Abstract
Commercial application of genetic algorithms (GAs) to engineering design problems, including optimal design of pipe networks, could be facilitated by the development of algorithms that require the least number of parameter tuning. This paper presents an attempt to eliminate the need for defining a priori the proper penalty parameter in GA search for pipe networks optimal designs. The method is based on the assumption that the optimal solution of a pipe network design problem lies somewhere on, or near, the boundary of the feasible region. The proposed method uses the ratio of the best feasible and infeasible designs at each generation to guide the direction of the search towards the boundary of the feasible domain by automatically adjusting the value of the penalty parameter. The value of the ratio greater than unity is interpreted as the search being performed in the feasible region and vice versa. The new adapted value of the penalty parameter at each generation is therefore calculated as the product of its current value and the aforementioned ratio. The genetic search so constructed is shown to converge to the boundary of the feasible region irrespective of the starting value of the constraint violation penalty parameter. The proposed method is described here in the context of pipe network optimisation problems but is equally applicable to any other constrained optimisation problem. The effectiveness of the method is illustrated with a benchmark pipe network optimization example from the literature.
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Abebe, A.J., Solomatine, D.P.: Application of global optimization to the design of pipe networks, In: 3rd International Conference on Hydroinformatics, pp. 989–996, Copenhagen, Denmark, 1999
Afshar, M.H.: An element-by-element algorithm for the analysis of pipe networks. Int. J. Eng. Sci. 12, 87–100 (2001)
Alperovits, E., Shamir, U.: Design of optimal water distribution systems. Water Resour. Res. 13, 885–900 (1977)
Back, T., Hoffmeister, F., Schwefel, H.-P.: A survey of evolution strategies. In: Proceedings of Fourth International Conference on Genetic Algorithms, pp. 2–9, San Mateo, CA (1991)
Bhave, P.R.: Optimal expansion of water distribution systems. J. Environ. Eng. 111, 177–197 (1985)
Boulos, P.F., Wu, Z.Y., Orr, C.H., Ro, J.J.: Least-cost design and rehabilitation of water distribution systems using genetic algorithms. In: Proceedings of the AWWA IMTech. Conference, Seattle, WA, 16–19 April 2000
Box, M.J.: A new method of constrained optimisation and a comparison with other methods. J. Comput. 8, 42 (1965)
Dandy, G.C., Simpson, A.R., Murphy, L.J.: A review of pipe network optimisation techniques. In: Proceedings of Watercomp 93, pp. 373–383, Melbourne, Australia, 1993
Dandy, G.C., Simpson, A.R., Murphy, L.J.: An improved genetic algorithm for pipe network optimization. Water Resour. Res. 32, 449–458 (1996)
Fujiwara, O., Aimahakoon, J., Edirisinghe, N.C.P.: A modified linear programming gradient method for optimal design of looped water distribution networks. Water Resour. Res. 23(6), 997–982 (1987)
Fujiwara, O., Khang, D.B.: A two-phase decomposition method for optimal design of looped water distribution networks. Water Resour. Res. 26, 539–549 (1990)
Gen, M., Cheng, R.: Genetic Algorithms and Engineering Design. Wiley, New York (1997)
Gessler, J.: Optimization of pipe network. Paper presented at international symposium on urban hydrology, hydraulics and sediment control, University of Kentucky, Lexington, KY, 1982
Gessler, J.: Pipe network optimization by enumeration. Water Resour. Res. 23, 977–982 (1985)
Halhal, D., Walters, G.A., Quazar, D., Savic, D.A.: Water network rehabilitation with structured messy genetic algorithm. J. Water Resour. Plan. Manag. 123, 137–146 (1997)
