Optimizing Gravity-Fed Sewer Systems using GRG and PGSL: A Path to Cost-Effective Design
Received: 13 January 2025 | Revised: 12 February 2025 | Accepted: 24 February 2025 | Online: 4 June 2025
Corresponding author: Pakorn Ditthakit
Abstract
In this paper, Generalized Reduced Gradient (GRG) and Probabilistic Global Search Lausanne (PGSL) optimization algorithms are employed to enhance sewer network design, focusing on link length, path, diameter, and cost. The former are compared with linear and dynamic programming, with the results indicating PGSL as the most cost-efficient, achieving optimal lengths of 70.00 m for Link I, 48.97 m for Link II, and 76.41 m for Link III, with paths of 1-2, 1-2, and 1-3, respectively, and a total cost of $15,688.17. In comparison, other algorithms incurred higher costs, while the optimal diameters remained consistent across all methods, ensuring structural integrity. The minor variations in lengths and paths reflect network design robustness. The importance of selecting the right optimization algorithm based on cost, length, path, and diameter is emphasized. PGSL is introduced for the first time in this context, demonstrating superior cost-effectiveness and significant implications for sewer network optimization. The findings provide valuable insights to engineers and planners, promoting more efficient and sustainable infrastructure development.
Keywords:
cost-efficiency analysis, GRG algorithm, infrastructure design, PGSL algorithm, sewer network optimizationDownloads
References
A. Gupta, N. Bokde, D. Marathe, and K. Kulat, "Leakage Reduction in Water Distribution Systems with Efficient Placement and Control of Pressure Reducing Valves Using Soft Computing Techniques,"Engineering, Technology & Applied Science Research, vol. 7, no. 2, pp. 1528–1534, Apr. 2017. DOI: https://doi.org/10.48084/etasr.1032
T. H. Nguyen, V. D. Le, X. H. Vu, and D. K. Nguyen, "Reliability-based Design Optimization of Steel-Concrete Composite Beams Using Genetic Algorithm and Monte Carlo Simulation,"Engineering, Technology & Applied Science Research, vol. 12, no. 6, pp. 9766–9770, Dec. 2022. DOI: https://doi.org/10.48084/etasr.5366
P. Armaos, "A Study of Joint Cost Inclusion in Linear Programming Optimization,"Engineering, Technology & Applied Science Research, vol. 3, no. 4, pp. 473–478, Aug. 2013. DOI: https://doi.org/10.48084/etasr.327
P. K. Swamee and A. K. Sharma, "Optimal Design of a Sewer Line Using Linear Programming,"Applied Mathematical Modelling, vol. 37, no. 6, pp. 4430–4439, Mar. 2013. DOI: https://doi.org/10.1016/j.apm.2012.09.041
L. Y. Liang, R. G. Thompson, and D. M. Young, "Optimising the Design of Sewer Networks Using Genetic Algorithms and Tabu Search,"Engineering, Construction and Architectural Management, vol. 11, no. 2, pp. 101–112, Jan. 2004. DOI: https://doi.org/10.1108/09699980410527849
C. Montes, Z. Kapelan, and J. Saldarriaga, "Impact of Self-Cleansing Criteria Choice on the Optimal Design of Sewer Networks in South America,"Water, vol. 11, no. 6, Jun. 2019, Art. no. 1148. DOI: https://doi.org/10.3390/w11061148
D. Singh, P. S. Mahar, and R. P. Singh, "Optimal Design of Gravity-Fed Sewer Lines Using Linear Programming,"Journal of The Institution of Engineers (India): Series A, vol. 100, no. 4, pp. 719–729, Dec. 2019. DOI: https://doi.org/10.1007/s40030-019-00391-x
C. Allen and S. Malekpour, "Unlocking and Accelerating Transformations to the SDGs: a Review of Existing Knowledge,"Sustainability Science, vol. 18, no. 4, pp. 1939–1960, Jul. 2023. DOI: https://doi.org/10.1007/s11625-023-01342-z
P. K. Navin and Y. P. Mathur, "Design Optimization of Sewer System Using Particle Swarm Optimization,"in Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Singapore, 2016, pp. 173–182. DOI: https://doi.org/10.1007/978-981-10-0451-3_17
S.-F. Yeh, C.-W. Chu, Y.-J. Chang, and M.-D. Lin, "Applying Tabu Search and Simulated Annealing to the Optimal Design of Sewer Networks,"Engineering Optimization, vol. 43, no. 2, pp. 159–174, Feb. 2011. DOI: https://doi.org/10.1080/0305215X.2010.482989
Y. F. Guo, G. A. Walters, S. T. Khu, and E. C. Keedwell, "Efficient Multiobjective Storm Sewer Design Using Cellular Automata and Genetic Algorithm Hybrid,"Journal of Water Resources Planning and Management, vol. 134, no. 6, pp. 511–515, Nov. 2008. DOI: https://doi.org/10.1061/(ASCE)0733-9496(2008)134:6(511)
