Optimal Design of Sewer Network Size using Ant Colony Optimization Algorithm: Comparing Performance of Four Different Algorithms
Author
Abstract
In this paper, the features of Ant Colony Optimization Algorithm (ACOA) are used to find optimal size for sewer network. Two different formulations are proposed. In the first formulation, pipes diameters and in the second formulation, nodal elevations of sewer network are taken as decision variables of the problem. In order to evaluate the performance of different ACOAs, four algorithms of Ant System, Elitist Ant System, Ranked Ant System and Max-Min Ant System are used to solve this optimization problem. Different test examples are solved using two proposed formulations for each ACOAs and the results are presented and compared with other available results. The results indicate the efficiency of the proposed methods in the solation of sewer network design optimization problem and the results of Max-Min Ant System are better in comparison with other ACOAs.
Keywords
1. Haestad, Wastewater Collection System Modelling and Design, Waterbury: Haestad methods, 2004.
2. Guo, Y., Walters, G., and Savic, D., “Optimal Design of Storm Sewer networks: Past, Present and Future”, Proceeding of 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, pp. 1-10, 2008.
3. Desher, D. P., and Davis, P. K., “Designing Sanitary Sewers with Microcomputers”, Journal of Environmental Engineering, Vol. 112, No. 6, pp. 993-1007, 1986.
4. Elimam, A. A., Charalambous, C., and Ghobrial, F. H., “Optimum Design of Large Sewer Networks” Journal of Environmental Engineering, Vol. 115, No. 6, pp. 1171-1189, 1989.
5. Dajani, J. S., and Hasit, Y., “Capital Cost Minimization of Drainage Networks”, ASCE Journal of Environmental Engineering, Vol. 100, No. 2, pp. 325-337, 1974.
6. Swamee, P. K., and Sharma, A. K., “Optimal Design of a Sewer Line using Linear Programming” Journal of Applied Mathematical Modelling, Vol. 37, pp. 4430-4439, 2013.
7. Price, R. K., “Design of Storm Water Sewers for Minimum Construction Cost”, proceeding of 1st International Conference on Urban Strom Drainage, Southampton, United Kingdom, pp. 636-647, 1978.
8. Swamee, P. K., “Design of Sewer Line”, Journal of Environmental Engineering, Vol. 127, No. 9, pp. 776-781, 2001.
9. Walsh, S. and Brown, L. C., “Least Cost Method for Sewer Design”, Journal of Environmental Engineering Division, Vol. 99, No. 3, pp. 333-345, 1973.
10. Mays, L. W., and Wenzel, H. G., “Optimal Design of Multilevel Branching Sewer Systems”, Water Resource Research, Vol. 12, No. 5, pp. 913-917, 1976.
11. Templeman, A. B., and Walters, G. A., “Optimal Design of Storm Water Drainage Networks for Roads”, Proceeding institute. of Civil Engineers, London, pp. 573-587, 1979.
12. Gupta, A., Mehndiratta, S. L., and Khanna, P., “Gravity Waste Water Collection Systems Optimization”, ASCE Journal of Environmental Engineering, Vol. 109, No. 5, pp. 1195-1208, 1983.
13. Yen, B. C., Cheng, S. T., Jun, B. H., Voohees, M. L., and Wenzel, H. G., “Illinois Least Cost Sewer System Design model”, User’s guide, Department of Civil Engineering, University of Texas at Austin, 1984.
14. Kulkarni, V. S., and Khanna, P., “Pumped Wastewater Collection Systems Optimization”, ASCE Journal of Environmental Engineering, Vol. 111, No. 5, pp. 589-601, 1985.
15. Botrous, A., El-Hattab, I., and Dahab, M., “Design of Wastewater Collection Networks using Dynamic Programming Optimization Technique”, Proceeding of the ASCE national conference on Environmental and Pipeline Engineering, Kansas City, MO, United States, American Society of Civil Engineers, pp. 503–512, 2000.
16. Diogo A. F., Walters G. A., de Sousa E. R., and Graveto V. M., “Three-Dimensional Optimization of Urban Drainage Systems”, Computer-Aided Civil and Infrastructure Engineering, Vol. 15, No. 6, pp. 409-426, 2000.
