کاربرد الگوریتم های GA، SMPSO و HGAPSO در بهره برداری بهینه از مخازن سدها

نوع مقاله : مقالات پژوهشی


دانشگاه ارومیه


مسئله بهره‌برداری از مخازن سدها به لحاظ تنوع تصمیم‌گیری و توابع هدف دارای پیچیدگی‌هایی است که گاهی اوقات حل آن ها با روش‌های بهینه سازی سنتی امکان‌پذیر نیست و نیازمند صرف وقت و هزینه بسیار است. بنابراین استفاده از ابزارهای نوین و روش‌های پیشرفته در حل این مسائل امری اجتناب ناپذیر می باشد. در این مقاله از یک نسخه ساده اصلاحی الگوریتم بهینه سازی ازدحام ذرات (SMPSO)، الگوریتم ژنتیک (GA) و یک الگوریتم هیبرید جدید به نام HGAPSO برای بهره برداری از مخزن سد دز با هدف تأمین آب استفاده گردید. الگوریتم HGAPSO بر مبنای ترکیبی بسیار ساده اما کارامد از دو الگوریتم GA و SMPSO می باشد که باعث شده است محدودیت هایی که هر کدام از این روش ها به تنهایی دارند کاهش یابد و در مقابل کارایی آن افزایش یابد. در این پژوهش از بین 40 سال آمار، داده های 5 سال ابتدایی (60 دوره ماهیانه) جریان ورودی به مخزن سد دز مورد استفاده قرار گرفت و پس از اعمال قیود در فرآیند بهینه سازی با استفاده از تابع پنالتی، برنامه مورد نظر برای 10 بار به صورت مستقل اجرا گردید. حداکثر تعداد تکرار برای هر بار اجرای برنامه 400 و تعداد جمعیت اولیه برای هر سه روش 100 انتخاب گردید. مقادیر میانگین تابع هدف برای الگوریتم های GA، SMPSO و HGAPSO به ترتیب 3457/1، 1581/1 و 9882/0 به دست آمد که HGAPSO با سرعت همگرایی بیشتری نسبت به دو روش GA و SMPSO در یافتن جواب بهینه تابع هدف عمل نمود. همچنین اختلاف بین نمودار میزان آب رها شده در برابر تقاضای ماهیانه با استفاده از روش HGAPSO بسیار کمتر از نمودارهای GA و SMPSO گردید. در نهایت نتایج نشان می دهد که HGAPSO در یافتن جواب بهینه نسبت به GA و PSO و سایر روش های پژوهش های پیشین موفق تر عمل نموده است.


عنوان مقاله [English]

The Application of GA, SMPSO and HGAPSO in Optimal Reservoirs Operation

نویسندگان [English]

  • Alireza Moghaddam
  • Majid Montaseri
  • Hossein Rezaei
Urmia University
چکیده [English]

