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Masoud Asadzadeh Bryan A. Tolson University of Waterloo
Multi-Objective Calibration of a Real Water Distribution Network Genevieve Pelletier François-Julien Delisle Manuel J. Rodriguez Laval University Masoud Asadzadeh Bryan A. Tolson University of Waterloo
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Outline Problem Definition (Single- vs. Multi-Objective Optimization) Optimization Algorithm Case Study (WDN Calibration) Discussion of Results Future Work WATER 2010QC July 5-7
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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
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WATER 2010QC July 5-7 Optimization Algorithm: DDS STOP Y
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
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Multi-Objective Optimization
Minimize: F(x)=[f1(x),f2(x),…,fN(x)] f1 f2 f1 f2 Non-Conflicting Objectives Conflicting Objectives WATER 2010QC July 5-7
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WATER 2010QC July 5-7 Optimization Algorithm: PA-DDS N Y Y STOP N
Perturb the current ND solution Update the set of ND solutions if necessary 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? N Y Y STOP N Continue? WATER 2010QC July 5-7
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Case Study: Problem Definition
Delisle, 2009 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
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Mean Absolute Error: MAE =
Case Study: Objective Functions Σ |Hi - hi(x)| i = 1 # obs Mean Absolute Error: MAE = # obs Hi : Observed data point hi (x) : Simulated data point x : x1, x2, …, x4700: Vector of decision variables WATER 2010QC July 5-7
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Previous Results: Single Objective Calibration, Flow OR Pressure
Which Solution? WATER 2010QC July 5-7
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WATER 2010QC July 5-7 New Results
Bi-Objective Optimization with PA-DDS can be more Effective than Single-Objective Optimization with DDS WATER 2010QC July 5-7
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Some Data Points are Hard to Match
Discussion of Results Some Data Points are Hard to Match WATER 2010QC July 5-7
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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
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Improve the Optimization Algorithm
Future Work Improve the Optimization Algorithm PA-DDS has Comparable Results with NSGAII and SPEA2 WATER 2010QC July 5-7
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