Paddy Water Environ (2005) 3: 29–38 DOI 10.1007/s10333-005-0070-y ARTICLE Janejira Tospornsampan · Ichiro Kita · Masayuki Ishii · Yoshinobu Kitamura Optimization of a multiple reservoir system operation using a combination of genetic algorithm and discrete differential dynamic programming: a case study in Mae Klong system, Thailand Received: 12 April 2004 / Accepted: 13 December 2004 / Published online: 12 February 2005 C Springer-Verlag 2005 Abstract A combination of genetic algorithm and dis- Introduction crete differential dynamic programming approach (called GA-DDDP) is proposed and developed to optimize the The coordinated operation of a multiple reservoir system operation of the multiple reservoir system. The demonstra- for efficient management of available water to maximize tion is carried out through application to the Mae Klong the net benefit or minimize the total deficits of the system system in Thailand. The objective of optimization is to is a complex decision-making process. The decision poli- obtain the optimal operating policies by minimizing the cies involve many variables, objectives and considerable total irrigation deficits during a critical drought year. The risk and uncertainty. They must satisfy various constraints performance of the proposed algorithm is compared with on system operation while maximizing releases for various the modified genetic algorithm. The results show that the purposes such as irrigation, energy production or minimiz- proposed GA-DDDP provides optimal solutions, converg- ing spills and losses. Ideally, the reservoirs in a system ing into the same fitness values within a short time. The should be designed and operated together to maximize net GA is able to produce satisfactory results that are very social benefits. This aim can be reached by using optimiza- close to those obtained from GA-DDDP but required alot tion approaches. more computation time to obtain the precise results. The Many successful applications of optimization techniques difficulties in selecting optimal parameters of GA as well have been extensively carried out in reservoir studies. as finding a feasible initial trial trajectory of DDDP are Among them, dynamic programming (DP) has long been significant problems and time-consuming. The significant recognized as a powerful technique and used extensively advantage obtained from GA-DDDP is saving of computa- in the optimization of complex water resource systems. DP tional resource as GA-DDDP requires no need for optimiz- is a systematic recursive procedure for optimizing a mul- ing parameters and deriving feasible initial trial trajectories. tistage decision process. Many variants of DP have been Because DDDP is a part of GA-DDDP, the good perfor- developed to alleviate the major drawback of DP, the “curse mance of GA-DDDP is obtained when applied to a small of dimensionality.” In the works of reservoir management, system where numbers of discretizations and variables have DP includes incremental DP (IDP), discrete differential no influence to the dimensionality problem of DDDP. DP (DDDP), incremental DP and successive approxima- tions (IDPSA), multi interval DP (MIDP), stochastic DP Keywords Multi-purpose . Operating policy . Optimum . (SDP), reliability constrained DP, differential DP (DDP), Rule curve constrained DDP (CDDP), and the progressive optimality algorithm. Among variant versions of DP, IDP, IDPSA, DDDP, and MIDP attempt to alleviate the curse of dimen- J. Tospornsampan () sionality based on the same increment concept for state The United Graduate School of Agricultural Sciences, Tottori variables. DDDP is known as a generalization of IDP. University, In recent years, Genetic Algorithms (GAs) have become Koyama-minami, Tottori 680-8553, Japan increasingly popular as a powerful optimization approach. e-mail: [email protected] GAs are search algorithms based on the mechanics of nat- I. Kita · M. Ishii ural selection and natural genetics (Goldberg 1989). GAs Faculty of Life and Environmental Science, Shimane University, use a vocabulary borrowed from natural genetics, perform Matsue, Shimane 690-8504, Japan a multi-directional search by maintaining a population of Y. Kitamura potential solutions and encourage formation of informa- Faculty of Life and Environmental Science, Tottori University, tion and exchange between these directions (Michalewicz Koyama-minami, Tottori 680-8553, Japan 1996). 