Multi-objective Optimisation

In this week’s #TechnicalTuesday, Andrew Slaughter discusses the power of trade-off optimisation models versus traditional simulation models to investigate our national supply-demand balance.

Trade-Off Optimisation Is a Powerful Modelling Tool with Wide-Ranging Applications

Models can allow you to mathematically simulate the properties of a system over time, and are often used to identify ways in which a system can be improved. For example, we may investigate how many transfers and local water supply options (such as dams and water reuse schemes) we need to achieve the future, national supply-demand balance. Use of traditional simulation models for this is, however, limited because the model will only provide results for a limited, set combination of options that we investigate. We would likely also want to consider some objectives within our modelling, in this case minimising costs of transfers and local supply options. Clearly, there are different extents to which you can invest in local supply options and transfers, each with different costs. Finding an optimal ‘suite’ of options according to a set of objectives involves trade-offs between these objectives. What we need here is a tool that considers all possible combinations of options within a simulation model and identifies optimal sets of options according to trade-offs in objectives we set.

When Trade-Off Creates a Winning Result

Trade-off optimisation is such a tool, which is becoming increasingly accessible as computing resources become more affordable. Under trade-off optimisation, we can distinguish between simulation and ‘search’ modes within simulation models. If we tell the model what our decision variables are - in our example, these would be the different local supply options and transfers we invest in and their capacities - and what our objectives are (minimising local supply option cost and minimising transfer cost), the model search mode can run the simulation model thousands of times, with each simulation investigating a different combination of those options, all the while keeping track of our objectives.

Continuing with our example, under search mode, the model will identify options which minimise local supply cost and transfer costs such that performance in one objective cannot be improved without worsening the performance in the other objective. These are called non-dominated solutions and are represented by the red points in the trade-off plot (right-hand graph) below. Each point in the graph below represents a ‘suite’ of different local supply options and transfers. A major advantage of trade-off optimisation is that the selection of any of these optimal ‘suites’ is a policy decision. For example, for whatever reason, there may be a decision to limit transfers and choose a point further to the left of the graph with a lower transfer cost and higher local supply cost.

The example above is for only two objectives, but we can in theory investigate as many objectives as we like - although in practice, this is limited by computing resources and time. When interrogating the trade-offs among more than two objectives, we can use a parallel plot (shown below is a hypothetical example). Here, each coloured line represents the performance of one non-dominated solution; intersections of the lines with vertical axes represent the objective performance, and the arrow points to the optimisation objective.

Free vs Proprietary Software

While some companies offer proprietary trade-off optimisation software and services, there are free optimisation libraries available. These include the Python Platypus multi-objective evolutionary algorithms, which can be connected to the free and Open Source Pywr water allocation model. WRc has integrated water quality simulation into Pywr in a completely dynamic way so that water quality can inform water allocation decisions (Pywr-WQ). This development, along with the possibility of conducting trade-off optimisation in Pywr, offers exciting possibilities for identifying optimal water quality solutions.