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YAPAY ARI KOLONİSİ ALGORİTMASI KULLANILARAK SU DAĞITIM ŞEBEKELERİNİN OPTİMİZASYONU

Yıl 2020, Cilt: 9 Sayı: 1, 377 - 392, 30.01.2020
https://doi.org/10.28948/ngumuh.568917

Öz

Su dağıtım
şebekeleri, şehir yaşamında kullanmak için gerekli olan suyun kullanıcılarına
dağıtımıını sağlayan yapılardır. Gerekli olan suyun kaynağından kullanıcılara
iletilmesini sağlayan tesisler arasında, su dağıtım şebekelerinin maliyetinin
toplam maliyete oranının oldukça yüksek olduğu bilinmektedir. Su dağıtım
şebekelerindeki belirli sınırlamalar, tasarımda kullanılan parametrelerin
fazlalığı ve ortaya çıkan yüksek miktardaki maliyet değerleri, su dağıtım
şebekelerinde maliyet optimizasyonunu zorunlu kılmıştır. Bu çalışmada, yeni bir
yöntem olan Yapay Arı Kolonisi optimizasyon yöntemini kullanarak daha önce çok
sayıda araştırmacı tarafından kullanılmış olan Alperovits ve Shamir şebekesi,
Hanoi şehri su dağıtım şebekesi ve bir yenileme projesi olarak New York şehri
su dağıtım şebekesi üzerinde maliyet optimizasyonu yapılmış ve sonuçlar
değerlendirilmiştir.

