optimal design and expansion of water distribution systems using ...
OPTIMAL DESIGN AND EXPANSION OF WATER DISTRIBUTION SYSTEMS USING GENETIC ALGORITHM
by A. Murat KAHRAMAN
September, 2003 İZMİR
ABSTRACT
In last decades, rapid increase in world population, urbanization and depletion of fresh water resources indicates that the optimization of water distribution networks is an essential element of water resources protection. Although up to now numerous computer aided tools on hydraulic design of water distribution networks and optimization methods have been developed. These methods could not be used widely due to some difficulties in the application of these methods/tools in real-size water distribution networks. Optimization of water distribution systems using genetic algorithms gains acceptance all over the world recent years. Genetic algorithms are powerful population oriented search algorithm based upon Darwin’s theory “Survival of the fittest”. The genetic algorithm selects, combines and manipulates possible solutions in a search for the lower cost network. Many tests of the application of the genetic algorithm optimization process to real-life network designs have shown that the GA is effective at finding low cost solutions. The technique has consistently found lower cost solution than the trial-and-error simulation approach typically used by design engineers. This study describes development of a computer program, called SuGA, which uses Genetic Algorithm for the least-cost design and expansion of water distribution system. Program was tested with several problems from the literature, comparing solutions was fairly near for small-scale water distribution systems. SuGA is a windows program under construction of Microsoft Visual Basic that optimizes water distribution systems using genetic algorithm. It uses Epanet2 (Distributed by The U.S. EPA) for hydraulic calculations, and OptiGA (Optiwater) ActiveX control for Genetic Algorithm optimization. SuGA can be used for new design, expansion or rehabilitation of existing water distribution systems for optimization. Keywords: Water, distribution, systems, least cost, design, optimization, genetic algorithms, pipes, nodes, networks
ÖZET Dünyada hızla nüfusun artmasına karşılık temiz su kaynaklarının giderek azalması göz önünde bulundurulursa su dağıtım şebekelerinin optimizasyonunun öneminin arttığı açıktır. Araştırmacılar önce şebeke hidroliğini çözmek için bilgisayar programları oluşturmuşlar, daha sonra su dağıtım şebekelerinin optimizasyonu konusunda çeşitli optimizasyon yöntemleri ve bunları kullanan programlar hazırlamışlardır. Ancak bunların bir çoğu gerçek şebeke sistemlerine uygulanması çok zor olan teknikler olması sebebiyle piyasalarda yaygın kullanım alanı bulamamıştır. Son yıllarda ise yeni bir yaklaşım sayabileceğimiz Genetik Algoritmaların (GAs) şebeke optimizasyonunda kullanımı giderek artmaktadır. Genetik algoritmalar, çözüm uzayının büyük olduğu her türlü karmaşık problemde iyi sonuçlar vermektedir. Günümüzde genetik algoritmalar su dağıtım sistemlerinin dizaynı, genişletilmesi, rehabilitasyonu, su sızıntılarını minimize etmek için kontrol vanalarının yerleşimi, karmaşık sistemler için pompa çalışma zamanlarının düzenlenmesi, hazne işletilmesi, numune alma ve klorlama istasyonlarının yerleşimi, farklı kaynaklardan alınan suların kalitesinin optimize edilmesi gibi çok geniş bir alanda yaygın olarak kullanılmaktadır. Avustralya, Kanada ve Amerika’ nın çeşitli eyaletlerinde su dağıtım şebekelerinin genetik algoritma ile dizaynı, rehabilitasyonu, genişletilmesi, işletilmesi gibi çalışmalarda %15 ile %50 arası tasarruf sağlanmıştır (Simpson, 2000). Genetik Algoritmaların yapısı oldukça basittir, Darvin’in “en iyiler hayatta kalır” prensibine göre işlerler. Basit bir Genetik Algoritmada en iyiyi belirleyen bir uygunluk fonksiyonu, seçme, çaprazlama ve mutasyon operatörleri bulunur. Genetik Algoritmalar belirli bir populasyon topluluğu ile başlarlar (populasyonlar genelde ilk defa rasgele oluşturulur), bir sonraki jenerasyon topluluktaki en iyi bireyler, seçme havuzunda birbirleriyle çaprazlanmak için çeşitli seçme yöntemlerinden (rulet, turnuva gibi) biriyle seçilirler, daha sonra en iyi bireyler birbirleriyle eşleştirilerek daha iyi bireyler oluşması sağlanır ve kuşaklar boyu sürekli en iyiye doğru gidilir. Genetik Algoritmalar çözümün nerede sonuçlanacağını bilmezler, yakınsamanın sağlandığı an çözüm olarak kabul edilir. Dolayısıyla genetik algoritmalar en iyi
çözümü vereceğini garanti etmezler, ancak optimum bir sonuç sağlarlar. Çözüm uzayının trilyonlar olduğu bir kümede en iyi sonucu bulabilmek ayrı bir meseledir! Bu çalışmaların ışığında, su dağıtım şebekelerinin dizaynı ve genişletilmesinde kullanılabilecek, genetik algoritma ile optimizasyon yapan SuGA adlı Visual BASIC ortamlı bir bilgisayar programı hazırlanmıştır. Hazırlanan program, dağıtım şebekesinin hidrolik hesapları için EPA’nın su dağıtım şebekesi programı EPANET2’yi, genetik algoritma için de Optiwater firmasının OptiGA adlı ActiveX denetimini kullanmaktadır. Hazırlanan program ile her bir boru için dizaynda kullanılabilecek boru çapları ve fiyatlarını kullanarak, her düğüm noktası için ayrı ayrı verilebilen minimum ve maksimum basınç ve her boru için ayrı ayrı verilebilen minimum ve maksimum hız sınırları arasında optimize edilmiş bir şebeke sunabilmektedir. Optimizasyonda hız ve basınç sınırlarının verilen tolerans sınırlarında aşılmasında verilen bir ceza puanı ile şebeke toplam maliyeti artırılmakta, böylece hidrolik açıdan uygun bir şebeke çözümüne ulaşılabilmektedir. Literatürde yer alan birçok şebeke sistemi hazırlanan program ile hesaplanarak test edilmiş ve literatürde yer alan çeşitli genetik algoritma ile çözüm yapan programın sonuçlarına yakın sonuçlar elde edilmiştir. Genetik algoritma ile yapılan optimizasyonlarda çözüm uzayı çok geniş olduğundan birbirine çok yakın çeşitli çözümlere ulaşılabilmektedir. Bu nedenle programın tamamen aynı verilerle yeniden çalıştırılmasıyla yeni bir çözüme daha ulaşılabilmektedir. Bu nedenle de en iyiye karar verebilmek oldukça güçtür. Ancak bulunan bir çok çözümde mühendisçe iyi bir yaklaşım olabilmektedir. Hazırlanan program su dağıtım şebekelerinin dizaynında, mevcut bir şebekenin genişletilmesinde ve hatta rehabilitasyonunda bir mühendis denetiminde optimizasyon amaçlı kullanılabilir. Anahtar Kelimeler: Su, dağıtım, sistemleri, en düşük maliyet, dizayn, optimizasyon, genetik algoritmalar, borular, düğüm noktaları, ağ şebeke.
1. Introduction As a vital part of water supply systems, water distribution networks represent one of the largest infrastructure assets of industrial society. The Water Infrastructure Network (WIN) report Clean and Safe Water for the 21st Century (April 2000) warns of huge funding shortfalls for replacement of drinking water infrastructure and needed improvements to meet federal water regulations. The required capital investment for drinking water systems alone is estimated to be $24 billion per year for the next 20 years—this amount dwarfs the $13 billion per year that water systems currently invest for infrastructure capital needs (The optimatics letter, 2001)
Figure 1.1. Percent of Infrastructure Funding Needs by Area Source: EPA’s 1997 Drinking Water Infrastructure Needs Survey Optimization Could Save $2B per Year. Genetic algorithm (GA) optimization, for example, can be applied to develop superior, low-cost solutions for capital improvement plans (CIPs), main replacement plans, and more. Cost savings of 20% or higher are not uncommon for both small and large distribution systems. (To apply the optimization does require a hydraulic model of the system.) Optimization analysis can help utilities reduce transmission, distribution and storage improvement costs, which amount to more than 60% of total infrastructure costs (see Figure 1.1). Assuming that cost savings of 25% can be achieved on just over half of all projects, the potential savings comes to $2 billion per year for the USA.
