Paddy Water Environ (2014) 12:125–137 DOI 10.1007/s10333-013-0366-2 ARTICLE Optimizing the rule curves of multi-use reservoir operation using a genetic algorithm with a penalty strategy Trieu Anh Ngoc • Kazuaki Hiramatsu Masayoshi Harada • Received: 14 October 2012 / Revised: 27 February 2013 / Accepted: March 2013 / Published online: 21 March 2013 Ó Springer Japan 2013 Abstract This study aims to propose a methodology for establishing the optimal rule curves of reservoir operation based on a multi-use reservoir system Located on the upper Saigon River, Dau Tieng Reservoir plays an important role in economic and social aspects: (1) flood control; (2) domestic and industrial demands; (3) flushing out salt water intrusion from the downstream area; and (4) agriculture irrigation We propose a reservoir operation model using a constrained genetic algorithm (CGA), in which the fitness function was constrained by penalty functions The proposed model was formulated by including various water demands configured into the objective function The penalty functions were designed for various constraints and integrated into the objectives of the operation process to perform the fitness function The model’s T A Ngoc Laboratory of Water Environment Engineering, Course in Bioproduction Environmental Sciences, Department of Agro-environmental Sciences, Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan T A Ngoc Faculty of Water Resources Engineering, Water Resources University, 175 TaySon, Dong Da, Hanoi, Vietnam T A Ngoc (&) Division of Applied Sciences & Technology, Water Resources University, Second Base, No Truong Sa, Ward 17, Binh Thanh, Ho Chi Minh, Vietnam e-mail: anhngoc267@yahoo.com K Hiramatsu Á M Harada Laboratory of Water Environment Engineering, Division of Bioproduction Environmental Sciences, Department of Agro-environmental Sciences, Faculty of Agriculture, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan performance was simulated for the last 20 years with 1-month intervals and evaluated through a generalized shortage index (GSI) The derived results of three CGA cases with associated environmental flow requirements significantly improved the efficiency and effectiveness of water supply capability to various water demands as compared to current operation Among the three cases, CGA case achieved much better water releases from the reservoir as indicated by a small derived GSI value (0.33), the smallest shortage of environmental water (0.11 m3/s) and the highest water usage (63.8 %) Thus, the derived results of CGA case were presented as the best rule curves for reservoir operation To summarize, CGA was demonstrated as an effective and powerful tool for optimal strategy searching for multi-use reservoir operations Keywords Objective function Á Water shortages Á Constrained genetic algorithm Á Environmental requirement Á Dau Tieng Reservoir Introduction Reservoirs are one of the most efficient measures for developing and managing integrated water resources They have become the most important facilities for increasing the reliability of water supply for various purposes such as agriculture, industry, human activities, and environmental requirements, and for reducing the vulnerability of water users in droughts (Guo et al 2004; Hsu and Wei 2007; Wei and Hsu 2009) In past decades, water is becoming an increasingly scarce resource as a result of the growing demand for its use for various purposes (Li et al 2010), and serious water shortages are occurring more frequently owing to restrictions on effective water use To overcome 123 126 the problem of water shortages during dry seasons, researchers have focused on improving water resource management, especially with regard to optimization of reservoir operations (Chang et al 2005; Chen and Chang 2007) Thus, the rule curves of reservoir operation are very important tools with which to support operators in effectively making decisions about operating policies The research is mainly concentrated on developing ways to meet the demands of human activities, while environmental requirements have received less attention In an attempt to minimize the negative impacts related to environmental aspects, environmental base flow requirements must be considered in the management of water storage facilities (Bauer and Olsson 2008; Gibbins et al 2001; McCartney et al 2005; Suen and Eheart 2006) In the past several years, many researchers have attempted to analyze human-related activities and environmental flow requirements to help optimize facility operational schemes Most of these attempts have quantified environmental flow requirements by assigning an extra water quantity constraint to the minimum reservoir water release rate (Homa et al 2005; Jager and Smith 2008) However, these methods allusively assigned lower priority levels to riverine ecosystems than to human needs (Yin and Yang 2011) To overcome an obstacle encountered when using previous methods, some researchers have developed reservoir operation simulation models that maintained environmental flow requirements Cardwell et al (1996) presented a model consisting of the corresponding frequencies and unmet water supplies as well as the available habitats for various typical fish species at different life stages Suen and Eheart (2006) utilized reservoir operating rule curves as the basis for developing an alternative approach Chang et al (2010) employed constraints as penalty functions to set weights for maintaining environmental base flow requirements To design an operation model with an effective balance of water reservoir releases and water reservoir storage, it is necessary to consider the various water demands and different water storage levels In the current decades, revolutionary computational techniques are being rapidly developed using artificial intelligence techniques for search optimization Popular global optimization algorithms, such as artificial neural networks (Chinh et al 2009; Chaves and Chang 2008), particle swarm optimizations (Kumar et al 2005), and genetic algorithms (Chang et al 2005), have been applied to water resources management sciences and engineering Most optimization algorithms have