INTRODUCTION
Flood and water shortage are still serious problems in Southeast Asia specially
Thailand. Integrated water resources management is an accepted method to solve
these problems. There are 2 categories of integrated management including demand
and supply management. These managements are addressed in the possible practice
and high efficiency (Dooge, 2002). In the supply management,
a reservoir simulation model is widely used to analyze the behavior of reservoir
system on the computer. Rule curves of reservoir are fundamental guidelines
for long term reservoir operation in order to minimize water shortage and flood
plane in the future. Generally, rule curves are searched by reservoir simulation
model and optimization techniques. In the past, the rule curves are obtained
from reservoir simulation model by trial error process (Jain
et al., 1998). This method is straightforward and applicable for
both single multiple reservoirs. However, the reservoir simulation method does
not guarantee to yield the optimal rule curves because of the experienced person
who adjusted the rule curves.
Dynamic Programming (DP) is another optimization technique that applied to
search the nonlinear problems of water resource as well as to search the optimal
rule curves (Bellman, 1957; Yakowitz,
1982; Esogbue, 1989). Unfortunately, the application
of DP to multireservoir system is limited due to a dimension problem. To overcome
this problem Chleeraktrakoon and Kangrang (2007) applied
the DP with a Principle Progressive Optimality (DPPPO) to determine the optimal
rule curves of the multiple reservoir systems. However, this technique is complicated
application.
Genetic Algorithms (GAs) is another search technique that applied to search
optimal rule curves of the reservoir system (Chang et
al., 2003, 2005; Chen, 2003).
The best part of GAs model is that it can handle any type of objective function
of the search. In addition, the applied GAs can handle any condition of reservoir
simulation such as initial reservoir capacity and the period of inflow record.
The GAs embedded the simulation model was applied to search the optimal rule
curves for finding the suitable length of historic inflow record (Kangrang
and Chaleeraktrakoon, 2008). The accepted objective functions are a shortage
index, frequency of water shortage, average water shortage and magnitude of
water deficit. However, the appropriate objective function for searching the
curves is average water shortage. Also, a smoothing function constraint is required
to include into the proposed GAs for fitting the rule curves (Kangrang
and Chaleeraktrakoon, 2007). However, an alternative technique to reduce
the fluctuation of rule curves in the output process is to limit the boundary
of searching. To reduce searching boundary can activate the process to reach
the optimal solution fast.
This study thus proposed the genetic algorithm to connect with simulation model for searching the optimal rule curves of reservoir. A conditional constraint was applied to the search process for reducing the fluctuation of the obtained rule curves. A minimum average water shortage was adopted be the objective function of the search process. Comparison results of the Conditional Genetic Algorithms (CGAs) and the simulation model were presented to demonstrate the effectiveness of the proposed model at the end of the paper. The proposed model was applied to determine the optimal rule curves of the Lampao Reservoir (in the Northeast Region of Thailand).
MATERIALS AND METHODS
Reservoir simulation model: This study developed reservoir simulation
model to describe the behavior of the reservoir system. This reservoir simulation
model was constructed on the concept of HEC3 (US Army Corps
of Engineers, 1974) and it can be used to simulate the reservoir operation
effectively. The reservoir operating policies are based on the reservoir rule
curves and the principles of water balance concept. The reservoir system operated
along the standard operating policy as expressed in Eq. 1:
where, R_{v,τ} is the release discharges form the reservoir during year v and period τ (τ = 1 to 12, representing January to December), D_{τ} is the water requirement of month τ, x_{τ} is lower rule curve of month τ, y_{τ} is upper rule curve of month τ and W_{v,τ} is the available water calculated by simple water balance as described in Eq. 2:
where, S_{υ,τ} is the stored water at the end of month τ, Q_{υ,τ} is monthly reservoir inflow; E_{τ} is average value of evaporation loss and DS is the minimum reservoir storage capacity (the capacity of dead storage).
In the Eq. 1, if available water is in a range of the upper and lower rule level, then demands are satisfied in full. If available water over the top of the upper rules level, then the water is spilled from the reservoir to downstream river in order to maintain water level at upper rule level. If available water is below the lower rule level, release water is reduced. The policy usually reserves the available water (W_{v,τ}) for reducing the risk of water shortage in the future, when 0≤W_{υ,τ}<x_{τ}–D_{τ}.
The release water of reservoir were used to calculate the situations of water shortage and excess release water such as the number of failure year, the number of excess release water, as well as the average annual shortage. These results will be then recorded for using in developed CGAs model.
Development of conditional genetic algorithms model: The developed CGAs
to connect simulation model are described as follows. The GAs requires encoding
schemes that transforms the decision variables into chromosome. Then, the genetic
operations (reproduction, crossover and mutation) are performed. These genetic
operations will generate new sets of chromosomes. The most common encoding schemes
use binary strings (Jain et al., 1998). In this
study, each decision variable represents a monthly level of the rule curves
of reservoirs.
After the chromosomes (rule curves) of the initial population have been determined,
the release water is calculated by the simulation model using these rule curves.
Then, the release water is used to calculate the objective function for evaluating
GAs fitness. Next, the reproduction including selection, crossover and mutation
is performed for creating a new rule curve parameters in next generation. This
procedure is repeated until the criterion is satisfied as shown in Fig.
1. There are 24 parameters (rule curve levels) for one reservoir which are
represented by the chromosomes. This study used population size = 80, crossover
probability = 0.9, mutation probability = 0.01 (Jain et
al., 1998).
The objective function of searching the optimal rule curve is the minimum of
average water shortage (AverMCM/year) (Kangrang and Chaleeraktrakoon,
2007) obtaining from the simulation model which described as follows:
where, n is the total number of considered year. Sh_{υ} is water deficit during year υ.
To reduce the fluctuation of the obtained rule curves, the boundary of the search for each generation is limited. The range of searching for lower and upper rule curves is fixed base on the previous rule curves. These ranges cover the existing rule curves for the old reservoir that similar to pattern of existing rule curves. For the new reservoir, these ranges are inner the active storage for the new reservoir that dead storage for lower bound and normal high water level for upper bound. This method was applied to determine the optimal rule curves of the Lampao Reservoir, Kalasin Province (in the Northeast Region of Thailand). The monthly flow records, monthly water requirements from the reservoirs, their characteristic reservoir, monthly evaporation rate, percolation data and rainfall data were used in the study. This research project was conducted from Jan 2008 to Jan 2009.
ILLUSTRATIVE APPLICATION
The proposed CGAs model was applied to search the optimal rule curve of the Lampao Reservoir that located in the Chi River Basin (in the Northeast Region of Thailand).
Figure 2 shows the locations of the Lampao Reservoir. In
the following, the obtained assessment results of the considered waterdeficit
and excessrelease properties for existing (HEC3), GAs and CGAs cases were
presented. As shown in Fig. 3, the schematic diagram of flows
within the total drainage basin of the Lampao reservoir system. The Lampao Reservoir
has the capacity of 1,400 MCM (million cubic meters or 10^{6} 10^{3}).
This reservoir is located on the Pao River. The verification needs monthly flow
records and the other related data such as monthly water requirements supplied
by the reservoirs, their characteristic curves and monthly evaporation rate.
For the inflow record data, sequences of 23 year (19862008) monthlyflow records
of reservoir were used. The locations of the flow gauging stations are shown
in Fig. 2. The 500 samples of generated inflow were used to
evaluate the proposed model. The stochastic inflows were generated by the MAR
(1) (Chaleeraktrakoon, 1999). The other average hydrological
data for each month included series of evaporation losses and precipitation
of the reservoirs were used for the simulation model.