Kaynakça

  • OZDAĞLAR, D., BENZEDEN, E., KAHRAMAN, A.M., "Kompleks Su Dağıtım Şebekelerinin Genetik Algoritma ile Optimizasyonu", Technical Journal, 3851-3867,2006.
  • AYVAZ, M.T,, KARAHAN, H., GURARSLAN, G., "Su dağıtım şebekelerinin armoni araştırması optimizasyon tekniği ile optimum tasarımı", 5. Kentsel Altyapı Ulusal Sempozyumu, 1-2 Kasım 2007, Antakya-Hatay, 2007.
  • KEEDWELL, E., KHU, S.,"Novel cellular automata approach to optimal water distribution network design", J. Comput. Civ. Eng., 20(1), 49-56, 2006.
  • MOHAN, S., JINESH BABU, K.S., "Water distribution network design using heuristic-based algorithm" J. Comput. Civ. Eng., 23(5), 249-257, 2009.
  • WU, Z.Y., SIMPSON, A.R., "Component genetic-evolutionary optimization of water distribution systems", J. Comput. Civ. Eng., 15(2), 89-101, 2001.
  • AFSHAR, M.H., "Application of a compact genetic algorithm to pipe network optimization problems", Transaction A: Civil Engineering, 16(3): 264-271, 2009.
  • SIMPSON, A.R., DANDY, G.C., MURPHY, L.J., "Genetic algorithms compared to other techniques for pipe optimization", J. Water Resour. Plann. Manage., 120(4), 423-443, 1994.
  • DANDY, G.C., SIMPSON, A.R., MURPHY, L.J., "An improved genetic algorithm for pipe network optimization", Water Resources Research, 32(2), 449-458, 1996.
  • GOLDBERG, D.E., KUO, C.H., "Genetic algorithms in pipeline optimization" J. Comput. Civ. Eng., 1(2), 128–141, 1987.
  • REZAEI, G., AFSHAR, M.H., ROHANI, M., "Layout optimization of looped networks by constrained ant colony optimisation algorithm", Advances in Engineering Software, 70, 123-133, 2014.
  • AFSHAR, M.H., "Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: application to storm water network design", Advances in Water Resources, 30, 954-965, 2007.
  • ZECCHIN, A.C., MAIER, H.R., SIMPSON, A.R, LEONARD, M., NIXON, J.B., "Ant colony optimization applied to water distribution system design: comparative study of five algorithms", J. Water Resour. Plann. Manage., 133(1), 87-92, 2007.
  • MAIER, H.R., SIMPSON, A.R., ZECCHIN, A.C., FOONG, W.K., PHANG, K.Y., SEAH, H.Y., TAN, C.L, "Ant colony optimization for design of water distribution systems", J. Water Resour. Plann. Manage., 129(3), 200-209, 2003.
  • EZZELDIN, R., DJEBEDJIAN, B., SAAFAN, T., "Integer discrete particle swarm optimization of water distribution networks", Journal of Pipeline Systems Engineering and Practice, 5(1), 04013013, DOI: 10.1061/(ASCE)PS.1949-1204.0000154, 2014.
  • MONTALVO, I., IZQUIERDO, J., PEREZ, R., TUNG, M.M., "Particle swarm optimization applied to the design of water supply systems", Computers and Mathematics with Applications, 56, 769-776, 2008.
  • QIAO, J.F., WANG, Y.F., CHAI, W., SUN, L.B., "Optimal water distribution network design with improved particle swarm optimization", Int. Journal of Comp. Sci. and Eng. 6(1-2), 34-42, 2011.
  • TOSPORNSAMPAN, J., KITA, I., ISHII, M., KITAMURA, Y., "Split-pipe design of water distribution network using simulated annealing", Int. Journal of Envir. Ecol. Geol. and Mining Eng., 1(4), 31-41, 2007.
  • CUNHA, M.C., SOUSA, J., "Water distribution network design optimization: simulated annealing approach", Journal of Water Resources Planning and Management, 125(4),215-221, 1999.
  • GEORGESCU, S.C., "HBMOA Applied to Design A Water Distribution Network For A Town of 50000 Inhabitants", U.P.B. Sci. Bull., Series D, Vol. 74, Iss.1, 91-102, 2012.
  • GEORGESCU, S.C., POPA, R. "Water Distribution Networks Optimal Design Using The Honey Bee Mating Optimization Algorithm" 4th International Conference on Energy and Environment CIEM2009, November 12-14, Bucharest, 2009.
  • CHUNG, G., LANSEY, K., "Application of the shuffled frog leaping algorithm for the optimization of a general large-scale water supply system", Water Resources Management, 23: 797-823, 2009.
  • SURİBABU, C.R., NEELAKANTA, T.R., "Optimal upgradation and expansion of existing water distribution networks using differential evolution algorithm", Asian Journal of Applied Sciences, 7(6): 375-390, 2014.
  • ZHENG, F., SIMPSON, A.R., ZECCHIN, A.C., "A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems", Water Resources Research, 47(8), 2011.
