GENETIC ALGORITHM OPTIMIZATION OF THE FORT COLLINS - LOVELAND WATER DISTRIBUTION SYSTEM
by
Laurie J Murphy, Angus R Simpson, Graeme C Dandy, Jeffrey P Frey, Terry W Farill
Prepared for American Water Works Association Conference on Computers in the Water Industry Chicago, USA April 1996
Citation: Murphy, L. J., Simpson, A. R., Dandy, G. C., Frey, J. P., and Farill, T. W. (1996) "Genetic algorithm optimization of the Fort Collins - Loveland Water distribution system." Proc., Conference in Computers in the Water Industry, AWWA, Chicago, April.
GENETIC ALGORITHM OPTIMIZATION OF THE FORT COLLINSLOVELAND WATER DISTRIBUTION SYSTEM Laurie J. Murphy\ Angus R. Simpson, Graeme C. Dandy PhD Candidate, Senior Lecturer, Associate Professor Department of Civil and Environmental Engineering, University of Adelaide Adelaide, Australia 5005 Jeffery P. Frey, President Frey Water Engineering, Inc. Arlington Heights, Illinois Terry W. Farrill Systems Engineer Fort Collins-Loveland Water District Fort Collins, Colorado INTRODUCTION Optimization techniques applied to water distribution networks have been the topic of much research over the last 25 years. These include linear programming, non-linear programming, dynamic programming and partial enumeration guided by heuristic search. Unfortunately few of these techniques have found their way into everyday practice by consultants and water utilities. The development of genetic algorithm (GA) optimization applied to water distribution networks at the University of Adelaide over the last five years offers a method for practical use to optimize water distribution network designs. Previously genetic algorithm optimization has been shown to be a successful way of significantly reducing costs of water distribution systems[I].[5]. Previous applications of genetic algorithm optimization have been for relatively small networks. In this paper application of genetic algorithm optimization is considered for a large 326 pipe network with five pressure zones, 10 water sources/tanks, 3 pumping stations and 14 pressure reducing valves. The network is located in Fort CollinsLoveland, Colorado. GENETIC ALGORITHM OPTIMIZATION Genetic algorithm (GA) optimization is a powerful popUlation oriented search technique or optimization algorithm based upon mechanisms of natural selection and genetics. When genetic algorithm optimization is applied to design of water distribution systems it can identify low cost combinations of pipe sizes, pipe materials, pumps, pump operation schedules, tank operating levels and pressure valve settings . . Each decision variable is coded as part of a binary string (there are also other possible coding methods) with an associated lookup or choice table with corresponding costs and hydraulic characteristics[3]. An example is shown in Table 1. A population, of say 100 strings, that represent 100 different possible design alternatives are randomly generated. The cost of each design option·in the popUlation is determined. In addition, each design is analysed by a computer hydraulic simulation program to assess if any of the design constraints are not satisfied. If for example, actual pressures are less than minimum allowable pressures then a penalty cost is added to the estimated cost of the design. Successive populations are generated using genetic operators· such as selection, crossover and mutation[3],[5]. "Survival of the fittest" relentlessly drives the GA to improved solutions. FORT COLLINS-LOVELAND WATER DISTRICT NETWORK The Fort Collins-Loveland Water District (FCLWD) supplies water for municipal use to an area of about 60 square miles between Fort Collins and Loveland in northern Colorado. The population is expanding and the water supply system will require
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expansion to meet the increasing demand. An assessment of the expansion needs for the year 2015 in terms of a Master Plan was carried out in 1993 by a local consultant. The Master Plan proposed system expansions in three construction phases over a fifteen year time horizon. Recommendations were made for (1) future sources of supply, (2) new storage sites, (3) pump station upgrades and new pumps, (4) locations and settings for pressure reducing valves, and (5) new pipes and duplication of existing pipes. A DESIGN BY TRADITIONAL SIMULATION METHODS In the development of the 1993 Master Plan for the FCLWD 2015 system expansion a hydraulic simulation computer model called EPANET was used. EPANET has gained widespread use over the past few years. Hydraulic computer simulation of water distribution networks is now at a mature stage of development with a number of computer models available commercially, e.g. Stoner SWS, Cybemet, KYPIPE2, Watermax and WaterWorks. The computer model for FCLWD included 326 pipes, 263 nodes, 10 water sources, 3 pump stations and 14 pressure reducing valves dividing the system into five major pressure zones. The design was required to supply peak hour demands, while maintaining at least 40 psi but less than 100 psi at all nodes. The consultant's recommended design based on traditional hydraulic simulation modeling sized 13 new pipes and suggested 33 new pipes parallel to existing pipes in the system totaling 29.4 miles in length as shown in Fig. I. The estimated installed cost of pipes was $5.85 million. Extended period