extensive abilities to solve complex planning and management problems, and have received considerable attention because of their potential as optimization techniques However, they have not really produced a significant breakthrough in solving complex nonlinear problems because they not address 123 Paddy Water Environ (2014) 12:125–137 the issues of constraints in a systematic way (Chang et al 2010) Only recently have several methods been proposed for handing nonlinear constraints by evolutionary algorithms for numerical optimization in water resources management (Chang 2008; Chang et al 2010; Katsifarakis and Petala 2006; Afshar 2012) The aim of this study was to design a reservoir operation model with interactive balancing of water releases and water storage, including environmental base flow requirements and flood control storage The optimizing reservoir operation rule curves for multi-use water resources management are proposed using a genetic algorithm with a penalty strategy The methodology of the proposed model was incorporated in a constrained genetic algorithm (CGA), where water demands were assumed as constraints to water reservoir storage/discharge operations The penalty functions were designed with various constraints integrated into their objectives of operation processes to perform the fitness function The model performance was evaluated through a generalized shortage index (GSI) of water demands Materials and methodology Study area The Saigon–Dong Nai River, shown in Fig 1, is one of the largest river systems in the south of Vietnam, and has two main reach rivers The Saigon River has a large reach of the Saigon–Dong Nai River, which flows through Ho Chi Minh City area The upstream portion of the Saigon River is intercepted by the Dau Tieng Reservoir, which spans about 130 km of the main course The Dau Tieng Reservoir has a total watershed of 2,700 km2 and a water surface area of about 270 km2 and its elevations are in the range of 24–100 m above mean sea level It has received an annual average rainfall of 1,800 mm in last 30 years; however, the rainfall was uneven, such that 77 % occurred between July and November Therefore, the difference between the wet and dry seasonal inflow discharge is very large, as shown in Fig This study predominantly focuses on the between water reservoir storage and water releases to gain the best level of water storage for flood control and provide for the different water demands corresponding to various weighted goals To evaluate the applicability of the reservoir operation model using a genetic algorithm with a penalty strategy, the data for the monthly inflow, evaporation, and outflow based on the current operation records including water storage levels and outflows from the reservoir during the period of 1989–2008 were used for the simulation These data were collected by Dau Tieng Irrigation Exploitation and Management under the Ministry of Agriculture and Paddy Water Environ (2014) 12:125–137 127 Fig Location of the Dau Tieng Reservoir watershed Fig Time series of annual wet and dry seasonal flows during the period of 1989–2008 Rural Development, Vietnam (MARD), and were also provided by Division of Applied Science and Technology, Water Resources University–Second Base, Vietnam Water storage and water supplies The Dau Tieng Reservoir, which was constructed beginning in 1981 and completed in 1985 by a credit fund of the World Bank, is one of the largest reservoir systems in Vietnam, especially in the south of Vietnam The Dau Tieng Reservoir has a total storage capacity of 2.2 109 m3 and an effective storage capacity of 1.58 109 m3 It supplies water for various purposes, including irrigation, industrial and domestic demands, environmental base flow requirements for flushing out saltwater intrusion, recreation, and especially flood control There are four provinces in the downstream area: Tay Ninh, Binh Duong, Long An, and Ho Chi Minh City, with a total direct irrigation area of about 640 km2 Several human water demand facilities located in the protected downstream area use the water released from this reservoir The reservoir was originally designed to achieve the following goals, in descending order of priorities: (1) flood control; (2) human demands, including domestic and industrial demands; and (3) agriculture irrigation In this sense, the reservoir has been operated according to the Dau Tieng Reservoir operating rule curves (DTOR) However, during operation of the reservoir, the downstream area of Ho Chi Minh City was critically affected by saline water intrusion, which emphasized the dramatic vulnerability of the economic sectors and human activities along with the damage to the river’s ecosystems Hence, policymakers (MARD 1995) reassigned the third priority to the DTOR to elevate the importance of flushing out saltwater intrusion in the downstream area of Ho Chi Minh City However, the water released from the reservoir for preventing saltwater intrusion is effective only when the downstream area is supplied with a minimum continuous flow, which implies that the environmental base flow requirements have certainly not been considered in the current operation DTOR 123 128 Paddy Water Environ (2014) 12:125–137 The minimum flow requirements are generally comprehended as a minimum water flow rate that significantly prevents an injury to the regional ecosystem The minimum base flow requirement should be determined based on a wide variety of existing information, including biologic and topographical information, scientific literature, and water flow data, in order to estimate the overall impact of the flow rate on aquatic communities and the regional environment (Chang et al 2010) The minimum base flow requirements used in this study were proposed for the water resources managers by MARD and the Ministry of Natural Resources and Environment, Vietnam (MONRE), and they mainly serve the purpose of flushing out saltwater intrusion in the area downstream from the Dau Tieng Reservoir The minimum base flow requirements are also understood as environmental flow requirements that follow the guidelines set by MONRE Table lists the expected minimum environmental flow requirements