Choosing an Optimization Method for Water Resources Problems Based on the Features of Their Solution Spaces
Publication: Journal of Irrigation and Drainage Engineering
Volume 144, Issue 2
Abstract
One of the main challenges for solving complex water-resources optimization is choosing an appropriate solution method. An important feature of optimization problems is the convexity and extent of their solution spaces. The solution space is the set whose elements are all the reservoir releases that meet the optimization problem’s constraints and are thus feasible. The solution space of optimization problems can be convex or nonconvex. This study presents a method for determining the convexity or nonconvexity of the optimization problem solution space. The convexity and the extent of the solution space for a water-supply and a hydropower-production reservoir operation problem are evaluated by the proposed method. It is shown that the solution spaces of the former and latter problems are convex and nonconvex, respectively. The dependence of the solution spaces of the two reservoir operation problems on changes in evaporation, water demand for the water-supply reservoir, power plant capacity (PPC) for the hydropower reservoir, dead storage, reservoir capacity, and reservoir inflow is evaluated. The results demonstrate that the generalized reduced gradient (GRG) method finds an optimal value faster and more accurately than does the genetic algorithm (GA) when solving the water-supply problem, and that the GRG search is trapped in a local optimum when solving the hydropower-production problem.
Get full access to this article
View all available purchase options and get full access to this article.
References
Asgari, H. R., Bozorg-Haddad, O., Pazoki, M., and Loáiciga, H. A. (2015). “Weed optimization algorithm for optimal reservoir operation.” J. Irrig. Drain. Eng., 04015055.
Azizipour, M., Ghalenoei, V., Afshar, M. H., and Solis, S. S. (2016). “Optimal operation of hydropower reservoir systems using weed optimization algorithm.” Water Resour. Manage., 30(11), 3995–4009.
Bhattacharjya, R. K., and Datta, B. (2005). “Optimal management of coastal aquifers using linked simulation optimization approach.” Water Resour. Manage., 19(3), 295–320.
Bozorg-Haddad, O. (2014). Water resources systems optimization, Tehran Univ., Tehran, Iran (in Persian).
Bozorg-Haddad, O., Afshar, A., and Mariño, M. A. (2006). “Honey-bees mating optimization (HBMO) algorithm: A new heuristic approach for water resources optimization.” Water Resour. Manage., 20(5), 661–680.
Bozorg-Haddad, O., Afshar, A., and Mariño, M. A. (2008). “Honey-bee mating optimization (HBMO) algorithm in deriving optimal operation rules for reservoirs.” J. Hydroinf., 10(3), 257–264.
Bozorg-Haddad, O., Afshar, A., and Mariño, M. A. (2009). “Optimization of non-convex water resource problems by honey-bee mating optimization (HBMO) algorithm.” Eng. Comput., 26(3), 267–280.
Bozorg-Haddad, O., Hosseini-Moghari, S. M., and Loáiciga, H. A. (2016). “Biogeography-based optimization algorithm for optimal operation of reservoir systems.” J. Water Resour. Plann. Manage., 04015034.
Cai, X., McKinney, D. C., Lasdon, L. S., and Watkins, J. D. W. (2001). “Solving large nonconvex water resources management models using generalized benders decomposition.” J. Oper. Res., 49(2), 235–245.
Chu, W. S., and Yeh, W. (1978). “A non-linear programming algorithm for real-time hourly reservoir operations.” J. Am. Water Resour. Assoc., 14(5), 1048–1063.
Del Valle, Y., Harley, R. G., and Venayagamoorthy, G. K. (2009). “Comparison of enhanced-PSO and classical optimization methods: A case study for STATCOM placement.” Proc., 15th Int. Conf. on Intelligent System Applications to Power Systems, IEEE, Piscataway, NJ.
Esat, V., and Hall, M. J. (1994). “Water resources system optimization using genetic algorithms.” J. Hydroinf., 94(1), 225–231.
Fallah-Mehdipour, E., Bozorg-Haddad, O., and Mariño, M. A. (2012). “Real-time operation of reservoir system by genetic programming.” Water Resour. Manage., 26(14), 4091–4103.
Garousi-Nejad, I., Bozorg-Haddad, O., Loáiciga, H. A., and Mariño, M. A. (2016). “Application of the firefly algorithm to optimal operation of reservoirs with the purpose of irrigation supply and hydropower production.” J. Irrig. Drain. Eng., 04016041.
