Concern Condition for Applying Optimization Techniques with Reservoir Simulation Model for Searching Optimal Rule Curves

Abstract

This paper presents a comprehensive review of optimization algorithms utilized in reservoir simulation-optimization models, specifically focusing on determining optimal rule curves. The study explores critical conditions essential for the optimization process, including inflow data, objective and smoothing functions, downstream water demand, initial reservoir characteristics, evaluation scenarios, and stop criteria. By examining these factors, the paper provides valuable insights into the effective application of optimization algorithms in reservoir operations. Furthermore, the paper discusses the application of popular optimization algorithms, namely the genetic algorithm (GA), particle swarm optimization (PSO), cuckoo search (CS), and tabu search (TS), highlighting how researchers can utilize them in their studies. The findings of this review indicate that identifying optimal conditions and considering future scenarios contribute to the derivation of optimal rule curves for anticipated situations. The implementation of these curves can significantly enhance reservoir management practices and facilitate the resolution of water resource challenges, such as floods and droughts.

1. Introduction

Water resource problems, including floods and droughts, have become increasingly prevalent due to population growth and economic expansion [1,2]. Effective management of water resources requires a balanced approach encompassing both supply management and demand management strategies [3]. While the construction of water storage and hydraulic control structures on the supply management side necessitates significant financial investments [4], demand management approaches focus on non-construction measures such as improving irrigation efficiency, altering crop patterns, and optimizing reservoir operation through the use of rule curves [5,6].

Rule curves play a crucial role in guiding reservoir operation by determining the appropriate amount of water to release in response to long-term water demand [7,8]. These curves are designed to meet the criteria of water demand, accounting for both flood and drought scenarios. Optimal rule curves are utilized to ensure effective reservoir operation, controlling water release based on specific criteria [9]. The utilization of rule curves for long-term reservoir operation, while effective in normal conditions, may not be suitable for extreme situations, such as flooding or drought due to their inflexibility [10]. These circumstances demand adaptive strategies that can dynamically respond to rapidly changing conditions and ensure optimal reservoir management. Consequently, the use of adaptive rule curves becomes more appropriate to support reservoir management in such extreme circumstances [11].

The search for optimal rule curves involves tackling a nonlinear optimization problem [12,13]. Conventional approaches that rely on human adjustment through trial and error are susceptible to suboptimal solutions due to the influence of operator experience and subjectivity [14]. To overcome this challenge, dynamic programming (DP) has emerged as an effective method for solving nonlinear problems in water resource management, including the identification of optimal rule curves [15,16].

In recent years, heuristic algorithms (HA) have gained popularity for solving optimization problems due to their simplicity and ease of implementation [17,18]. In the field of water resources management, optimization algorithms have been integrated with simulation models to search for optimal rule curves in reservoir operations [19,20]. Examples of such algorithms include the simulated annealing algorithm (SA) [21,22], the shuffled frog leaping algorithm (SFLA) [23,24], and the melody search algorithm (MeS) [13,20]. Additionally, evolutionary algorithms such as genetic algorithm (GA) [25,26], differential evolution (DE) [27,28], genetic programming (GP) [29,30], and cultural algorithm (CA) [31,32] have been utilized in combination with reservoir simulation models to search for optimal rule curves. Recently, swarm algorithms have emerged as promising approaches for optimizing rule curves using reservoir simulation models. Several notable swarm algorithms have been employed in the field of optimization. These include particle swarm optimization (PSO) [33], cuckoo search algorithm (CS) [34,35], firefly algorithm (FA) [36], flower pollination algorithm (FPA) [37], gray wolf optimizer (GWO) [38], wind-driven optimization (WDO) [39,40], ant colony optimization (ACO) [41,42,43], honey-bee mating optimization (HBMO) [44,45,46], and Harris Hawks optimization (HHO) [47], among others. These swarm algorithms have shown effectiveness in various optimization problems.

This paper offers a thorough review of optimization techniques used in reservoir simulation-optimization models to determine optimal rule curves. A crucial aspect of attaining these curves lies in identifying the appropriate search conditions. This review aims to summarize the necessary conditions for searching, with a focus on the application of optimization techniques connected to reservoir simulation models in various studies. The factors considered include inflow data, objective function, smoothing function, downstream water demand, initial reservoir conditions, and evaluation scenarios [11,34,48]. This paper will present the application of popular techniques such as GA, PSO, CS, and TS to these search conditions, providing guidance for researchers in this field. Additionally, this paper will discuss the optimal conditions for future situations.

