Like many other cities, the Amsterdam conglomeration is faced with rising demand for water as a result of population growth and developing industry. Expectations are for water demand to grow even more in hot, dry periods as a result of climate change. The current production and distribution network was not designed to cater to this new level of growing demand. Thus, Waternet is faced by the challenge of how to develop a good approach to growth.
Amsterdam’s water supply currently comes from two production sites, one to the west and one to the east of the city. Waternet intends to meet increasing demand mainly from the east, because that will lead to a better balance between the two production sites. Apart from the capacity of the production sites, the distribution network also needs to be expanded. There are various possible ways of doing this. As a first step in the process of deciding on the best solution, in collaboration with KWR Waternet drew up a definition of the problem, and subsequently worked through a large number of possible solutions with the Gondwana numerical optimisation platform . The horizon for the whole exercise was 2050.
Solutions through numerical optimisation
KWR has developed the Gondwana computational software tool in order to automatically and systematically answer all kinds of design questions regarding the network (numerical optimisation). Gondwana combines a genetic algorithm with hydraulic computation to automatically generate a large number of possible design solutions. It works as follows:
The starting point is the existing network. By making some arbitrary changes to it, a first ‘generation’ of potential new networks is generated.
Examples of changes include: changing the diameter of some pipes on the basis of a list of available diameters, ‘opening up’ potential extra pipes, or changing completely different design aspects such as installing a particular sensor. This first generation of networks is then worked through and assessed with regard to certain pre-established conditions, such as certainty of supply and performance criteria such as costs, and pressure problems resolved. Networks that do not meet the hard conditions stipulated are rejected. Networks that do meet them are compared with each other on the basis of performance criteria. The best performing networks are used to generate a new generation of solutions (by adjusting improving more pipelines and combining networks). In the same way, the new generation is then worked through and assessed too. In this way, generation after generation, the collection of solutions becomes better and better. Ultimately this leads to a collection of possible ideal networks: a Pareto front. The user can compare the different designs on the Pareto front and decide to what extent an improvement in one objective justifies a concession on another.
The technique of designing solutions with numerical optimisation is not new. There are many scientific publications on the subject. These publications deal mainly with smaller standard networks. Practical applications with existing extensive networks are still only available to a very limited extent, however. The difficulties of applying it in practice are twofold: first, translating the problem into mathematical form, and then interpreting the results, taking account of the assumptions made. Collaboration between Waternet (problem owner) and KWR (translation of the problem into a mathematical definition of a problem) is thus essential and requires mutual consultation. In order to transform Waternet’s problem into a mathematically solvable problem definition, it is necessary to jointly define goals, conditions, decision variables and the starting situation of the network.
Defining the starting situation
The first step in defining an optimisation problem is a good description of the starting situation. For this we chose to give a simplified description of the current network, with as consumption the expected peak consumption of 2050. The model was then expanded with nodes (a distribution network exists out of pipes and nodes. Nodes are points where the demand of houses and or businesses are concentrated) with extra consumption (see illustration 1) representing the urban expansion plans. Doubling of the current production capacity in the east and a possible new pumping station in the north of the city were also incorporated as part of the starting situation. Finally a few possible future pipelines (local solutions) were included in the model with an effective diameter of zero. These local solutions can be activated during the optimisation by increasing the diameter if they contribute added value to the solution. This gives Waternet the possibility of assessing the effectiveness of the local solutions and finding an optimal combination. In this optimisation, the adjustment of the diameters of the local solutions and the existing pipelines serves as the decision variable: that which can be adjusted by the algorithm to generate new potential solutions.
Waternet’s goal is to maintain certainty of supply through to 2050 and beyond. More precisely, to ensure that at the peak time on the peak day in 2050, enough water can be supplied with sufficient pressure. Analyses of the current network, adding in the expected extra demand of 2050 (so including urban development as well as the increase in demand for water due to climate change) show that the current network is incapable of dealing with it and that there are many points where the necessary pressure is not attained. Because in the 30 years to 2050 Waternet will have only limited room in terms of time, money and people, with which to adapt the network, we also looked at which adaptations were the most effective. Or to put it another way: how can we resolve as many deficient pressure points with as few changes as possible. The optimisation chosen therefore assesses the solutions by reference to two objectives:
- minimising the sum of pressures below 230 kPa (33.36 psi), and
- Minimising the number of kilometres of pipe that need to be adapted.
