit more complicated, visual analysis.

The decision variables (i.e., those system model variables perturbed by the MOEA) were triggers for watering restrictions (e.g., system inflow and storage) along with reservoir pool boundaries in our highest priority reservoirs. Preliminary results showed much promise for using MOEAs in the planning process. System operating criteria were found that resulted in improvements to nearly all metrics as compared to our current best guess starting values. CSU staff received the results and methods favorably. An additional benefit was that the extensive stress testing of the system model led to discovery of a couple of errors within our model. While we recognize the presence of uncertainties in this analysis framework and the subsequent impacts to the location of an approximated Pareto surface, the uncertainties do not diminish the usefulness of MOEAs in this application. From a practical planning perspective, we observed the ability to move out of the inferior decision space and closer to an approximate Pareto surface with much greater efficiency than would be realized in a more typical planning approach.

Implementation of this study was conducted on a typical server-class, Windows-based, 12-core computer. This server was a one-and-a-half years old, repurposed, off the shelf, server-class machine from the CSU inventory. Parallelization in a master-slave computing configuration, while not sophisticated, is a large leap forward for a midsized water utility performing water supply system modeling.

Through CSU’s progressive thinking, we have realized the benefit of investing in the tools and a data management system for current and future planning activities. These methods will allow CSU to perform these types of MOEA-based analyses deemed untenable in the recent past. Previously, similar analyses would have required parameterization of the MOEAs, which can be problem-dependent, and require an investment of additional resources to properly configure. This is not to say the problem would not have been approachable, but rather was likely beyond the capabilities of midsized utilities due the additional level of specialized skill to perform the analysis. Furthermore, as climate models continue to improve, CSU will have the ability to more readily update its analyses.

In order for MOEAs to become more commonplace for practitioners, a few things are needed from the water resources research community. The benefits and importance of using legacy simulation models should not be underestimated. Significant effort is often required to gain acceptance and trust of simulation models. Those using model platforms with source code availability or the equivalent (e.g., MODSIM with custom code) will have a significantly easier time implementing these techniques. Most planning processes will evolve, questions will change, and the need for modeling flexibility will be required. I challenge the modeling community to develop or adapt model platforms for use with this new generation of MOEA wrappers. For those water providers that are embarking on new planning studies, consider the flexibility to take advantage of these powerful MOEAs when choosing a modeling platform. Model authors should consider making access to source code available in order to enable the use of these powerful techniques. Flexibility in future modeling systems is critically important. GUIs should not be integrated into the code structure, but should act more as data interfaces allowing future wrapping of optimization models.

CSU has invested in the future, and since utilities never stop planning, there will always be complex problems to be analyzed beyond those currently envisioned. A high skill level is required for these types of analyses. However, the necessary skills are certainly not out of the reach of those currently practicing in water resources engineering who are willing to adapt their analytical thinking and methods. A working knowledge of Pareto optimality is necessary. Fortunately information is widely available, as the Pareto optimality concept has been around for nearly 100 years. Currently, some programming skill is required in order to interface the MOEAs and the simulations models. Some knowledge of basic network computing would be required for parallelization. Good analytical skills are required to formulate reasonable objective functions and then process the results in a meaningful way in order to evaluate the metrics together with any state variables. We cannot remove the human element from the most complex analyses, and there must be a willingness to deeply investigate results.

As all water resources professionals are aware, increased competition for water supplies and increased understanding of greater water supply uncertainties combine to create a heightened level of contention between competing users and concerned stakeholders. Therefore, a need for finding the best compromises or tradeoffs between competing management objectives will only increase. MOEAs are the new big hammer in the tool box.