2. Inflow Data

Inflow data is a crucial input for reservoir simulation models that utilize the water balance concept as the primary equation for calculating the water budget in the reservoir [13,49,50], as shown in Equation (1).

$$W_{\nu ,\tau }=S_{\nu ,\tau -1}+Q_{\nu ,\tau }-R_{\nu ,\tau }-E_{\tau }$$

(1)

where $W_{\upsilon ,\tau }$ is the available water during year ν and month τ; $S_{\upsilon ,\tau -1}$ is the stored water at the end of month τ − 1; $Q_{\upsilon ,\tau }$ is the monthly inflow to the reservoir; and $E_{\tau }$ is the average evaporation loss.

In the application of simulation models, the reservoir system is connected to optimization techniques to determine optimal monthly rule curves [51]. The most crucial and necessary information for this is meteorological data, such as rainfall and evaporation rates. Additionally, information about the amount of runoff flowing into the reservoir is also required, and this data must be collected from the past to the present or should be received from forecast models [52]. However, this data may have varying recording and collection lengths, with some reservoirs having data for only a few years, while others have data for over 50 years [53,54]. In such cases, the average or synthesis of the data must be used, as the meteorological data is recorded differently.

However, most of the rule curves obtained using unequal-length water data to find a response yield different optimum rule curve responses and have differing effectiveness. Therefore, selecting the appropriate interval of runoff data is crucial in determining the appropriate rule curves. A guideline for determining the appropriate runoff data length is to experiment with runoff data of different lengths entering the reservoir. These experiments may include using runoff data during years of drought events or high-water events, including experiments that use synthetic runoff data [55,56].

The length of inflow data was investigated in determining the appropriate monthly control curves of Bhumibol and Sirikit Reservoirs by considering the length of runoff data during low water years [48]. They applied a genetic algorithm to a reservoir system simulation model and considered eight separate cases. The cases were: (1) using the year with all historical data (45 years), (2) using the year when the low water event occurred (26 years), (3) using the low water period of 21 years, (4) using the low water period of 17 years, (5) using the low water period of 14 years, (6) using the low water period of 10 years, (7) using the low water period of 7 years, and (8) using the low water period of 4 years.

The study evaluated the efficiency of the rule curves obtained from all eight cases by operating Bhumibol and Sirikit Reservoirs using 500 sets of 45-year synthetic runoff data to assess the situation of water scarcity and excess flow in the lower Chao Phraya Basin. The evaluation results in both water shortage and excess flow situations are shown in

Table 1. Frequency, magnitude, and successive periods of water shortage for different dry-year inflow conditions [48].

Duration Lengths of Inflow Records (Years)	Frequency		Magnitude (MCM/Year)		Duration (Year)
	(Times/Year)		Average	Maximum	Average	Maximum
4	μ	0.157	34	495	2.2	3.4
	σ	0.084	28	379	1.0	1.7
7	μ	0.191	35	431	2.1	3.6
	σ	0.089	23	257	0.9	1.8
10	μ	0.118	22	313	2.0	2.8
	σ	0.072	18	210	1.0	1.6
14	μ	0.124	23	329	2.0	2.9
	σ	0.072	18	205	0.9	1.6
17	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7
21	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7
26	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7
45	μ	0.113	19	289	1.9	2.7
	σ	0.070	16	219	0.9	1.6

Note: μ = mean, σ = standard deviation.

and

Table 2. Frequency, magnitude, and successive periods of excess release for different dry-year inflow conditions [48].

Duration Lengths of Inflow Records (Years)	Frequency		Magnitude (MCM/Year)		Duration (Year)
	(Times/Year)		Average	Maximum	Average	Maximum
4	μ	0.833	1179	4537	7.9	16.5
	σ	0.073	196	1842	4.2	6.6
7	μ	0.819	1172	4524	7.0	15.1
	σ	0.074	197	1831	3.1	5.7
10	μ	0.815	1121	4437	7.0	15.4
	σ	0.079	196	1850	3.0	5.9
14	μ	0.819	1124	4537	7.3	15.6
	σ	0.078	197	1892	3.4	6.1
17	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9
21	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9
26	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9
45	μ	0.811	1110	4706	7.0	15.0
	σ	0.079	202	1905	3.1	5.6

Note: μ = mean, σ = standard deviation.