2. What is Genetic Algorithm Genetic algorithms (GAs) are optimization techniques based on the concepts of natural selection and genetics. Genetic algorithms are inspired by Darwin's theory of evolution. In this approach, the variables are represented as genes on a chromosome. Solution to a problem solved by genetic algorithms uses an evolutionary process (it is evolved). GAs features a group of candidate solutions (population) on the response surface. Through natural selection and the genetic operators, mutation and recombination, chromosomes with better fitness are found. Natural selection guarantees that chromosomes with the best fitness will propagate in future populations. Using the recombination operator, the GA combines genes from two parent chromosomes to form two new chromosomes (children) that have a high probability of having better fitness than their parents. Mutation allows new areas of the response surface to be explored. This is repeated until some condition (for example number of populations or improvement of the best solution) is satisfied. 2.1. Simple Genetic Algorithm The mechanics of a simple genetic algorithm are surprisingly simple, involving nothing more complex than copying strings and swapping partial strings (Goldberg, 1989). Basic components of simple genetic algorithm are as follows (Obitko, 1998). 2.1.1. Encoding a chromosome A chromosome should in some way contain information about solution that it represents. The most used way of encoding is a binary string. A chromosome then could look like this : Table 2.1. Encoding a chromosome Chromosome 1 1101100100110110 Chromosome 2 1101111000011110 Each chromosome is represented by a binary string. Each bit in the string can represent some characteristics of the solution. Another possibility is that the whole string can represent a number.
Of course, there are many other ways of encoding. The encoding depends mainly on the solved problem. For example, one can encode directly integer or real numbers; sometimes it is useful to encode some permutations and so on. 2.1.2. Reproduction During reproduction, recombination (or crossover) first occurs. Genes from parents combine to form a whole new chromosome. The newly created offspring can then be mutated. Mutation means that the elements of DNA are a bit changed. These changes are mainly caused by errors in copying genes from parents. The fitness of an organism is measured by success of the organism in its life (survival). 2.1.3. Selection Parents are selected according to their fitness. The better the chromosomes are, the more chances to be selected they have. Imagine a roulette wheel where all the chromosomes in the population are placed. The size of the section in the roulette wheel is proportional to the value of the fitness function of every chromosome - the bigger the value is, the larger the section is. See the following picture for an example.
Figure 2.1. Roulette Wheel Selections A marble is thrown in the roulette wheel and the chromosome where it stops is selected. Clearly, the chromosomes with bigger fitness value will be selected more times.
This process can be described by the following algorithm. 1. [Sum] Calculate the sum of all chromosome fitness’s in population - sum S. 2. [Select] Generate random number from the interval (0, S) - r. 3. [Loop] Go through the population and sum the fitness’s from 0 - sum s. When the sum s is greater then r, stop and return the chromosome where you are. Of course, the step 1 is performed only once for each population. 2.1.4. Crossover After we have decided what encoding we will use, we can proceed to crossover operation. Crossover operates on selected genes from parent chromosomes and creates new offspring. The simplest way how to do that is to choose randomly some crossover point and copy everything before this point from the first parent and then copy everything after the crossover point from the other parent. Crossover can be illustrated as follows: ( | is the crossover point): Table 2.2. Crossover Chromosome 1 11011 | 00100110110 Chromosome 2 11011 | 11000011110 Offspring 1
11011 | 11000011110
Offspring 2
11011 | 00100110110
There are other ways how to make crossover, for example we can choose more crossover points. Crossover can be quite complicated and depends mainly on the encoding of chromosomes. Specific crossover made for a specific problem can improve performance of the genetic algorithm. 2.1.5. Mutation After a crossover is performed, mutation takes place. Mutation is intended to prevent falling of all solutions in the population into a local optimum of the solved
problem. Mutation operation randomly changes the offspring resulted from crossover. In case of binary encoding we can switch a few randomly chosen bits from 1 to 0 or from 0 to 1. Mutation can be then illustrated as follows: Table 2.3. Mutation Original offspring 1 1101111000011110 Original offspring 2 1101100100110110 Mutated offspring 1 1100111000011110 Mutated offspring 2 1101101100110110 The technique of mutation (as well as crossover) depends mainly on the encoding of chromosomes. For example when we are encoding permutations, mutation could be performed as an exchange of two genes. 2.1.6. Elitism The idea of the elitism has been already introduced. When creating a new population by crossover and mutation, we have a big chance, that we will loose the best chromosome. Elitism is the name of the method that first copies the best chromosome (or few best chromosomes) to the new population. The rest of the population is constructed in ways described above. Elitism can rapidly increase the performance of GA, because it prevents a loss of the best found solution. 2.2. Steps in Using Genetic Algorithms for Network Optimization The following steps summarize an implementation of a genetic algorithm for optimizing the design of a water distribution network system (based on Simpson, Murphy and Dandy 1993; Simpson, Dandy and Murphy 1994): 1. Develop a coding scheme to represent the decision variables to be optimized and the corresponding lookup tables for the choices for the design variables. 2. Choose the form of the genetic algorithm operators; e.g. population size (say N=100 or 500); selection scheme - tournament selection or biased Roulette
wheel; crossover type - one-point, two-point or uniform; and mutation type bit-wise or creeping. 3. Choose values for the genetic algorithm parameters (e.g. crossover probability – pc; mutation probability - pm; penalty cost factor K). 4. Select a seed for the random number generator. 5. Randomly generate the initial population of WDS network designs. 6. Decode each string in the population by dividing into its sub-strings and then determining the corresponding decision variable choices (using the lookup tables). 7. For the decoded strings, compute the network cost of each of the designs in the population. 8. Analyze each network design with a hydraulic solver for each demand loading case to compute network flows, pressures and pressure deficits (if any). 9. Compute a penalty cost for each network where design constraints are violated. 10. Compute the fitness of each string based on the costs in steps 7 and 9; often taken as the inverse of the total cost (network cost plus penalty cost). 11. Create a mating pool for the next generation using the selection operator that is driven by the “survival of the fittest.” 12. Generate a new population of designs from the mating pool using the genetic algorithm operators of crossover and mutation. 13. Record the lowest cost solutions from the new generation. 14. Repeat steps 6 to 13 to produce successive generations of populations of designs stop if all members of the population are the same. 15. Select the lowest cost design and any other similarly low cost designs of different configuration. 16. Check if any of the decision variables have been selected at the upper bound of the possible choices in the lookup table. If so, expand the range of choices and re-run of genetic algorithm. 17. Repeat steps 4 to 16 for say, ten different starting random number seeds. 18. Repeat steps 4 to 17 for successively larger and larger population sizes. Some of the main steps in the genetic algorithm process are now described in more detail.
2.2.1. Coding Schemes A genetic algorithm coding scheme is required for each of the design variables within the water distribution system to be selected as part of the design. Examples of design variables that may need to be selected include: 1. Diameter, material and class of new pipes. 2. Diameter, material and class of duplicate pipes (that is – pipes in parallel to existing pipes). 3. The possibility of cleaning or eliminating existing pipes. 4. Possible locations of source pumps and/or booster pumps. 5. Sizes of pumps (that is –the rated head and rated discharge) 6. The operating schedule for pumps. 7. Possible locations of storage tanks. 8. Sizes and normal operating levels for the tanks. 9. Possible locations of pressure regulating valves (for example, pressure reducing valves, pressure sustaining valves, flow control valves) 10. Pressure settings for the pressure regulator valves. Each decision variable to be selected is coded within a finite-length string. Genetic algorithm optimization can be applied to the design of the following systems: •
Urban water distribution systems.
•
Piped off-farm irrigation systems.
•
Design of new water distribution systems, calibrating existing models, and locating monitoring stations.
•
Expansion of existing systems.
•
Rehabilitation of existing systems.
•
Optimizing the operation of existing systems.
•
Scheduling pumps for large or complex distribution systems.
•
Setting operational points for water tanks, pumps, and pressure valves.
•
Blending of water sources to meet water quality standards at minimum costs.
•
Locating and sizing system storage to meet equalization, fire flow, and emergency needs most efficiently.
•
Optimizing the location of control valves in a water supply network in order to maximize leakage reduction.
3. Introduction to SuGA SuGA is a windows program under construction of Microsoft Visual Basic that optimizes water distribution systems using genetic algorithm. SuGA is not a water distribution network simulation modeler; it performs as a next step after simulation
EPANET
modeling.
SuGA
Have Terminati on criteria been met?