T.-C. Pan and J.-J. Kao, "GA-QP Model to Optimize Sewer System Design,"Journal of Environmental Engineering, vol. 135, no. 1, pp. 17–24, Jan. 2009. DOI: https://doi.org/10.1061/(ASCE)0733-9372(2009)135:1(17)
L. Wang, Y. Zhou, and W. Zhao, "Comparative Study on Bionic Optimization Algorithms for Sewer Optimal Design,"in 2009 Fifth International Conference on Natural Computation, Aug. 2009, vol. 3, pp. 24–29. DOI: https://doi.org/10.1109/ICNC.2009.89
R. Moeini and M. H. Afshar, "Sewer Network Design Optimization Problem Using Ant Colony Optimization Algorithm and Tree Growing Algorithm,"in EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV, Heidelberg, 2013, pp. 91–105. DOI: https://doi.org/10.1007/978-3-319-01128-8_7
E. Tan, D. Sadak, and M. T. Ayvaz, "Optimum Design of Sewer Systems by Using Differential Evolution Algorithm,"Teknik Dergi, vol. 31, no. 5, pp. 10229–10250, 2020. DOI: https://doi.org/10.18400/tekderg.541507
I. Basupi, "Integrating water-saving schemes in the design of sanitary sewers,"Water and Environment Journal, vol. 34, no. 4, pp. 536–549, 2019. DOI: https://doi.org/10.1111/wej.12483
E. Tan, D. Sadak, and M. T. Ayvaz, "Optimum Design of Storm Sewer Systems by Using Harmony Search Optimization Approach,"presented at the 38th IAHR World Congress, Panama, Sep. 2019, pp. 6226–6233. DOI: https://doi.org/10.3850/38WC092019-0500
W. H. Hassan, M. H. Jassem, and S. S. Mohammed, "A GA-HP Model for the Optimal Design of Sewer Networks,"Water Resources Management, vol. 32, pp. 865–879, Feb. 2018. DOI: https://doi.org/10.1007/s11269-017-1843-y
S.-F. Yeh, Y.-J. Chang, and M.-D. Lin, "Optimal Design of Sewer Network by Tabu Search and Simulated Annealing,"in 2013 IEEE International Conference on Industrial Engineering and Engineering Management, Bangkok, Dec. 2013, pp. 1636–1640. DOI: https://doi.org/10.1109/IEEM.2013.6962687
M. Zakwan and M. Niazkar, "A Comparative Analysis of Data-Driven Empirical and Artificial Intelligence Models for Estimating Infiltration Rates,"Complexity, vol. 2021, no. 1, 2021, Art. no. 9945218. DOI: https://doi.org/10.1155/2021/9945218
M. Niazkar and M. Zakwan, "Assessment of Artificial Intelligence Models for Developing Single-Value and Loop Rating Curves,"Complexity, vol. 2021, no. 1, 2021, Art. no. 6627011. DOI: https://doi.org/10.1155/2021/6627011
R. Barati, "Application of excel solver for parameter estimation of the nonlinear Muskingum models,"KSCE Journal of Civil Engineering, vol. 17, no. 5, pp. 1139–1148, Jul. 2013. DOI: https://doi.org/10.1007/s12205-013-0037-2
S. Adarsh, "Design of Minimum Seepage Loss Irrigation Canal Sections Using Probabilistic Search,"International Journal of Optimization in Civil Engineering, vol. 2, no. 1, pp. 15–28, Mar. 2012.
H. Benzeguir, S. M. Elachachi, D. Nedjar, and M. Bensafi, "Reliability of Buried Pipes in Heterogeneous Soil Subjected to Seismic Loads,"Engineering, Technology & Applied Science Research, vol. 11, no. 1, pp. 6708–6713, Feb. 2021. DOI: https://doi.org/10.48084/etasr.4000
M. Shivashankar, M. Pandey, and M. Zakwan, "Estimation of settling velocity using generalized reduced gradient (GRG) and hybrid generalized reduced gradient–genetic algorithm (hybrid GRG-GA),"Acta Geophysica, vol. 70, pp. 2487–2497, Oct. 2022. DOI: https://doi.org/10.1007/s11600-021-00706-2
B. Raphael and I. F. C. Smith, "A Direct Stochastic Algorithm for Global Search,"Applied Mathematics and Computation, vol. 146, no. 2, pp. 729–758, Dec. 2003. DOI: https://doi.org/10.1016/S0096-3003(02)00629-X
B. Domer, B. Raphael, K. Shea, and I. F. C. Smith, "A Study of Two Stochastic Search Methods for Structural Control,"Journal of Computing in Civil Engineering, vol. 17, no. 3, pp. 132–141, Jul. 2003. DOI: https://doi.org/10.1061/(ASCE)0887-3801(2003)17:3(132)
B. Raphael and I. F. C. Smith, "Engineering Applications of a Direct Search Algorithm, PGSL,"in International Conference on Computing in Civil Engineering, Cancun, Mexico, 2005. DOI: https://doi.org/10.1061/40794(179)61
L. Mays and Y. Tung, Hydrosystems Engineering and Management. New York: McGraw-Hill, 1992.
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Copyright (c) 2025 Teerapat Keawsriyong, Warit Wipulanusart, Satjapan Leelatanon, Nukul Suksuwan, Jakkarin Weekaew , Quoc Bao Pham, Pakorn Ditthakit

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