THE BATTLE OF THE WATER NETWORKS (BWN-II): PADDS BASED SOLUTION APPROACH Bryan A. Tolson, Ayman Khedr, Masoud Asadzadeh

Multi-Stage Solution Methodology Stage 1: trial and error analyst testing to identify a feasible solution to the problem under nominal conditions (no power failure) –Fix pump configuration, identify candidate decision variables (DVs), set bounds on DVs Stage 2: optimize with MO PADDS algorithm (Asadzadeh & Tolson, 2012) –23 DVs governing various tank and pipe sizes (discrete DVs) as well as pump control thresholds (continuous DVs) Stage 3: polish non-dominated solutions from Stage 2 with more PADDS optimization using 49 new DVs (discrete) to refine the pumping schedule –Turn off pumps if possible during periods when unit electricity cost is maximum –Turn on pumps if helpful during periods when unit electricity cost is maximum Stage 4: for each non-dominated solution from Stage 3, optimize diesel generator configuration required to maintain feasibility in a power outage: –Optimize by implicit enumeration, consider 8 possible generator configurations –Perform final non-dominated sort Stage 5: selecting one of the final non-dominated feasible solutions by minimizing the BWN-II evaluation metric given by contest organizers: 2

Results 3 Cost, $ GHG 10 6 kg CO 2 /yr WA - Stage 0: Estimate original network performance before expansion/demand increase (combined C-Town (2010 WDSA BWCN) and D-Town info. Time: not counted* Stage 1: analyst manual optimize, fix pump sizes –one initial solution, feasible (all pumps backed up) Time: hrs Stage 2: PADDS mixed integer optimization –1 trial of default algorithm configuration –10,000 solutions evaluated by 168-hr EPS in EPANET2 –Found 124 candidate ND solutions PC Time: 48 hrs Stage 3: PADDS to tune pumping schedule –1 trial of default algorithm configuration –10,000 solutions evaluated by 168-hr EPS in EPANET2 –Found 232 candidate ND solutions PC Time: 47 hrs Stage 4: Generator configuration for all ND sols –Evaluate up to hr power outages  up to 8 configs –Found 159 feasible candidate ND solutions PC Time: 10 hrs Stage 5: Select final solution Time: < 1 hr Pumping: 145,000 NA , ,638 (221,687) most improvements here Small cost improvements

Key Points 4 Multi-stage approach important: –easy way to combine analyst knowledge/intuition with opt. algorithm –Broke problem into solvable subproblems (not sizing pumps and tanks simultaneously) Final solution required: –4-5 weeks of analyst* time (coding for EPANET toolkit mainly) –Only 20,000 total solutions evaluated by PADDS MO algorithm –105 hours of serial computing time on an Intel® Core(TM) 2 Quad CPU 2.50GHz and 8 MB RAM desktop PC Results repeatable (re-solved after paper submitted): The 5-stage procedure can be iterated based on alternative initial designs proposed by analyst in Stage 1 Cost, $ GHG 10 6 kg CO 2 /yr WA - Submitted356, Re-solved358,