, respectively, in terms of frequency, magnitude, and duration of events. From 10 years onward, there was no significant difference in efficiency. However, the magnitude of excess flow from the 7-year and 4-year runoff data usage was higher than other usage periods.

Based on the presented tables, it can be inferred that a minimum duration of 10 years for dry-year inflow records is advisable. However, previous research has indicated that the recommended duration for inflow records should exceed 30 years. This suggests that longer-term data is preferred for a more comprehensive and accurate assessment of reservoir operations under dry-year conditions [8,48,57].

Hence, it is more suitable to use runoff data for a period of at least 10 years or more to derive the optimal rule curves that can address both water shortage and excess flow situations. However, using all available historical inflow records is the most effective approach to alleviating these situations, as depicted in Figure 1.

Recently, the application of future streamflow data, which considers the impacts of climate and land use changes, has been incorporated into the aforementioned process. The performance comparison between current rule curves and future rule curves, based on the future inflow data of the B2 scenario for the period 2017–2041, reveals that the future rule curves exhibit greater applicability in mitigating water shortage situations compared to the current rule curves [11]. These findings suggest that utilizing future inflow data to determine appropriate rule curves can effectively address future scenarios and their associated challenges more effectively than other types of rule curves.

Forecast-based reservoir operation refers to the practice of using weather forecasts, hydrological predictions, and other relevant data to inform real-time decision-making in reservoir management. By integrating forecast information into operational strategies, reservoir operators can optimize water releases, storage levels, and hydropower generation, leading to improved water resource management and enhanced resilience to changing hydrological conditions. This approach enables proactive and adaptive reservoir operations that take into account anticipated future conditions, contributing to efficient water allocation, flood control, and ecosystem preservation [58,59,60].

Several studies highlight the significance of incorporating future conditions and improving forecast accuracy in reservoir operation. They propose some operating policies, such as the Hedging Rule [61], and forecast models to handle nonstationary inflow conditions and the effects of climate change. The studies demonstrate improvements in water deficit, system vulnerability, and operation performance compared to conventional rule curves and standard operation policies [59]. The models incorporate forecasted inflows using feature selection methods, ensemble learning techniques, and optimization algorithms to determine effective forecast horizons [61,62]. The research emphasizes the need to consider nonstationary time series, future conditions, and climate-atmospheric indices in reservoir management and decision-making processes [63,64]. These approaches provide valuable insights and tools for enhancing the flexibility and performance of reservoir systems [65].

3. Objective Function

Reservoir operation plays a crucial role in managing water resources, addressing both quantity and quality objectives, which are inherently interconnected [66]. The use of reservoir rule curves is a common approach for effective reservoir management, with the primary goal of minimizing long-term water scarcity. This entails ensuring that the remaining water quantity in the reservoir adheres to the prescribed rule curves for each month. In order to decide the optimal rule curves for both unused and existing stores, it is essential to assess their proficiency in moderating water shortages and excess streams, taking into consideration the frequency, greatness, and length of these occasions [67,68].

Water resources management, particularly reservoir operation optimization, involves tackling a complex, multi-objective optimization problem [69]. In the context of reservoir operations, the selection of objective functions is crucial when applying optimization techniques. Typically, the objective function aims to minimize both water scarcity and overflow, representing the dual goals of ensuring adequate water supply while preventing excessive releases from the reservoir. This objective function serves as a guiding principle in finding optimal rule curves for reservoir operations, striking a balance between meeting water demand and avoiding wasteful or damaging water releases. However, there are several terms related to water scarcity that can be used as objective functions, such as the shortage index, the average water shortage, the highest water shortage, the frequency of water shortages, the squared water shortage, and any combination of these terms whereas, the overflow also has many terms, such as the average excess water, the most elevated excess water, the frequency of excess water, and the squared overflow. In this manner, selecting the most appropriate term will result in obtaining a reasonable set of rule curves that can clarify the shortage of water in detail, driving to a littler overabundance stream term as well [70,71].

