Masoud Asadzadeh

Bryan A. Tolson

University of Waterloo

Multi-Objective Calibration of a Multi-Objective Calibration of a Real Water Distribution NetworkReal Water Distribution Network

Genevieve Pelletier

François-Julien Delisle

Manuel J. Rodriguez

Laval University

• Problem Definition (Single- vs. Multi-Objective Optimization)Problem Definition (Single- vs. Multi-Objective Optimization)

OutlineOutlineOutlineOutline

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• Optimization AlgorithmOptimization Algorithm

• Case Study (WDN Calibration)Case Study (WDN Calibration)

• Discussion of ResultsDiscussion of Results

• Future WorkFuture Work

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Single-Objective OptimizationSingle-Objective OptimizationSingle-Objective OptimizationSingle-Objective Optimization

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• Minimize: f (x)

We are looking for a single best value of the objective function f(x) and the corresponding solution

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Optimization Algorithm: DDSOptimization Algorithm: DDSOptimization Algorithm: DDSOptimization Algorithm: DDS

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Perturb the current best solution

Initialize starting solution

Continue?STO

P

– Globally search at the startstart of the search by perturbing allall decision variables (DV) from their current best values

– Perturb each DV from a normal probability normal probability distribution centered on the current value of DV

– Locally search at the endend of the search by perturbing typically only oneonly one DV from its current best value

NN

YY

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Multi-Objective OptimizationMulti-Objective OptimizationMulti-Objective OptimizationMulti-Objective Optimization

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• Minimize: F(x)=[f1(x),f2(x),…,fN(x)]

f1

f2

f1

f2

Non-Conflicting Objectives

Non-Conflicting Objectives Conflicting ObjectivesConflicting Objectives

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Optimization Algorithm: PA-DDSOptimization Algorithm: PA-DDSOptimization Algorithm: PA-DDSOptimization Algorithm: PA-DDS

Perturb the current ND solution

Update the set of ND solutions if

necessary

Continue?STOP

New solution is ND?

Pick the New solution

Pick a ND solution based on

crowding distance

Initialize starting

solutions

YYNN

Create the non-dominated (ND)

solutions set

YYNN

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Case Study: Problem DefinitionCase Study: Problem DefinitionCase Study: Problem DefinitionCase Study: Problem Definition

Delisle, 2009Delisle, 2009 Determine proper pipe diameterDetermine proper pipe diameter

Adequately simulate observationsAdequately simulate observations

Have better understanding of the systemHave better understanding of the system

230,000 People230,000 People

Modeled in EPANET2 (Université Laval)Modeled in EPANET2 (Université Laval)

4700 pipes, 3691 Nodes, 379 Km, 34.2 Km4700 pipes, 3691 Nodes, 379 Km, 34.2 Km22

15 Flow Rate Measurements15 Flow Rate Measurements

19 Pressure Measurements19 Pressure Measurements

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Case Study: Objective FunctionsCase Study: Objective FunctionsCase Study: Objective FunctionsCase Study: Objective Functions

Mean Absolute Error: MAE =

Σ |Hi - hi(xx)|i = 1

# obs

# obs

Hi : Observed data point

hi (xx) : Simulated data point

xx : x1, x2, …, x4700: Vector of decision variables

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Previous Results: Single Objective Previous Results: Single Objective Calibration, Flow OR PressureCalibration, Flow OR Pressure

Previous Results: Single Objective Previous Results: Single Objective Calibration, Flow OR PressureCalibration, Flow OR Pressure

Which Solution?

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New ResultsNew ResultsNew ResultsNew Results

Bi-Objective Optimization with PA-DDS can be more Effective than Single-Objective Bi-Objective Optimization with PA-DDS can be more Effective than Single-Objective Optimization with DDSOptimization with DDS

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Discussion of ResultsDiscussion of ResultsDiscussion of ResultsDiscussion of Results

Some Data Points are Hard to MatchSome Data Points are Hard to Match

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Future Work and DiscussionFuture Work and DiscussionImprove the Case StudyImprove the Case Study

Future Work and DiscussionFuture Work and DiscussionImprove the Case StudyImprove the Case Study

• Decrease the problem size by decision variable groupingDecrease the problem size by decision variable grouping

4700 Decision Variables to Fit 34 Data Points4700 Decision Variables to Fit 34 Data Points

Why some data points are hard to match?Why some data points are hard to match?

• Check the data qualityCheck the data quality

• Collect more measurementsCollect more measurements

• Check the model in the vicinity of the data pointCheck the model in the vicinity of the data point

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Future WorkFuture WorkImprove the Optimization AlgorithmImprove the Optimization Algorithm

Future WorkFuture WorkImprove the Optimization AlgorithmImprove the Optimization Algorithm

PA-DDS has Comparable Results with NSGAII and SPEA2PA-DDS has Comparable Results with NSGAII and SPEA2

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