MORDM Basics V: WaterPaths Tutorial

The MORDM framework poses four fundamental questions that each corresponds to a section within the framework shown in Figure 1:

  1. What actions can we take to address the problem?
  2. What worlds are we implementing those actions in?
  3. What are acceptable levels of performance for those actions in all worlds?
  4. What controls failures across those worlds?
Figure 1: The MORDM framework (Herman et. al., 2013).

In the previous blog post, we used state-aware ROF triggers to implement drought mitigation and supply management actions for one hydroclimatic and demand scenario. In the first MORDM blog post, we generated multiple deeply-uncertain synthetic realizations of hydroclimatic and demand scenarios. The next logical question would be: how do these actions fare across all worlds and across time?

Setting up the system

To explore this question, we will expand the scope of our test case to include Cary’s two neighboring utilities – Durham and Raleigh – within the Research Triangle. The three utilities aim to form a cooperative water supply and management agreement in which they would like to optimize the following objectives, as stated in Trindade et al (2019):

  1. Maximize supply reliability, REL
  2. Minimize the frequency of implementing water use restrictions, RT
  3. Minimize the net present value of infrastructure investment, NPV
  4. Minimize the financial cost of drought mitigation and debt repayment, FC
  5. Minimize the worst first-percentile cost of the FC

In this example, each objective is a function of short-term risks of failure triggers (stROF) and long term risks of failure triggers (ltROF). The stROFs trigger short-term action, typically on a weekly or monthly basis. The ltROFs trigger action on a multi-year, sometimes decadal, timescale. Recall from a previous post that ROF triggers are state-aware, probabilistic decision rules that dictate how a system responds to risk. Here, we optimize for a Pareto-approximate set of ROF triggers (or risk thresholds) that will result in a range of performance objective tradeoffs. An example of a stROF is the restriction ROF trigger we explored in the post prior to this one.

In addition, an example of an ltROF would be the infrastructure construction ltROF. When this ltROF threshold is crossed, an infrastructure project is ‘built’. Potential infrastructure projects are ordered in a development pathway (Zeff et al 2016), and the ltROF triggers the next infrastructure option in the sequence. The term ‘pathway’ is used as these infrastructure sequences are not fixed, but are state-dependent and can be shuffled to allow the optimization process to discover multiple potential pathways.

Over the next two blog posts, we will explore the interaction between the water-use restriction stROF and the infrastructure ltROF, and how this affects system performance. For now, we will simulate the Research Triangle test case and optimize for the ‘best’ set of ROF triggers using WaterPaths and Borg MOEA.

Using WaterPaths and Borg MOEA

We will be using the WaterPaths utility planning and management tool (Trindade et al, 2020) to simulate the performance of the Research Triangle test case. For clarification, the default simulation within WaterPaths is that of the Research Triangle. The folder that you will be downloading from GitHub already contains all the input, uncertainty and decision variable files required. This tool will be paired with the Borg MOEA (Hadka and Reed, 2013) to optimize the performance objectives in each simulation to obtain a set of Pareto-optimal long- and short-term ROF triggers that result in a non-dominated set of tradeoffs. Jazmin made a few posts that walks through compiling Borg and the installation of different parallel and series versions of Borg that might be helpful to try out before attempting this exercise.

Once you have Borg downloaded and set up, begin by downloading the GitHub repository into a file location on your machine of choice:

git clone

Once all the files are downloaded, compile WaterPaths:

make gcc

To optimize the WaterPaths simulation with Borg, first move the Borg files into the main WaterPaths/borg folder:

mv -r Borg WaterPaths/borg/

This line of code will make automatically make folder called borg within the WaterPaths folder, and copy all the external Borg files into it.

