GENETIC ALGORITHM OPTIMIZATION: ITS ...

GENETIC ALGORITHM OPTIMIZATION: ITS APPLICATION TO DESIGN AND OPERATION OF WATER DISTRIBUTION SYSTEMS

by

Jeffery P Frey Angus R Simpson Graeme C Dandy Laurie J Murphy

Presented at 1996 Computer Conference American Water Works Association April 21-24, 1996 Chicago Illinois

Citation: Frey, J.P., Simpson, A.R., Dandy, G.C. and Murphy, LJ. (1996). "Genetic algorithm optimization: its application to design and operation of water distribution systems." Proc., 1996 Computer Conference, American Water Works Association, Chicago, Illinois, April, 187-191. (ISBN 0-89867-854-4)

GENETIC ALGORITHM OPTIMIZATION: ITS APPLICATION TO DESIGN AND OPERATION OF WATER DISTRIBUTION SYSTEMS Jeffery P. Frey, President Frey Water Engineering, Inc. Arlington Heights, lllinois

Angus R. Simpson, Graeme C. Dandy, Laurie J. Murphy Senior Lecturer, Associate Professor, PhD Candidate Department of Civil and Environmental Engineering, University of Adelaide Adelaide, Australia

Genetic algorithm pipe network optimization is a new analysis technique for distribution system design and operation. Developed by researchers at the University of Adelaide in Australia over the past five years, the genetic algorithm (GA) optimization technique has recently been applied to a number of real-world distribution system expansion planning and system rehabilitation projects on a consulting services basis. The results of these studies have demonstrated the cost-saving potential of the GA technique. In each case, the GA-optimized design solutions had projected capital and life cycle costs 6% to 49% lower than the original design solutions prepared using computer simulation programs alone. Projected cost savings identified using GA optimization ranged from $113,000 to $2,880,000 for the five recent design review studies described in this paper. Development and Acceptance of Genetic Algorithm Optimization GA optimization is a directed search technique which usually gets classified in the field of artificial intelligence. Back in the 1970s, John Holland at the University of Michigan came up with the idea to use computer-based artificial evolution to search for solutions to complex problems. (1) The computer starts with an initial population of solutions which are then manipulated and combined repeatedly over many generations in order to evolve improved solutions. Using genetic operators which mimic the natural processes of reproduction and mutation, successive generations of solutions inherit more and more desirable characteristics, such as low cost or high reliability. Holland's groundbreaking work opened up an entire new field of optimization research in genetic algorithms. Today, after nearly 20 years of research in universities throughout the world, genetic algorithms have become an established design technique in various industries. Successful engineering applications of GA optimization are numerous:(2) • • • •

John Deere is using GA optimization to optimize production scheduling Texas Instruments uses GA to design circuits to minimize computer chip sizes General Electric has used GA optimization for gas turbine design to increase fuel efficiency, which led to the development of the Boeing 777 engine US West uses GA to design fiber-optic cable networks, which has cut design times from 2 months to 2 days, and saved them $1 million to $10 million on each network.

GA Optimization Applied to the NYC Water Supply Tunnels System The New York City water supply tunnels problem provides a straightforward illustration of how GA optimization is used to identify low cost solutions for distribution system expansion planning. Figure 1 shows the basic NYC system layout as it existed in the