Past research studies suggest that the above objective functions are most suitable for finding the appropriate answer. The analysis results for each objective function will be presented as follows:

3.1. The Shortage Index

The shortage index (SI), which was proposed by the US Armed Forces Corps of Engineers [72], can be summarized as:

$$SI=\frac{100}{n}{\displaystyle \sum }_{i=1}^n{\left(\frac{S{h}_i}{D_i}\right)}^2$$

(2)

In the given context, where n represents the total number of considered periods (time steps), Sh_i denotes the water deficit during period i, and D_i represents the target demand during period i. It is generally assumed that a month is the operational time step for the reservoir.

3.2. The Average Water Shortage

The average water shortage (Aver) can be described as:

$$Aver=\frac{1}{n}{\displaystyle \sum }_{i=1}^{n}S{h}_i$$

(3)

where n is the total number of considered periods, Sh_i is water deficit during period i.

3.3. The Highest Water Shortage

The highest water shortage (Max) is the maximum magnitude of water shortage during the considered period that can be described as:

$$MaxSh=Maximum \left(Shi\right), for i=1,\dots , n$$

(4)

where n is the total number of considered periods, Sh_i is water deficit during period i.

3.4. The Frequency of Water Shortage

The frequency of water shortage (Fre) is the frequency of water shortage during the considered period that can be described as:

$$Fre=\frac{p_i}{n}$$

(5)

where n is the total number of the considered year, $p_i$ is total number of annual failure (shortage).

3.5. The Total Square Deficit

The total square deficit (RMS) can describe as:

$$RMS={\displaystyle \sum }_{i=1}^n{\left(D_i-R_i\right)}^2 , \forall R_i<D_i$$

(6)

where n is the total number of the considered periods, $D_i$ is the target demand during period i, and $R_i$ is released water during ith period.

3.6. The Combination of Water Shortage Terms (SUM)

The Combination of Water Shortage Terms (SUM) is described as follows:

$$SUM=\frac{1}{4}\left(\frac{Aver}{\mathit{full}\left(Aver\right)}+\frac{MaxSh}{\mathit{full}\left(MaxSh\right)}+Fre+\frac{RMS}{\mathit{full}\left(RMS\right)}\right)$$

(7)

where full(Aver) is the sum of average water shortages, full(Max) is the sum of maximum water shortages, and full(RMS) is the sum of squared water shortages.

Figure 2 and Figure 3 display the results of the optimal rule curves for Bhumibol and Sirikit Reservoirs, respectively. These figures provide visual representations of the optimized reservoir operating policies, showcasing the relationship between reservoir storage levels and corresponding release strategies for efficient water management [48]. The obtained results were achieved by applying an optimization technique to a simulation model of the reservoir system. The optimization process involved searching for suitable rule curves by considering six objective functions individually, as described by Equations (2)–(7). This approach allowed for a comprehensive evaluation of different criteria and objectives to identify the most effective rule curves for reservoir operations. It can be seen from the figures that the rule curves from different objective functions have similar shapes due to the effect of the runoff trend on the reservoir. However, the values of these rule curves differ greatly in some months. When using these curves to evaluate the efficiency of operating Bhumibol and Sirikit reservoirs using the past 21 years of runoff data, the evaluation results are shown in

Table 3. Frequency, magnitude, and successive period of excess release for different dry-year inflow conditions [48].

Objective Functions		Frequency	Magnitude (MCM/Year)		Duration (Year)
		(Times/Year)	Average	Maximum	Average	Maximum
SI	μ	0.142	25	391	2.0	3.1
	σ	0.080	21	243	0.9	1.7
Aver	μ	0.208	29	207	2.1	3.8
	σ	0.082	14	102	0.7	1.8
Max	μ	0.807	139	437	8.5	18.1
	σ	0.092	30	98	5.4	7.6
Fre	μ	0.123	45	707	1.9	2.8
	σ	0.070	35	457	0.8	1.5
RMS	μ	0.196	31	333	2.1	3.7
	σ	0.087	19	177	0.8	1.7
SUM	μ	0.156	28	353	2.0	3.3
	σ	0.078	19	218	0.8	1.7

Note: μ = mean, σ = standard deviation.

and

Table 4. Frequency, magnitude, and successive periods of excess release for all objective functions [48].