Next, cd into the /borg folder and run make in your terminal. This should a generate a file called libborgms.a. Make a folder called lib within the WaterPaths folder, and move this file into the WaterPaths/lib folder

cp libborgms.a ../lib/

Next, cd back into the main folder and use the Makefile to compile the WaterPaths executable with Borg:

make borg

Great! Now, notice that the /rof_tables_test_problem folder is empty. You will need to generate ROF tables within the WaterPaths environment. To do so, run the script provided in the GitHub repository into your terminal. The script provided should look like this:

#SBATCH -n 16 -N 2 -p normal
#SBATCH --job-name=gen_rof_tables
#SBATCH --output=output/gen_rof_tables.out
#SBATCH --error=error/gen_rof_tables.err
#SBATCH --time=04:00:00
#SBATCH --mail-type=all

       	-t 2344\
       	-r 1000\
       	-C 1\ 
	-m 0\
	-s sample_solutions.csv\
       	-O rof_tables_test_problem/\
       	-e 0\
       	-U TestFiles/rdm_utilities_test_problem_opt.csv\
       	-W TestFiles/rdm_water_sources_test_problem_opt.csv\
       	-P TestFiles/rdm_dmp_test_problem_opt.csv\
	-p false

Replace all the ‘YOUR…’ parameters with your system-specific details. Make two new folders: output/ and error/. Then run the script above by entering

sbatch ./

into your terminal. This should take approximately 50 minutes. Once the ROF tables have been generated, run the script provided. It should look like this:

#SBATCH -n 16 -N 3 -p normal
#SBATCH --job-name=sedento_valley_optimization
#SBATCH --output=output/sedento_valley_optimization.out
#SBATCH --error=error/sedento_valley_optimization.err
#SBATCH --time=04:00:00
#SBATCH --mail-type=all


mpirun ./waterpaths -T ${OMP_NUM_THREADS}\
  -t 2344 -r ${N_REALIZATIONS} -d ${DATA_DIR}\
  -C -1 -O rof_tables_test_problem/ -e 3\
  -U TestFiles/rdm_utilities_test_problem_opt.csv\
  -W TestFiles/rdm_water_sources_test_problem_opt.csv\
  -P TestFiles/rdm_dmp_test_problem_opt.csv\
  -b true -o 200 -n 1000

As usual, replace all the ‘YOUR…’ parameters with your system-specific details. Run this script by entering

sbatch ./

into the terminal. This script runs the Borg MOEA optimization for 1,000 function evaluations, and will output a .set file every 200 function evaluations. At the end of the run, you should have two files within your main folder:

  1. NC_output_MS_S3_N1000.set contains the Pareto-optimal set of decision variables and the performance objective values for the individual utilities and the overall region.
  2. NC_runtime_MS_S3_N1000.runtime contains information on the time it took for 1000 simulations of the optimization of the Research Triangle to complete.

The process should take approximately 1 hour and 40 minutes.


Congratulations, you are officially the Dr Strange of the Research Triangle! You have successfully downloaded WaterPaths and Borg MOEA, as well as run a simulation-optimization of the North Carolina Research Triangle test case across 1000 possible futures, in which you were Pareto-optimal in more than one. You obtained the .set files containing the Pareto-optimal decision variables and their respective performance objective values. Now that we have optimized the performance of the Research Triangle system, we are ready to examine the performance objectives and the Pareto-optimal ROF trigger values that result in this optimal set of tradeoffs.

In the next blog post, we will process the output of the .set files to visualize the objective space, decision variable space, and the tradeoff space. We will also conduct robustness analysis on the Pareto-optimal set to delve further into the question of “What are acceptable levels of performance for those actions in all worlds?”. Finally, we will explore the temporal interactions between the water use restrictions stROF and the infrastructure construction ltROF, and how supply and demand are both impacted by – and have an effect on – these decision variables.


Hadka, D., & Reed, P. (2013). Borg: An auto-adaptive Many-objective evolutionary computing framework. Evolutionary Computation, 21(2), 231–259.

Trindade, B. C., Gold, D. F., Reed, P. M., Zeff, H. B., & Characklis, G. W. (2020). Water pathways: An open source stochastic simulation system for integrated water supply portfolio management and infrastructure investment planning. Environmental Modelling & Software, 132, 104772.

Trindade, B. C., Reed, P. M., & Characklis, G. W. (2019). Deeply uncertain pathways: Integrated multi-city regional water supply infrastructure investment and portfolio management. Advances in Water Resources, 134, 103442.

Zeff, H. B., Herman, J. D., Reed, P. M., & Characklis, G. W. (2016). Cooperative drought adaptation: Integrating infrastructure development, conservation, and water transfers into adaptive policy pathways. Water Resources Research, 52(9), 7327–7346.

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