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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 anew population (P_i+1).  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).
2. Values of each decision variable from the new population (P_i+1) are used for selection, crossover and mutation by Insight (i.e. the third bullet point in Step 3(c) in the section on Theory of NSGA-II) to create a new offspring population (Q_i+1) of decision variables. The resultant values of decision variables are passed to Source.
3. Source is run for each individual (or group of runs when multiple scenarios are being investigated).
4. 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.
5. Insight processes decision variables and objective functions from the current and previous generations (i.e. repeats Step 1 above), searching for “dominated solutions” and “non-dominated solutions”.
6. If all generations have been run, the resultant set of “non-dominated solutions” is the final set and is the Pareto front of optimal solutions.  Otherwise the process repeats Steps 2-5 above.

Data

Input data

At a minimum, Insight requires the following information to run an optimisation:

• One or more Source scenarios containing decision variables and objective functions
• Access to the Source command line tool
• An Insight settings file (containing the Source project location, objective functions and decision variables)
• The number of generations
• The population size of each generation

The decision variables and objective functions must be defined in the Source project as global expressions.  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 editor.

More details on data are provided in the Source User Guide.

Parameters

Output data

Outputs include values of decision variables and objective functions for each individual for each generation, to enable viewing in graphical displays and tables and further processing.  The graphical displays include a plot that is updated after each individual is run in Source which shows the progressive development of the Pareto Front. 

Once more than one generation is complete Insight allows for the hypervolume (Emmerich et al, 2005; Fonseca et al, 2006; Knowles et al, 2006) to be viewed.  This provides an indication of how the results are converging towards the Pareto optimal solution.  The hypervolume is calculated based on the distance between a maximum non-optimal solution and the modelled results, and the larger the hypervolume, the closer the results are to reaching the Pareto optimal solution.  Graphing this provides a useful indication of how much the optimal solutions are changing.  If the hypervolume plot is flattening out then this is an indication that more generations are unlikely to produce better results.

All items selected for recording in the Source Recording Manager by the modeller from single and multi-replicate model runs are written to file by Source so that results are able to be analysed for selected outputs:

• For all replicates
• For any selected replicate
• Statistics across all replicates

The structure of the file is:

Rows 1 – 5 Header lines with run and output information.  These are used to record metadata such as project file name and description, scenario name and description, user name, run date and time, initial storage volumes (to be used for item 5 – water balance report) etc.

Row 6 – Fortran free format statement for time series data in the file (i.e. *).

Row 7 – number of columns of data inclusive of date and replicate number (ncol)

Row 8 – 8 + ncol - 1 – descriptors for each column

Subsequent rows – time series data of the following form:

Timestep 1, replicate 1  season, year, replicate, requested outputs
Timestep 2, replicate 1  season, year, replicate, requested outputs
Timestep 3, replicate 1  season, year, replicate, requested outputs
Tiimestep …, replicate 1 season, year, replicate, requested outputs
Timestep 1, replicate 2  season, year, replicate, requested outputs
Timestep 2, replicate 2  season, year, replicate, requested outputs
Timestep 3, replicate 3  season, year, replicate, requested outputs
Tiimestep …, replicate 4 season, year, replicate, requested outputs
… and so on.

A separate stand-alone tool is available that produces the following statistics and output for modeller selected items or all items in the above file:

• For all replicates, or for a selected replicate, with a user-definable year (only full years considered)
  1. Overall maximum
  2. Mean and standard deviation of annual maximums for all/selected replicate(s)
  3. Specified percentile of annual maximums for all/selected replicate(s)
  4. Overall minimum
  5. Mean and standard deviation of annual minimums for all/selected replicate(s)
  6. Specified percentile of annual minimums for all/selected replicate(s)
  7. Mean and standard deviation of value for all/selected replicate(s)
  8. Items I – VII  for a specified annual date
  9. Items I – VI  for accumulated values for a specified annual date range

• Export to a separate file modeller selected time series selected by replicate number and/or item.  This file has same format as above. 

Reference list

Blackmore, J. M., Dandy, G. C., Kuczera, G. and Rahman, J. (2009). Making the most of modelling: a decision framework for the water industry. In 18th World IMACS / MODSIM International Congress on Modelling and Simulation, edited by R. S. Anderssen, et al. Cairns, Australia: Modelling and Simulation Society of Australia and New Zealand and International Association for Mathematics and Computers in Simulation.

Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2): 182-197.

Emmerich, M., Beume, N. and Naujoks, B. (2005). An EMO algorithm using the Hypervolume measure as selection criterion. Carlos A. Coello Coello, Arturo Hernández Aguirre, Eckart Zitzler (Eds): Evolutionary Multi-Criterion Optimization, Third International Conference, EMO 2005, Guanajuato, Mexico, March 9-11, 2005. Proceedings. Lecture Notes in Computation Science, 3410: 62-76.

Fonseca, C.M., Paquete, L. and López-Ibáñez, M. (2006). An improved dimension-sweep algorithm for the Hypervolume indicator. Proceedings of the IEEE Congress on Evolutionary Computation, Vancouver, Canada, July 16-21, 2006. 1157-1163.

Knowles, J.D., Thiele, L. and Zitzler, E. (2006). A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimisers, TIK Report Number 214, ETH Zurich.

Loucks, D.P. and van Beek, E. (2005). Water resources systems planning and management: an introduction to methods, models and applications.  UNESCO, Paris and WL | Delft Hydraulics, The Netherlands.  680 pp. ISBN 92-3-103998-9. Available at: ecommons.library.cornell.edu/handle/1813/2799.