Optimisation is a tool we apply to a very broad range of problems within our research group. In this article you’ll find out what it can do, how to apply it, and why.

Here in the Intelligent Water Decisions Research Group, we are constantly pulling optimisation from our toolbox. The group has enormous experience in developing and applying optimisation to a large suite of engineering, environmental and planning problems. We pioneered the use of genetic algorithms for water distribution design, and some of our members have worked commercially in this space. We have developed new algorithms that are faster and smarter than ever before, and that are suitable for solving large real-world problems. We have access to world-leading computing facilities that enable us to solve problems that would have been impossible just a few years ago.

Let’s explore the reasons why optimisation is a great tool. And if you need to help applying it in your problem-solving and decision making, we are always available to help you.

What can optimisation do?

Optimisation is all about making the best plans, designs and decisions. Let’s look at each of these three areas.

Using optimisation to make the best plans

When planning, we know the general outcomes we want to achieve. Then we then work out the steps we will take to achieve them. We plan because the outcomes we want to achieve will not happen by themselves: They involve the coordination of a whole range of people, resources, tasks, policies, and/or projects to best meet our outcomes.

And here’s where optimisation comes in: There’s always a different way to reach our outcomes, but wouldn’t it be great to have a tool that can help us select the best way? We want to have the best people available to us; to choose the best set of projects or options to achieve our outcomes with low financial and time costs; to coordinate how these occur in the best possible way.

Optimisation can help!

Using optimisation to make the best designs

When designing, we need to choose a number of components. Then, for each of these components, we may need to specify a number of design parameters (like size or material), and put them together so that they function as a system.  Again, there are many designs that will get the job done, but some of these will be superior to others. Usually we do not have time to explore all possible solutions (even if it is possible to identify them!).

Optimisation can help screen and rank different design options.

Using optimisation to make the best decisions

Decisions do not often a involve a simple choice between two options, but tend to form decision trees that can be very complex. (In fact, we are not always aware of how complex they are until we map them out.) Navigating through this decision tree to achieve the best balance of outcomes (for there are usually multiple factors to consider when making a decision) is extremely difficult.

Optimisation can be used to help navigate complex decision trees.

7 reasons why you should use optimisation too

As you have seen, optimisation has direct and meaningful application. But why should you do it too?

Reason 1: You can save a bucket load of money (or best meet other goals that you may have)

For example, it has been shown that optimisation reduces the cost of water distribution system designs (whether irrigation or municipal) by as little as 15%, and as much as 50%. Saving your organisation, or your customer, a bucket load of money is a significant way of making your brand competitive.

But there are many reasons why optimisation is disregarded too quickly. The remaining six reasons show you why.

Reason 2: You do not need to simplify your decision or problem

It is often thought that you need to simplify your problem in order to apply optimisation. This is not true.

Traditional optimisation techniques did require assumptions to be made about particular properties of your problem (eg. linearity, convexity, differentiable, etc), but newer breeds of algorithms do not. For example, these days evolutionary algorithms are very commonly used optimisers, and are even available by default within newer versions of Excel and Libreoffice/Openoffice. They are our most used optimsation algorithm for the problems that we solve, for they can work with any simulation model used to evaluate our objectives and constraints,  and are one of the best performing algorithms for solving non-smooth problems. A non-smooth problem is a difficult optimisation problem.

Practically, this is convenient. It means you can use whatever computational system you want to use to evaluate your objectives, when using an evolutionary algorithm (such as a genetic alrgorithm) for your problem.

The only caveat is that the computational system needs to be relatively fast. It needs to evaluate your objectives and constraints in a matter of minutes. This can often cause problems if you calculate your objectives using a complex simulation model. But there are a number of solutions to this.

How can we speed up the computational system?

First, evolutionary algorithms can be very easily parallelised: that is, we can split the work up across hundreds of CPUs. High performance computing and cloud computing (such as those offered by Amazon) provide hundreds of CPUs if we need them, with ever decreasing costs.  We also have techniques to approximate your objective function with high accuracy using very fast running neural networks (this is the meta-modelling or surrogate model approach).  Also, in these cases it is wise to reflect on whether you can simplify your objective functions and constraints,  or use a simpler, faster running model to evaluate them.

