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Masoud Asadzadeh Bryan A. Tolson University of Waterloo

Multi-Objective Calibration of a Real Water Distribution Network. Masoud Asadzadeh Bryan A. Tolson University of Waterloo. Genevieve Pelletier François-Julien Delisle Manuel J. Rodriguez Laval University. Outline. Problem Definition (Single- vs. Multi-Objective Optimization).

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Masoud Asadzadeh Bryan A. Tolson University of Waterloo

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  1. Multi-Objective Calibration of a Real Water Distribution Network Masoud Asadzadeh Bryan A. Tolson University of Waterloo Genevieve Pelletier François-Julien Delisle Manuel J. Rodriguez Laval University

  2. Outline • Problem Definition (Single- vs. Multi-Objective Optimization) • Optimization Algorithm • Case Study (WDN Calibration) • Discussion of Results • Future Work WATER 2010QC July 5-7

  3. Single-Objective Optimization f (x) • Minimize: We are looking for a single best value of the objective function f(x) and the corresponding solution WATER 2010QC July 5-7

  4. Optimization Algorithm: DDS Initialize starting solution Perturb the current best solution Y • Globally search at the start of the search by perturbing all decision variables (DV) from their current best values Continue? STOP N • Locally search at the end of the search by perturbing typically only one DV from its current best value • Perturb each DV from a normal probability distribution centered on the current value of DV WATER 2010QC July 5-7

  5. Multi-Objective Optimization F(x)=[f1(x),f2(x),…,fN(x)] • Minimize: f2 f2 f1 f1 Non-Conflicting Objectives Conflicting Objectives WATER 2010QC July 5-7

  6. Optimization Algorithm: PA-DDS Update the set of ND solutions if necessary Perturb the current ND solution Initialize starting solutions Create the non-dominated (ND) solutions set Pick a ND solution based on crowding distance Pick the New solution New solution is ND? Y N Y STOP Continue? N WATER 2010QC July 5-7

  7. Case Study: Problem Definition 230,000 People Modeled in EPANET2 (Université Laval) 4700 pipes, 3691 Nodes, 379 Km, 34.2 Km2 • Determine proper pipe diameter 15 Flow Rate Measurements • Adequately simulate observations 19 Pressure Measurements • Have better understanding of the system WATER 2010QC July 5-7 Delisle, 2009

  8. Case Study: Objective Functions Mean Absolute Error: MAE = # obs Σ |Hi - hi(x)| i = 1 # obs Hi : Observed data point hi (x) : Simulated data point x : x1, x2, …, x4700: Vector of decision variables WATER 2010QC July 5-7

  9. Previous Results: Single Objective Calibration, Flow OR Pressure Which Solution? WATER 2010QC July 5-7

  10. New Results Bi-Objective Optimization with PA-DDS can be more Effective than Single-Objective Optimization with DDS WATER 2010QC July 5-7

  11. Discussion of Results Some Data Points are Hard to Match WATER 2010QC July 5-7

  12. Future Work and Discussion Improve the Case Study Why some data points are hard to match? • Check the data quality • Check the model in the vicinity of the data point • 4700 Decision Variables to Fit 34 Data Points • Decrease the problem size by decision variable grouping • Collect more measurements WATER 2010QC July 5-7

  13. Future Work Improve the Optimization Algorithm PA-DDS has Comparable Results with NSGAII and SPEA2 WATER 2010QC July 5-7

  14. ?

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