  • ZHENG, F., ZECCHİN A.C., SIMPSON, A.R., "Self-adaptive differential evolution algorithm applied to water distribution system optimization", J. Comput. Civ. Eng., 27(2): 148-158, 2013.
  • BAEK, C.W., JUN, H.D., KIM, J.H., "Development of a PDA model for water distribution systems using harmony search algorithm", KSCE Journal of Civil Engineering. 14(4):613-625, 2010.
  • GEEM, Z.W., CHO, Y., "Optimal design of water networks using parameter-setting-free harmony search for two major parameters", J. Water Resour. Plann. Manage., 137(4): 377–380, 2010.
  • GEEM, Z.W., "Comparison harmony search with other meta-heuristics in water distribution network design", Water Distribution Systems Analysis Symposium 2006.
  • SUNG, Y.H., LIN, M.D., LIN, Y.H., LIU, Y.L., "Tabu search solution of water distribution network optimization", J. Environ. Eng. Manage., 17(3): 177–187, 2007.
  • CUNHA, M.C., RIBEIRO, L., "Tabu search algorithms for water network optimization", European Journal of Operational Research, 157: 746-758, 2004.
  • MOHAN, S., JINESH BABU, K.S., "Optimal water distribution network design with honey-bee mating optimization", J. Comput. Civ. Eng. 24(1): 117-126, 2010.
  • PAN, Q.K., TASGETIREN, M.F., SUGANTHAN, P.N., CHUA, T.J., "A discrete artificial bee colony algortihm for the lot-streaming flow shop scheduling problem", Information Sciences, 181(12): 2455-2468, 2011.
  • KARABOGA, D., "An Idea Based on Honey Bee Swarm for Numerical Optimization", Techinical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.
  • AKAY, B., "Performance Analysis of Artificial Bee Colony Algorithm on Numerical Optimization Problems", Ph.D. thesis, Erciyes University, Graduate School of Natural and Applied Sciences, Turkey, 2009.
  • ALPEROVITS, E., SHAMIR, U., "Design of optimal water distribution systems", Water Resources Research, 13(6): 885-900, 1977.
  • SAVIC, D.A., WALTERS, G.A., "Genetic algorithms for least-cost design of water distribution networks", J. Water Resour. Plann. Manage., 123 (2): 67-77, 1997.
  • EUSUFF, M.M, LANSEY, K.E., "Optimization of water distribution network design using the shuffled frog leaping algorithm", J. Water Resour. Plann. Manage., 129(3):210–225, 2003.
  • MONBALIU, J., JO, J., FRAISSE, C.W., VADAS, R.G., "Computer aided design of pipe networks", Proc., Int. Symp. on Water Resource Systems Application, 2009.
  • MURPHY, L.J., SIMPSON, A.R, "Genetic Algorithms in Pipe Network Optimization", Res. Rep. No. R93 Dept. of Civ. and Envir. Engrg. Univ. of Adelaide Australia, 1992.
  • SEDKI, A., OUAZAR, D., "Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems", Advanced Engineering Informatics, 26: 582-591, 2012.
  • FUJIWARA, O., KHANG, D.B., "A two-phase decomposition method for optimal design of looped water distribution networks", Water Resources Research, 26(4):539-549, 1990.
  • LIONG, S., ATIQUZZAMAN, M., "Optimal design of water distribution network using shuffled complex evolution", Journal of the Institution of Engineers, 44(1): 93-107, 2004.
  • PERELMAN, L., OSTFELD, A., "An adaptive heuristic cross-entropy algorithm for optimal design of water distribution systems", Engineering Optimization, 39(4): 413-428, 2007.
  • JINESH BABU, K.S., VIJAYALAKSHMI, D.P., "Self-Adaptive PSO-GA hybrid model for combinatorial water distribution network design", Journal of Pipeline Systems Engineering and Practice, 4(1): 57-67, 2013.
  • SCHAAKE J.C., LAI, F.H., "Linear Programming and Dynamic Programming Applications to Water Distribution Network Design", Rep.116, Dept. of Civ. Engrg. Massachusetts Inst. Of Technol. Cambridge Mass, 1969.
  • QUINDRY, G.E., LIEBMAN, J.C., BRILL, E.D., "Optimization of looped water distribution systems", Journal of the Environmental Engineering Division ASCE, 107(4): 665-679, 1981.
  • VASAN, A., SIMONOVIC, S.P., "Optimization of water distribution network using differential evolution", J. Water Resour. Plann. Manage., 136(2):279-287, 2010.
  • YILMAZ, V., "Su Dağıtım Şebekelerinin Metasezgisel Yöntemlerle Optimizasyonu. [Optimization of Water Distribution Networks Using Metaheuristic Methods]", PhD thesis. The Graduate School of Natural and Applied Science, Selcuk University, Konya, Turkey (in Turkish), 2015.

OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM

Yıl 2020, Cilt: 9 Sayı: 1, 377 - 392, 30.01.2020
https://doi.org/10.28948/ngumuh.568917

Öz

Water
distribution networks are such structures, which maintain the distribution of
the water necessary for use in the city-life to its users. Among the
facilities, which maintain the transmission of the utility water from its
resource to the users, water distribution networks are known to have quite high
ratio of cost to the overall cost. Certain limitations in the water
distribution networks, excessiveness of the parameters being in use in the
design, and the high amounts of cost being incurred, have altogether
necessitated the cost optimization in the water distribution networks. In this
study, cost optimization using the Artificial Bee Colony (ABC) optimization
method, which is a novel method, was performed on Alperovits and Shamir
network, Hanoi city water distribution network as well as New York city water
distribution network as a rehabilitation practice, which were previously used
by numerous researchers, and the results were evaluated.

Kaynakça

  • OZDAĞLAR, D., BENZEDEN, E., KAHRAMAN, A.M., "Kompleks Su Dağıtım Şebekelerinin Genetik Algoritma ile Optimizasyonu", Technical Journal, 3851-3867,2006.
  • AYVAZ, M.T,, KARAHAN, H., GURARSLAN, G., "Su dağıtım şebekelerinin armoni araştırması optimizasyon tekniği ile optimum tasarımı", 5. Kentsel Altyapı Ulusal Sempozyumu, 1-2 Kasım 2007, Antakya-Hatay, 2007.
  • KEEDWELL, E., KHU, S.,"Novel cellular automata approach to optimal water distribution network design", J. Comput. Civ. Eng., 20(1), 49-56, 2006.
  • MOHAN, S., JINESH BABU, K.S., "Water distribution network design using heuristic-based algorithm" J. Comput. Civ. Eng., 23(5), 249-257, 2009.
  • WU, Z.Y., SIMPSON, A.R., "Component genetic-evolutionary optimization of water distribution systems", J. Comput. Civ. Eng., 15(2), 89-101, 2001.
  • AFSHAR, M.H., "Application of a compact genetic algorithm to pipe network optimization problems", Transaction A: Civil Engineering, 16(3): 264-271, 2009.
  • SIMPSON, A.R., DANDY, G.C., MURPHY, L.J., "Genetic algorithms compared to other techniques for pipe optimization", J. Water Resour. Plann. Manage., 120(4), 423-443, 1994.
  • DANDY, G.C., SIMPSON, A.R., MURPHY, L.J., "An improved genetic algorithm for pipe network optimization", Water Resources Research, 32(2), 449-458, 1996.
  • GOLDBERG, D.E., KUO, C.H., "Genetic algorithms in pipeline optimization" J. Comput. Civ. Eng., 1(2), 128–141, 1987.
  • REZAEI, G., AFSHAR, M.H., ROHANI, M., "Layout optimization of looped networks by constrained ant colony optimisation algorithm", Advances in Engineering Software, 70, 123-133, 2014.
  • AFSHAR, M.H., "Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: application to storm water network design", Advances in Water Resources, 30, 954-965, 2007.
  • ZECCHIN, A.C., MAIER, H.R., SIMPSON, A.R, LEONARD, M., NIXON, J.B., "Ant colony optimization applied to water distribution system design: comparative study of five algorithms", J. Water Resour. Plann. Manage., 133(1), 87-92, 2007.
  • MAIER, H.R., SIMPSON, A.R., ZECCHIN, A.C., FOONG, W.K., PHANG, K.Y., SEAH, H.Y., TAN, C.L, "Ant colony optimization for design of water distribution systems", J. Water Resour. Plann. Manage., 129(3), 200-209, 2003.
  • EZZELDIN, R., DJEBEDJIAN, B., SAAFAN, T., "Integer discrete particle swarm optimization of water distribution networks", Journal of Pipeline Systems Engineering and Practice, 5(1), 04013013, DOI: 10.1061/(ASCE)PS.1949-1204.0000154, 2014.
  • MONTALVO, I., IZQUIERDO, J., PEREZ, R., TUNG, M.M., "Particle swarm optimization applied to the design of water supply systems", Computers and Mathematics with Applications, 56, 769-776, 2008.
  • QIAO, J.F., WANG, Y.F., CHAI, W., SUN, L.B., "Optimal water distribution network design with improved particle swarm optimization", Int. Journal of Comp. Sci. and Eng. 6(1-2), 34-42, 2011.
  • TOSPORNSAMPAN, J., KITA, I., ISHII, M., KITAMURA, Y., "Split-pipe design of water distribution network using simulated annealing", Int. Journal of Envir. Ecol. Geol. and Mining Eng., 1(4), 31-41, 2007.
  • CUNHA, M.C., SOUSA, J., "Water distribution network design optimization: simulated annealing approach", Journal of Water Resources Planning and Management, 125(4),215-221, 1999.
  • GEORGESCU, S.C., "HBMOA Applied to Design A Water Distribution Network For A Town of 50000 Inhabitants", U.P.B. Sci. Bull., Series D, Vol. 74, Iss.1, 91-102, 2012.
  • GEORGESCU, S.C., POPA, R. "Water Distribution Networks Optimal Design Using The Honey Bee Mating Optimization Algorithm" 4th International Conference on Energy and Environment CIEM2009, November 12-14, Bucharest, 2009.
  • CHUNG, G., LANSEY, K., "Application of the shuffled frog leaping algorithm for the optimization of a general large-scale water supply system", Water Resources Management, 23: 797-823, 2009.