OptiGA
Random Population
Yes Cost
Has the Generation Number Reach Max Generation
No
No
Cost = Cost + Penalty Cost
Yes
Selection Crossover Mutation
Generation = Generation + 1
SOLUTION Figure 3.1. Flow Scheme of SuGA Before run the program firstly water network data must be entered in Epanet2 and it must be run without any error. Export the network from Epanet2 must be done as an INP file, so we have the data which is necessary to run the SuGA. How to create pipe’s cost considering distribution systems are shown next
Table 3.1. Excavation and filling cost table
POZ NO
YAPILAN IŞIN CINSI
MIKTARI BR
BIRIM FIYAT
TUTARI (TL)
14.012/2
El ile her derinlikte toprakta dar derin kazı yapılması
0,080
m³
5604843
448387,44
14.013/2
El ile her derinlikte küskülük zeminde dar derin kazı yapılması
0,060
m³
8070975
484258,5
14.015/2
El ile her derinlikte yumuşak kayada dar derin kazı yapılması
0,030
m³
12801223
384036,69
14.016/2
El ile her derinlikte sert kayada dar derin kazı yapılması
0,020
m³
16711046
334220,92
14.017/2
El ile her derinlikte çok sert kayada dar derin kazı yapılması
0,010
m³
24530695
245306,95
151/3
Makine ile her derinlikte toprakta dar derin kazı yapılması
0,320
m³
2093923
670055,36
156/3
Makine ile her derinlikte küskülükte dar derin kazı yapılması
0,240
m³
3463327
831198,48
15.010/6
Makine ile her derinlikte yumuşak kayada dar derin kazı yapılması
0,120
m³
4316857
518022,84
15.014/3
Makine ile her derinlikte sert kayada dar derin kazı yapılması
0,080
m³
8632540
690603,2
15.018/3
Makine ile her derinlikte çok sert kayada dar derin kazı yapılması
0,040
m³
9955897
398235,88
15.140/İB-1
Stabilize malzeme ile hendek ve temel dolgusu yapılması
0,100
m³
2560385
256038,5
14.1714/1
Kazı malzemesinden makine ile hendek ve temel dolgusu yapılması
0,600
m³
1858533
1115119,8
15.140/İB-4
Her kategoride kum-çakılın el ile sıkıştırılarak hendek ıslahı,
0,300
m³
4627530
1388259
2
m³
TOPLAM
7763743,56
Land Class : Soil : 40% , Sand : 30% , Soft Rock : 15% , Hard Rock : 10% , The Hardest Rock : 5% to be taken Ditch excavation is done by 20% hand, 80% machine.
Excavation and filling cost for 1m³ is found 7763744 TL
Figure 3.2. Ditch excavation
Excavation and filling cost for 1m and different diameters 1 Euro = 1,600,000 TL 80 mm 1m PE-100
0,713 m3 * 7763744 = 5.535.549 TL = 3,46 Euro
100 mm 1m PE-100 0,726 m3 * 7763744 = 5.636.478 TL = 3,52 Euro 125 mm 1m PE-100 0,743 m3 * 7763744 = 5.768.462 TL = 3,60 Euro 150 mm 1m PE-100 0,762 m3 * 7763744 = 5.915.973 TL = 3,70 Euro 200 mm 1m PE-100 0,792 m3 * 7763744 = 6.148.885 TL = 3,84 Euro 250 mm 1m PE-100 0,894 m3 * 7763744 = 6.940.787 TL = 4,34 Euro 300 mm 1m PE-100 1,001 m3 * 7763744 = 7.771.508 TL = 4,86 Euro 400 mm 1m PE-100 1,232 m3 * 7763744 = 9.564.933 TL = 5,98 Euro 500 mm 1m PE-100 1,485 m3 * 7763744 = 11.529.160 TL = 7,20 Euro
Table 3.2. Dizayn Group PE-100 pipes cost (Euro) list
DIZAYN GROUP PE100 PIPES COST LIST Diameter (mm) PN16 (Euro) PN10 (Euro) PN8 (Euro) PN6 (Euro) 80 3,95 2,75 2,34 1,78 100 6,78 4,68 3,83 2,85 125 10,48 7,12 5,84 4,42 150 15,15 10,30 8,44 6,40 200 26,75 18,14 14,90 11,29 250 41,80 28,17 23 17,67 300 59,34 40,13 32,75 25,20 400 106,83 72,15 59,07 45,21 500 166,98 113,02 92,06 70,63 Total cost for 1m length pipe concerning water distribution systems 80 mm 1m PE-100 3,46 + 2,75 = 6,21 Euro 100 mm 1m PE-100 3,52 + 4,68 = 8,20 Euro 125 mm 1m PE-100 3,60 + 7,12 = 10,72 Euro 150 mm 1m PE-100 3,70 + 10,30 = 14 Euro 200 mm 1m PE-100 3,84 + 18,14 = 21,98 Euro 250 mm 1m PE-100 4,34 + 28,17 = 32,51 Euro 300 mm 1m PE-100 4,86 + 40,13 = 44,99 Euro 400 mm 1m PE-100 5,98 + 72,15 = 78,13 Euro 500 mm 1m PE-100 7,20 + 113,02 = 120,22 Euro
3.1. Implementation of SuGA Example water distribution network system is made to show to how the program works. In the WDS, nine different diameters (table 6.3) were thought to be used. You can use Appendix A, which contains basic tutorial, to understand running SuGA. The layout of WDS and WDS’s data such as pipes and junctions ID’s, pipes length and junctions demand are given Appendices B. You can look Appendices C and D to compare SuGA’s solution and final solution of this WDS. Solutions contain diameters, velocities, pressures, flows, heads, and unit headloss. The search space of this 77 piped WDS, because of nine different diameters, is 977. With assistance of SuGA, we were able to obtain the following solution represent table 6.4. We run the program with tournament selection type, two points crossover type, 40 population sizes, 10.000 generations and 20 runs. Since the program does not make a telescopic solution, diameters can be distributed unbalanced; some engineering approachment must be made on the solution by modeler. To achieve this, not spending too much effort (eliminate lots of trial and error steps), we can find a suitable solution a bit higher (1314 Euro) than the found by SuGA. The solution data we found with some engineering approachment is in table 6.4. with comparing results found by SuGA. So, we see that SuGA is an effective program for finding lower cost solution; SuGA almost nearly reached this solution at the one of these 20 runs.
Table 3.3. Cost Data for Pipe DIAMETER
COST
(MM)
(UNITS)
80 100 125 150 200 250 300 400 500
6,21 8,20 10,72 14,00 21,98 32,51 44,99 78,13 120,22
Table 3.4. Compare SuGA and Final Solution Initial SuGA SuGA Delta Pipe Initial Cost ID Diameter Diameter Diameter Diameter Cost Cost 10 80 80 2.484 2.484 0 11 80 80 2.484 2.484 0 12 80 80 2.484 2.484 0 23 80 80 2.484 2.484 0 24 80 80 2.484 2.484 0 25 80 80 2.484 2.484 0 36 250 300 13.004 17.996 4992 37 250 200 13.004 8.792 -4212 38 200 200 8.792 8.792 0 39 200 150 8.792 5.600 -3192 54 100 100 2.050 2.050 0 55 80 80 1.552,5 1.552,5 0 57 100 100 2.050 2.050 0 58 80 80 1.552,5 1.552,5 0 60 150 150 3.500 3.500 0 61 150 100 3.500 2.050 -1450 62 80 80 1.552,5 1.552,5 0 63 150 150 3.500 3.500 0 64 150 80 3.500 1.552,5 -1947,5 65 80 80 1.552,5 1.552,5 0
Delta Initial SuGA Velocities Velocities Velocities 0,49 0,60 0,69 0,69 0,60 0,49 1,95 1,24 1,54 1,24 1,09 0,77 1,09 0,77 0,84 0,73 0,69 0,84 0,73 0,69
0,63 0,63 0,65 0,66 0,77 0,47 1,38 1,59 1,22 1,42 0,97 0,76 1,01 0,80 1,16 0,88 0,83 1,25 0,85 0,67
0,14 0,03 0,04 0,03 0,17 0,02 0,57 0,35 0,32 0,18 0,12 0,01 0,08 0,03 0,32 0,15 0,14 0,41 0,12 0,02
Node ID 5 6 7 8 14 15 16 17 18 24 25 26 27 28 34 35 36 37 38 44
Initial SuGA Pressures Pressures 28,67 27,38 25,51 23,09 31,91 30,20 27,72 25,81 23,15 33,77 31,01 28,29 25,81 23,30 36,51 32,07 30,15 26,45 23,97 33,77
28,70 26,62 24,54 22,36 32,50 30,85 26,77 24,72 22,54 34,32 32,71 28,87 26,08 23,70 36,51 34,63 30,71 28,30 23,82 34,13