Fig. 2: 
Location of the Lampao reservoir 

Fig. 3: 
Schematic diagram of flows in the Lampao River Basin (Other
requirements consist of salinity, pollution control and navigation demands) 
The considered waterrequirement information of the studied basin was collected
from the report of the Royal Irrigation Department of Thailand (RID).
RESULTS AND DISCUSSION
Figure 4 shows the optimal rule curves of CGAs compared with
the rule curves of GAs and simulation model (HEC3). The pattern of the new
rule curves is similar to the existing curves of the simulation, but the obtained
rule curves of GAs technique are fluctuate. However, the lower rule curves of
both techniques during dry season (JanMay) are the lower than theirs existing
curves. Beside, the upper rule curves of using CGAs and GAs are higher than
the existing curves. Then obtained rule curves were used to simulate the Lampao
River Basin system. The monthly inflow were generated by SVD (MAR 1) (Chaleeraktrakoon,
1999) for evaluating water shortage and flood frequency. The results show
the circumstances of water shortage and flood frequency (frequency of water
shortage, average water shortage, the frequency of excess water and the average
water release). The frequency of water shortage, the average water shortage
and the maximum water shortage of rule curve from CGAs model are 0.443±0.083
time years^{1}, 106±22 and 471±115 MCM year^{1},
respectively.