  • SURİBABU, C.R., NEELAKANTA, T.R., "Optimal upgradation and expansion of existing water distribution networks using differential evolution algorithm", Asian Journal of Applied Sciences, 7(6): 375-390, 2014.
  • ZHENG, F., SIMPSON, A.R., ZECCHIN, A.C., "A combined NLP-differential evolution algorithm approach for the optimization of looped water distribution systems", Water Resources Research, 47(8), 2011.
  • ZHENG, F., ZECCHİN A.C., SIMPSON, A.R., "Self-adaptive differential evolution algorithm applied to water distribution system optimization", J. Comput. Civ. Eng., 27(2): 148-158, 2013.
  • BAEK, C.W., JUN, H.D., KIM, J.H., "Development of a PDA model for water distribution systems using harmony search algorithm", KSCE Journal of Civil Engineering. 14(4):613-625, 2010.
  • GEEM, Z.W., CHO, Y., "Optimal design of water networks using parameter-setting-free harmony search for two major parameters", J. Water Resour. Plann. Manage., 137(4): 377–380, 2010.
  • GEEM, Z.W., "Comparison harmony search with other meta-heuristics in water distribution network design", Water Distribution Systems Analysis Symposium 2006.
  • SUNG, Y.H., LIN, M.D., LIN, Y.H., LIU, Y.L., "Tabu search solution of water distribution network optimization", J. Environ. Eng. Manage., 17(3): 177–187, 2007.
  • CUNHA, M.C., RIBEIRO, L., "Tabu search algorithms for water network optimization", European Journal of Operational Research, 157: 746-758, 2004.
  • MOHAN, S., JINESH BABU, K.S., "Optimal water distribution network design with honey-bee mating optimization", J. Comput. Civ. Eng. 24(1): 117-126, 2010.
  • PAN, Q.K., TASGETIREN, M.F., SUGANTHAN, P.N., CHUA, T.J., "A discrete artificial bee colony algortihm for the lot-streaming flow shop scheduling problem", Information Sciences, 181(12): 2455-2468, 2011.
  • KARABOGA, D., "An Idea Based on Honey Bee Swarm for Numerical Optimization", Techinical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.
  • AKAY, B., "Performance Analysis of Artificial Bee Colony Algorithm on Numerical Optimization Problems", Ph.D. thesis, Erciyes University, Graduate School of Natural and Applied Sciences, Turkey, 2009.
  • ALPEROVITS, E., SHAMIR, U., "Design of optimal water distribution systems", Water Resources Research, 13(6): 885-900, 1977.
  • SAVIC, D.A., WALTERS, G.A., "Genetic algorithms for least-cost design of water distribution networks", J. Water Resour. Plann. Manage., 123 (2): 67-77, 1997.
  • EUSUFF, M.M, LANSEY, K.E., "Optimization of water distribution network design using the shuffled frog leaping algorithm", J. Water Resour. Plann. Manage., 129(3):210–225, 2003.
  • MONBALIU, J., JO, J., FRAISSE, C.W., VADAS, R.G., "Computer aided design of pipe networks", Proc., Int. Symp. on Water Resource Systems Application, 2009.
  • MURPHY, L.J., SIMPSON, A.R, "Genetic Algorithms in Pipe Network Optimization", Res. Rep. No. R93 Dept. of Civ. and Envir. Engrg. Univ. of Adelaide Australia, 1992.
  • SEDKI, A., OUAZAR, D., "Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems", Advanced Engineering Informatics, 26: 582-591, 2012.
  • FUJIWARA, O., KHANG, D.B., "A two-phase decomposition method for optimal design of looped water distribution networks", Water Resources Research, 26(4):539-549, 1990.
  • LIONG, S., ATIQUZZAMAN, M., "Optimal design of water distribution network using shuffled complex evolution", Journal of the Institution of Engineers, 44(1): 93-107, 2004.
  • PERELMAN, L., OSTFELD, A., "An adaptive heuristic cross-entropy algorithm for optimal design of water distribution systems", Engineering Optimization, 39(4): 413-428, 2007.
  • JINESH BABU, K.S., VIJAYALAKSHMI, D.P., "Self-Adaptive PSO-GA hybrid model for combinatorial water distribution network design", Journal of Pipeline Systems Engineering and Practice, 4(1): 57-67, 2013.
  • SCHAAKE J.C., LAI, F.H., "Linear Programming and Dynamic Programming Applications to Water Distribution Network Design", Rep.116, Dept. of Civ. Engrg. Massachusetts Inst. Of Technol. Cambridge Mass, 1969.
  • QUINDRY, G.E., LIEBMAN, J.C., BRILL, E.D., "Optimization of looped water distribution systems", Journal of the Environmental Engineering Division ASCE, 107(4): 665-679, 1981.
  • VASAN, A., SIMONOVIC, S.P., "Optimization of water distribution network using differential evolution", J. Water Resour. Plann. Manage., 136(2):279-287, 2010.
  • YILMAZ, V., "Su Dağıtım Şebekelerinin Metasezgisel Yöntemlerle Optimizasyonu. [Optimization of Water Distribution Networks Using Metaheuristic Methods]", PhD thesis. The Graduate School of Natural and Applied Science, Selcuk University, Konya, Turkey (in Turkish), 2015.
Toplam 47 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İnşaat Mühendisliği
Bölüm İnşaat Mühendisliği
Yazarlar