Delta Pressures 0,03 0,76 0,97 0,73 0,59 0,65 0,95 1,09 0,61 0,55 1,70 0,58 0,27 0,40 0 2,56 0,56 1,85 0,15 0,36
Table 3.4. Continues Pipe Initial SuGA Initial SuGA ID Diameter Diameter Diameter Diameter Cost Cost 66 80 80 1.552,5 1.552,5 67 80 80 1.552,5 1.552,5 68 80 80 1.552,5 1.552,5 69 80 80 1.552,5 1.552,5 70 80 100 1.552,5 2.050 71 80 80 1.552,5 1.552,5 72 80 80 1.552,5 1.552,5 73 80 80 1.552,5 1.552,5 74 80 80 1.552,5 1.552,5 75 80 80 1.552,5 1.552,5 76 80 80 1.552,5 1.552,5 77 80 80 1.552,5 1.552,5 78 80 80 1.552,5 1.552,5 79 80 80 1.552,5 1.552,5 80 80 80 1.552,5 1.552,5 81 80 80 1.552,5 1.552,5 82 80 80 1.552,5 1.552,5 83 80 80 1.552,5 1.552,5 93 80 80 2.484 2.484 94 80 125 2.484 4.288 95 80 125 2.484 4.288 96 80 125 2.484 4.288 102 80 80 2.484 2.484
Delta Cost 0 0 0 0 497,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1804 1804 1804 0
Initial SuGA Delta Velocities Velocities Velocities 0,77 0,41 0,31 0,77 0,41 0,31 0,43 0,03 0,29 0,43 0,03 0,29 0,44 0,20 0,13 0,44 0,20 0,13 0,74 0,73 0,70 0,70 0,74
0,76 0,82 0,20 0,52 0,76 0,50 0,85 0,65 0,22 0,78 0,75 0,09 0,17 0,60 0,22 0,09 0,62 0,21 0,55 1,17 0,98 0,90 0,57
0,01 0,41 0,11 0,25 0,35 0,19 0,42 0,62 0,07 0,35 0,72 0,20 0,27 0,40 0,09 0,35 0,42 0,08 0,19 0,44 0,28 0,20 0,17
Node ID 45 46 47 48 54 55 56 57 58 65 66 67 68 1 3 9 10 11 12 13 19 20 21
Initial SuGA Pressures Pressures 31,01 28,29 25,81 23,30 31,91 30,20 27,72 25,81 23,15 28,67 27,38 25,51 23,09 21,11 21,61 19,05 21,73 19,35 22,48 20,53 21,73 19,35 21,61
32,41 29,30 26,39 23,78 32,11 30,19 28,40 24,62 22,54 28,76 27,56 24,59 22,37 20,05 20,43 19,03 20,76 19,05 21,19 19,06 20,77 19,05 20,44
Delta Pressures 1,40 1,51 0,58 0,48 0,20 0,01 0,68 1,19 0,61 0,09 0,18 0,92 0,72 1,06 1,18 0,02 0,97 0,30 1,29 1,47 0,96 0,30 1,17
Table 3.4. Continues Pipe Initial SuGA Initial SuGA ID Diameter Diameter Diameter Diameter Cost Cost 103 80 150 2.484 5.600 104 80 125 2.484 4.288 105 80 125 2.484 4.288 111 80 80 2.484 2.484 112 125 80 4.288 2.484 113 125 100 4.288 3.280 114 100 100 3.280 3.280 120 80 80 2.484 2.484 121 125 80 4.288 2.484 122 125 80 4.288 2.484 123 100 100 3.280 3.280 1 300 300 224.950 224.950 2 80 80 2.484 2.484 4 100 100 3.280 3.280 5 80 100 2.484 3.280 6 80 100 2.484 3.280 7 80 100 2.484 3.280 8 200 150 8.792 5.600 13 150 125 5.600 4.288 14 80 100 2.484 3.280 15 80 100 2.484 3.280 16 100 100 3.280 3.280 17 80 100 2.484 3.280
Delta Cost 3116 1804 1804 0 -1804 -1008 0 0 -1804 -1804 0 0 0 0 796 796 796 -3192 -1312 796 796 0 796
Initial SuGA Delta Velocities Velocities Velocities 0,73 0,70 0,70 0,57 0,92 0,80 0,83 0,57 0,92 0,80 0,83 1,67 0,62 0,62 0,71 0,55 0,68 0,94 0,91 0,55 0,68 0,62 0,71
1,06 1,10 0,95 0,56 0,91 0,72 0,75 0,61 0,58 0,87 0,73 1,67 0,67 0,73 0,59 0,88 0,66 1,07 0,85 0,89 0,66 0,73 0,59
0,33 0,40 0,25 0,01 0,01 0,08 0,08 0,04 0,34 0,07 0,10 0 0,05 0,11 0,12 0,33 0,02 0,13 0,06 0,34 0,02 0,11 0,12
Node ID 22 23
Initial SuGA Pressures Pressures 19,05 21,11
19,03 20,06
Delta Pressures 0,02 1,05
Table 3.4. Continues SuGA Initial SuGA Pipe Initial ID Diameter Diameter Diameter Diameter Cost Cost 18 80 80 2.484 2.484 20 80 80 1.552,5 1.552,5 21 100 80 2.050 1.552,5 22 100 80 2.050 1.552,5 27 100 80 2.050 1.552,5 28 100 80 2.050 1.552,5 29 80 80 1.552,5 1.552,5 31 80 80 1.552,5 1.552,5 32 80 80 1.552,5 1.552,5 33 80 80 1.552,5 1.552,5 34 80 80 1.552,5 1.552,5 442.592 441.278
Delta Cost 0 0 -497,5 -497,5 -497,5 -497,5 0 0 0 0 0 -1314
SuGA Delta Initial Velocities Velocities Velocities 0,62 0,38 0,20 0,54 0,54 0,20 0,38 0,29 0,60 0,60 0,29
0,67 0,33 0,30 0,35 0,34 0,30 0,33 0,07 0,04 0,04 0,07
0,05 0,05 0,10 0,19 0,20 0,10 0,05 0,22 0,56 0,56 0,22
Node ID
Initial SuGA Pressures Pressures
Delta Pressures
4.1. Conclusion The combinatorial optimization problem of least-cost design of water distribution networks is formulated by several researchers and it is shown that GAs are particularly suited to this type of problem (Savic and Walters, 1997). GA does not provide the absolute answers to the problems that are being investigated, but it is more a powerful new tool for moving towards the best solution. GAs are not replacement traditional simulation modeling program, instead, they are performed next step after hydraulic solver. However, instead of relying on the modeler to evaluate different scenarios on a trial and error basis, GA optimization automates the solution search process by instructing the computer to successively generate and evaluate possible solutions. This study describes development of a computer program, called SuGA, which uses Genetic Algorithm for the least-cost design and expansion of water distribution system. SuGA does not expose telescopic (enlarged diameters from end point to tank) solution. It needs to be corrected by an engineer, so the final solution may be higher than solution found by SuGA. Program was tested with several problems from the literature, comparing solutions was fairly near for small-scale water distribution systems. In conclusion, SuGA can be used for new design, expansion or rehabilitation of existing water distribution systems for optimization
4.2. Recommendations SuGA use single objective function, constraints take part inside fitness function as a penalty. Constraints and pipes can be coded separately in multiobjective function. Usage of multiobjective function on WDS should be considered. Binary coding scheme has some disadvantage such as the hamming cliff effect and redundant values. Real value or Gray coding scheme can be used instead of binary coding Simple genetic algorithm is not effective on large-scale water distribution systems. Several researchers studied on modified genetic algorithm such as structured messy genetic algorithm, fast messy genetic algorithm, and they give good solution on large-scale water
distribution systems. Developing a new genetic algorithm which is more suitable for WDS should be investigated. SuGA does not provide telescopic solution. Adding a function to SuGA can provide telescopic solution, so it will be helped close to final solution. SuGA has capable optimal design and expansion of WDS. Other usage of GA on WDS such as pump scheduling, leakage reduction, water quality control etc. can be added to SuGA with some developing coding scheme. 5. References 1. Goldberg, D. E. (1989). Genetic Algorithms in Search Optimization and Machine Learning. Addison Wesley, MA, USA. 2. Melanie Mitchell, (1996). “An introduction to genetic algorithm” Cambridge, MA:MIT P. 3. Obitko, Marek and Slavík, Pavel. Visualization of Genetic Algorithms in a Environment. In: Spring Conference on Computer Graphics, SCCG'99.
