Sewer Networks Optimization by Particle Swarm Optimization with Abilities of Fly-Back Mechanism and Harmony Memory

Document Type : Research Paper

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Abstract

Lack of an efficient sewer network in urban areas threatens public health and may give rise to contagious diseases. Various optimization methods have been developed for use in designing sewers networks in response to a number of requirements such as the high costs of constructing sewer networks, financial limitations, the presence of both discrete and continuous decision variables, and the nonlinear time complexity of such design problems. In this study, the particle swarm optimization algorithm (PSO) with the capability of “fly-back” mechanism equipped with the harmony search (HPSO) is used for the optimization of sewers network designs. The objective function consists of minimizing the excavation and embedding costs of commercial pipes. The fly-back mechanism and the harmony memory method are used to prevent leaving out variables from the feasible space of the problem in an attempt to enhance model efficiency. Model constraints are satisfied at two levels, which leads to the desirable convergence of the PSO algorithm as compared to the conventional penalty methods in alternative evolutionary algorithms. In order to determine the admissible decision variables, the Manning equation is used as a hydraulic model. The performance of the proposed algorithm is shown by presenting two examples of sewer networks. Compared to the PSO algorithm used in sewer network optimization models, the proposed model exhibits a tangible improvement in cost reduction and a higher computational stability.

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1- Elimam, A., Charalambous, C., and Ghobrial, F. (1989). “Optimum design of large sewer networks.” J. of Environmental Engineering, 115(6), 1171-1190.
2- Swamee, P.K., and Sharma, A.K. (2013). “Optimal design of a sewer line using linear programming.” J. of Applied Mathematical Modelling, 37(6), 4430-4439.
3- Li, G., and Matthew, R.G. (1990). “New approach for optimization of urban drainage systems.” J. of Environmental Engineering, 116(5), 927-944.
4- Mays, L.W., and Wenzel, H.G. (1976). “Optimal design of multilevel branching sewer systems.” J. of Water Resources Research, 12(5), 913-917.
5- Heaney, J., Wright, L., Sample, D., Field, R., and Fan, C. (1999) “Innovative methods for the optimization of gravity storm sewer design.” Proc., 8th International Conference on Urban Storm Drainage, USEPA.
6- Setoodeh, M. (2004). “Optimal design of sewer networks.” M.S. Thesis, Iran University of Science and Technology, Tehran, Iran. (In Persian)
7- Liang, L.Y., Thompson, R.G., and Young, D.M. (2004). “Optimising the design of sewer networks using genetic algorithms and tabu search.” J. of Engineering, Construction and Architectural Management, 11(2), 101-112.
8- Haghighi, A., and Bakhshipour, A.E. (2012). “Optimization of sewer networks using an adaptive genetic algorithm.” J. of Water Resources Management, 26(12), 3441-3456.
9- Haghighi, A. (2011). “Development of an unconditional mathematical model to design sewer networks.”
J. of Water and Wastewater, 83, 28-39. (In Persian)
10- Afshar, M. (2010). “A parameter free continuous ant colony optimization algorithm for the optimal design of storm sewer networks: Constrained and unconstrained approach.” J. of Advances in Engineering Software, 41(2), 188-195.
11- Afshar, M., Shahidi, M., Rohani, M., and Sargolzaei, M. (2011). “Application of cellular automata to sewer network optimization problems.” J. of Scientia Iranica, 18(3), 304-312. (In Persian)
12- Eberhart, R.C., and Kennedy, J. (1995). “A new optimizer using particle swarm theory.” Proceedings of the 6th International Symposium on Micro Machine and Human Science, IEEE, New York, 39-43.
13- Izquierdo, J., Montalvo, I., Pérez, R., and Fuertes, V.S. (2008). “Design optimization of wastewater collection networks by PSO.” J. of Computers and Mathematics with Applications, 56(3), 777-784.
14- Li, L., Huang, Z., Liu, F., and Wu, Q. (2007). “A heuristic particle swarm optimizer for optimization of pin connected structures.” J. of Computers and Structures, 85(7), 340-349.
15- Moeini, R., and Afshar, M. (2012). “Layout and size optimization of sanitary sewer network using intelligent ants.” J. of Advances in Engineering Software, 51, 49-62.
16- He, S., Prempain, E., and Wu, Q. (2004). “An improved particle swarm optimizer for mechanical design optimization problems.” J. of Engineering Optimization, 36(5), 585-605.
17- He, S., Wu, Q., Wen, J., Saunders, J., and Paton, R. (2004). “A particle swarm optimizer with passive congregation.” J. of Biosystems, 78(1), 135-147.
18- Geem, Z.W., Kim, J.H., and Loganathan, G. (2001). “A new heuristic optimization algorithm: Harmony search.” J. of Simulation, 76(2), 60-68.
19- Afshar, M., and Rohani, M. (2012). “Optimal design of gravitational sewer networks with general cellular automata.” J. of Water and Wastewater, 90, 12-25. (In Persian)
20- Trelea, I.C. (2003). “The particle swarm optimization algorithm: convergence analysis and parameter selection.” J.of Information Processing Letters, 85(6), 317-325.
21- Mansouri, M.R., and Khanjani, M.J. (1999). “Optimization of sewer system by the nonlinear programming.” J. of Water and Wastewater, 30, 20-30 (In Persian).