Objective Functions		Frequency	Magnitude (MCM/Year)		Duration (Year)
		(Times/Year)	Average	Maximum	Average	Maximum
SI	μ	0.848	1038	4757	9.0	18.2
	σ	0.072	205	2002	5.2	7.1
Aver	μ	0.843	1188	4446	8.8	17.2
	σ	0.073	194	1825	5.6	7.0
Max	μ	0.856	1160	5403	8.3	17.1
	σ	0.065	208	2031	4.2	6.5
Fre	μ	0.814	1036	4882	7.1	15.4
	σ	0.078	205	1932	3.2	5.9
RMS	μ	0.836	1289	5578	7.9	16.3
	σ	0.071	231	2014	4.2	6.3
SUM	μ	0.848	1082	4602	8.7	17.7
	σ	0.071	196	1922	4.4	6.7

Note: μ = mean, σ = standard deviation.

, respectively. When using the rule curves from the objective function, the average overflow of the lower Chao Phraya is relatively lower than the other objective functions, and some terms are the lowest, such as the mean water scarcity, peak water shortage, average water shortage event interval, excess flow frequency, etc. Thus, the rule curves from the average water shortage objective function can optimally alleviate water shortage and overflow situations based on the frequency of the event, the magnitude of the event, and the duration of the event. In conclusion, the new rule curves obtained from the optimization approach connected to the reservoir simulation model when using the average water shortage value as an objective function for finding the answer are optimal. Since it can alleviate the situation of water shortage and overflow better than the rule curves obtained by using other objective functions.

However, the term “overflow”, which refers to characteristics such as average excess water, highest excess water, frequency of excess water, and squared excess water, can also be utilized as an objective function similar to Equations (2)–(7).

4. Smoothing Function

A smoothing function was employed to mitigate fluctuations in the rule curve outputs caused by seasonal streamflow patterns. This function also regulated the onset and conclusion of the flood season, setting the lowest level at the beginning and the highest level at the end. This trend was observed in both the upper and lower rule curves. To describe the smoothing function for adjusting the rule curves, the monthly water levels for the lower and upper curves were fixed and represented by ‘x’ and ‘y’ values, respectively. In the early drought season, the water level in January (x₁, y₁) needed to be higher than that in February (x₂, y₂), gradually decreasing until June (x₆, y₆). Subsequently, in July (x₇, y₇), which marks the start of the flood season, the water level should be higher than that in June (x₆, y₆). In August (x₈, y₈), the water level rises further compared to July (x₇, y₇), reaching its peak during the last rainy season in October (x₁₀, y₁₀) and extending until the end of December (x₁₂, y₁₂). This pattern aligns with the seasonal streamflow patterns observed in Thailand [2,48,73]. To incorporate the smoothing function constraints into the fitness function, the following procedure was employed in the reservoir simulation model to optimize the rule curves:

• Initialize the rule curves based on the desired smoothing pattern.
• Simulate the reservoir operations using the rule curves.
• Calculate the fitness of the simulated rule curves by considering multiple objective functions, including the smoothing function constraints.
• Adjust the rule curves using an optimization algorithm to improve the fitness.
• Repeat steps 2–4 until the desired fitness criteria are met.
• Obtain the final optimized rule curves that satisfy the smoothing function constraints and provide optimal reservoir operation.

By integrating the smoothing function constraints into the fitness function, the optimization process ensures that the resulting rule curves adhere to the desired pattern while simultaneously optimizing other objectives of reservoir operations.

$$x_1>x_2>x_3>x_4>x_5>x_6<x_7<x_8<x_9<x_{10}<x_{11}<x_{12}$$

(8)

$$y_1>y_2>y_3>y_4>y_5>y_6<y_7<y_8<y_9<y_{10}<y_{11}<y_{12}$$

(9)

The specific values of the water levels for the smoothing function constraints are as follows:

-

x₁, y₁: Beginning level in January (early drought season)

-

x₅, y₅: Level in May

-

x₆, y₆: Beginning level in June (end of drought season, beginning of flood season, and start of the lower rule curve for the flood season)

-

x₁₂, y₁₂: Level in December (end of the upper rule curve for the flood season)

These values define the desired water levels at specific months within the year and are used to ensure a smooth transition and an appropriate representation of the seasonal streamflow patterns in the rule curves.