Introduction: The reservoir operation is a multi-objective optimization problem with large-scale which consider reliability and the needs of hydrology, energy, agriculture and the environment. There were not the any algorithms with this ability which consider all the above-mentioned demands until now. Almost the existing algorithms usually solve a simple form of the problem for their limitations. In the recent decay the application of meta-heuristic algorithms were introduced into the water resources problem to overcome on some complexity, such as non-linear, non-convex and description of these problems which limited the mathematical optimization methods. In this paper presented a Simple Modified Particle Swarm Optimization Algorithm (SMPSO) with applying a new factor in Particle Swarm Optimization (PSO) algorithm. Then a new suggested hybrid method which called HGAPSO developed based on combining with Genetic algorithm (GA). In the end, the performance of GA, MPSO and HGAPSO algorithms on the reservoir operation problem is investigated with considering water supplying as objective function in a period of 60 months according to inflow data.
Materials and Methods: The GA is one of the newer programming methods which use of the theory of evolution and survival in biology and genetics principles. GA has been developed as an effective method in optimization problems which doesn’t have the limitation of classical methods. The SMPSO algorithm is the member of swarm intelligence methods that a solution is a population of birds which know as a particle. In this collection, the birds have the individual artificial intelligence and develop the social behavior and their coordinate movement toward a specific destination. The goal of this process is the communication between individual intelligence with social interaction. The new modify factor in SMPSO makes to improve the speed of convergence in optimal answer. The HGAPSO is a suggested combination of GA and SMPSO to remove the limitation of GA and SMPSO. In this paper the initial population which caused randomly in all metha-heuristic algorithms consider fixing for the three mentioned algorithms because the elimination of random effect in initial population may make increase or decrease the convergence speed. The objective function is the minimum sum of the difference between the downstream demand reservoir and system release in the period time. Also the constrains problem is continuity equation, minimum and maximum of reservoir storage and system release.
Results and Discussion: The performance of GA, SMPSO and HGAPSO evaluated based on the objective function for Dez reservoir in the south east of Iran. In this study the programming of GA, SMPSO and HGAPSO was written in Matlab software and then was run for the time period with a maximum of 400 iterations. The minimum of the objective function for GA, SMPSO and HGAPSO was obtained 1.19, 1.05 and 0.9 respectively, and the maximum of objective function was calculated 1.66, 1.26 and 1.10 respectively. The results showed that the minimum of the objective function by HGAPSO was estimated 32 and 16 percent lower than the counts which calculated by GA and SMPSO. The standard deviation of SMPSO and HGAPSO were near to each other and less than GA which shows the diversity between solutions for SMPSO and HGAPSO are much less than GA. Also the HGAPSO had the better performance rather than previous method in terms of minimum, maximum, average and standard deviation. The convergence speed of HGAPSO for finding the optimal solution is much faster of GA and SMPSO. The difference graphs between system release and monthly demand in HGAPSO is much less than GA and SMPSO. Also the storage calculated in HGAPSO and SMPSO is highly close to each other but in GA method the storage calculated more in the first and second years.
Conclusions: The convergence speed in finding the optimal solution in SMPSO in more than GA but in other hand the probability of caughting in local optima for SMPSO is great whereas GA can make the diverse optimal solutions. For this reason, in this paper was trying to improve the performance of the GA and SMPSO and remove their disadvantage based on combining them and presenting a new hybrid method. The results showed the HGAPSO method which presented in this paper to use without any complexity and additional operator to GA and SMPSO has the ability to use for reservoir operation with large-scale. In addition it is suggested which the HGAPSO apply to other water resources engineering problems.

کلیدواژه‌ها [English]