Learning Bratislava :
Comenius University, 1999, p. 101-106. ISBN 80-223-1357-2. 4. Rossman, L. A. (1994). EPANET USERS MANUAL, Risk Reduction Engineering Laboratory, U.S. Environmental Protection Agency, USA. 5. Savic, D. A., and Walters, G. A. (1997). “Genetic algorithms for least-cost design of water distribution networks.” J. Water Resour. Plng. and Mgmt., ASCE, 123(2), 67-77. 6. Simpson, A. R., Murphy, L. J., and Dandy G. C. (1993). “Pipe Network Optimization using Genetic Algorithms.” Paper presented at ASCE, Water Resources Planning and Management Specialty Conference, ASCE, Seattle, USA. 7. Simpson, A. R., Dandy G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.” J. Water Resour. Plng. and Mgmt., ASCE, 120(4), 423-443. 8. Simpson, A.R. (2000). "Optimization of design of water distribution systems using genetic algorithms." Slovenian Society of Hydraulic Research, Seminar Series, Vol.1, Ljubljana, Slovenia, 10pp. 9. The optimatics letter Issue No:12 (April-June, 2001) Advances in Optimization for Water Distribution System Design & Operations 10. http:\\www.optiwater.com
by A. Murat KAHRAMAN
September, 2003 İZMİR
ABSTRACT
In last decades, rapid increase in world population, urbanization and depletion of fresh water resources indicates that the optimization of water distribution networks is an essential element of water resources protection. Although up to now numerous computer aided tools on hydraulic design of water distribution networks and optimization methods have been developed. These methods could not be used widely due to some difficulties in the application of these methods/tools in real-size water distribution networks. Optimization of water distribution systems using genetic algorithms gains acceptance all over the world recent years. Genetic algorithms are powerful population oriented search algorithm based upon Darwin’s theory “Survival of the fittest”. The genetic algorithm selects, combines and manipulates possible solutions in a search for the lower cost network. Many tests of the application of the genetic algorithm optimization process to real-life network designs have shown that the GA is effective at finding low cost solutions. The technique has consistently found lower cost solution than the trial-and-error simulation approach typically used by design engineers. This study describes development of a computer program, called SuGA, which uses Genetic Algorithm for the least-cost design and expansion of water distribution system. Program was tested with several problems from the literature, comparing solutions was fairly near for small-scale water distribution systems. SuGA is a windows program under construction of Microsoft Visual Basic that optimizes water distribution systems using genetic algorithm. It uses Epanet2 (Distributed by The U.S. EPA) for hydraulic calculations, and OptiGA (Optiwater) ActiveX control for Genetic Algorithm optimization. SuGA can be used for new design, expansion or rehabilitation of existing water distribution systems for optimization. Keywords: Water, distribution, systems, least cost, design, optimization, genetic algorithms, pipes, nodes, networks
ÖZET Dünyada hızla nüfusun artmasına karşılık temiz su kaynaklarının giderek azalması göz önünde bulundurulursa su dağıtım şebekelerinin optimizasyonunun öneminin arttığı açıktır. Araştırmacılar önce şebeke hidroliğini çözmek için bilgisayar programları oluşturmuşlar, daha sonra su dağıtım şebekelerinin optimizasyonu konusunda çeşitli optimizasyon yöntemleri ve bunları kullanan programlar hazırlamışlardır. Ancak bunların bir çoğu gerçek şebeke sistemlerine uygulanması çok zor olan teknikler olması sebebiyle piyasalarda yaygın kullanım alanı bulamamıştır. Son yıllarda ise yeni bir yaklaşım sayabileceğimiz Genetik Algoritmaların (GAs) şebeke optimizasyonunda kullanımı giderek artmaktadır. Genetik algoritmalar, çözüm uzayının büyük olduğu her türlü karmaşık problemde iyi sonuçlar vermektedir. Günümüzde genetik algoritmalar su dağıtım sistemlerinin dizaynı, genişletilmesi, rehabilitasyonu, su sızıntılarını minimize etmek için kontrol vanalarının yerleşimi, karmaşık sistemler için pompa çalışma zamanlarının düzenlenmesi, hazne işletilmesi, numune alma ve klorlama istasyonlarının yerleşimi, farklı kaynaklardan alınan suların kalitesinin optimize edilmesi gibi çok geniş bir alanda yaygın olarak kullanılmaktadır. Avustralya, Kanada ve Amerika’ nın çeşitli eyaletlerinde su dağıtım şebekelerinin genetik algoritma ile dizaynı, rehabilitasyonu, genişletilmesi, işletilmesi gibi çalışmalarda %15 ile %50 arası tasarruf sağlanmıştır (Simpson, 2000). Genetik Algoritmaların yapısı oldukça basittir, Darvin’in “en iyiler hayatta kalır” prensibine göre işlerler. Basit bir Genetik Algoritmada en iyiyi belirleyen bir uygunluk fonksiyonu, seçme, çaprazlama ve mutasyon operatörleri bulunur. Genetik Algoritmalar belirli bir populasyon topluluğu ile başlarlar (populasyonlar genelde ilk defa rasgele oluşturulur), bir sonraki jenerasyon topluluktaki en iyi bireyler, seçme havuzunda birbirleriyle çaprazlanmak için çeşitli seçme yöntemlerinden (rulet, turnuva gibi) biriyle seçilirler, daha sonra en iyi bireyler birbirleriyle eşleştirilerek daha iyi bireyler oluşması sağlanır ve kuşaklar boyu sürekli en iyiye doğru gidilir. Genetik Algoritmalar çözümün nerede sonuçlanacağını bilmezler, yakınsamanın sağlandığı an çözüm olarak kabul edilir. Dolayısıyla genetik algoritmalar en iyi
çözümü vereceğini garanti etmezler, ancak optimum bir sonuç sağlarlar. Çözüm uzayının trilyonlar olduğu bir kümede en iyi sonucu bulabilmek ayrı bir meseledir! Bu çalışmaların ışığında, su dağıtım şebekelerinin dizaynı ve genişletilmesinde kullanılabilecek, genetik algoritma ile optimizasyon yapan SuGA adlı Visual BASIC ortamlı bir bilgisayar programı hazırlanmıştır. Hazırlanan program, dağıtım şebekesinin hidrolik hesapları için EPA’nın su dağıtım şebekesi programı EPANET2’yi, genetik algoritma için de Optiwater firmasının OptiGA adlı ActiveX denetimini kullanmaktadır. Hazırlanan program ile her bir boru için dizaynda kullanılabilecek boru çapları ve fiyatlarını kullanarak, her düğüm noktası için ayrı ayrı verilebilen minimum ve maksimum basınç ve her boru için ayrı ayrı verilebilen minimum ve maksimum hız sınırları arasında optimize edilmiş bir şebeke sunabilmektedir. Optimizasyonda hız ve basınç sınırlarının verilen tolerans sınırlarında aşılmasında verilen bir ceza puanı ile şebeke toplam maliyeti artırılmakta, böylece hidrolik açıdan uygun bir şebeke çözümüne ulaşılabilmektedir. Literatürde yer alan birçok şebeke sistemi hazırlanan program ile hesaplanarak test edilmiş ve literatürde yer alan çeşitli genetik algoritma ile çözüm yapan programın sonuçlarına yakın sonuçlar elde edilmiştir. Genetik algoritma ile yapılan optimizasyonlarda çözüm uzayı çok geniş olduğundan birbirine çok yakın çeşitli çözümlere ulaşılabilmektedir. Bu nedenle programın tamamen aynı verilerle yeniden çalıştırılmasıyla yeni bir çözüme daha ulaşılabilmektedir. Bu nedenle de en iyiye karar verebilmek oldukça güçtür. Ancak bulunan bir çok çözümde mühendisçe iyi bir yaklaşım olabilmektedir. Hazırlanan program su dağıtım şebekelerinin dizaynında, mevcut bir şebekenin genişletilmesinde ve hatta rehabilitasyonunda bir mühendis denetiminde optimizasyon amaçlı kullanılabilir. Anahtar Kelimeler: Su, dağıtım, sistemleri, en düşük maliyet, dizayn, optimizasyon, genetik algoritmalar, borular, düğüm noktaları, ağ şebeke.
1. Introduction As a vital part of water supply systems, water distribution networks represent one of the largest infrastructure assets of industrial society. The Water Infrastructure Network (WIN) report Clean and Safe Water for the 21st Century (April 2000) warns of huge funding shortfalls for replacement of drinking water infrastructure and needed improvements to meet federal water regulations. The required capital investment for drinking water systems alone is estimated to be $24 billion per year for the next 20 years—this amount dwarfs the $13 billion per year that water systems currently invest for infrastructure capital needs (The optimatics letter, 2001)
Figure 1.1. Percent of Infrastructure Funding Needs by Area Source: EPA’s 1997 Drinking Water Infrastructure Needs Survey Optimization Could Save $2B per Year. Genetic algorithm (GA) optimization, for example, can be applied to develop superior, low-cost solutions for capital improvement plans (CIPs), main replacement plans, and more. Cost savings of 20% or higher are not uncommon for both small and large distribution systems. (To apply the optimization does require a hydraulic model of the system.) Optimization analysis can help utilities reduce transmission, distribution and storage improvement costs, which amount to more than 60% of total infrastructure costs (see Figure 1.1). Assuming that cost savings of 25% can be achieved on just over half of all projects, the potential savings comes to $2 billion per year for the USA.