Reason 3: Optimisation can deal with multiple objectives (and/or many constraints)

Real world problems need to take into account a number of factors. Fortunately, multi-objective evolutionary algorithms exist, and are a mature technology. In fact, they are prevalent. Within my field, it is very rare these days to find anyone publishing who uses single-objective optimisation.

When I say multi-objective, I’m not talking about aggregating each of our objectives into a single criterion, using something like a weighted average. We are talking about characterising the full set of trade-offs between the objectives.

Take an example from an optimisation study I did,[1] selecting water sources and infrastructure for small-scale water systems. This study explored the costs and greenhouse gas emissions of using a range of alternative water sources, such as recycled greywater and rainwater in a greenfield development setting. Optimisation was applied here to select what water sources to use, and to size the infrastructure required to collect, treat, store and pump this water to residential allotments.

In doing this, we found the best possible trade-offs between cost, greenhouse gas emissions and water savings. Now, we know the minimum amount of extra money we need to spend for each kilolitre of water we do not need to take from our traditional mains water supplies.[1]

Reason 4: Optimisation comes up with feasible, realistic solutions

Some people have had poor experiences of using optimisation. This is often because previous optimisation studies that they’re familiar with came up with solutions you would not actually implement.

For example:

  1. New pipes being located in streets where excavation will cause excessive disruption to traffic or be too expensive
  2. Water tanks being located where there are likely to be community objections

I can understand these impressions. But, unrealistic solutions are often caused by poor formulations of the your optimisation problem. In particular, we find that unrealistic solutions are caused by unspoken objectives and constraints that were not considered when formulating the optimisation problem.

To solve this, you can go back and reformulate the problem. You can also preserve a range of ‘just-sub-optimal’ solutions from across the entire decision space as the optimisation runs. By doing this, you can be presented with a diverse range of near-optimal solutions, and it is likely that at least one of these will be a solution that you would want to implement.

The goal of optimisation is not necessarily to come up with the final design. Our aim is often to come up with a base design that can then be modified to achieve all objectives and constraints, which are hard to formulate within a formal optimisation approach. Because we have the optimised base design (or plan, or decision pathway), we still achieve many of the benefits of optimisation.

And this brings up another important aspect.

Reason 5: Optimisation is not a substitute for thinking about your problem seriously

When considering the millions of dollars that can be saved through implementing a ‘best’ design, rather than just a ‘suitable’ design, thinking carefully is important. Optimisation asks us to the take time to ponder the nature of our problems and decision tasks; to take the time to form robust formulations of the optimisation problem and identify realistic options for the optimizer to consider. We also need to carefully select and parameterise the right solver for the problem.

By this, I mean that we should not think of optimization as a tool where we can just press a button and out pops the best solution to the problem.

So how do we ensure that our formulations are robust? Well, I think this involves participatory approaches between analysts, decision makers, experts, and other stakeholders.  There is growing interest within academia on how to best facilitate interaction between these players in order to develop robust problem formulations (as described in this article). [2] This blog is just one method of such facilitated interaction within our research group.

Reason 6: Optimisation can deal with uncertainty

It makes sense to optimize even when your objectives or constraints contain uncertainty. At first, it may seem that optimisation cannot deal with uncertainty: Uncertainty means we cannot categorically say that a particular solution is best. But optimisation can find solutions that perform very well over a broad range of conditions.  This is a better outcome, as there is almost always uncertainty in real-world problems, and what we want to do is find solutions that are reliable and resilient, despite uncertainty.

Using a trial-and-error approach makes it even harder to find a solution that performs well across a range of uncertain conditions. Optimisation is able to find such solutions. This strengthens  the argument to use optimisation for these types of problems.

How do we take uncertainty into account within optimisation problems?

Well, when we can describe the nature of the uncertainty using probability distributions, we often use regret-based approaches.  Essentially, we calculate how much we may regret a solution (based on the objective functions), given the range of uncertain conditions possible. Then we aim to minimise this regret. This is a so-called ‘robust optimization approach’, because the ‘optimal solution’ is robust across a range of uncertain conditions.