simulation (EPS) was not considered in the initial 1993 design. Future studies should consider EPS analysis to ensure tanks refill following a peak day. OPTIMIZATION OF THE DESIGN BY GENETIC ALGORITHMS The data required for the genetic algorithm optimization is very similar to the data required for simulation using a hydraulic computer model such as EPANET. The data includes: node connectivity, node elevations and peak hour demands, existing pipe lengths, diameters and roughness coefficients, reservoir and tank data, connections to other pipe sources, pump system curves and operation schedules; and PRY locations and settings. Data is also required for possible choices of components for the expansion (e.g. pipes, pumps, pressure reducing valves), the associated costs and hydraulic characteristics. The genetic algorithm analysis was used to optimize the following design variables for the FCLWD expansion for 2015: • diameters of new pipes • diameters of pipes to be placed in parallel to existing pipes (no pipe is also an option) • optimal pressure settings for pressure reducing valves. The same basic layout and configuration for other components in the system were maintained for the GA design as were assumed for the 1993 Master Plan design. For the FCLWD network expansion 10 pipe size choices were considered for new pipes in the range of 6" to 30" and 13 pipe sizes for pipes parallel to existing pipes in the range 0" to 30". Thus the genetic algorithm solution was constrained to include at least a minimum size 6" pipe at new pipe locations but was permitted to eliminate duplicate pipes if possible. Exactly the same design criteria were used for the genetic algorithm design analysis as for the 1993 Master Plan development. The GA design was verified by an independent check using EPANET. All design criteria for the low cost GA design were satisfied and in particular all actual pressures exceeded the minimum allowable pressures for all supply nodes in the network. The 20 lowest cost solutions found during the genetic algorithm run are stored. Usually between 200,000 and 500,000 networks are considered during the GA run with a run time of typically 10 hours on a Sparc 20 workstation. A detailed description of the FCLWD network and optimization process is given in Simpson et al. (1995).
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RESULTS The genetic algorithm design came up with a solution with pipe sizes for the 13 new pipes as shown in Fig. 2. These are significantly different from the Master Plan design based on traditional design methods. Nine existing pipes were identified as requiring pipes in parallel and this compared to 33 pipes in the Master Plan design. The genetic algorithm also optimized the settings of the 14 PRVs to the nearest 5 psi. The total length of new pipes in the GA design is 18.8 miles at an estimated installed cost of $2.97 million. CONCLUSION A case study for the application of genetic algorithm optimization to the Fort Collins Loveland Water District pipe network expansion plan for 2015 has led to significant cost savings. The original design carried out by consultants with computer hydraulic simulation software using traditional trial and error improvement design techniques based on engineering judgement resulted in a design costing $5.85 million. The genetic algorithm optimization technique design reduced the network expansion cost to $2.97 million, a saving of 49%. Genetic algorithm optimization has a number of advantages including (1) significantly lower cost solutions (2) it identifies a range of alternative solutions of similar low cost from which the designer can choose (3) discrete options such as commercially available pipe diameters and pumps are considered in the optimization and (4) the computer hydraulic simulation model methodology is fully utilised by the genetic algorithm. REFERENCES [1] Murphy, L.J., Simpson, AR. and Dandy, G.c. (1993). "Design of a water
[2] [3] [4]
[5] [6]
distribution network using genetic algorithms," Water, Australian Water and Waste Water Association, August, 40-42. Murphy, L.J., Dandy, G.c. and Simpson, AR. (1994). "Optimum design and operation of pumped water distribution systems." Proc., Conf on Hydraulics in Civil Engineering, Brisbane, Australia, February, 149-155. Simpson, AR., Dandy, G.C. and Murphy, L.J. (1994). "Genetic algorithms compared to other techniques for pipe optimization," Journal of Water Resources Planning and Management, ASCE, 120 (4), July/August, 423-443. Simpson, AR., Dandy, G.c., Murphy, L.J. and Kitto, R. (1995). "Urban water distribution network optimisation - a case study," Proceedings, 16th Federal Convention, Australian Water and Wastewater Association, Sydney, April, Volume 2,167-174. Dandy, G.C., Simpson, AR. and Murphy, LJ. (1996). "An improved genetic algorithm for pipe network optimization." Accepted for publication in Water Resources Research - to appear early in 1996 Simpson, A.R., Dandy, G.C., Murphy, L.J. and Frey, J.P. (1995). Genetic algorithm optimization study of the year 2015 water distribution system expansion planfor Fort Collins-Loveland water district, Department of Civil and Environmental Engineering, The University of Adelaide, Feb., 102pp. Table 1. A genetic algorithm representation decoding lookup table
Binary coding
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