in the dry season during the period of January–May The existing DTOR (Fig 3), which was approved by MARD, consists of four curves: the retarding water level (RWL), the upper water level (UWL), the lower water level (LWL), and the critical water level (CWL) The dead water level (Dead Level) is the point at which all sediment accumulates to the maximum level allowed by the design conditions This means that once the water level of the reservoir is below the dead water level, the reservoir operation will encounter its lowest controllable level However, this water storage will only be supplied for human demand if required Based on the DTOR, the operating regulations can be summarized as follows: (1) (2) When the water level in the reservoir reaches the retarding water level, the spillway is immediately opened in an attempt to rapidly reduce the water level to the upper water level When the water level in the reservoir exceeds the upper water level, water release should be kept at a high priority level in an attempt to maintain the water level at the upper water level Fig The rule curves of the Dau Tieng Reservoir’s operation (DTOR) (3) (4) (5) When the water level in the reservoir is between the lower water and the critical water levels, water release is restricted In this case, the water supply should satisfy human demand and be reduced for agricultural demand When the water level in the reservoir is below the critical water level, agricultural water demand must be critically reduced in an attempt to maintain the water level above the dead water level, but the water supply remains for satisfying human and domestic demands When the water level in the reservoir drops to the dead level of the reservoir, the water release is stopped for supplying all water users except for human demand Genetic algorithm optimization search Constrained genetic algorithms The genetic algorithm (GA) was originally developed and introduced in 1975 by John Holland (Holland 1975) It is a population-based optimization method that mimics the Table The expected minimum environmental base flow requirements for the Saigon River Case Environmental base flow requirement Method References 30 m3/s in dry season Historical flows during the period from 1989–2008 Rule regulations of handbook (MARD 1995) 50 m3/s in dry season 35 m3/s in dry season 15 m3/s in wet season Considering the needs for preventing salt water intrusion in the downstream Ho Chi Minh City area Considering the needs for preventing salt water intrusion and improving water quality in the Saigon River Recommendations of Vietnamese scientists on the research project of EIA on Water quality of the Saigon River 2006–2008 (MONRE 2009) Proposed in this study 123 Paddy Water Environ (2014) 12:125–137 processes of natural selection and natural evolution The GA is used to search large nonlinear spaces where expert knowledge is lacking or is difficult to encode (Chu-Tian et al 2006) The GA optimization search uses the idea of fitness to analyze a variety of solutions and generate a new and better solution The GA begins with a randomly generated initial set of solutions called the population and progresses to enhance the fitness of solutions through interaction by conducting operators, including selection, crossover, and mutation However, restrictions on unfeasible search spaces imposed by constrained conditions were encountered in GA optimization, and this usually engendered early convergences or ineffective searches During the past few years, several methods such as rejection, repair, and penalization strategies have been presented for handling constraints when using GAs to solve constrained optimization problems (Deep and Dipti 2008) The advantage of the rejection and repair approaches was that only feasible solutions were generated Thus, the most popular approaches to handling constraints in the GA community were to use penalty functions (Chang 2008) The objective to be achieved by means of penalty functions was to penalize infeasible solutions in an attempt to proportionally reduce their fitness values when constraint violations were found This strategy guided the search toward providing better solutions (see Fig 4) Unfortunately, the constraints that represent interior penalty functions impede the capability of the GA search within the feasible domain (Abedian et al 2006) When the constraints were exterior penalty functions, the penalty values were designed to add to violated solutions by considering the number of violated constraints and their distance to the feasible domain (Chang 2008) The most common methods for using genetic algorithms with penalty strategies were written in nonlinear programing as follows: 129 FðWÞ ¼ f ðWÞ þ PðWÞ ð1Þ where W is the water storage in the reservoir, F(W) is the fitness function, f(W) is the objective function, and P(W) is the penalty function However, there is no common guideline for finding a suitable and effective penalty function In general, the equation of the penalty function is designed as follows: XL XI PðWÞ ¼ p ðWi Þ ð2Þ l¼1 i¼1 li & Wi feasible region pli ðWÞ ¼ ð3Þ pli ðWi Þ Wi 62 feasible region where i is the current simulation time step, L is the total number of sub-penalty functions, I is the total number of simulation steps, and pli(Wi) is the lth sub-penalty function at the ith time step In the following, the water storage Wi at the ith time step will be sometimes described as the water storage Wmn at the mth month in the nth year The reservoir operation model The reservoir operation simulation model was developed to describe the reservoir’s behaviors This model was designed based on a water balance equation, and its equation is written as follows: Wi ¼ WiÀ1 þ WiInflow À Ei À Ri ð4Þ where Wi is the water storage at the ith period, Wi-1 is the water storage in the (i-1)th period, and is the water volume by rainfall runoff at the ith period The inflow to the Dau Tieng Reservoir was simulated through hydrological rainfall runoff models (the Tank model and the NAM model, of which, NAM is an abbreviation for ‘‘Nedbor–Afstromings Model’’, a Danish phrase meaning ‘‘precipitation runoff model’’ originally developed at the Institute of