Sometimes, we are unable to characterise uncertainty. For example, it is virtually impossible to set probabilities of future climate, as we cannot predict what political decisions are going to be made and what actions are going to occur to abate carbon emissions. This contrasts with weather forecasts, where meteorologists will often give a probability of rainfall at some future time.

When we are unable to characterise uncertainty, we usually use a scenario-based approach. In these cases, we might form a number of scenarios. An example could be planning the development of water resources into the future: We might have different climate scenarios forcing the hydrological models that  assess water availability as well as different scenarios characterizing future population growth). We could use optimisation for selecting what water sources to develop, and when to develop them. We might then assess how robust each of these solutions are across all other scenarios (remember, our optimal solutions at this stage are only optimal with respect to one scenario). Based on this robustness information, we could choose a solution with which to proceed, and then use an adaptive approach to modify these solutions as we get more definite information about our uncertainties.

A similar approach to this can be found in a recent  article by my PhD classmate, Eva Beh.[3]

Reason 7: It is within reach of your organisation

Optimisation need not be daunting. It is something that you can use in your organisation. Here are some ways you can get started:

How to get started if you are new to optimisation

Start to think with an ‘optimisation’ approach. As you go about your work-tasks, ask yourself questions like:

  • What are the goals/objectives?
  • What is in my power to control which can help achieve these?
  • What constraints am I under to achieve these?

Then see if you can formulate indicators or criteria to quantify these goals and constraints.

Explore the solver add-ins to your spreadsheet software. Play around with them for a few of your own optimisation problems, to familiarise yourself with the general concept of optimisation. We even have add-ins for genetic algorithms and ant colony algorithms that are powerful enough to solve some of the most challenging problems. And they are right within your spreadsheet!

Contact us if you are interested in using these.

Consider reading some entry-level texts on optimisation. A good one is Planning and Design of Engineering Systems[4].

How to improve your optimisation opportunities

Make sure you market the benefits that you have achieved with optimisation to your supervisors, clients, etc.  Otherwise, the benefits are hidden, and the organisation remains oblivious to the opportunities that this technique brings. If you do market the benefits achieved, then you will be given the time needed to develop optimisation approaches.

How to refine your optimisation skills

Consider doing a Masters degree or PhD with us! We have plenty of opportunities for a range of different interests in optimisation. They range from improved algorithmic performance, to application to real-world problems, to participatory approaches to formulation.

How to get help in applying optimisation to your problems

Here at the Intelligent Water Decisions Group, we’d love to see a world where decisions are made optimally, and are based on the best intelligence.  Our doors are always open to you, especially within the field of Water or Natural Resources Management. We are happy to discuss your planning, design or decision problem. There are many ways in which can collaborate, so get in touch for more information.

 

Let me know how you use optimisation!

As a researcher, I am very interested in the way optimisation is being applied in industry. It helps me understand where industry is at, which benefits our students with better training, and industry with better collaboration. Email me at jeffrey.newman [at] adelaide.edu.au with your stories of how you have applied optimisation in your work.

I thank Emeritus Professor Graeme Dandy whose comments improved this article.

 

References

[1] Newman, J. P.; Dandy, G. C.; Maier, H.R. (2014) Multiobjective optimization of cluster-scale urban water systems investigating alternative water sources and level of decentralization. Water Resources Research. Volume 50, Issue 10, pages 7915-7938. doi:10.1002/2013WR015233

[2] Wu, W; Maier, H.R; Dandy, G. C.; Leonard, R.; Bellette, K.; Cuddy, S. Maheepala, S. (2016) Including stakeholder input in formulating and solving real-world optimisation problems: Generic framework and case study. Environmental Modelling and Software. Volume 79, pages 197-213. doi:10.1016/j.envsoft.2016.02.012

[3] Beh, E.H.Y; Maier, H.R.; Dandy, G.C. (2015) Scenario driven optimal sequencing under deep uncertainty. Environmental Modelling and Software. Volume 68, pages 181-195. doi:10.1016/j.envsoft.2015.02.006

[4] Dandy, G.; Walker, D.; Daniell, T. and Warner, R. (2007) Planning and Design of Engineering Systems. 2. Ed. CRC Press.