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# Optimization a Mathematical Abstraction, or an Idea Whose Time Has Come?

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Courtesy of Innovyze

Hydraulic models that use advanced modeling packages such as Infoworks are helping growing numbers of water supply planners and operators better understand how their networks operate and can operate in the future, under a wide range of conditions.

One of the techniques modelers use for exploring how networks can operate better, a technique that is currently the subject of much discussion, is optimization – calculating the maximum or minimum value of a particular function, such as a cost function, and determining the network conditions that deliver that optimum. Some argue that optimization is a valuable tool that at the very least speeds up the process of searching for the best solution, and at best can find better solutions than endless manual changes and re-runs of a model will ever find. Others see it as a mathematical step too far, given the state of development of modeling and model usage, and argue that modeling is really about understanding network performance and its determinants rather than taking a single “black box” mathematical answer to a problem. So let me set out the Wallingford Software view of optimization, which is something of a middle way between these two poles.

Optimization is a well proven and useful mathematical technique that has proven applications across many industry sectors. The algorithms work, provided of course that the objective function expresses the cost function accurately; and the principle of using computers wherever possible to do the routine computation in order to allow engineers more time to do what they do best is central to the Wallingford approach. So why have we not banged the drum for optimization?

The answer is that, as with other areas where math is applied to engineering, it must be used with careful consideration of all the practicalities. Let’s look at two examples of areas where optimization is being trialed – the operational issue of optimizing pumping costs, and the planning issue of a least cost network topology.

Pumping cost optimization usually looks at balancing improved use of pumps and the variable costs of electricity at different times to minimize costs. There have been a number of trials of this in the past, and some are ongoing, but we know of no real success stories in this area. The problems we hear of stem from the fact that success depends on an operational model working in real time, and reacting to real time input from telemetry. We know of no operations department that is using such a model with the required level of trust in the model logic and outputs for optimization to be effective. The problem lies not with optimization, but with the stage of development of modeling. Optimization of operational models must await the development and use of robust and trusted operational models.

Using optimization to solve a planning question, such as finding the least cost investment to satisfy the water needs of a new development, is closer to successful implementation. But again, there are problems. The first arises because most hydraulic network optimization is based not on the analytical solution of equations but using a model and simulation to hunt for the best solution. They use a process called “optioneering” – selecting the best model case to run next. Because this could take many time-consuming re-runs of the model, the model used is often simplified, or run over a short time period. In either case, simplification undermines the trust in the results. Second is the issue of practicality. There are many real-world constraints on any proposed projects, and an engineering eye is needed through the mathematical process of optimization to ensure that the result is feasible. Without this, the results may be engineering nonsense. Finally, the process gives no indication of the sensitivity of the solution to the minor changes that implementation practicality usually imposes on the theoretical optimum.

Having stated the caveats, and there are more that could be stated, we nevertheless believe that optimization within a well bounded solution space with limited degrees of freedom will soon deliver useful results. But only for those utilities that have already invested in a well-built model that is proven and trusted.

The major benefits that modeling delivers to planning and operations engineers come from running a tried and tested hydraulic model to understand better the behavior of the network. This will continue to be the case into the foreseeable future. The proven and accepted validity of the model has got to be the base-line. Once such a model is established, optimization is then one of a number of useful techniques that can be used to explore planning and operational options. Optimization isn´t going to change the hydraulic modeling world dramatically, but it certainly has a place for engineers and modelers to make the best use of their network models.