1960s. The problem is to expand system capacity to meet a given set of future demands by adding one or more parallel pipes to the existing network of21 tunnels and pipes. Given a range of allowable new pipe diameters (from 36 to 204 inches) and corresponding installed pipe cost per foot, the GA optimization generates a large number of possible combinations of parallel pipes to augment the existing system capacity. Each set of parallel pipes in this initial population of solutions is evaluated to test its hydraulic performance and its cost. Solutions exhibiting good hydraulic performance and relatively low cost are deemed fit solutions and are assigned a high probability of passing through to the next generation. Solutions having poor hydraulic performance and/or high cost are deemed to be unfit and given a lower probability of survival. Parent solutions for the next generation are then selected based on hydraulic and cost performance. Reproduction is carried out by pairing up the selected solutions, splitting each into parts, and recombining them to form a generation of offspring solutions. Next, the offspring solutions undergo a mutation step where the values of a small percentage of individual bits (i.e., pipe diameters in this case) are randomly changed. Once again the solutions are evaluated to check hydraulic performance and cost. The best solutions are identified and carried forward to the next generation. These steps are repeated over and over to breed superior combinations of new parallel pipes in a process akin to natural selection where only the fittest solutions survive. The remarkable thing about the GA optimization technique is the efficiency of its search process. Figure 2 shows the progress of the GA search in narrowing in on the lowest cost hydraulically viable solutions for the NYC tunnels expansion problem. The genetic operators are able to rapidly drive the solution cost down below $40 million in fewer than 100,000 solution evaluations. Considering that the total number of pipe combinations for this problem is 1.9x1025 (i.e., 1621 for 16 allowable pipe diameters at any of 21 pipe locations), it is incredible that the GA search is able to identify near-optimal solutions after evaluating so few potential solutions.

In optimizing the NYC tunnels expansion problem, the GA optimization technique identified five feasible design alternatives with pipe costs ranging from $38.8 to $39.9 million.(2) Figure 3 presents solution GA-1 ($38.8 million) indicating diameters in inches for the six parallel pipes chosen to increase system capacity. Figure 4 presents an interesting alternative optimized solution, GA-8. This solution calls for only five parallel pipes at a cost of $33.6 million, but happens to be marginally infeasible. Pressures at three of the nodes are slightly out of allowable range. The computed hydraulic heads at nodes 16, 17 and 19 are 258.99 ft, 271.79 ft and 254.07 ft, which are no more than 1.01 ft less than the specified allowable values of 260.0 ft, 272.8 ft and 255.0 ft, respectively. Decision-makers could thus make an informed choice and relax the minimum head criteria just slightly in order to accept solution GA-8 and save an additional $5 million in pipe costs. It may be noted that from 1969 to 1990, various researchers have used the NYC tunnels problem to test their optimization techniques. Costs for the recommended feasible solutions have ranged from $78.1 to $39.2 million. This means the GA optimization solutions described above have lower costs than any previous solution presented for this problem.

Results of Five GA Pipe Network Optimization Review Studies The capability of the GA optimization technique to identify improved distribution system planning and design solutions is demonstrated by the results of several recent GA review

studies. For each of the five GA reviews described, an original design solution had been prepared by experienced network designers using current hydraulic simulation programs, namely WATSYS and EPANET. The results of the GA review studies are summarized in Table 1; brief descriptions of the studies follow. The Seaford Rise GA studies analyzed expansion plans for two separate pressure zones in a suburban development near Adelaide, South Australia. The original network designs were prepared by the Engineering and Water Supply Department of South Australia (E&WS, now called SA Water Corporation) in 1992-93. The E&WS El. 126 Zone design called for 13 new pipes to connect to 14 existing mains.l4 ) The design was based on a peak hour loading condition with a minimum pressure head of 20.0 m required at all demand nodes. Using the same layout, the GA optimization re-sized the 13 new pipes by evaluating tens of thousands of alternatives choosing among eight pipe sizes from 150 to 600 mm. The GA reduced seven of the 13 proposed new pipes by one pipe size from the original design solution resulting in a projected 12.0% savings in pipe costs. The Seaford Rise El. 80 Zone design by E&WS was prepared using the same design criteria and range of pipe sizes as the El. 126 Zone design. [5) The planned expansion solution called for 27 new pipes to connect to the 78 existing pipes already serving the zone. In the GA analysis, new pipe locations and the addition of pipes parallel to existing pipes were evaluated. Several alternative optimized solutions were identified as the analysis investigated the effects of relaxing the pressure criteria at one node and reducing the minimum allowable pipe diameter by one size. The projected cost savings for the GAoptimized design directly comparable to the original E&WS design was 6.0%. A local consulting firm prepared the original Fort Collins-Loveland Water District Master Plan update in 1993. The Plan recommended future water sources, storage sites, pumping stations, pressure reducing valves (PRVs), and new and parallel pipes to meet the projected year 2015 demands.l6) The system model included 326 pipes, 263 nodes, 10 water sources, 3 pump stations and 14 PRVs which divided the system into five major pressure ZOnes. The recommended year 2015 expansion plan called for 13 new pipes and 33 parallel pipes totaling 29.4 miles in length. The GA optimization analysis identified an improved solution which re-sized the 13 new pipes, reduced the number of parallel pipes from 33 to 9, and cut the total length of pipe to 18.8 miles. The GA also optimized PRY settings to improve hydraulic performance throughout the system. The optimized expansion plan resulted in projected pipe cost savings of nearly $3 million or 49%. The last two network designs reviewed using GA optimization were for low-pressure pipe irrigation rehabilitation projects.!') In each case, the GA identified improved pipe diameters for the given layouts to substantially cut costs. Parts of the optimized Loveday system are now constructed. For the Corbie Hill study, the GA also optimized the tank height by incorporating pumping energy costs into the optimization search. Conclusion GA pipe network optimization has proven successful in identifying a choice of superior low cost solutions for both simple and complex distribution system planning, design and operations problems. The GA technique incorporates cost data with the data from a computer hydraulic simulation model to direct an automated search of tens or hundreds of thousands of potential solutions. The efficient GA search finds the best combinations of pipe, tank, pump and valve locations, sizes and settings, as well as optimizing water source selections and pumping operations to minimize capital and/or life cycle costs.