Hydrodynamic and Hydraulic Engineering at the Technical University of Denmark) constructed by Ngoc et al (2011, 2013) The precipitation directly to the reservoir was considered in the rainfall runoff models Ei is the evaporation observed by the ‘‘Piche’’ evaporimeter (Stanhill 1962; Papaioannou et al 1996) in the ith period and Ri is the water release in the ith period, as expressed as below: & Agr Dom þ REnv WiÀ1 WiUpper Ri þ RInd i þ Ri i Ri ¼ Agr Spil Dom Ri þ RInd þ REnv þ Ri WiÀ1 [ WiUpper i þ Ri i ð5Þ Fig The structure of the proposed model combined CGA search Ind Dom where RAgr and REnv are the volumes of the i , Ri , Ri i water released in month for agricultural, industrial, domestic, and environmental demands, respectively, and RSpil is the released water from the spillway gate to avoid i 123 130 Paddy Water Environ (2014) 12:125–137 the breakdown of the reservoir The water demands for agriculture, industry, and domestic use were calculated for 1-month intervals based on the actual demand states, while the environmental flow requirements were estimated for two seasons (dry and wet) WiUpper is the upper limit at the ith period corresponding to the upper water level in the rule curves of reservoir operation shown in Fig Supply priorities of water users were set in descending order as domestic, industrial, environmental, and agricultural supplies It means that the water demand with lower priority was supplied only when the water demands with higher priorities had been adequately met Constraints The reservoir was operated according to the regulations defined by the reservoir operation curves promulgated by MARD, complying with physical characteristic limitations such as water balance and permissible terms of water storages and releases Retard ð6Þ ðwet season) ð7Þ Wi ! W Lower ðdry season) ð8Þ WiWet ! 0:9W0Wet ð9Þ W Dead Wi WiDry W Wi Upper W W0Dry ð10Þ Wi ! W Critical Dead ð11Þ Max Upper Lower where W , W , W , and W are the water storages corresponding to the dead water level, the retarding water level, the upper water level, the lower water level, respectively W0Wet is the water storage limit to be maintained at the end of the wet season to avoid long-term water shortage in the next dry season, W0Dry is the water storage limit that must be maintained at the end of dry season to serve for retarding the flood flow in each wet season, and W0Wet is the water storage of the reservoir at the ith step of the last period in each wet season Because the annual rainfall of the Dau Tieng Reservoir watershed fluctuates widely through the years, the value of 0.9 was set in Eq to insure that the search process of the CGA is better and to decrease the effect of the penalty functions WiDry is the water storage in the reservoir at the ith step of the last period in each dry season Objective function The objective function was designed by considering the different water demands to avoid long-term water shortage and to specifically focus on short-term water shortage It consists of all the water demands of the different users 123 downstream from the Dau Tieng Reservoir area, including the environmental flow requirement Hence, the objective function should be considered the core value to meet the total water demands of different users and to anticipate serious water shortages, while each different water demand and the enforced terms based on the rule curves are considered constraints when optimizing the reservoir operation Moreover, long-term water shortage might cause inconvenience for users, and will eventually result in damage agricultural crops, the ecosystem, industrial manufacturing, etc Therefore, the sub-objective functions are defined as the shortages in each period to the power of the number of continuous water insufficiency periods in an attempt to strongly restrict long-term water insufficiency, which may seriously damage vulnerable agricultural products and activities in the downstream area The objective function f(W) was formulated as follows: f ðWÞ ¼ fEnv ðWÞ þ fAgr ðWÞ; f ðW Þ ! Min ð12Þ The sub-objective functions of fEnv(W) and fAgr(W) were set as follows: Release Ind Dom Env If Wmn À Wmn À Wmn \Wmn > > = Rest Release Ind Dom Wmn ¼ Wmn À Wmn À Wmn Â Ã È É P M N Env Rest nmn Env > fEnv ðWÞ ¼ Maxn¼1 ÂK > m¼1 ðWmn À Wmn Þ ; Else fEnv ðWÞ ¼ ð13Þ Release Ind Dom Env Agr If Wmn À Wmn À Wmn À Wmn \Wmn > > > > Rest Release Ind Dom Env > = Wmn ¼ Wmn À Wmn À Wmn À Wmn nXM  o à n mn Agr Rest fAgr ðWÞ ¼ MaxNn¼1 ðWmn À Wmn Þ ÂK Agr > > > m¼1 > > ; Else fAgr ðWÞ ¼ ð14Þ where N is the total number of computed years(=20), M (=12) is the total number of computed periods in a year, Relase Ind Dom Wmn is the total volume of water released, Wmn , Wmn , Env Agr Wmn , and Wmn correspond to the water volumes for the industrial demand, the domestic demand, the environmental flow demand and the agricultural demand, respectively; nmn is the number of continuous water insufficiency periods wherewater shortages continuously occurs at step m of year n, and K Env and K Agr are the weighted factors corresponding to environmental and agricultural demand MaxNn¼1 f .g is the maximum value in N years of the quantity inside the parentheses Agricultural and environmental demands accounted for most of the total water demand (53 % for agricultural demand, 35 % for environmental requirements in case 2) and were considered in the objective function, while the domestic (5 %) and industrial (7 %) demands counted for smaller proportions (Ngoc 2012) and were always met Paddy Water Environ (2014) 12:125–137 131 with plentiful water in almost all of the past years’ operations Although the environmental requirements counted for much of the total water demand, they were mostly not considered in setting the regulation policy for proposing the rule curves for the reservoir’s current operation This means that the Dau Tieng Reservoir has normally operated to supply water for human, domestic, and industrial demands Once the downstream area was deeply affected by salinity intrusion and the industrial zones could not use the water for their production owing to high salinity levels, the Dau Tieng Reservoir Irrigation Exploitation and Management Company would