2. What is Genetic Algorithm Genetic algorithms (GAs) are optimization techniques based on the concepts of natural selection and genetics. Genetic algorithms are inspired by Darwin's theory of evolution. In this approach, the variables are represented as genes on a chromosome. Solution to a problem solved by genetic algorithms uses an evolutionary process (it is evolved). GAs features a group of candidate solutions (population) on the response surface. Through natural selection and the genetic operators, mutation and recombination, chromosomes with better fitness are found. Natural selection guarantees that chromosomes with the best fitness will propagate in future populations. Using the recombination operator, the GA combines genes from two parent chromosomes to form two new chromosomes (children) that have a high probability of having better fitness than their parents. Mutation allows new areas of the response surface to be explored. This is repeated until some condition (for example number of populations or improvement of the best solution) is satisfied. 2.1. Simple Genetic Algorithm The mechanics of a simple genetic algorithm are surprisingly simple, involving nothing more complex than copying strings and swapping partial strings (Goldberg, 1989). Basic components of simple genetic algorithm are as follows (Obitko, 1998). 2.1.1. Encoding a chromosome A chromosome should in some way contain information about solution that it represents. The most used way of encoding is a binary string. A chromosome then could look like this : Table 2.1. Encoding a chromosome Chromosome 1 1101100100110110 Chromosome 2 1101111000011110 Each chromosome is represented by a binary string. Each bit in the string can represent some characteristics of the solution. Another possibility is that the whole string can represent a number.
Of course, there are many other ways of encoding. The encoding depends mainly on the solved problem. For example, one can encode directly integer or real numbers; sometimes it is useful to encode some permutations and so on. 2.1.2. Reproduction During reproduction, recombination (or crossover) first occurs. Genes from parents combine to form a whole new chromosome. The newly created offspring can then be mutated. Mutation means that the elements of DNA are a bit changed. These changes are mainly caused by errors in copying genes from parents. The fitness of an organism is measured by success of the organism in its life (survival). 2.1.3. Selection Parents are selected according to their fitness. The better the chromosomes are, the more chances to be selected they have. Imagine a roulette wheel where all the chromosomes in the population are placed. The size of the section in the roulette wheel is proportional to the value of the fitness function of every chromosome - the bigger the value is, the larger the section is. See the following picture for an example.
Figure 2.1. Roulette Wheel Selections A marble is thrown in the roulette wheel and the chromosome where it stops is selected. Clearly, the chromosomes with bigger fitness value will be selected more times.
This process can be described by the following algorithm. 1. [Sum] Calculate the sum of all chromosome fitness’s in population - sum S. 2. [Select] Generate random number from the interval (0, S) - r. 3. [Loop] Go through the population and sum the fitness’s from 0 - sum s. When the sum s is greater then r, stop and return the chromosome where you are. Of course, the step 1 is performed only once for each population. 2.1.4. Crossover After we have decided what encoding we will use, we can proceed to crossover operation. Crossover operates on selected genes from parent chromosomes and creates new offspring. The simplest way how to do that is to choose randomly some crossover point and copy everything before this point from the first parent and then copy everything after the crossover point from the other parent. Crossover can be illustrated as follows: ( | is the crossover point): Table 2.2. Crossover Chromosome 1 11011 | 00100110110 Chromosome 2 11011 | 11000011110 Offspring 1
11011 | 11000011110
Offspring 2
11011 | 00100110110
There are other ways how to make crossover, for example we can choose more crossover points. Crossover can be quite complicated and depends mainly on the encoding of chromosomes. Specific crossover made for a specific problem can improve performance of the genetic algorithm. 2.1.5. Mutation After a crossover is performed, mutation takes place. Mutation is intended to prevent falling of all solutions in the population into a local optimum of the solved
problem. Mutation operation randomly changes the offspring resulted from crossover. In case of binary encoding we can switch a few randomly chosen bits from 1 to 0 or from 0 to 1. Mutation can be then illustrated as follows: Table 2.3. Mutation Original offspring 1 1101111000011110 Original offspring 2 1101100100110110 Mutated offspring 1 1100111000011110 Mutated offspring 2 1101101100110110 The technique of mutation (as well as crossover) depends mainly on the encoding of chromosomes. For example when we are encoding permutations, mutation could be performed as an exchange of two genes. 2.1.6. Elitism The idea of the elitism has been already introduced. When creating a new population by crossover and mutation, we have a big chance, that we will loose the best chromosome. Elitism is the name of the method that first copies the best chromosome (or few best chromosomes) to the new population. The rest of the population is constructed in ways described above. Elitism can rapidly increase the performance of GA, because it prevents a loss of the best found solution. 2.2. Steps in Using Genetic Algorithms for Network Optimization The following steps summarize an implementation of a genetic algorithm for optimizing the design of a water distribution network system (based on Simpson, Murphy and Dandy 1993; Simpson, Dandy and Murphy 1994): 1. Develop a coding scheme to represent the decision variables to be optimized and the corresponding lookup tables for the choices for the design variables. 2. Choose the form of the genetic algorithm operators; e.g. population size (say N=100 or 500); selection scheme - tournament selection or biased Roulette
wheel; crossover type - one-point, two-point or uniform; and mutation type bit-wise or creeping. 3. Choose values for the genetic algorithm parameters (e.g. crossover probability – pc; mutation probability - pm; penalty cost factor K). 4. Select a seed for the random number generator. 5. Randomly generate the initial population of WDS network designs. 6. Decode each string in the population by dividing into its sub-strings and then determining the corresponding decision variable choices (using the lookup tables). 7. For the decoded strings, compute the network cost of each of the designs in the population. 8. Analyze each network design with a hydraulic solver for each demand loading case to compute network flows, pressures and pressure deficits (if any). 9. Compute a penalty cost for each network where design constraints are violated. 10. Compute the fitness of each string based on the costs in steps 7 and 9; often taken as the inverse of the total cost (network cost plus penalty cost). 11. Create a mating pool for the next generation using the selection operator that is driven by the “survival of the fittest.” 12. Generate a new population of designs from the mating pool using the genetic algorithm operators of crossover and mutation. 13. Record the lowest cost solutions from the new generation. 14. Repeat steps 6 to 13 to produce successive generations of populations of designs stop if all members of the population are the same. 15. Select the lowest cost design and any other similarly low cost designs of different configuration. 16. Check if any of the decision variables have been selected at the upper bound of the possible choices in the lookup table. If so, expand the range of choices and re-run of genetic algorithm. 17. Repeat steps 4 to 16 for say, ten different starting random number seeds. 18. Repeat steps 4 to 17 for successively larger and larger population sizes. Some of the main steps in the genetic algorithm process are now described in more detail.
2.2.1. Coding Schemes A genetic algorithm coding scheme is required for each of the design variables within the water distribution system to be selected as part of the design. Examples of design variables that may need to be selected include: 1. Diameter, material and class of new pipes. 2. Diameter, material and class of duplicate pipes (that is – pipes in parallel to existing pipes). 3. The possibility of cleaning or eliminating existing pipes. 4. Possible locations of source pumps and/or booster pumps. 5. Sizes of pumps (that is –the rated head and rated discharge) 6. The operating schedule for pumps. 7. Possible locations of storage tanks. 8. Sizes and normal operating levels for the tanks. 9. Possible locations of pressure regulating valves (for example, pressure reducing valves, pressure sustaining valves, flow control valves) 10. Pressure settings for the pressure regulator valves. Each decision variable to be selected is coded within a finite-length string. Genetic algorithm optimization can be applied to the design of the following systems: •
Urban water distribution systems.
•
Piped off-farm irrigation systems.
•
Design of new water distribution systems, calibrating existing models, and locating monitoring stations.
•
Expansion of existing systems.
•
Rehabilitation of existing systems.
•
Optimizing the operation of existing systems.
•
Scheduling pumps for large or complex distribution systems.
•
Setting operational points for water tanks, pumps, and pressure valves.
•
Blending of water sources to meet water quality standards at minimum costs.
•
Locating and sizing system storage to meet equalization, fire flow, and emergency needs most efficiently.
•
Optimizing the location of control valves in a water supply network in order to maximize leakage reduction.
3. Introduction to SuGA SuGA is a windows program under construction of Microsoft Visual Basic that optimizes water distribution systems using genetic algorithm. SuGA is not a water distribution network simulation modeler; it performs as a next step after simulation
EPANET
modeling.
SuGA
Have Terminati on criteria been met?