17. Heaney, J. P., Wright, L. T., Sample, D., Field, R., and Fan, C. Y., “Innovative Methods for the Optimization of Gravity Storm Sewer Design”, Proceedings the 8th International Conference on Urban Storm Drainage, Sydney, Australia, pp. 1896-903, 1999.
18. Liang, L. Y., Thompson, R. G., and Young, D. M., “Optimising the Design of Sewer Networks using Genetic Algorithms and Tabu Search”, Engineering, Construction and Architectural Management, Vol. 11, No. 2, pp. 101-112, 2004.
19. Afshar, M. H., Afshar, A., Marino, M. A., and Darbandi, A. A. S., “Hydrograph-Based Storm Sewer Design Optimization by Genetic Algorithm”, Canadian Journal Civil Engineering, Vol. 33, No. 3, pp. 310-325, 2006.
20. Haghighi, A., and Bakhshipour, A. E., “Optimization of Sewer Networks using an Adaptive Genetic Algorithm”, Water Resource Management, Vol. 26, No. 12, pp. 3441-3456, 2012.
21. Guo, Y., “Sewer Network Optimal Design Based on Cellular Automata Principles”, Proceeding of 2005 XXXI IAHR Congress, Seoul, Korea, pp. 6582-6593, 2005.
22. Guo, Y., Walters, G. A., Khu, S. T., and Keedwell, E., “Optimal Design of Sewer Networks using Hybrid Cellular Automata and Genetic Algorithm”, Proceeding of IWA World Water Congress, Beijing, China, 2006.
23. Afshar, M. H., Shahidi, M., Rohania, M., and Sargolzaei, M., “Application of Cellular Automata to Sewer Network Optimization Problems”, Scientia Iranica, Transactions A: Civil Engineering, Vol. 18, No. 3, pp. 304-312, 2011.
24. Afshar, M. H., “Improving the Efficiency of Ant Algorithms using Adaptive Refinement: Application to Storm Water Network Design”, Advances in Water Resources, Vol. 29, pp. 1371-1382, 2006.
25. 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, Vol. 30, No. 4, pp. 954-965, 2007.
26. Afshar, M. H., “A Parameter Free Continuous Ant Colony Optimization Algorithm for the Optimal Design of Storm Sewer Networks: Constrained and Unconstrained Approach”, Advances in Engineering Software, Vol. 41, pp. 188-195, 2010.
27. Izquierdo, J., Montalvo, I., Perez, R., and Fuertes, V. S., “Design Optimization of Wastewater Collection Networks by PSO”, Computers and Mathematics with Applications, Vol. 56, No. 3, pp. 777-784, 2008.
28. نفیسی، م.، احمدی، آ. "بهینه سازی شبکه های فاضلاب با الگوریتم دسته ذرات با قابلیت پرواز بازگشتی و مجهز به حافه هارمونی" مجله آب و فاضلاب، ش. 94، ص. 76-87، 1393.
29. Karovic, O., and Mays, L. W., “Sewer System Design using Simulated Annealing in Excel”, Water Resource Management, Vol. 28, pp. 4551-4565, 2014.
30. Colorni, A., Dorigo, M., and Maniezzo, V., “Ant System: An Autocatalytic Optimizing Process”, Technical Report 91-016, Politecico di Milao, Italy, 1991.
31. Moeini, R., and Afshar, M. H., “Application of an Ant Colony Optimization Algorithm for the Optimal Operation of Reservoirs: A Comparative Study of Three Proposed Formulations”, Scientia Iranica. Transactions A: Civil Engineering, Vol. 16, No. 4, pp. 273-285, 2009.
32. Afshar, M. H., and Moeini, R., “Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems”, Journal Water Resource Management, Vol. 22, No. 1, pp. 1835-1857, 2008.
33. Moeini, R., and Afshar, M. H., “Constrained Ant Colony Optimization Algorithm for the Layout and Size Optimization of Sanitary Sewer Networks”, Urban Water, Vol. 10, No. 3, pp.154-173, 2013.
37. Robinson, D. K., and Labadie, J. W., “Optimal Design of Urban Storm Water Drainage System”, International Symposium on Urban Hydrology, Hydraulics, and Sediment Control, University of Kentucky, Lexington, KY, USA, pp. 145-156, 1981.