be asked to release additional water for flushing out saltwater intrusion Therefore, human and industry demand were not considered to reduce the complexity of the formula and the proposed model Penalty strategy and fitness function The constraints were divided and placed into the subpenalty functions The constraints corresponding to Eq confine the search space to the designed ranges The constraints corresponding to Eqs 7–11 are penalized by subpenalty functions when the obtained variants in the model violate terms of the designed penalty mechanism throughout the model by decreasing the fitness values Thus, the constraints will lead the CGA search process toward a feasible solution space Furthermore, in the computation process, when various genes reach the limits of their conditions, the respective penalties are strictly put into the fitness function to promptly reduce the fitness value Thus, the sub-penalty functions in Eq are designed using the water storage and penalty weights K as follows In wet seasons, the aim is to maintain a certain water level for flood control, and when Wi [ WiUpper , the penalty function is set as: p1i ðWÞ ¼ ðWi À WiUpper Þ Â K Upper ð15Þ However, the aim is to always keep the water level below the retarding water level to avoid breakdown of the reservoir, and when Wi [ WiRetard , the penalty function is set as: p2i ðWÞ ¼ ðWi À WiRetard Þ Â K Retard ð16Þ In dry seasons, the aim is to hoard up the water to a certain level to prevent water shortages, and when Wi \WiLower , the penalty function is p3i ðWÞ ¼ ðWiLower À Wi Þ Â K Lower ð17Þ The aim is to avoid long-term water shortages, and hence, water should be hoarded up to a certain level all the time When Wi \WiCritical , the penalty function is set as: p4i ðWÞ ¼ ðWiCritical À Wi Þ Â K Critical ð18Þ This reservoir is operated under regulations developed over several years time to avoid water shortages in the long-term When Wi \W0Wet at the last period of the wet season, then the penalty function is set as: p5i ðWÞ ¼ ð0:9WiWet À Wi Þ Â K Wet ð19Þ In addition, to maintain water storage space for the wet season as part of the function of retarding flood flow, when Wi [ W0Dry at the last period of the dry season, the penalty function is set as: p6i ðWÞ ¼ ðWi À W0Dry Þ Â K Dry ð20Þ To avoid exceeding the limitation of the physical reservoir characteristic, when Wi \W Dead , the penalty function is set as: p7i ðWÞ ¼ ðW Dead À Wi Þ Â K Dead ð21Þ While sub-penalty functions are as above-designed, the fitness function F(W) was used in this research determined as Eq 22, meaning that it may substantially increase the chance of searching a better solution with savings in resource expenditure The fitness function was defined by inversion of the value of objective function plus penalty function, and the largest value of fitness function is the best solution FðWÞ ¼ ; FðWÞ ! Max f ðWÞ þ PðWÞ ð22Þ Variables for CGA optimization and their coding The CGA requires coding to transform the variables to a structural scheme for operation Binary strings are the most common coding scheme, and hence, they were applied in this study There were 20 years (N = 20) and each year had 12 step intervals (months, M = 12), so the total number of variables (WiRelease ) was 240 Constraints on the water release rates were required within maximum and minimum water release capacity of the Dau Tieng Reservoir and were set at 2,700 m3/s and 0, respectively As previously stated, the aim of the CGA was to solve the optimization problem by searching for an optimal solution in terms of the water releases from the reservoir, considering all of the input variables The variables were joined together by defining a chromosome as an array of values to be optimized The chromosome consisted of NT(=M N) variables [WiRelease , i = 1, NT] with the Release range WMin (=0) B WiRelease B WiRelease (=2,700 m3/s) Each variable WiRelease was represented as a single binary string of length b(=24) according to the following formula: 123 132 Paddy Water Environ (2014) 12:125–137 Release WiRelease ¼ WMin þ Decimalð1010 .110Þ Release Release WMax À WMin  2b À Table CGA parameters CGA-Parameter Setting value Bit-length for one parameter 24 Population size 500 Generation 5,000 Crossover rate 0.8 Mutation rate 0.05 Selection method Roulette Wheel Constraint method Penalty function ð23Þ where Decimal(binary string) is the decimal value of the binary string Each chromosome value is represented for a coded possible solution It will take a long period of computing time or be ineffective when a large number of variables are set Therefore, our case considered 240 variables Setting parameters of the genetic algorithm Table Values of the K (weighting) factors Factor Value Factor Value KEnv 20 KLower Agr 10 KCritical K Upper KRetard 100 K K Wet The GA’s parameters consist of the population size, the mutation and crossover rates, and the generation size These parameters play an important role in determining the best input variables of the model Table shows the parameters for the GA optimization Based on considering the importance of each element in the model as abovementioned and through several test runs, the weighting factors K were determined as shown in Table 10 KDry 10 KDead 1,000 Table The annual water shortages (9106m3) W Shortage and the annual water usage rates (%) W Usage for the current operation and CGA cases Case Current operation CGA_ current CGA_case1 CGA_case2 CGA_case3 Water usage (%) Water usage (%) Water usage (%) Water shortages (9106 m3) 58.1 142.4 Type Year Water usage (%) Water shortages (9106 m3) Water usage (%) Drought 1992 62.9 148.6 62.4 94.4 74.3 10.6 1995 67.4 178.7 74.7 67.6 66.7 117.2 68.3 135.3 76.9 57.6 2003 74.0 189.5 84.3 56.2 81.2 74.0 65.3 191.5 84.6 58.8 2004 80.2 266.4 86.8 119.0 94.3 83.7 93.1 117.3 79.4 158.3 2005 60.2 230.0 71.1 65.6 74.0 47.0 65.6 130.0 66.5 100.4 2006 56.3 245.2 63.2 100.9 62.2 107.6 56.3 176.0 65.6 89.2 2007 55.2 220.3 60.4 96.8 52.3 155.5 56.3 154.0 59.7 106.0 1989 51.1 221.4 60.1 69.7 60.8 64.2 59.8 99.6 58.1 88.8 1993 54.1 173.7 56.7 92.3 60.8 60.3 59.1 101.6 56.9 94.7 1994 68.7 96.9 62.7 105.9 58.3 135.8 67.6 101.1 65.8 89.3 1996 51.4 178.7 57.3 