This gives an insight into how much needs to be invested/adapted to attain the desired pressure performance.
Defining the constraints
The network must attain the objectives set but also within a number of constraints. Waternet intends to meet the increasing demand mainly from the east side of the system, because that will lead to a better balance between the two production sites. An analysis of the network shows however that, because of the network’s current hydraulic resistance, it would only be possible to supply the extra water from the western production site. If supply from the west were delimited and equal proportions forced between east and west, an unattainably high pressure would be needed in the eastern pumping station. One of the constraints is that with equal distribution the pressure at this supply point should not exceed 350 kPa (50.77 psi). At the same time, Waternet wishes to take explicit account of security of supply in certain situations of serious disruption of the distribution system, such as non-availability of a pumping station or an important pipeline. To take account of this, 21 disruptive scenarios were elaborated and the six with the most adverse impacts selected for inclusion in the optimisation. The performance of the potential networks in these adverse scenarios is then adopted as a constraint.
Results of the optimisation
With the starting situation, decision variables, objectives and constraints described (table 1), the optimisation platform (Gondwana) can now start calculating.
Table 1. Overview of the final definition of the optimisation problem
|Starting situation||Hydraulic network with future extra consumption and future pumping stations added|
|Decision variables||New diameters and extra pipes|
|Objective 1||As few points as possible with pressure below 230 kPa in undisrupted situation|
|Objective 2||As few adaptations as possible to the network|
|Constraint 1||Assured supply in six worst case disruptive scenarios|
|Constraint 2||Acceptable pressure in the eastern pumping station|
The optimisation gives 48 solutions per generation and a total of 4,500 generations. This means that a total of 216,000 potential network models were calculated. This ultimately gives a Pareto front of optimised networks, with some networks scoring better for pressure (illustration 2, horizontal axis) but needing more kilometres of adaptation (vertical axis) or vice versa. Within the possibilities indicated by the Pareto front, Waternet has a preference for solutions in which between 100 and 300 kilometres of pipe are adapted. There are two reasons for this. Firstly, solutions involving more than 300 kilometres of adaptation require extra investment and hardly perform any better as regards pressure, while at under 100 kilometres with each small adaptation a respectable profit can still be made. Secondly, 100-300 kilometres of adaptation in the next 30 years means a challenging but not impossible task for Waternet.
Illustration 2: All optimal models and their scores for the two goals defined
On the Pareto front, there are 156 potential networks with between 100 and 300 kilometres of adaptations, all with different performances as regards pressure and different numbers of kilometres to be adapted. To determine which pipes are it is important to tackle, for each pipe we calculated the number of solutions in which that pipe was adapted. The Pareto front also shows which previously devised local solutions will actually be selected and are thus effective in resolving sub-standard pressure. Some local solutions are not much chosen (because there are better ways), while others are nearly always used.
Thanks to this study, Waternet has a better view of the investment needed in order to continue to assure supply in 2050. It is now clear which existing stretches of pipeline must be expanded and which local solutions have added value. With this knowledge, packages of measures can be put together and elaborated.
Waternet is faced with the challenge of keeping the growth of their distribution infrastructure in pace with that of the city. Together with KWR, Waternet restated this challenge as a mathematical problem that could be solved using the Gondwana numerical optimisation platform. The iterative, systematic approach delivers credible and usable outcomes. The challenge of maintaining ‘security of supply’ in 2050 is tough, but not impossible. It turns out that a large part of the solution may tally with the planned replacement programme. At the same time, it became clear which new trajectories can best be considered.
 Practical Application of Optimisation Techniques to Drinking Water Distribution Problems (easychair.org)