38. Miles, S. W., and Heaney, J. P., “Better than Optimal Method for Designing Drainage Systems”, Water Resource Planning and Management, Vol. 114, No. 5, pp. 477-499, 1988.
39. Afshar, M. H., “Rebirthing Particle Swarm Optimization Algorithm: Application to Storm Sewer Network Design” Canadian journal of civil engineering, Vol. 35. No.10. pp.1120-1127.
2. Guo, Y., Walters, G., and Savic, D., “Optimal Design of Storm Sewer networks: Past, Present and Future”, Proceeding of 11th International Conference on Urban Drainage, Edinburgh, Scotland, UK, pp. 1-10, 2008.
3. Desher, D. P., and Davis, P. K., “Designing Sanitary Sewers with Microcomputers”, Journal of Environmental Engineering, Vol. 112, No. 6, pp. 993-1007, 1986.
4. Elimam, A. A., Charalambous, C., and Ghobrial, F. H., “Optimum Design of Large Sewer Networks” Journal of Environmental Engineering, Vol. 115, No. 6, pp. 1171-1189, 1989.
5. Dajani, J. S., and Hasit, Y., “Capital Cost Minimization of Drainage Networks”, ASCE Journal of Environmental Engineering, Vol. 100, No. 2, pp. 325-337, 1974.
6. Swamee, P. K., and Sharma, A. K., “Optimal Design of a Sewer Line using Linear Programming” Journal of Applied Mathematical Modelling, Vol. 37, pp. 4430-4439, 2013.
7. Price, R. K., “Design of Storm Water Sewers for Minimum Construction Cost”, proceeding of 1st International Conference on Urban Strom Drainage, Southampton, United Kingdom, pp. 636-647, 1978.
8. Swamee, P. K., “Design of Sewer Line”, Journal of Environmental Engineering, Vol. 127, No. 9, pp. 776-781, 2001.
9. Walsh, S. and Brown, L. C., “Least Cost Method for Sewer Design”, Journal of Environmental Engineering Division, Vol. 99, No. 3, pp. 333-345, 1973.
10. Mays, L. W., and Wenzel, H. G., “Optimal Design of Multilevel Branching Sewer Systems”, Water Resource Research, Vol. 12, No. 5, pp. 913-917, 1976.
11. Templeman, A. B., and Walters, G. A., “Optimal Design of Storm Water Drainage Networks for Roads”, Proceeding institute. of Civil Engineers, London, pp. 573-587, 1979.
12. Gupta, A., Mehndiratta, S. L., and Khanna, P., “Gravity Waste Water Collection Systems Optimization”, ASCE Journal of Environmental Engineering, Vol. 109, No. 5, pp. 1195-1208, 1983.
13. Yen, B. C., Cheng, S. T., Jun, B. H., Voohees, M. L., and Wenzel, H. G., “Illinois Least Cost Sewer System Design model”, User’s guide, Department of Civil Engineering, University of Texas at Austin, 1984.
14. Kulkarni, V. S., and Khanna, P., “Pumped Wastewater Collection Systems Optimization”, ASCE Journal of Environmental Engineering, Vol. 111, No. 5, pp. 589-601, 1985.
15. Botrous, A., El-Hattab, I., and Dahab, M., “Design of Wastewater Collection Networks using Dynamic Programming Optimization Technique”, Proceeding of the ASCE national conference on Environmental and Pipeline Engineering, Kansas City, MO, United States, American Society of Civil Engineers, pp. 503–512, 2000.
16. Diogo A. F., Walters G. A., de Sousa E. R., and Graveto V. M., “Three-Dimensional Optimization of Urban Drainage Systems”, Computer-Aided Civil and Infrastructure Engineering, Vol. 15, No. 6, pp. 409-426, 2000.
17. Heaney, J. P., Wright, L. T., Sample, D., Field, R., and Fan, C. Y., “Innovative Methods for the Optimization of Gravity Storm Sewer Design”, Proceedings the 8th International Conference on Urban Storm Drainage, Sydney, Australia, pp. 1896-903, 1999.
18. Liang, L. Y., Thompson, R. G., and Young, D. M., “Optimising the Design of Sewer Networks using Genetic Algorithms and Tabu Search”, Engineering, Construction and Architectural Management, Vol. 11, No. 2, pp. 101-112, 2004.