Ghosh, A., and Dehuri, S. (2004). “Evolutionary algorithms for multi-criterion optimization: A survey.” Int. J. Comput. Inf. Sci., 2(1), 38–57.
Giuliani, M., Castelletti, A., Pianosi, F., Mason, E., and Reed, P. M. (2015). “Curses, tradeoffs, and scalable management: Advancing evolutionary multiobjective direct policy search to improve water reservoir operations.” J. Water Resour. Plann. Manage., 04015050.
Hillier Frederick, S., and Lieberman Gerald, J. (2005). Introduction to operations research, 7th Ed., McGraw-Hill, New York.
Houck, M. H. (1979). “A chance constrained optimization model for reservoir design and operation.” Water Resour. Res., 15(5), 1011–1016.
Jordehi, A. R., and Jasni, J. (2012). “Approaches for FACTS optimization problem in power systems.” Power Engineering and Optimization Conf. (PEDCO), IEEE, Piscataway, NJ.
Karatzas, G. P., and Pinder, G. F. (1993). “Groundwater management using numerical simulation and the outer approximation method for global optimization.” Water Resour. Res., 29(10), 3371–3378.
Kuczera, G. (1989). “Fast multireservoir multiperiod linear programing models.” Water Resour. Res., 25(2), 169–176.
Labadie, J. W. (2004). “Optimal operation of multireservoir systems: State-of-the-art review.” J. Water Resour. Plann. Manage., 93–111.
Lasdon, L. S., Fox, R. L., and Ratner, M. W. (1974). “Nonlinear optimization using the generalized reduced gradient method.” Revue française d’automatique, d’informatique et de recherche opérationnelle. Recherche opérationnelle, 8(V3), 73–103.
Little, J. D. (1955). “The use of storage water in a hydroelectric system.” J. Oper. Res., 3(2), 187–197.
Mantawy, A. H., Soliman, S. A., and El-Hawary, M. E. (2003). “An innovative simulated annealing approach to the long-term hydroscheduling problem.” Int. J. Electr. Power Energy Syst., 25(1), 41–46.
MATLAB [Computer software]. MathWorks, Natick, MA.
Oliveira, R., and Loucks, D. P. (1997). “Operating rules for multi reservoir systems.” Water Resour. Res., 33(4), 839–852.
Ostadrahimi, L., Mariño, M. A., and Afshar, A. (2012). “Multi-reservoir operation rules: Multi-swarm PSO-based optimization approach.” Water Resour. Manage., 26(2), 407–427.
Seifollahi-Aghmiuni, S., Bozorg-Haddad, O., and Loáiciga, H. A. (2016). “Development of a sample multiattribute and multireservoir system for testing operational models.” J. Irrig. Drain. Eng., 04015039.
Simonovic, S. P. (1992). “Closing gap between theory and practice.” J. Water Resour. Plann. Manage., 262–280.
Stedinger, J. R., Sule, B. F., and Loucks, D. P. (1984). “Stochastic dynamic programming models for reservoir operation optimization.” Water Resour. Res., 20(11), 1499–1505.
Wardlaw, R., and Sharif, M. (1999). “Evaluation of genetic algorithms for optimal reservoir system operation.” J. Water Resour. Plann. Manage., 25–33.
Wurbs, R. A. (1993). “Reservoir system simulation and optimization models.” J. Water Resour. Plann. Manage., 455–472.
Yeh, W. W. G. (1985). “Reservoir management and operations models: A state-of-the-art review.” Water Resour. Res., 21(12), 1797–1818.
Yeh, W. W. G., Graves, A. L., Toy, D., and Becker, L. (1980). “Central Arizona project: Operations model.” J. Water Resour. Plann. Manage. Div., 106(2), 521–540.
Yeniay, O. (2005). “A comparative study on optimization methods for the constrained nonlinear programming problems.” Math. Probl. Eng., 2005(2), 165–173.
Young, G. K. (1967). “Finding reservoir operating rules.” J. Hydraul. Div., 93(6), 297–322.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 144 • Issue 2 • February 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 20, 2017
Accepted: Jul 25, 2017
Published online: Nov 17, 2017
Published in print: Feb 1, 2018
Discussion open until: Apr 17, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.