Kessler, A., Shamir, U.: Analysis of the linear programming gradient method for optimal design of water supply networks. Water Resour. Res. 25, 1469–1480 (1989)
Lippai, I., Heaney, J., Laguna, M.: Robust water system design with commercial intelligent search optimizers. J. Comput. Civil Eng. 13, 133–135 (1999)
Mahjoub, Z.: Contribution à étude d’optimization des réseaux mailles. Thèse (Docteur d’Etat), Inst. Nat. Polytech. de Toulouse, Toulouse, France, pp. 51–142 (1983)
Maier, H.R., Simpson, A.R., Zecchin, A.C., Foong, W.K., Phang, K.Y., Seah, H.Y., Tan, C.L.: Ant colony optimization for design of water distribution systems. J. Water Resour. Plan. Manag. 129(3), 200–209 (2003)
Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4, 1–32 (1996)
Murphy, L.J., Simpson, A.R.: Pipe optimisation using genetic algorithms. Research report 93, Dept. of Civil Engrg., Univ. of Adelaide, Adelaide, Australia (1992)
Murphy, L.J., Simpson, A.R., Dandy, G.C.: Design of a network using genetic algorithms. Water 20, 40–42 (1993)
Quindry, G.E., Brill, E.D., Liebman, J.C.: Optimization of looped water distribution systems. J. Environ. Eng. 107, 665–679 (1981)
Quindry, G.E., Brill, E.D., Liebman, J.C., Robinson, A.R.: Comments on the ‘Design of optimal water distribution systems’, by E. Alperovits and U. Shamir. Water Resour. Res. 15, 1651–1654 (1979)
Saphir, Y.N.: Optimization of water distribution systems (in Hebrew), 150 p. M.Sc. thesis, Technion, Haifa, Israel (1983)
Savic, D.A., Walters, G.A.: Genetic algorithms for least-cost design of water distribution networks. J. Water Resour. Plan. Manag. 123, 67–77 (1997)
Schaake, J., Lai, D.: Linear programming and dynamic programming applications to water distribution network design. Report 116, Dept. of Civil Engrg., Massachusetts Inst. Technol., Cambridge, MA (1969)
Schoenauer, M., Michalewicz, Z.: Evolutionary computation at the edge of feasibility. In: Proceedings of Fourth Conference on Parallel Problem Solving from Nature, Berlin, Germany, 1996
Simpson, A.R., Dandy, G.C., Murphy, L.J.: Genetic algorithms compared to other techniques for pipe optimization. J. Water Resour. Plan. Manag. 120(4), 423–443 (1994)
Simpson, A.R., Murphy, L.J., Dandy, G.C.: Pipe network optimisation using genetic algorithms. In: Proceedings of Water Resource Planning and Management Specialty Conference, American Society of Civil Engineers, Seattle, WA, 1993
Walters, G.A., Halhal, D., Savic, D., Quazar, D.: Improved design of any town distribution network using structured messy genetic algorithms. Urban Water 1, 23–38 (1999)
Wu, Z.Y., Boulos, P.F., Orr, C.H., Ro, J.J.: Using Genetic Algorithms to Rehabilitate Distribution Systems. J. Am. Water Works Assoc. 93(11), 74–85 (2002)
Wu, Z.Y., Simpson, A.R.: A self-adaptive boundary search genetic algorithm and its application to water distribution systems. J. Hydraul. Res. 40, 191–203 (2002)
Wu, Z.Y., Wang, Y.T.: Arch dam optimisation design under strength fuzziness and fuzzy safety measure. In: Proceedings of International Conference on Arch Dams, pp. 129–131, Hehai Univ., Nanjing, China, 1992
Yates, D.F., Templeman, A.B., Boffey, T.B.: The computational complexity of the problem of determining least capital cost designs for water supply networks. Eng. Optim. 7, 142–155 (1984)
Zhu, B.F., Li, Z.M., Zhang, B.C.: Structural Optimal Design: Theory and Applications. Hydro-electrical Press, Beijing (1984)
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Afshar, M.H., Mariño, M.A. A parameter-free self-adapting boundary genetic search for pipe network optimization. Comput Optim Appl 37, 83–102 (2007). https://doi.org/10.1007/s10589-007-9016-1
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DOI: https://doi.org/10.1007/s10589-007-9016-1