19. Afshar, M. H., Afshar, A., Marino, M. A., and Darbandi, A. A. S., “Hydrograph-Based Storm Sewer Design Optimization by Genetic Algorithm”, Canadian Journal Civil Engineering, Vol. 33, No. 3, pp. 310-325, 2006.
20. Haghighi, A., and Bakhshipour, A. E., “Optimization of Sewer Networks using an Adaptive Genetic Algorithm”, Water Resource Management, Vol. 26, No. 12, pp. 3441-3456, 2012.
21. Guo, Y., “Sewer Network Optimal Design Based on Cellular Automata Principles”, Proceeding of 2005 XXXI IAHR Congress, Seoul, Korea, pp. 6582-6593, 2005.
22. Guo, Y., Walters, G. A., Khu, S. T., and Keedwell, E., “Optimal Design of Sewer Networks using Hybrid Cellular Automata and Genetic Algorithm”, Proceeding of IWA World Water Congress, Beijing, China, 2006.
23. Afshar, M. H., Shahidi, M., Rohania, M., and Sargolzaei, M., “Application of Cellular Automata to Sewer Network Optimization Problems”, Scientia Iranica, Transactions A: Civil Engineering, Vol. 18, No. 3, pp. 304-312, 2011.
24. Afshar, M. H., “Improving the Efficiency of Ant Algorithms using Adaptive Refinement: Application to Storm Water Network Design”, Advances in Water Resources, Vol. 29, pp. 1371-1382, 2006.
25. 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, Vol. 30, No. 4, pp. 954-965, 2007.
26. Afshar, M. H., “A Parameter Free Continuous Ant Colony Optimization Algorithm for the Optimal Design of Storm Sewer Networks: Constrained and Unconstrained Approach”, Advances in Engineering Software, Vol. 41, pp. 188-195, 2010.
27. Izquierdo, J., Montalvo, I., Perez, R., and Fuertes, V. S., “Design Optimization of Wastewater Collection Networks by PSO”, Computers and Mathematics with Applications, Vol. 56, No. 3, pp. 777-784, 2008.
28. نفیسی، م.، احمدی، آ. "بهینه سازی شبکه های فاضلاب با الگوریتم دسته ذرات با قابلیت پرواز بازگشتی و مجهز به حافه هارمونی" مجله آب و فاضلاب، ش. 94، ص. 76-87، 1393.
29. Karovic, O., and Mays, L. W., “Sewer System Design using Simulated Annealing in Excel”, Water Resource Management, Vol. 28, pp. 4551-4565, 2014.
30. Colorni, A., Dorigo, M., and Maniezzo, V., “Ant System: An Autocatalytic Optimizing Process”, Technical Report 91-016, Politecico di Milao, Italy, 1991.
31. Moeini, R., and Afshar, M. H., “Application of an Ant Colony Optimization Algorithm for the Optimal Operation of Reservoirs: A Comparative Study of Three Proposed Formulations”, Scientia Iranica. Transactions A: Civil Engineering, Vol. 16, No. 4, pp. 273-285, 2009.
32. Afshar, M. H., and Moeini, R., “Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems”, Journal Water Resource Management, Vol. 22, No. 1, pp. 1835-1857, 2008.
33. Moeini, R., and Afshar, M. H., “Constrained Ant Colony Optimization Algorithm for the Layout and Size Optimization of Sanitary Sewer Networks”, Urban Water, Vol. 10, No. 3, pp.154-173, 2013.
37. Robinson, D. K., and Labadie, J. W., “Optimal Design of Urban Storm Water Drainage System”, International Symposium on Urban Hydrology, Hydraulics, and Sediment Control, University of Kentucky, Lexington, KY, USA, pp. 145-156, 1981.
38. Miles, S. W., and Heaney, J. P., “Better than Optimal Method for Designing Drainage Systems”, Water Resource Planning and Management, Vol. 114, No. 5, pp. 477-499, 1988.
39. Afshar, M. H., “Rebirthing Particle Swarm Optimization Algorithm: Application to Storm Sewer Network Design” Canadian journal of civil engineering, Vol. 35. No.10. pp.1120-1127.
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