  • Dez reservoir, Genetic algorithm
  • Hybrid algorithm
  • Objective function
  • Simple modified particle Swarm optimization algorithm
1- Afshar M.H. 2009. Elitist mutated particle swarm optimisation algorithms: application to reservoir operation problems, P I Civil Eng-Wat M; 162(6): 409- 417.
2- Afshar M. H. 2013. Extension of the constrained particle swarm optimization algorithm to optimal operation of multi-reservoirs system. International Journal of Electrical Power & Energy Systems, 51, 71- 81.
3- Afshar M.H., and Moeini R. 2008. Partially and fully constrained ant algorithms for the optimal solution of large scale reservoir operation problems, Water Resour Manage; 22(12): 1835– 1857.
4- Afshar M. H., and Motaei I. 2011. Constrained big bang-big crunch algorithm for optimal solution of large scale reservoir operation problem. Int. Journal Optim. Civil Eng, 2, 357- 375.
5- Afshar A., Emami Skardi M. J., and Masoumi F. 2014. Optimizing water supply and hydropower reservoir operation rule curves: An imperialist competitive algorithm approach. Engineering Optimization, (ahead-of-print), 1- 18.
6- Bellman R.E. 1957. Dynamic Programming, Princeton University Press, Princeton, New Jersey.
7- Changa L.C., Chang F.J., Wang K.W., and Daib S.Y. 2010. Constrained genetic algorithms for optimizing multi-use reservoir operation, Journal Hydrology Engineering; 390(1-2): 66– 74.
8- Chiu Y.C., Chang L.C., and Chang F.J. 2007. Using a hybrid genetic algorithm-simulated annealing algorithm for fuzzy programming of reservoir operation, Hydrol Process; 21(23): 3162– 3172.
9- Dahe P.D., and Srivastava D.K. 2002. Multi reservoir multi yield model with allowable deficit in annual yield, Journal Water Research Pl-ASCE; 128(6): 406- 414.
10- Dorfman R. 1962. Mathematical Models: The Multi-Structure Approach, in Design of Water Resources Systems (edited by A. Maass), Harvard University Press, Cambridge, Massachusetts.
11- Esmin A. A., and Matwin S. 2013. HPSOM: a hybrid particle swarm optimization algorithm with genetic mutation. International Journal Innov Comput Inf Control (IJICIC), 9(5), 1919- 1934.
12- Ganji A., Khalili D., and Karamouz M. 2007. Development of stochastic dynamic Nash game model for reservoir operation. I. The symmetric stochastic model with perfect information, Adv Water Resour; 30(3): 528- 542.
13- Ghahraman B., and Sepaskhah A. 2004. Linear and non-linear optimization models for allocation of a limited water supply, Irrigation Drainage; 53(1): 39– 54.
14- Goldberg D. E., Korb B., and Deb K. 1989. Messy genetic algorithms: Motivation, analysis, and first results. Complex systems, 3(5), 493- 530.
15- Haddad O.B., Afshar A., and Marino M.A. 2006. Honey-bees mating optimization (HBMO) algorithm: a new heuristic approach for water resources optimization ,Water Resour Manag; 20(5): 661– 680.
16- Juang C. F. 2004. A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 34(2), 997- 1006.
17- Kerachian R., and Karamouz M. 2006. Optimal reservoir operation considering the water quality issues: A stochastic conflict resolution approach, Water Resour. Res; 42: 1- 17.
18- Kumar D.N., Falguni B., and Srinivasa K.R. 2010. Optimal Reservoir Operation for Flood Control Using Folded Dynamic Programming ,Water Resour Manage; 24(6):1045– 1064.
19- Marino M.A., and Mahammadi B. 1983. Reservoir management: A reliability programming approach, Water Resour Res; 19(3): 613- 620.
20- Martin Q.W. 1987. Optimal daily operation of surface-water systems, Journal Water Res Pl-ASCE; 113 (4): 453- 470.
21- Moghaddam A., Alizadeh A., Ziaei A.N., and Farid A. 2014. The Effect of PSO Algorithm Parameters in Optimal Design of Water Distribution Systems. 8th National Congress on Civil Engineering, Babol, Iran, May 7-8. (in Persian)
22- Mouatasim A. El. 2011. Boolean Integer Nonlinear Programming for Water Multi‐Reservoir Operation, Journal Water Res Pl-ASCE; doi: 10.1061/ (ASCE) WR.1943-5452.0000160.
23- Oliveira R., and Loucks D.P. 1997. Operating rules for multireservoir systems, Water Resour Res; 33(4): 839– 852.
24- Premalatha K., and Natarajan A. M. 2009. Hybrid PSO and GA for global maximization. Int. J. Open Problems Compt. Math, 2(4), 597- 608.
25- Reddy J.M., and Kumar D.N. 2007. Multi-objective particle swarm optimization for generating optimal trade-offs in reservoir operation, Hydrol. Process; 21(21): 2897– 2909.
26- Reddy M., and Kumar D. 2009. Performance evaluation of elitist-mutated multi-objective particle swarm optimization for integrated water resources management. Journal of Hydro informatics, 11(1), 79- 88.
27- Re Velle C., Joeres E., and Kirby W. 1969. The linear decision rule in reservoir management and design: 1, Development of the Stochastic Model, Water Resour Res; 5(4): 767- 777.
28- Sharif M., and Wardlaw R. 2000. Multireservoir systems optimization using genetic algorithms: case study, Journal Comput Civil Eng 2000; 14(4): 255– 263.
29- Shi Y., and Eberhart R., .1998. A modified particle swarm optimizer, in: Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence. pp. 69– 73.
30- Teegavarapu R.S.V., and Simonovic S.P. 2002. Optimal operation of reservoir systems using simulated annealing, Water Resour Manage; 16(5): 401- 428.
31- Tilmanta A., Faouzib E.H., and Vanclooster M. 2002. Optimal operation of multipurpose reservoirs using flexible stochastic dynamic programming, Appl Soft Comput; 2(1): 61- 74.
32- Tu M.Y., Hsu N.S., and Yeh W.W.G. 2003. Optimization of reservoir management and operation with hedging rules, J Water Res Pl-ASCE; 129(2): 86- 97.
33- Van den Bergh F., and Engelbrecht A. P. 2004. A cooperative approach to particle swarm optimization. Evolutionary Computation, IEEE Transactions on, 8(3), 225- 239.