A New Algorithm for Water Distribution System Optimization: Discrete Dynamically Dimensioned Search (DDDS). EWRI 2008 May 12, 2008. Dr. Bryan Tolson 1 Masoud A. Esfahani 1 Dr. Holger Maier 2 Aaron Zecchin 2 Department of Civil & Environmental Engineering University of Waterloo, Canada
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EWRI 2008
May 12, 2008
Dr. Bryan Tolson1
Masoud A. Esfahani1
Dr. Holger Maier2
Aaron Zecchin2
Department of Civil & Environmental Engineering University of Waterloo, Canada
School of Civil, Environmental and Mining Engineering, University of Adelaide
0.User inputs:
- maximum function evaluations
- decision variable ranges
- perturbation size parameter (0.2*)
Discrete probability distribution of candidate solution option numbers for a single decision variable with 16 possible values and a current best solution of xbest=8. Default DDDS-v1 r-parameter of 0.2*
Start of SearchEnd of Search
Best Current Solution (red)
Pipe 1
Pipe 2
Pipe 3
Pipe 4
Example Candidate Solutions
Pipe 1
Pipe 2
Pipe 3
Pipe 4
Pipe 1
Pipe 2
Pipe 3
Pipe 4
Start of SearchEnd of Search
Best Current Solution (red)
Example Candidate Solutions
Given pipe layout, its connectivity & nodal demands choose pipe diameters (the decision variables) that:
Minimize Total Pipe Costs
Subject to:
Note that the hydraulic solver (e.g. EPANET2) determines a flow regime that automatically satisfies hydraulic constraints (conservation of mass, energy)
evaluated with all pipes at max diameter
min required pressureactual pressure for solution
second modification:
2.At end of the search, avoid wasting excessive function evaluations on candidate solutions with only one pipe perturbed from best solution
No algorithm parameter tuning in steps above
NFS
Specify maximum # of model evaluations, M
Empirical CDF of best obj. func. values
60,000 function evaluations not long enough for C2
(different result for NYTP)
2P change heuristic very effective polisher at end* of search
best of 6 algorithms in Zecchin et al. 2007
Algorithm response to smaller user-specified computational budget
all studies use EPANET2
normally distributed perturbations with adequate variance ensures global search
Pipe 1
Pipe 2
Pipe 3
Pipe 4