We can also use a pseudo-pipe which has a very large Hazen-Williams coefficient and extremely expensive as one of the commercially available pipes to.
Closure to “Optimization of Water Distribution Networks Using Integer Linear Programming” by Hossein M. V. Samani and Alireza Mottaghi May 2006, Vol. 132,No. 5. pp. 501-509. DOI, 10.1061/(ASCE)0733-9429(2006)132:5(501) Hossein Mohammad Vali Samani 1 1
Professor, Dept. of Civil Engineering, Faculty of Engineering, Shahid Chamran Univ., Ahvaz, Iran.
I would like to thank the discussers for their interesting and valuable comments. The validity of the integer linear programming approach was demonstrated by examples 1 and 2. The reason for selecting a simple example (Example 1) is that depicting all possible result combinations in a paper for a larger problem is not possible. It should be noted that even for the chosen simple example, sixteen possible combinations are shown. The second example represents a network that has been studied by many other researchers such as Alprovits and Shamir (1977), Goulter et al.(1986), Kessler and Shamir(1989), Eiger et al.(1994), and Savic and Walters(1997). The authors had to choose such an example in order to be able to compare the results with those obtained by others from accuracy and run time points of view. Actually, the main goal of presenting rather small examples in the paper is to introduce the integer linear programming approach as a new tool in this field that can be used for solving the water distribution system optimization problems. I do not see any problem to apply the ILPA for solving large real problems. On the contrary, the approach should be more appropriate for solving WDP because it is simple and computationally fast compared to other widely used algorithms as was demonstrated in the paper.
The convergence of Example 2 is illustrated in Table 14. The example was solved by using different initial diameters. All runs converged to the same results rapidly. I believe that this may approve the ability of the approach to obtain the global optimum. I agree with the discussers that one of the weak points in the ILPA is including all source nodes and pipes in the pressure constraint [equations (5)] and it is much easier if, instead of paths, only one pipe is included in every equation. As a matter of fact, I have used the mixed integer real linear programming for solving WDN optimization and I hope this will be published soon. I thank the discussers for finding the “bugs” in the paper. I believe that mentioning about the substitution of the valve with an equivalent length of pipe is not necessary because there are a lot of other minor losses in a water distribution network and none of them is usually mentioned. I would like to comment on the issue of viewing the ILPA as a step backward, both in terms of research and practical application of optimization to design of WDN. It is a wellknown fact that the linear programming approach is in general easier and much faster than other approaches in solving WDN optimization. The network shown in Fig. 2 of the paper, which has been studied by many other researchers, was solved by using different initial diameters. All runs converged to the same results. Table 14 indicates that the number of iterations is between 2 and 5 for different initial diameters. It can also be seen in Table 14 that the run time is between 0.96 and 2.4 seconds [Pentium 4 (Processor 2.4 GHz, Ram 512 MB)]. I have also employed this approach to Hanoi network that includes 34 pipes and studied by many other researchers such as Savic and Walters (1997), Abebe and Solomanite (1998), Cunha and Sousa (1999), and Liong and Atiquzzman (2004). The
run time of obtaining the optimal design using the same PC was 4 minutes. This demonstrates that the proposed method is fast compared to other widely used algorithms. Regarding the issue of the problem in the solution when the initial decision variables are poorly selected, the author has discussed how to overcome the problem at the end of the paper. We can also use a pseudo-pipe which has a very large Hazen-Williams coefficient and extremely expensive as one of the commercially available pipes to overcome the mentioned problem. In this case, the optimization program will select the pseudo-pipe because it will lead to a very small head loss. Therefore, pressures at nodes after this pipe will not be so low to violate the pressure constraint and consequently the computer program will proceed until a feasible solution is found. However, the combination of pipes, which include the pseudo-pipe, will not be the optimal one because it is extremely expensive. Therefore, the program will proceed without influencing the global optimum even if the WDN is large.
References Abebe A.J., and Solomanite, D.P. (1998). "Application of Global Optimization to the Design of Pipe Networks" , 3rd Int. Conf. on Hydroinformatics, Copenhagen, Denmark. Alperovits, F., and Shamir, U. (1977). “Design of optimal water distribution systems.” Water Resour. Res., 13(6), 885-900. Cunha, M. D. C., and Sousa, J. (1999) "Water Distribution Network Design Optimization: Simulated Annealing Approach", Journal of Water Res. Planning and Management, ASCE, Vol.125(4), 1999, p215-221.
Eiger,G., U. Shamir & Ben-Tal (1994). “Optimal design of water distribution networks.” Water Res. Research, 30(9), 2637-2646. Goulter, I. C., Lussier, B. M., and Morgan, D. R. (1986). “Implications of head loss path choice in the optimization of water distribution networks.” Water Resour. Res., 22(5), 819-822. Kessler, A., and Shamir, U. (1989). “Analysis of the linear programming gradient method for optimal design of water supply networks.“ Water Resour. Res., 25(7), 1469- 1480. Liong, S. Y. & Atiquzzman, M. D. (2004). “Optimal design of water distribution network using Shuffled complex evolution.” Journal of the Inistitution of Engineers, Singapore, Vol. 44. issue 1. 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.
