Multi-objective optimisation/trade-off analysis - Insight - SRG

Overview

Description and rationale

Insight is eWater’s multiple-objective optimisation 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.

Insight allows the modeller to define which parameters are to be considered in the optimisation framework. These parameters are called "decision variables". For example, the requirement might be to develop operating rules for a new desalination plant that meet the objective of minimising cost, or to identify what the optimal operating rules are for transferring water between storages to meet supply security objectives and minimising environmental impacts. By creating decision variables for these operating rules, the optimiser will try hundreds or thousands of different operating rules based on the chosen decision variables and determine how the rules perform against a set of user-specified objectives.

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 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.

Principal developer

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. 

Insight was originally developed by eWater CRC and has subsequently been enhanced by eWater Ltd to meet the needs of the Melbourne Water Corporation.

Scientific Provenance

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).

Version

Source v3.8.8.

Dependencies

Insight requires a functioning Source model to work with.

Availability/conditions

Use this heading if the functionality is a plugin or requires any 3rd party software applications.

Structure & processes

Theory of NSGA-II

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):

1. A fast non-dominated sorting approach.  This is used to find population members in the best, second best, third best, etc., non-domination levels.
2. 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.

3. A computational algorithm summarised as follows:

   1. Initially create a random parent population, P₁ of size N and sort this population using the fast non-dominated sorting approach.

   2. Use binary tournament selection, recombination (crossover) and mutation operators, to create the first offspring population, Q₁, of size N.

   3. 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 R_i = P_i U Q_i, where R_i has size 2N, and sort this combined population using the fast non-dominated sorting approach.
      • Start assembling a new population P_i+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 P_i+1 is used for selection, crossover and mutation to create a new offspring population Q_i+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.

Definitions

Insight Functionality

User requirements are summarised in Table 1. Interactions between Insight and Source are shown in Figure 2.

Table 1. User requirements

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. 

Figure 2: Flowchart of interactions between Insight and Source for multi-scenario optimisation

Key features are:

1. The same set of DVs applies to all scenarios for each run of a batch of scenarios
2. The values of the OF(s) are aggregated for each population member for all scenarios in a run of a batch of scenarios
3. Statistics-based OFs are determined within Insight.

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 optimisation for information on how to use it.

Process

(Also refer to Figure 2)

1^st generation

1. Values of decision variables, randomly chosen by Insight from within their allowable value ranges (where these ranges are input by the modeller), are passed to Source (Step 3(a) in the section on Theory of NSGA-II). Insight provides one set of values for every “individual”, where the number of individuals is equal to the population size input by the modeller.
2. Source is run for each individual (this is a group of runs for each individual when multiple scenarios are being investigated: one for each scenario).
3. Values of objective functions and result variables needed for evaluating statistical objective functions are passed back from each run of Source to Insight.
4. New values of decision variables are derived by selection, crossover and mutation to create the first offspring population (Step 3(b) in the section on Theory of NSGA-II).
5. Source is run for each individual in this population (group of runs when multiple scenarios are being investigated).
6. Values of objective functions and result variables needed for evaluating statistical objective functions are passed back from Source to Insight at the end of the run(s) for each individual.

Subsequent generations

For the i’th generation where 1 ≤ i ≤ ng (and the total number of generations, ng, is input by the modeller):

1. Insight processes decision variables and objective functions using the procedure described in the first two bullet points in Step 3(c) in the section on Theory of NSGA-II to create a new population ().  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).