References [1] Holland. J.H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor. [2] Begley, Sharon (1995). "Software au Naturel." Newsweek, May 8, 70-71. [3] Dandy, G.C., Simpson, AR and Murphy, L.J. (1996). "An Improved Genetic Algorithm for Pipe Network Optimization." Accepted by Water Resources Research. [4] Murphy, L.J., Simpson, AR and Dandy, G.C. (1993). "Design of a Pipe Network using Genetic Algorithms." Water, August, 40-42. [5] Simpson, A.R., Dandy, G.C., Murphy, L.J. and Kitto, R. (1995). "Urban Water Distribution Network Optimization-A Case Study." Proceedings, 16th Federal Convention, Australian Water and Wastewater Association, Sydney, Australia, April, Volume 2,167-174. [6) Simpson, AR, Dandy, G.C., Murphy, L.J. and Frey, J.P. (1995). "Genetic Algorithm Optimization Study of the Year 2015 Water Distribution System Expansion Plan for Fort Collins-Loveland Water District." Department of Civil and Environmental Engineering, University of Adelaide, February, 102 pp. [7) Frey, J.P., Simpson, AR, Dandy, G.C., and Murphy, L.J. (1995). "A Breakthrough in Irrigation Design from Down Under: GA Pressure Pipe System Optimization." Us. Committee on Irrigation and Drainage Newsletter, April-October, 11-13.

Table 1. Projected Cost Savings for Five GA Optimization Design Reviews

Real-World Network Design Reviewed by GA

$ Savings usingGA Technique

Seaford Rise Development, EL126 Zone Adelaide, South Australia

27

$932,000*

$819,000

12.0%

$113,000

Seaford Rise Development EL 80 Zone .Adelaide, South Australia

105

$1,944,000

$1,828,000

6.0%

$116,000

Fort Collins-Loveland Water District, Colorado

326

$5,851,000

$2,966,000

49.2%

$2,885,000

Loveday/Cobdogla Irrigation Network South Australia

56

$3,067,000

$2,729,000+

11.0%

$338,000

Corbie Hills Irrigation Network, Leeton, New South Wales

84

$2,093,000** $1,763,000**

15.8%

$330,000

* +

Original GA-Optimiz. % Savings No.of Pipes Solution Cost Solution Cost usingGA Technique

**

Solution costs and savings for the Australia networks are shown in equivalent U.S. dollars. Project construction based on GA-optimized irrigation design began in April 1995. Includes present value of estimated pumping costs.

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GA Optimization Search Progress for NYC Tunnels Problem

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18 Queens

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150,000

200,000

Num ber of Solution Evaluations

Figure 2. An Efficient GA Solution Search

Figure 1. Layout of NYC Tunnels

Manhattan

18

18

Queens

Queens

Figure 3. Solution GA-l at $38.8 million

Figure 4. Solution GA-8 at $33.6 million