30 GAs belong to the class of probabilistic algorithm, re- In this paper, the combination of GA and DDDP (for ferred to as stochastic optimization techniques in which simplification it is called GA-DDDP hereinafter) is pro- the solution space is searched by generating candidate so- posed to overcome their shortcomings and improve their lutions. They maintain a population of potential solutions efficiencies. The GA-DDDP is developed to optimize a while all other methods process a single point of the search multiple reservoir system, namely the Mae Klong system, space. As a result, we can obtain more than one solution in Thailand. The objective of optimization is to obtain the from GAs. Since GAs do not rely on any mathematical operating policies by minimizing the total irrigation deficit properties of the functions employed in the model, such in a critical drought year. The performance of the proposed as differentiability and continuity of the objective function, GA-DDDP is compared with a single GA. The operat- this makes the method more generally applicable and ro- ing policies obtained from optimization are compared with bust than other directed search methods. Because GAs are those obtained from the actual operation as well. heuristic search techniques (of their stochastic nature), the global optimum solution are not guaranteed to be found Description of the Mae Klong River Basin system using GAs. Nevertheless, GAs give alternative solutions close to the optimum after a reasonable number of evolu- The Mae Klong River Basin is located in the west of tions that can be accepted for most of the real-life problem. Thailand, covering a total area of 30,800 km2 in five The ability to provide a number of alternatives near opti- ◦ ◦ provinces and lying from latitude 16 23 Nto13 10 N and mal solutions, in addition to one best solution, of GAs is ◦ ◦ longitude 98 15 Eto10 17 E. Figure 1 shows location and accurately reflecting the real world. general features of the basin. The basin is composed of GAs have been increasingly applied to solve complex two main rivers: the Khwae Yai River and the Khwae Noi optimization problems in a broad spectrum of fields. In River having a length of 380 and 315 km respectively. The the water resources field, GAs with their modifications confluence of these two rivers is the starting point of the and extensions have been applied to pipe network op- main Mae Klong River which ends at the Gulf of Thailand timization problems (Goldberg and Kuo 1987; Simpson and has a length of 132 km. Two major large-scale Dams, et al. 1994; Dandy et al. 1996; Savic and Walters 1997; the Srinagarindra Dam and the Vajiralongkorn Dam, Montesinos et al. 1999), to groundwater management prob- are constructed in the basin, serving multi-purposes for lems (Mckinney and Lin 1994; Cieniawski et al. 1995), to groundwater contamination problems (Ritzel and Eheart 1994; Inoue et al. 2003), and to reservoir operation (Oliveira and Loucks 1997; Wardlaw and Sharif 1999; Sharif and Wardlaw 2000). In addition GAs have been used to calibrate a rainfall-runoff model (Wang 1991), linked with SWMM to calibrate a catchment’s parameters (Liong et al. 1995), used to estimate WGR model parameters to characterize the variation of rainfall fields (Yoo et al. 2003), integrated with an AnnAGNPS (Srivastava et al. 2002) to optimize the selection of best management practices (BMP), and linked with SDP (Huang et al. 2002) to the operation of a multi- ple reservoir system. GAs have been compared with many other optimization techniques as well. In most cases, GAs have performed well and resulted in near optimal solutions. In some cases, GAs have performed better than traditional techniques. Advantage of GAs over conventional optimization is their handling of complex, highly nonlinear problems that are more realistic. Although GAs are flexible enough to handle a wide variety of complex problems, increasing of com- plexity is expected to cost more in terms of the computation time required. GAs may be set up in a number of ways, but as yet there is no standard procedure (Sharif and Wardlaw 2000). Each user exploits the GA concepts in a different way, and it is hard to perceive which are the best implementations for particular applications. Users of GA are forced to try different alternatives, and certainly different GA parame- ter values, and to choose those that perform best for their particular application. On the other hand, this need for ex- perimentation and judgment is not unique to GA (Oliveira and Loucks 1997). Fig. 1 Location map of Mae Klong River Basin 31 irrigation, hydropower generation, domestic and industrial full potential command irrigation area of 4,304 km2. The water supply, recreation and salinity control. In addition, area is utilized in both dry and wet seasons. The average another re-regulating Dam, the Tha Thung Na Dam, is irrigation requirement of the GMKIP is 5,791 MCM/year. located downstream of the Srinagarindra Dam performing In future, according to the development plan, the total irri- as a tail end reservoir for reversible turbines of the gation area will be increased up to 5,984 km2. In addition Srinagarindra reservoir. These three Dams are operated by to the water requirement of the GMKIP, the requirements the Electricity Generating Authority of Thailand (EGAT). from upstream and downstream of the Mae Klong Dam are Besides, the Mae Klong Dam is the diversion Dam, 62.4 and 1,000.1 MCM/year, respectively. Moreover, the situated just downstream of the confluence of the major minimum flow requirement for salinity control of the basin tributaries. The water is diverted from this Dam to supply is about 30–50 m3/s.