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Insight is eWater’s multiple-objective optimisation and decision support framework. This framework allows for more efficient evaluation of planning options than the traditional manual trial and error approach that modellers often use. The optimisation tool enables a more thorough examination of potential planning scenarios and the resulting trade-offs between desired outcomes.
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Insight links a multi-objective optimiser (Deb et al., 2002) to Source’s external interface and optimises Source models by running them up to thousands of many times with different parameter values.
For example, if the requirement is to minimise both costs and adverse environmental impacts, then Insight will search for options which express the trade-offs between these two competing objectives. Each solution has different cost and performance outcomes. Insight does not make any judgements about how important each of the impact statistics are, instead it searches a range of options which have different types of impacts. Insight will only discard an option, ‘A’, if it is clearly inferior to an alternative option, ‘B’. That is, if ‘B’ performs better than ‘A’ on at least one of the statistics and there is no statistic where ‘A’ performs better than ‘B’. At the end of its run, Insight will produce a range of optimal solutions (the Pareto Front). Figure 1 shows an example (after Blackmore et al., 2009).
The optimisation results can be examined via a number of graphical tools to help the planners consider the trade-offs between objectives and the relationship between decisions and objectives.
Figure 1. Example Pareto Front diagram (after Blackmore et al., 2009)
Insight operates at the spatial and temporal scales of Source models. It runs Source models multiple times to search for optimal solutions.
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The multi-objective optimiser used in Insight was developed by Deb et al. (2002). It was originally adapted for use with Source by eWater CRC with permission.
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The multi-objective optimiser used in Insight is the Non-dominated Sorting Genetic Algorithm II (NSGA-II) developed by Deb et al. (2002). This is a Multi-Objective Evolutionary Algorithm (MOEA) that is based on the principles of the well known Genetic Algorithm (GA).
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Details of the derivation of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), including pseudo-code, are available in Deb et al. (2002). NSGA-II is a variant of the well known Genetic Algorithm (GA) and the principles of the GA are discussed in text books (e.g. Loucks and van Beek, 2005).
Key features of NSGA-II are (abridged from Deb et al., 2002):
- A fast non-dominated sorting approach. This is used to find population members in the best, second best, third best, etc., non-domination levels.
- Diversity preservation based on a crowded distance estimation procedure and a crowded comparison operator. This approach does not require any user-defined parameter for maintaining diversity among population members.
A computational algorithm summarised as follows:
Initially create a random parent population, P1 of size N and sort this population using the fast non-dominated sorting approach.
Use binary tournament selection, recombination (crossover) and mutation operators, to create the first offspring population, Q1, of size N.
Noting that elitism is introduced by comparing the current population with previously found non-dominated solutions then the procedure after the initial generation can be summarised by considering the i’th generation:
- Create a combined population Ri = Pi U Qi, where Ri has size 2N, and sort this combined population using the fast non-dominated sorting approach.
- Start assembling a new population Pi+1 of size N. The assembly process begins by including solutions at the best non-dominated level. If the number of these is less than N then they are all included. This process continues with solutions from the second best, etc. levels as long as all the solutions from these levels can be included (i.e. the combined total of these solutions is less than N). For the last level (i.e. the one where not all solutions can be included to make up the numbers to N), the solutions are sorted using the crowded comparison operator to identify the best ones to include in the new population.
- The new population Pi+1 is used for selection, crossover and mutation to create a new offspring population Qi+1 of size N. For selection a binary tournament selection operator is used but the selection criterion is now based on the crowded comparison operator.
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| Decision variables | The management levers which can be pulled in order to achieve the required objectives. Each decision variable must be defined as a global expressionFunction, with an allowable range of values it can take. |
| Dominated solution | When comparing results from two Source runs (or group of runs), ‘A’ and ‘B’, Insight will treat ‘A’ as a “dominated solution” only if it is clearly inferior to ‘B’; that is, if ‘B’ performs better than ‘A’ on at least one of the statistics and there is no statistic where ‘A’ performs better than ‘B’. In this case ‘B’ is a “non-dominated solution” and is a potential candidate for the Pareto front of optimal solutions (e.g. see Figure 1). |
| Generation | For each generation the decision variables are subject to selection, crossover and mutation. The number of generations is specified by the modeller. |
| Individual | A solution obtained from a single run of Source with a given set of decision variable values (an individual is a group of runs when multiple scenarios are being investigated: one run for each scenario). |
| Non-dominated solution | See definition of “dominated solution”. |
| Objective function | Mathematical expression of the objectives required to be achieved (e.g. minimising the operating cost of the system, maximising environmental benefits, or minimising time spent in water restrictions). Objective Functions are set up as global expressions Functions within Source. Note that only the value of the expression Function at the last time step is used for evaluating the objective function. Therefore, expressions Function should be defined in such a way that the value at the last time step of the simulation is the value that represents the required statistic for the entire simulation period. |
| Population | The number of possible feasible solutions to be derived by changing decision variable values (within their value constraints) in Insight and running Source. The population size is specified by the modeller and is equal to the total number of individuals. |
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A single scenario in a Source model could represent a particular system configuration, inflow sequence, demand model, etc. Insight can optimise the decision variable(s) (DVs) over multiple scenarios. The DVs and objective functions are chosen by the modeller.
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The functionality listed in Table 1 is all concerned with input and output data handling and how Insight and Source interact, and there is no new science involved. Therefore, the functionality in Insight is not discussed further here and reference should be made to the Insight: Objective Multi-objective optimisation for information on how to use it.
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The decision variables and objective functions must be defined in the Source project as global expressionsFunctions. Hence, in order for a Source parameter to be included in an optimisation problem, that parameter needs to be able to be defined through the expression Function editor.
More details on data are provided in the Source User Guide.
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