110.7 58.6 101.3 57.3 139.1 57.8 111.7 1998 56.4 188.7 63.3 67.6 63.3 67.3 53.7 166.5 60.1 95.0 2000 2002 49.0 59.4 97.8 150.7 46.8 66.4 89.8 48.1 43.5 66.1 121.2 50.3 46.7 61.0 118.7 115.3 46.6 60.7 105.4 93.8 2008 57.9 148.2 57.7 98.0 53.8 127.7 56.1 138.6 63.4 59.7 1990 56.5 150.9 55.3 104.3 54.8 107.5 56.7 121.4 65.5 28.9 1991 59.5 84.1 56.2 83.4 58.0 69.3 48.4 174.1 62.3 38.7 1997 75.6 131.4 77.4 74.3 72.3 104.5 74.0 122.2 74.7 94.1 1999 59.7 162.5 68.2 45.4 64.5 71.7 69.7 62.2 65.3 70.2 2001 57.9 70.0 57.5 55.8 55.0 77.2 52.5 125.2 47.6 142.1 60.7 166.7 64.4 82.3 63.7 87.7 61.9 127.9 63.8 91.3 Normal Wet Average 123 Water shortages (9106 m3) Water shortages (9106 m3) 70.0 Water shortages (9106 m3) 68.8 Paddy Water Environ (2014) 12:125–137 133 Table Annual water shortage based on environmental flow requirements (9106 m3) between current operations and CGA results Type Years Current Operations Current Drought Normal Wet CGA results Case1 Case2 Case Current Case1 Case2 Case 1992 27.3 30.9 110.9 42.9 0.0 0.0 0.0 10.5 1995 7.4 11.4 58.3 17.4 17.2 0.0 19.1 19.7 2003 23.7 30.7 110.7 42.7 0.0 2.9 33.9 0.0 2004 37.1 56.2 142.3 80.6 0.0 0.0 0.0 0.0 2005 31.6 38.6 149.3 55.1 0.0 0.0 19.2 0.7 2006 26.5 35.6 120.2 47.6 0.0 10.9 44.2 0.0 2007 1989 23.6 4.2 30.9 8.2 150.9 106.9 48.9 14.4 0.0 0.0 33.8 0.0 32.8 0.0 16.4 0.0 1993 0.0 0.0 55.5 0.0 0.0 0.0 0.0 0.0 1994 8.5 11.5 51.5 17.5 0.0 3.2 41.3 1.3 1995 27.8 46.9 126.9 58.9 0.0 0.0 15.5 14.1 1998 9.5 13.5 76.3 19.5 0.0 0.0 17.0 0.0 2000 5.7 8.7 48.7 14.7 0.0 3.3 0.0 0.0 2002 1.1 4.1 47.7 10.1 0.0 0.0 7.9 2.9 2008 8.1 12.1 83.8 18.1 0.0 12.0 8.0 0.0 1990 18.8 22.5 102.5 34.5 0.0 25.7 55.0 0.0 1991 14.5 18.5 58.5 29.3 0.0 0.0 61.5 0.0 1997 5.1 9.1 51.7 15.1 0.0 0.0 8.3 0.0 1999 0.0 0.0 36.7 2.7 0.0 0.0 0.0 0.8 0.0 0.0 12.1 0.0 30.4 0.0 0.0 6.0 14.0 19.5 85.1 28.5 2.4 4.8 18.2 3.6 2001 Average Underlined values denote different tendency (unexpected results) as compared to other values Fig Comparison of the GSI values between current operations and CGA results during 1989–2008 Evaluation indicators To evaluate the performance of the CGA, the search results were compared with current operations, i.e., the generalized shortage index (GSI) proposed by Hsu (1995) was used to express the status of the frequency and intensity of water shortages Its formula is given as follows: DPDn ¼ XM DDRnm  NDCnm   100 XN DPDn k GSI ¼ n¼1 100  M N m¼1 ð24Þ ð25Þ where DDRnm is the month shortage rate (%) at the mth month in the nth year, i.e., a ratio of the total shortage in the 123 134 Paddy Water Environ (2014) 12:125–137 month to the water demand in the month, NDCnm is the number of continuous shortage days in the month, M is the number of months in a year (=12), N is the number of simulation years, and k is a constant usually set as (Chang et al 2010) According to the above formula, a smaller value of GSI is considered to provide better operational performance In addition, the following formulas for water shortage and water usage were used to evaluate the simulated results: W Shortage ¼ W Total À W Release W Usage ð%Þ ¼ W Total  100 W Inflow ð26Þ ð27Þ where and are the annual water shortage and annual water usage rate, respectively; W Total is the total annual water demand including the human, industrial, agricultural demands, and the environmental base flow requirement; W Release is the annual water released from the reservoir; and W Inflow is the volume of the annual inflow from rainfall runoff Results Evaluating the results To estimate the performance of the proposed model for optimizing the Dau Tieng Reservoir operation rule curves during the period of 1989–2008, this study evaluated three cases of environmental base flow requirements as shown in Table The results obtained for the current operations and the CGA operations are shown in Table 4, and Fig Figure represents the annual GSI values calculated from the CGA results compared with the current operations In Fig 5, the ‘‘current’’ operation was operated by complying with the DTOR without considering the environmental flow requirement, and ‘‘CGA_Current’’ was operated under the rule curves of the current operation with the supporting CGA search It can be seen that most of the obtained GSI values from the CGA search for all cases were much smaller than those of current operations, except for the GSI values of case in 1991 and 2003 Most of obtained GSI values for the four cases simulated using the CGA method were lower and only six GSI values were larger and occurred in 2007 of case 1, in 1998 and 2003 of case 2, and in 1996, 2001, and 2004 of case In the comparison among the three environmental base flow cases, the corresponding GSI values were slightly increased for case (30 m3/s), case (50 m3/s), and case (35 m3/s in the dry season and 15 m3/s in the wet season) Table indicates the annual average water shortages W Shortage and the water usage W Usage for all of the cases 123 compared with current operations during the 20-year period In Table 4, the drought years have much smaller annual rainfall than the 20-year average annual rainfall, the wet years have much larger annual rainfall than the 20-year average annual rainfall, and the normal years have approximately the 20-year average annual rainfall The average water shortages were obtained using the long-term reservoir operation records, which were based on complying with the DTOR curves, and the CGA results According to the obtained results, without difficulty we can remark that water usage (%) of all three cases simulated by the CGA method attained higher values than those of current operations and thus demonstrated much better performance (60.7, 64.4, 63.7, 61.9, and 63.8 % for current operations, CGA-Current, case 1, case 2, and case 3, respectively) However, we could find some values of annual water shortages in the current operation that were lower than those of all of the cases simulated by CGA method, and the value of water usage in the current operations also achieved a higher level in a few years As shown in Fig and Table 4, the results obtained by the CGA method were clearly better than those obtained from the current operations using the DTOR curves The water