Extensive research have been conducted to optimize the water distribution networks, but none has simultaneously considered the economic-mechanical and hydraulic properties of the networks. Moreover, the entropy difference in the various networks has not been exactly calculated. Therefore, the present study suggests a modified entropy function for computing the information entropy of the water distribution networks to calculate the demand nods and entropy difference amongst the various networks considering the mechanical and hydraulic properties of the network. This modification is carried out by defining a coefficient in entropy function as the output amount in every node by the exponent of all the power wasted in the network. Furthermore, the most optimum diameter and the most economic state are obtained simultaneously using the ant colony algorithm (ACO). Thus, considering all the three mechanical, hydraulic, and economic properties of the network while keeping simplicity, a more realistic method will be offered using these two metaheuristic methods. The efficiency of the proposed method was evaluated in some of the sample water networks using the modified function
Moghtaderi-Zadeh, M. and Kiureghian, A., "Reliability upgrading of lifeline networks for post-earthquake serviceability", Earthquake Engineering and Structural Dynamics, Vol. 11, (1983), 557-566. https://doi.org/10.1002/eqe.4290110408
Selçuk, R.D.A.S. and Yücemen, M.S., "Reliability of lifeline networks under seismic hazard", Reliability Engineering and System Safety, Vol. 65, (1999), 213-227. https://doi.org/10.1016/S0951-8320(98)00098-2
Quimpo, R.G. and Shamsi, U.M., "Reliability-based distribution system maintenance", Journal of Water Resources Planning and Manage, ASCE, Vol. 117, (1991), 321-339. https://doi.org/10.1061/(ASCE)0733-9496(1991)117:3(321)
Tanyimboh, T., Burd, R., Burrows, R. and Tabesh, M., "Modelling and reliability analysis of water distribution systems", Water Science and Technology, Vol. 39, No. 4, (1999), 249-255. https://doi.org/10.1016/S0273-1223(99)00078-5
Awumah, K., Goulter, I. and Bhatt, S., "Assessment of reliability in water distribution networks using entropy based measures", Stochastic Hydrology and Hydraulics, Vol. 4, (1990), 309-320. https://doi.org/10.1007/BF01544084
Tanyimboh, T.T. and Templeman, A.B., "A quantified assessment of the relationship between the reliability and entropy of water distribution systems", Engineering Optimization, Vol. 33, No. 2, (2000), 179-199. https://doi.org/10.1080/03052150008940916
Awumah, K., Goulter, I. and Bhatt, S.K., "Entropy-based redundancy measures in water-distribution networks", Journal of Hydraulic Engineering, Vol. 117, No. 5, (1991), 595-614. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(595)
Javanbarg, M.B., Takada, S. and Kuwata, Y., “Seismic vulnerability evaluation of water delivery system”, The 12th Japan Earthquake Engineering Symposium, Tokyo, Japan, (2006).
Shannon, C., "A mathematical theory of communication", The Bell System Technical Journal, Vol. 27, No. 3, (1948), 379-423. DOI: 10.1002/j.1538-7305.1948.tb01338.x
Tanyimboh, T. and Templeman, A., "Calculating maximum entropy flows in networks", Journal of the Operational Research Society, Vol. 44, No. 4, (1993), 383-396. https://doi.org/10.1057/jors.1993.68
Khinchin, A.I., "The entropy concept in probability theory", Courier Corporation, (2013).
Tanyimboh, T. and Templeman, A., "Maximum entropy flows for single-source networks", Engineering Optimization, Vol. 22, No. 1, (1993), 49-63. https://doi.org/10.1080/03052159308941325
Walters, G., "Discussion on: Maximum entropy flows in single source networks3", Engineering Optimization+ A35, Vol. 25, No. 2, (1995), 155-163. https://doi.org/10.1080/03052159508941260
Yassin-Kassab, A., Templeman, A. and Tanyimboh, T., "Calculating maximum entropy flows in multi-source, multi-demand networks", Engineering Optimization, Vol. 31, No. 6, (1999), 695-729. https://doi.org/10.1080/03052159908941393
Hosseini, M. and Emamjomeh, H., "A method for assessmentof water distribution networks’ redundancyby using informational entropy", in 4th International Conference from Scientific Computing to Computational Engineering 4th IC-SCCE, Athens., (2010 of Conference).
Ang, W.K. and Jowitt, P.W., "Some new insights on informational entropy for water distribution networks", Engineering Optimization, Vol. 37, No. 3, (2005), 277-289. https://doi.org/10.1080/0305215512331328259
Hosseini, M. and Emamjomeh, H., "Entropy-based serviceability assessment of water distribution networks subjected to natural and man-made hazards", International Journal Engineering, Transactions B: applications, Vol. 27, No. 5, (2014), 675-688. DOI: 10.5829/idosi.ije.2014.27.05b.02
Ang, W.K. and Jowitt, P., "Some observations on energy loss and network entropy in water distribution networks", Engineering Optimization, Vol. 37, (2003), 375-389. https://doi.org/10.1080/0305215031000154668
Tanyimboh, T.T. and Templeman, A.B. “Calculating the reliability of single-source networks by the source head method”, Advances in Engineering. Software., Vol 29, (1998), 499-505. https://doi.org/10.1016/S0965-9978(98)00016-7
Bulm, C. and Roli, A., "Metaheuristics in combinatorial optimization overview and conceptual comparison", ACM Computing Surveys Vol. 35, (2003), 268-308. https://doi.org/10.1145/937503.937505
Mousavi. M., S. A., & Nateghi, F. (2023). Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm. International Journal of Engineering, 36(5), 979-990. doi: 10.5829/ije.2023.36.05b.14
MLA
S. A. Mousavi. M.; F. Nateghi. "Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm". International Journal of Engineering, 36, 5, 2023, 979-990. doi: 10.5829/ije.2023.36.05b.14
HARVARD
Mousavi. M., S. A., Nateghi, F. (2023). 'Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm', International Journal of Engineering, 36(5), pp. 979-990. doi: 10.5829/ije.2023.36.05b.14
VANCOUVER
Mousavi. M., S. A., Nateghi, F. Seismic and Economic Optimization of Water Distribution Networks Using Entropy and Ant Colony Algorithm. International Journal of Engineering, 2023; 36(5): 979-990. doi: 10.5829/ije.2023.36.05b.14