OptiGA
Random Population
Yes Cost
Has the Generation Number Reach Max Generation
No
No
Cost = Cost + Penalty Cost
Yes
Selection Crossover Mutation
Generation = Generation + 1
SOLUTION Figure 3.1. Flow Scheme of SuGA Before run the program firstly water network data must be entered in Epanet2 and it must be run without any error. Export the network from Epanet2 must be done as an INP file, so we have the data which is necessary to run the SuGA. How to create pipe’s cost considering distribution systems are shown next
Table 3.1. Excavation and filling cost table
POZ NO
YAPILAN IŞIN CINSI
MIKTARI BR
BIRIM FIYAT
TUTARI (TL)
14.012/2
El ile her derinlikte toprakta dar derin kazı yapılması
0,080
m³
5604843
448387,44
14.013/2
El ile her derinlikte küskülük zeminde dar derin kazı yapılması
0,060
m³
8070975
484258,5
14.015/2
El ile her derinlikte yumuşak kayada dar derin kazı yapılması
0,030
m³
12801223
384036,69
14.016/2
El ile her derinlikte sert kayada dar derin kazı yapılması
0,020
m³
16711046
334220,92
14.017/2
El ile her derinlikte çok sert kayada dar derin kazı yapılması
0,010
m³
24530695
245306,95
151/3
Makine ile her derinlikte toprakta dar derin kazı yapılması
0,320
m³
2093923
670055,36
156/3
Makine ile her derinlikte küskülükte dar derin kazı yapılması
0,240
m³
3463327
831198,48
15.010/6
Makine ile her derinlikte yumuşak kayada dar derin kazı yapılması
0,120
m³
4316857
518022,84
15.014/3
Makine ile her derinlikte sert kayada dar derin kazı yapılması
0,080
m³
8632540
690603,2
15.018/3
Makine ile her derinlikte çok sert kayada dar derin kazı yapılması
0,040
m³
9955897
398235,88
15.140/İB-1
Stabilize malzeme ile hendek ve temel dolgusu yapılması
0,100
m³
2560385
256038,5
14.1714/1
Kazı malzemesinden makine ile hendek ve temel dolgusu yapılması
0,600
m³
1858533
1115119,8
15.140/İB-4
Her kategoride kum-çakılın el ile sıkıştırılarak hendek ıslahı,
0,300
m³
4627530
1388259
2
m³
TOPLAM
7763743,56
Land Class : Soil : 40% , Sand : 30% , Soft Rock : 15% , Hard Rock : 10% , The Hardest Rock : 5% to be taken Ditch excavation is done by 20% hand, 80% machine.
Excavation and filling cost for 1m³ is found 7763744 TL
Figure 3.2. Ditch excavation
Excavation and filling cost for 1m and different diameters 1 Euro = 1,600,000 TL 80 mm 1m PE-100
0,713 m3 * 7763744 = 5.535.549 TL = 3,46 Euro
100 mm 1m PE-100 0,726 m3 * 7763744 = 5.636.478 TL = 3,52 Euro 125 mm 1m PE-100 0,743 m3 * 7763744 = 5.768.462 TL = 3,60 Euro 150 mm 1m PE-100 0,762 m3 * 7763744 = 5.915.973 TL = 3,70 Euro 200 mm 1m PE-100 0,792 m3 * 7763744 = 6.148.885 TL = 3,84 Euro 250 mm 1m PE-100 0,894 m3 * 7763744 = 6.940.787 TL = 4,34 Euro 300 mm 1m PE-100 1,001 m3 * 7763744 = 7.771.508 TL = 4,86 Euro 400 mm 1m PE-100 1,232 m3 * 7763744 = 9.564.933 TL = 5,98 Euro 500 mm 1m PE-100 1,485 m3 * 7763744 = 11.529.160 TL = 7,20 Euro
Table 3.2. Dizayn Group PE-100 pipes cost (Euro) list
DIZAYN GROUP PE100 PIPES COST LIST Diameter (mm) PN16 (Euro) PN10 (Euro) PN8 (Euro) PN6 (Euro) 80 3,95 2,75 2,34 1,78 100 6,78 4,68 3,83 2,85 125 10,48 7,12 5,84 4,42 150 15,15 10,30 8,44 6,40 200 26,75 18,14 14,90 11,29 250 41,80 28,17 23 17,67 300 59,34 40,13 32,75 25,20 400 106,83 72,15 59,07 45,21 500 166,98 113,02 92,06 70,63 Total cost for 1m length pipe concerning water distribution systems 80 mm 1m PE-100 3,46 + 2,75 = 6,21 Euro 100 mm 1m PE-100 3,52 + 4,68 = 8,20 Euro 125 mm 1m PE-100 3,60 + 7,12 = 10,72 Euro 150 mm 1m PE-100 3,70 + 10,30 = 14 Euro 200 mm 1m PE-100 3,84 + 18,14 = 21,98 Euro 250 mm 1m PE-100 4,34 + 28,17 = 32,51 Euro 300 mm 1m PE-100 4,86 + 40,13 = 44,99 Euro 400 mm 1m PE-100 5,98 + 72,15 = 78,13 Euro 500 mm 1m PE-100 7,20 + 113,02 = 120,22 Euro
3.1. Implementation of SuGA Example water distribution network system is made to show to how the program works. In the WDS, nine different diameters (table 6.3) were thought to be used. You can use Appendix A, which contains basic tutorial, to understand running SuGA. The layout of WDS and WDS’s data such as pipes and junctions ID’s, pipes length and junctions demand are given Appendices B. You can look Appendices C and D to compare SuGA’s solution and final solution of this WDS. Solutions contain diameters, velocities, pressures, flows, heads, and unit headloss. The search space of this 77 piped WDS, because of nine different diameters, is 977. With assistance of SuGA, we were able to obtain the following solution represent table 6.4. We run the program with tournament selection type, two points crossover type, 40 population sizes, 10.000 generations and 20 runs. Since the program does not make a telescopic solution, diameters can be distributed unbalanced; some engineering approachment must be made on the solution by modeler. To achieve this, not spending too much effort (eliminate lots of trial and error steps), we can find a suitable solution a bit higher (1314 Euro) than the found by SuGA. The solution data we found with some engineering approachment is in table 6.4. with comparing results found by SuGA. So, we see that SuGA is an effective program for finding lower cost solution; SuGA almost nearly reached this solution at the one of these 20 runs.
Table 3.3. Cost Data for Pipe DIAMETER
COST
(MM)
(UNITS)
80 100 125 150 200 250 300 400 500
6,21 8,20 10,72 14,00 21,98 32,51 44,99 78,13 120,22
Table 3.4. Compare SuGA and Final Solution Initial SuGA SuGA Delta Pipe Initial Cost ID Diameter Diameter Diameter Diameter Cost Cost 10 80 80 2.484 2.484 0 11 80 80 2.484 2.484 0 12 80 80 2.484 2.484 0 23 80 80 2.484 2.484 0 24 80 80 2.484 2.484 0 25 80 80 2.484 2.484 0 36 250 300 13.004 17.996 4992 37 250 200 13.004 8.792 -4212 38 200 200 8.792 8.792 0 39 200 150 8.792 5.600 -3192 54 100 100 2.050 2.050 0 55 80 80 1.552,5 1.552,5 0 57 100 100 2.050 2.050 0 58 80 80 1.552,5 1.552,5 0 60 150 150 3.500 3.500 0 61 150 100 3.500 2.050 -1450 62 80 80 1.552,5 1.552,5 0 63 150 150 3.500 3.500 0 64 150 80 3.500 1.552,5 -1947,5 65 80 80 1.552,5 1.552,5 0
Delta Initial SuGA Velocities Velocities Velocities 0,49 0,60 0,69 0,69 0,60 0,49 1,95 1,24 1,54 1,24 1,09 0,77 1,09 0,77 0,84 0,73 0,69 0,84 0,73 0,69
0,63 0,63 0,65 0,66 0,77 0,47 1,38 1,59 1,22 1,42 0,97 0,76 1,01 0,80 1,16 0,88 0,83 1,25 0,85 0,67
0,14 0,03 0,04 0,03 0,17 0,02 0,57 0,35 0,32 0,18 0,12 0,01 0,08 0,03 0,32 0,15 0,14 0,41 0,12 0,02
Node ID 5 6 7 8 14 15 16 17 18 24 25 26 27 28 34 35 36 37 38 44
Initial SuGA Pressures Pressures 28,67 27,38 25,51 23,09 31,91 30,20 27,72 25,81 23,15 33,77 31,01 28,29 25,81 23,30 36,51 32,07 30,15 26,45 23,97 33,77
28,70 26,62 24,54 22,36 32,50 30,85 26,77 24,72 22,54 34,32 32,71 28,87 26,08 23,70 36,51 34,63 30,71 28,30 23,82 34,13
Delta Pressures 0,03 0,76 0,97 0,73 0,59 0,65 0,95 1,09 0,61 0,55 1,70 0,58 0,27 0,40 0 2,56 0,56 1,85 0,15 0,36
Table 3.4. Continues Pipe Initial SuGA Initial SuGA ID Diameter Diameter Diameter Diameter Cost Cost 66 80 80 1.552,5 1.552,5 67 80 80 1.552,5 1.552,5 68 80 80 1.552,5 1.552,5 69 80 80 1.552,5 1.552,5 70 80 100 1.552,5 2.050 71 80 80 1.552,5 1.552,5 72 80 80 1.552,5 1.552,5 73 80 80 1.552,5 1.552,5 74 80 80 1.552,5 1.552,5 75 80 80 1.552,5 1.552,5 76 80 80 1.552,5 1.552,5 77 80 80 1.552,5 1.552,5 78 80 80 1.552,5 1.552,5 79 80 80 1.552,5 1.552,5 80 80 80 1.552,5 1.552,5 81 80 80 1.552,5 1.552,5 82 80 80 1.552,5 1.552,5 83 80 80 1.552,5 1.552,5 93 80 80 2.484 2.484 94 80 125 2.484 4.288 95 80 125 2.484 4.288 96 80 125 2.484 4.288 102 80 80 2.484 2.484
