1. Assessing the Impact of Alternative Pipe Groupings on Multi-Objective Water Distribution Network Masoud Asadzadeh Bryan Tolson

2. Outline  Objectives  Problem Description  Calibration Problem Setup  Optimization Algorithms  Numerical Experiment  Results and Discussion  Main Findings WDSA2012, Adelaide, South Australia, Sept. 24-27 2

3. Objectives Assessing the impact of reducing the number of decision variables on the quality of model calibration results Comparing PA-DDS and ε-NSGAII across a range of computational budgets WDSA2012, Adelaide, South Australia, Sept. 24-27 3

4. Problem Description WDSA2012, Adelaide, South Australia, Sept. 24-27 4 DMA1 DMA2 DMA3 DMA4 DMA5 The problem is simplified from the Battle 2010 and needs the Calibration of:  Roughness Coefficients of 429 pipes (there could be some partially closed pipes in DMA2)  Demand Pattern Multipliers of 5 DMAs

5.  The perfect EPANET2 input file and perfect observed data are taken from Ostfeld et al. (in press).  Pipes and DPMs are grouped: 32 1.Full Calibration Model with 32 decision variables: 27 a)Pipes in each DMA are grouped based on their size + 3 groups of pipes to make the partially closed pipes identifiable  27 Decision Variables 5 b)Each DMA has its own DPM  5 Decision Variables 7 2.Reduced Calibration Model with 7 decision variables: 6 a)Pipes are grouped based on their age 3 groups of pipes to make the partially closed pipes identifiable  6 Decision Variable 1 b)All DMAs has the same DPM  1 Decision Variable WDSA2012, Adelaide, South Australia, Sept. 24-27 5 Calibration Problem Setup

6. Calibration Problem Setup Calibration Problem Setup (cont’d)  EPANET2 toolkit and a MATLAB code are linked to: a)Modify the EPANET2 input file by changing pipe roughness coefficients and demand pattern multipliers based on decision variable values of each solution b)Simulate the modified input file c)Return the desired simulated data points for: 1.Tank levels and Pumping Station flows at the end of Hour1 2.Static Pressure 3.Fire Flow Test (FFT) Pressure 4.FFT flow d)Objective functions are : 1.SSRE Hour1 2.SSRE FFT WDSA2012, Adelaide, South Australia, Sept. 24-27 6

7. Optimization Algorithm: Pareto Archive Dynamically Dimensioned Search Optimization Algorithm: Pareto Archive Dynamically Dimensioned Search (Asadzadeh and Tolson 2009) Perturb current ND solution Update ND solutions Continue? STOP New solution is ND? Pick the New solution Pick a ND solution Initialize starting solutions Y N Create ND-solution set Y N 7

8. Optimization Algorithm: ε-NSGAII Optimization Algorithm: ε-NSGAII (Kollat and Reed 2005) 8 A variant of NSGAII with a modified solution archiving scheme: –Discretize the objective space into grid cells with the size of epsilon (ε) –Archives at most a single solution in each grid cell –Archives a new solution only if it: Dominates a previously archived solutions or Corresponds to a vacant grid cell

9. Numerical Experiment & Results Comparison Apply PA-DDS and ε-NSGAII to both full and reduced calibration problems: 1,00010,000 –With limited (1,000) and large (10,000) computational Budgets 10 –In multiple independent trials (10) Compare the aggregated results of reduced and full models Compare PA-DDS and ε-NSGAII in both limited and large computational budgets WDSA2012, Adelaide, South Australia, Sept. 24-27 9

10. Comparing Final Calibration Results of Full and Reduced Models Comparing Final Calibration Results of Full and Reduced Models (aggregated tradeoffs after 220,000 solution evaluaitons) WDSA2012, Adelaide, South Australia, Sept. 24-27 10

11. Hour 1 Tank Levels (m)Pumping Flow (lps) Data Point T1T2T3T4T5T6T7S1S2S3S4S5 Measured 2.820.723.512.761.565.462.9919233483530 Sim. (Full Model) 2.820.723.512.761.575.452.9919233483530 Sim. (Reduced Model)2.800.733.502.841.575.402.9318833483630 WDSA2012, Adelaide, South Australia, Sept. 24-27 11 Static Pressure (m) DMA1DMA2DMA3DMA4DMA5 Measured65666462247795857075878027 Sim. (Full Model)65666462237795857075878027 Sim. (Reduced Model)65666461237795857075867727 Comparing Final Calibration Results of Full and Reduced Models Comparing Final Calibration Results of Full and Reduced Models (Detailed Evaluation of Selected Solutions)

12. FFT Flow (lps) DMA1DMA2DMA3DMA4DMA5 Measured 24722858505428481234383745 Sim. (Full Model) 24922858505428481234383745 Sim. (Reduced Model) 24122259495328491236383845 WDSA2012, Adelaide, South Australia, Sept. 24-27 12 FFT Pressure (m) DMA1DMA2DMA3DMA4DMA5 Measured5051484912536555396358 22 Sim. (Full Model)5051484912536555396358 22 Sim. (Reduced Model)4951484912526454396158 22 Comparing Final Calibration Results of Full and Reduced Models Comparing Final Calibration Results of Full and Reduced Models (Detailed Evaluation of Selected Solutions cont’d)

13. Comparing Calibration Problem Difficulty WDSA2012, Adelaide, South Australia, Sept. 24-27 13

14. Comparing MO Algorithm Performance WDSA2012, Adelaide, South Australia, Sept. 24-27 14

15. Main Findings Reducing the number of decision variables would: –Make the calibration problem easier to solve –Reduce the quality of calibrated model significantly Both optimization algorithms found high quality results of the full model even with limited budget, but PA-DDS performed slightly better  It is recommended to not reduce the number of decision variables only due to the limited computational budget.  Also, if a stochastic optimization algorithm is used, it is recommended to have multiple optimization trials and aggregate the results. WDSA2012, Adelaide, South Australia, Sept. 24-27 15