AMALGAM: Multi-criteria optimization using multimethod adaptive search in MATLAB and Python

Description

This toolbox infers the Pareto trade-off surface corresponding to a vector of competing objective functions. In principle, each Pareto solution is a different weighting of the objectives used. Therefore, one could use differential weighting and approximte the Pareto front using many different trials with a single objective optimization algorithm. This approach, however, has shown to not be particularly efficient (exception is MOEA/D). This MATLAB and Python toolbox implements adaptive multimethod search to ensure a fast, reliable and computationally efficient solution to multiobjective optimization problems. This method is called a multi-algorithm, genetically adaptive multiobjective, or AMALGAM, method, to evoke the image of a procedure that blends the attributes of the best available individual optimization algorithms. AMALGAM finds a well-distributed set of Pareto solutions within a single optimization run, and achieves a good performance compared to commonly used methods such as SPEA2, NSGA-II and MOEA/D. The AMALGAM toolbox implements multi-core (thread) evaluation of the offspring to speed-up inference of CPU-intensive system models, and provides convergence diagnostics and graphical output. Built-in case studies involving (among others) multimodality, high-dimensionality, bounded parameter spaces, dynamic simulation models, and distributed multi-core computation illustrate the main capabilities and functionalities of the AMALGAM toolbox.

Getting Started

Installing: MATLAB

• Download and unzip the zip file 'MATLAB_code_AMALGAM_V2.0.zip' in a directory 'AMALGAM'.
• Add the toolbox to your MATLAB search path by running the script 'install_AMALGAM.m' available in the root of 'AMALGAM'
• You are ready to run the examples.

Executing program

• After intalling, you can simply direct to each example folder and execute the local 'example_X.m' file.
• Please Make sure you read carefully the instructions (i.e., green comments) in 'install_AMALGAM.m' and the manual !!!

Installing: Python

• Download and unzip the zip file 'Python_code_AMALGAM_V2.0.zip' to a directory called 'AMALGAM'.

Executing program

• Go to Command Prompt and directory of example_X in the root of 'AMALGAM'
• Now you can execute this example by typing 'python example_X.py'.
• Instructions can be found in the file 'AMALGAM.py' and in the manual !!!

Authors

• Vrugt, Jasper A. ([email protected])

Literature

1. Vrugt, J.A. (2024), Distribution-Based Model Evaluation and Diagnostics: Elicitability, Propriety, and Scoring Rules for Hydrograph Functionals, Water Resources Research, 60, e2023WR036710, https://doi.org/10.1029/2023WR036710
2. Vrugt, J.A., Multi-criteria optimization using the AMALGAM software package: Theory, concepts, and MATLAB implementation, UCI, 2015
3. Vrugt, J.A., B.A. Robinson, and J.M. Hyman (2009), Self-adaptive multimethod search for global optimization in real-parameter spaces, IEEE Transactions on Evolutionary Computation, 13(2), pp. 243-259, https://doi.org/10.1109/TEVC.2008.924428
4. Vrugt, J.A., P.H. Stauffer, T. Wöhling, B.A. Robinson, and V.V. Vesselinov (2008), Inverse modeling of subsurface flow and transport properties: A review with new developments, Vadose Zone Journal, 7(2), pp. 843-864, https://doi.org/10.2136/vzj2007.0078
5. Wöhling, T., J.A. Vrugt, and G.F. Barkle (2008), Comparison of three multiobjective optimization algorithms for inverse modeling of vadose zone hydraulic properties, Soil Science Society of America Journal, 72, 305 - 319, https://doi.org/10.2136/sssaj2007.0176
6. Wöhling, T., and J.A. Vrugt (2008), Combining multi-objective optimization and Bayesian model averaging to calibrate forecast ensembles of soil hydraulic models, Water Resources Research, 44, W12432, https://doi.org/10.1029/2008WR007154
7. Vrugt, J.A., and B.A. Robinson (2007), Improved evolutionary optimization from genetically adaptive multimethod search, Proceedings of the National Academy of Sciences of the United States of America, 104, pp. 708-711, https://doi.org/10.1073/pnas.061047110407
8. Vrugt, J.A., and B.A. Robinson (2007), Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging, Water Resources Research, 43, W01411, https://doi.org/10.1029/2005WR004838
9. Schoups, G.H., J.W. Hopmans, C.A. Young, J.A. Vrugt, and W.W. Wallender (2006), Multi-objective optimization of a regional spatially-distributed subsurface water flow model, Journal of Hydrology, pp. 20-48, 311(1-4), https://doi.org/10.1016/j.jhydrol.2005.01.001
10. Vrugt, J.A., M.P. Clark, C.G.H. Diks, Q. Duan, and B. A. Robinson (2006), Multi-objective calibration of forecast ensembles using Bayesian model averaging, Geophysical Research Letters, 33, L19817, https://doi.org/10.1029/2006GL027126
11. Vrugt, J.A., H.V. Gupta, L.A. Bastidas, W. Bouten, and S. Sorooshian (2003), Effective and efficient algorithm for multi-objective optimization of hydrologic models, Water Resources Research, 39(8), art. No. 1214, https://doi.org/10.1029/2002WR001746

Version History

• 1.0
  • Initial Release
• 2.0
  • Improved postprocessing capabilities
  • Python implementation

Built-in Case Studies

1. Example 1: ZDT1: test function
2. Example 2: ZDT2: test function
3. Example 3: ZDT3: test function
4. Example 4: ZDT4: test function
5. Example 5: ZDT6: test function
6. Example 6: ZDT6: test function, discrete parameter space
7. Example 7: DTLZ1: test function, 3 objectives
8. Example 8: DTLZ2: test function, 3 objectives
9. Example 9: DTLZ3: test function, 3 objectives
10. Example 11: Real-world example using rainfall-discharge modeling
11. Example 12: Watershed modeling using driven & nondriven hydrograph
12. Example 13: Bayesian model averaging: RMSE, IS and CRPS
13. Example 14: Multi-criteria BMA training temperature ensemble
14. Example 15: Multi-criteria BMA training sea-level pressure ensemble

Acknowledgments