Delta Cost 0 0 0 0 497,5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1804 1804 1804 0
Initial SuGA Delta Velocities Velocities Velocities 0,77 0,41 0,31 0,77 0,41 0,31 0,43 0,03 0,29 0,43 0,03 0,29 0,44 0,20 0,13 0,44 0,20 0,13 0,74 0,73 0,70 0,70 0,74
0,76 0,82 0,20 0,52 0,76 0,50 0,85 0,65 0,22 0,78 0,75 0,09 0,17 0,60 0,22 0,09 0,62 0,21 0,55 1,17 0,98 0,90 0,57
0,01 0,41 0,11 0,25 0,35 0,19 0,42 0,62 0,07 0,35 0,72 0,20 0,27 0,40 0,09 0,35 0,42 0,08 0,19 0,44 0,28 0,20 0,17
Node ID 45 46 47 48 54 55 56 57 58 65 66 67 68 1 3 9 10 11 12 13 19 20 21
Initial SuGA Pressures Pressures 31,01 28,29 25,81 23,30 31,91 30,20 27,72 25,81 23,15 28,67 27,38 25,51 23,09 21,11 21,61 19,05 21,73 19,35 22,48 20,53 21,73 19,35 21,61
32,41 29,30 26,39 23,78 32,11 30,19 28,40 24,62 22,54 28,76 27,56 24,59 22,37 20,05 20,43 19,03 20,76 19,05 21,19 19,06 20,77 19,05 20,44
Delta Pressures 1,40 1,51 0,58 0,48 0,20 0,01 0,68 1,19 0,61 0,09 0,18 0,92 0,72 1,06 1,18 0,02 0,97 0,30 1,29 1,47 0,96 0,30 1,17
Table 3.4. Continues Pipe Initial SuGA Initial SuGA ID Diameter Diameter Diameter Diameter Cost Cost 103 80 150 2.484 5.600 104 80 125 2.484 4.288 105 80 125 2.484 4.288 111 80 80 2.484 2.484 112 125 80 4.288 2.484 113 125 100 4.288 3.280 114 100 100 3.280 3.280 120 80 80 2.484 2.484 121 125 80 4.288 2.484 122 125 80 4.288 2.484 123 100 100 3.280 3.280 1 300 300 224.950 224.950 2 80 80 2.484 2.484 4 100 100 3.280 3.280 5 80 100 2.484 3.280 6 80 100 2.484 3.280 7 80 100 2.484 3.280 8 200 150 8.792 5.600 13 150 125 5.600 4.288 14 80 100 2.484 3.280 15 80 100 2.484 3.280 16 100 100 3.280 3.280 17 80 100 2.484 3.280
Delta Cost 3116 1804 1804 0 -1804 -1008 0 0 -1804 -1804 0 0 0 0 796 796 796 -3192 -1312 796 796 0 796
Initial SuGA Delta Velocities Velocities Velocities 0,73 0,70 0,70 0,57 0,92 0,80 0,83 0,57 0,92 0,80 0,83 1,67 0,62 0,62 0,71 0,55 0,68 0,94 0,91 0,55 0,68 0,62 0,71
1,06 1,10 0,95 0,56 0,91 0,72 0,75 0,61 0,58 0,87 0,73 1,67 0,67 0,73 0,59 0,88 0,66 1,07 0,85 0,89 0,66 0,73 0,59
0,33 0,40 0,25 0,01 0,01 0,08 0,08 0,04 0,34 0,07 0,10 0 0,05 0,11 0,12 0,33 0,02 0,13 0,06 0,34 0,02 0,11 0,12
Node ID 22 23
Initial SuGA Pressures Pressures 19,05 21,11
19,03 20,06
Delta Pressures 0,02 1,05
Table 3.4. Continues SuGA Initial SuGA Pipe Initial ID Diameter Diameter Diameter Diameter Cost Cost 18 80 80 2.484 2.484 20 80 80 1.552,5 1.552,5 21 100 80 2.050 1.552,5 22 100 80 2.050 1.552,5 27 100 80 2.050 1.552,5 28 100 80 2.050 1.552,5 29 80 80 1.552,5 1.552,5 31 80 80 1.552,5 1.552,5 32 80 80 1.552,5 1.552,5 33 80 80 1.552,5 1.552,5 34 80 80 1.552,5 1.552,5 442.592 441.278
Delta Cost 0 0 -497,5 -497,5 -497,5 -497,5 0 0 0 0 0 -1314
SuGA Delta Initial Velocities Velocities Velocities 0,62 0,38 0,20 0,54 0,54 0,20 0,38 0,29 0,60 0,60 0,29
0,67 0,33 0,30 0,35 0,34 0,30 0,33 0,07 0,04 0,04 0,07
0,05 0,05 0,10 0,19 0,20 0,10 0,05 0,22 0,56 0,56 0,22
Node ID
Initial SuGA Pressures Pressures
Delta Pressures
4.1. Conclusion The combinatorial optimization problem of least-cost design of water distribution networks is formulated by several researchers and it is shown that GAs are particularly suited to this type of problem (Savic and Walters, 1997). GA does not provide the absolute answers to the problems that are being investigated, but it is more a powerful new tool for moving towards the best solution. GAs are not replacement traditional simulation modeling program, instead, they are performed next step after hydraulic solver. However, instead of relying on the modeler to evaluate different scenarios on a trial and error basis, GA optimization automates the solution search process by instructing the computer to successively generate and evaluate possible solutions. This study describes development of a computer program, called SuGA, which uses Genetic Algorithm for the least-cost design and expansion of water distribution system. SuGA does not expose telescopic (enlarged diameters from end point to tank) solution. It needs to be corrected by an engineer, so the final solution may be higher than solution found by SuGA. Program was tested with several problems from the literature, comparing solutions was fairly near for small-scale water distribution systems. In conclusion, SuGA can be used for new design, expansion or rehabilitation of existing water distribution systems for optimization
4.2. Recommendations SuGA use single objective function, constraints take part inside fitness function as a penalty. Constraints and pipes can be coded separately in multiobjective function. Usage of multiobjective function on WDS should be considered. Binary coding scheme has some disadvantage such as the hamming cliff effect and redundant values. Real value or Gray coding scheme can be used instead of binary coding Simple genetic algorithm is not effective on large-scale water distribution systems. Several researchers studied on modified genetic algorithm such as structured messy genetic algorithm, fast messy genetic algorithm, and they give good solution on large-scale water
distribution systems. Developing a new genetic algorithm which is more suitable for WDS should be investigated. SuGA does not provide telescopic solution. Adding a function to SuGA can provide telescopic solution, so it will be helped close to final solution. SuGA has capable optimal design and expansion of WDS. Other usage of GA on WDS such as pump scheduling, leakage reduction, water quality control etc. can be added to SuGA with some developing coding scheme. 5. References 1. Goldberg, D. E. (1989). Genetic Algorithms in Search Optimization and Machine Learning. Addison Wesley, MA, USA. 2. Melanie Mitchell, (1996). “An introduction to genetic algorithm” Cambridge, MA:MIT P. 3. Obitko, Marek and Slavík, Pavel. Visualization of Genetic Algorithms in a Environment. In: Spring Conference on Computer Graphics, SCCG'99.
Learning Bratislava :
Comenius University, 1999, p. 101-106. ISBN 80-223-1357-2. 4. Rossman, L. A. (1994). EPANET USERS MANUAL, Risk Reduction Engineering Laboratory, U.S. Environmental Protection Agency, USA. 5. Savic, D. A., and Walters, G. A. (1997). “Genetic algorithms for least-cost design of water distribution networks.” J. Water Resour. Plng. and Mgmt., ASCE, 123(2), 67-77. 6. Simpson, A. R., Murphy, L. J., and Dandy G. C. (1993). “Pipe Network Optimization using Genetic Algorithms.” Paper presented at ASCE, Water Resources Planning and Management Specialty Conference, ASCE, Seattle, USA. 7. Simpson, A. R., Dandy G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.” J. Water Resour. Plng. and Mgmt., ASCE, 120(4), 423-443. 8. Simpson, A.R. (2000). "Optimization of design of water distribution systems using genetic algorithms." Slovenian Society of Hydraulic Research, Seminar Series, Vol.1, Ljubljana, Slovenia, 10pp. 9. The optimatics letter Issue No:12 (April-June, 2001) Advances in Optimization for Water Distribution System Design & Operations 10. http:\\www.optiwater.com