Fig. 4: 
Optimal rule curves of the Lampao reservoir 

Fig. 5: 
Number of generation for searching optimal rule curves 
The flood frequency of excess water release, the average excess
water release and the maximum excess release of rule curve’s CGAs are 0.800±0.061
time years^{1}, 698±27 and 2,593±280 MCM year^{1},
respectively (Table 1). The results also indicated that most situations of shortage and excess release
for CGAs model are smaller than the situations of HEC3 such as maximum water
shortage and average duration of water shortage.
Figure 5 shows the number of generation for searching optimal rule curves. The CGAs used 110 generations for reaching optimal rule curves, while the GAs model used 80 generations only.
The pattern of the new rule curves that using CGAs as shown in Fig.
4 is similar to the existing curves of the simulation because the boundary
of searching is limited according to existing rule curves according to the incorporated
smoothing function constraint to fit the rule curves (Kangrang
and Chaleeraktrakoon, 2007). However, the pattern of the obtained rule curves
using GAs technique is fluctuate due to widely boundary of searching (dead storage
level to normal high water level).
Table 1: 
Frequency, magnitude and duration of water shortage and excess
release of the systems 

μ: Mean, σ: SD 
The fluctuation of obtained rule curves in
this studysimilar to the obtained rule curves in the previous study (Chang et al., 2003). The lower rule curves of GAs technique during dry season (JanMay) and rainy
season (AugDec) are the lowest, this affected from the objective function of
the search that try to sufficiently release water to meet the demand. In addition,
the release condition in Eq. 1 directly controls remain water
for next month in reservoir simulation.
Most situations of shortage and excess release of CGAs model are smaller than
the situations of HEC3 such as maximum water shortage and average duration
of water shortage these because the obtained rule curves of CGAs are optimum
solution, whereas the rule curves of HEC3 are provided by trial error process
(US Army Corps of Engineers, 1974; Jain
et al., 1998). However, the situations of shortage and excess release
of GAs model are the smallest because the wide boundary of searching provided
the better solution. Although, GAs model provide the rule curves that get the
least shortage and excess release situations, these rule curves can not use
to practice because of theirs fluctuation.
For the number of iterations of each method, it indicates that the CGAs model
and GAs model are not significantly different to get the optimal solution. Also,
the run time of both models are used closely. According to the consideration
of different inflow record length in GAs searching (Kangrang
and Chaleeraktrakoon, 2008).
CONCLUSION
Rule curves are necessary guides for long term reservoir operation. The optimization techniques applied to search the optimal rule curves include simulation model, dynamic programming and genetic algorithm. This paper proposed a genetic algorithms connected simulation model to search the optimal rule curve. A minimum average water shortage was applied as the objective function of the search process. The limited bound of searching is used as the conditional constraint to reduce the fluctuation of the obtained rule curve. The developed CGAs model was applied to determine the optimal rule curves of the Lampao Reservoir (in the Northeast Region of Thailand). The results showed that the pattern of the obtained rule curves similar to the existing rule curve. The rule curves of traditional GAs model are fluctuate that can not use to practice. Then these obtained rule curves were used to simulate the reservoirs system by the synthetic inflow. The results indicated that the maximum water shortage and average duration of water shortage of CGAs model are smaller than the situations of HEC3. The excess release’s situations of the CGAs model are less than situations of HEC3 for all properties. Although, GAs model get the rule curves that have the least shortage and excess release situations, these rule curves can not use to practice because of theirs fluctuation.
ACKNOWLEDGMENTS
The authors would like to acknowledge the financial support by the faculty of Engineering, Mahasarakham University. Thanks are also due to Dr. Sudarat Compliew for helpful to calculate stochastic inflow.