Volkan Yılmaz 0000-0002-5407-860X

Meral Büyükyıldız 0000-0003-1426-3314

Ömer Kaan Baykan 0000-0001-5890-510X

Yayımlanma Tarihi 30 Ocak 2020
Gönderilme Tarihi 22 Mayıs 2019
Kabul Tarihi 10 Eylül 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 9 Sayı: 1

Kaynak Göster

APA Yılmaz, V., Büyükyıldız, M., & Baykan, Ö. K. (2020). OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 9(1), 377-392. https://doi.org/10.28948/ngumuh.568917
AMA Yılmaz V, Büyükyıldız M, Baykan ÖK. OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM. NÖHÜ Müh. Bilim. Derg. Ocak 2020;9(1):377-392. doi:10.28948/ngumuh.568917
Chicago Yılmaz, Volkan, Meral Büyükyıldız, ve Ömer Kaan Baykan. “OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9, sy. 1 (Ocak 2020): 377-92. https://doi.org/10.28948/ngumuh.568917.
EndNote Yılmaz V, Büyükyıldız M, Baykan ÖK (01 Ocak 2020) OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9 1 377–392.
IEEE V. Yılmaz, M. Büyükyıldız, ve Ö. K. Baykan, “OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM”, NÖHÜ Müh. Bilim. Derg., c. 9, sy. 1, ss. 377–392, 2020, doi: 10.28948/ngumuh.568917.
ISNAD Yılmaz, Volkan vd. “OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 9/1 (Ocak 2020), 377-392. https://doi.org/10.28948/ngumuh.568917.
JAMA Yılmaz V, Büyükyıldız M, Baykan ÖK. OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM. NÖHÜ Müh. Bilim. Derg. 2020;9:377–392.
MLA Yılmaz, Volkan vd. “OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, c. 9, sy. 1, 2020, ss. 377-92, doi:10.28948/ngumuh.568917.
Vancouver Yılmaz V, Büyükyıldız M, Baykan ÖK. OPTIMIZATION OF WATER DISTRIBUTION NETWORKS USING ARTIFICIAL BEE COLONY ALGORITHM. NÖHÜ Müh. Bilim. Derg. 2020;9(1):377-92.

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