shortages of the current operations and the CGA results were based on associating the various environmental base flow requirements and are shown in Table In all cases associated with the current operations curves, the average water shortages for providing the environmental flow requirements increased in ascending order from 14.0, 19.5, 85.1, and 28.5 for cases of current operation, case 1, case 2, and case 3, respectively In the cases of the CGA results, it also showed an ascending tendency like the current operations cases Nevertheless, the obtained values of 2.4, 4.8, 18.2, and 3.6 in the cases of CGA-Current, case 1, case 2, and case 3, respectively, were much smaller than those of the current operations cases Especially, the CGA results in case 3, with an average Fig The optimized CGA curves for Case Paddy Water Environ (2014) 12:125–137 135 Table Summarized CGA results Type GSI Agricultural unmet water (m3/s) Environmental unmet water (m3/s) Case Case Case Case Case Case Case Case Case Drought 0.40 0.61 0.41 12.1 19.8 14.5 0.2 0.7 0.2 Normal 0.30 0.35 0.29 13.0 17.5 13.2 0.1 0.4 0.1 Wet 0.26 0.24 0.29 12.3 17.2 10.7 0.2 0.8 0.0 20 years 0.33 0.41 0.33 12.51 18.19 13.02 0.15 0.58 0.11 water shortage as compared with the environmental flow requirement, was 3.6, lower than case of the CGA results (4.6) although its environmental base flow requirement was set at 30 m3/s in the dry season, lower than those for case (35 m3/s in the dry season and 15 m3/s in the wet season) Looking at Table 5, we can make the following observations: (1) the water shortages of the CGA results of current operations and case were higher than those of the current DTOR and case in 1995 (one of the drought years); (2) the water shortages of all three cases simulated by the CGA method decreased dramatically as compared with all cases of DTOR operation in normal years, remarkably in 2000 and 2008; (3) there are different fluctuations between the water shortages of the CGA results and current operations associating various environmental base flow requirements in wet years as indicated in 1990, 1999, and 2001; (4) all water shortages as compared with environmental requirements from the CGA cases decreased remarkably as compared to all cases of current operation Those aforesaid statements are presented in some years of Table as marked by underlines It appears that: (1) in the drought year of 1995, although the environmental flow requirement for case was set higher than for case 1, in that year the average inflows in the dry season were not smaller than in normal years; (2) in normal years, most of the obtained GSI values from the CGA method were very small, especially for case with the larger environmental flow requirement of 50 m3/s, and reached zero in 2000 and 2008 It might explain that the inflows in the dry seasons were higher than those of dry seasons in normal years; (3) in the wet years 1990, 1999, and 2001, the inflows in the wet seasons exceeded the effective capability of water reservoir storage However, the obtained GSI values of all cases for the CGA method achieved smaller values than those for the current operations and the only larger GSI value was for CGA case in 1991, when it was slightly increased (larger than in current operation case); (4) the Dau Tieng Reservoir was designed for operating for several years, meaning that it needs to hoard up water year-by-year to attain its full effective volume According to the above-mentioned analysis, the obtained CGA results for case (35 m3/s in dry and 15 m3/ s in wet season) achieved much better performance following the requirements for environmental base flow to flush out saltwater intrusion and improve the water quality downstream of the Dau Tieng Reservoir watershed for two seasons, dry and wet In addition, Table gives the mean values of the CGA results in comparison with the difference between the cases associated with the environmental base flow requirements The values for CGA case demonstrated it had both good performance and efficiency Consequently, Fig represents the best set of operating rule curves, those achieved from CGA case The simulated water levels resulting from CGA case for 20 years have been statistically counted and drawn as the CGA curves The results also demonstrate that the CGA curves have higher UWLs in the dry seasons, and also larger feasible operating spaces However, at the ends of dry seasons (April and May), the LWL of the CGA curve was lower than those of current operations Besides that, the operating space between the LWL and the CWL is larger It indicates that, by the CGA-obtained curves, simulated reservoir operation extended the working space to enhance the effective performance of year-by-year reservoir operations In summary, the results in the above tables and figures show that it is obvious that the values of both GSI and water shortages from the CGA method were much smaller than those achieved by the results of current operations over the 20-years study interval and the obtained CGA curves resulted in better performance than the DTOR curves Conclusion The rapid development of computational techniques in the current decades has prompted a great deal of potential for optimizing complex numerical models This study constructed a model of reservoir operation based on the guiding rational reservoir operation principle using a penalty-type genetic algorithm (Chang 2008) for multi-use reservoir management The proposed model, with constraints integrated into its objective function, was configured with a penalty strategy to form the fitness function The designed constraints allow punishing of a fitness value once it reaches an infeasible space in an attempt to guide 123 136 the GA toward a promising solution space during search processing The CGA search is very efficient using the penalty mechanism, which is able to avoid the probability of choosing a worse solution, as the above results demonstrate According to previous studies, the environmental base flow requirements were set as follows for the proposed model: case 1—30 m3/s in the dry season, case 2—50 m3/s in the dry season, and case 3—35 m3/s in the dry and 15 m3/s in wet season The reservoir operation model was integrated into the CGA method simulation and carried out an effective level of performance It was demonstrated by a dramatic decrease of the GSI values in all three CGA cases associated with the different environmental base flow requirements in comparison with the current operations On the other hand, the results also indicated that water shortages for the three cases were reduced significantly and the water demands were supplied reasonably To be more specific, the simulated results of CGA case showed the best performance where most of the GSI and water shortage values decreased remarkably Comparing the simulated results from all of the cases shows that the CGA curves were more efficient than current operations, in which the CGA results for case were slightly more effective at operating than the others Therefore, we trust that the obtained CGA curves as determined from case provided the best performance In terms of future study, the above-proposed model will be applied for a watershed with multiple multi-purpose reservoirs The rainfall runoff forecast modules might be additionally developed and integrated into the reservoir operation model Weekly simulated water releases from the reservoir will be considered to have good consistency with weekly downstream demands in order to accurately simulate the reservoirs’ behavior in real time With this approach, the model can gain a highly capable and effective application to actual cases Besides that, the larger number of variables will be a big challenge for the CGA optimization search Moreover, the complex interactions of the multi-reservoir system will require more complex formulas in the model that may reduce the capability of the CGA’s search to the most promising space Acknowledgments The authors greatly appreciate the support under FY2012-2014 JSPS Core-to-Core Program ‘‘Collaborative Project for Soil and Water Conservation in Southeast Asian Watersheds’’ and FY2011-2015 JSPS Grant-in-Aid for Scientific Research (B) (Project number: 23380144) References Abedian A, Ghiasi MH, Dehghan-Manshadi B (2006) Effect of a linear-exponential penalty function on the 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(2) the water shortages of all three cases simulated by the CGA method decreased dramatically as compared with all cases of DTOR operation in normal years, remarkably in 2000 and 2008; (3) there are different fluctuations between the water shortages of the CGA results and current operations... represents the best set of operating rule curves, those achieved from CGA case 3 The simulated water levels resulting from CGA case 3 for 20 years have been statistically counted and drawn as the CGA curves The results also demonstrate that the CGA curves have higher UWLs in the dry seasons, and also larger feasible operating spaces However, at the ends of dry seasons (April and May), the LWL of the CGA curve... was lower than those of current operations Besides that, the operating space between the LWL and the CWL is larger It indicates that, by the CGA-obtained curves, simulated reservoir operation extended the working space to enhance the effective performance of year-by-year reservoir operations In summary, the results in the above tables and figures show that it is obvious that the values of both GSI and... the current operations On the other hand, the results also indicated that water shortages for the three cases were reduced significantly and the water demands were supplied reasonably To be more specific, the simulated results of CGA case 3 showed the best performance where most of the GSI and water shortage values decreased remarkably Comparing the simulated results from all of the cases shows that... explain that the inflows in the dry seasons were higher than those of dry seasons in normal years; (3) in the wet years 1990, 1999, and 2001, the inflows in the wet seasons exceeded the effective capability of water reservoir storage However, the obtained GSI values of all cases for the CGA method achieved smaller values than those for the current operations and the only larger GSI value was for CGA case... in the dry season, case 2—50 m3/s in the dry season, and case 3—35 m3/s in the dry and 15 m3/s in wet season The reservoir operation model was integrated into the CGA method simulation and carried out an effective level of performance It was demonstrated by a dramatic decrease of the GSI values in all three CGA cases associated with the different environmental base flow requirements in comparison with. .. operations associating various environmental base flow requirements in wet years as indicated in 1990, 1999, and 2001; (4) all water shortages as compared with environmental requirements from the CGA cases decreased remarkably as compared to all cases of current operation Those aforesaid statements are presented in some years of Table 5 as marked by underlines It appears that: (1) in the drought year of 1995,... environmental base flow to flush out saltwater intrusion and improve the water quality downstream of the Dau Tieng Reservoir watershed for two seasons, dry and wet In addition, Table 6 gives the mean values of the CGA results in comparison with the difference between the cases associated with the environmental base flow requirements The values for CGA case 3 demonstrated it had both good performance and efficiency... constructed a model of reservoir operation based on the guiding rational reservoir operation principle using a penalty- type genetic algorithm (Chang 2008) for multi-use reservoir management The proposed model, with constraints integrated into its objective function, was configured with a penalty strategy to form the fitness function The designed constraints allow punishing of a fitness value once it reaches an... forecast modules might be additionally developed and integrated into the reservoir operation model Weekly simulated water releases from the reservoir will be considered to have good consistency with weekly downstream demands in order to accurately simulate the reservoirs’ behavior in real time With this approach, the model can gain a highly capable and effective application to actual cases Besides that,