The moving average is an additional smoothing function utilized to reduce fluctuations in the rule curves and obtain optimal results. The smoothing function imperative for fitting the rule curves can be displayed as follows:

$$\left|\frac{x_{\tau -2}+x_{\tau -1}+x_{\tau }}{3}-x_{\tau }\right|\le 0.1T \mathrm{for} \tau =3,\dots 12$$

(10)

$$\left|\frac{x_{12}+x_{\tau -1}+x_{\tau }}{3}-x_{\tau }\right|\le 0.1T \mathrm{for} \tau =2$$

(11)

$$\left|\frac{x_{12}+x_{12-\tau }+x_{\tau }}{3}-x_{\tau }\right|\le 0.1T \mathrm{for} \tau =1$$

(12)

$$\left|\frac{y_{\tau -2}+y_{\tau -1}+y_{\tau }}{3}-y_{\tau }\right|\le 0.1T \mathrm{for} \tau =3,\dots 12$$

(13)

$$\left|\frac{y_{12}+y_{\tau -1}+y_{\tau }}{3}-y_{\tau }\right| \le 0.1T \mathrm{for} \tau =2$$

(14)

$$\left|\frac{y_{12}+y_{12-\tau }+y_{\tau }}{3}-y_{\tau }\right| \le 0.1T \mathrm{for} \tau =1$$

(15)

where x is the lower rule curve level, y is the upper rule curve level, and T is the active storage of each reservoir. These smoothing functions are integrated into the fitness function in the search procedure.

Figure 4 and Figure 5 showcase the results of the optimization process using genetic algorithms (GAs) for the Bhumibol and Sirikit Reservoirs, comparing the optimal rule curves obtained with and without the smoothing function constraint. Additionally, the existing curves generated from the HEC-3 simulation approach are also included for comparison [73]. These figures illustrate that the optimal rule curves obtained with the smoothing function imperative show a smoother profile compared to those obtained without the constraint. In addition, the pattern of the obtained rule curves using the smoothing imperative closely follows the existing rule curves. This indicates that the smoothing function constraint effectively reduces the variation in both the upper and lower rule curves, resulting in improved curve smoothness and alignment with the existing curves.

The rule curves were subjected to an appraisal to assess the events of water shortage and excess discharge by comparing important characteristics, such as recurrence, magnitude, and term with those of the optimal curves. The assessment was performed employing a Monte Carlo simulation, producing 500 tests of month-to-month streams from stations P.12 and SK [60]. The results of the appraisal provide the interval of the insights (cruel ± standard deviation). In the following section, the obtained evaluations for water shortfall and excess-release properties within the three cases are displayed. These results shed light on the execution and viability of the rule curves in tending to water shortage and abundance discharge situations.

Figure 6 and Figure 7 delineate the appraisal interims of water shortage characteristics for the simulation approach utilizing genetic algorithms (GAs) with and without the smoothing function constraint, as well as the HEC-3 simulation approach. These figures illustrate that the proposed procedure yields fewer water shortage characteristics, counting shorter durations and smaller magnitudes of water shortages, when compared to the existing approach. This shows that the GAs-based simulation with the smoothing function constraint successfully reduces the effect of relationships in water shortage situations. Furthermore, the figures outline that the water shortage characteristics obtained with and without the smoothing constraint do not show critical contrasts. In Figure 8 and Figure 9, the insights of excess releases are presented for the three sets of rules. It is clear that both GAs-based simulation techniques do not result in greater excess releases compared to the existing approach [73]. These discoveries demonstrate that the optimization process utilizing GAs keeps a sensible level of control over excess discharges while still accomplishing advancements in tending to water shortage situations.

5. Downstream Water Demand

Reservoir management should be based on the natural variability of water resources and water demand. Rule curves play a fundamental and essential role in water balance analysis for improving reservoir operation performance [74,75,76]. However, these rule curves require important information and calculations, such as end-of-basin water demand, rainfall, and inflow into the basin. Nevertheless, this information may still be insufficient or ineffective due to the absence of past and present participation processes. By involving stakeholders and estimating water demand based on their input, considering current and future realities, reservoir management can be improved by releasing water according to the appropriate demand for each period [77,78].

Participation in water management in various projects is a means of promoting inclusive and effective projects or activities. For example, participation can be sought during the planning and development processes, as well as in the management of water resources, to reduce community conflicts and enhance community learning. These guidelines contribute to more widely accepted and effective water resource management [79].

This study applied the genetic programming (GP) technique with a reservoir simulation model to search for rule curves that consider downstream water demand using a participation process [80]. The case study focused on the Huay Ling Jone reservoir in Yasothorn province, located in the northeast area of Thailand.

The study included an exploration of water demand and the level of participation in water management. Based on the Taro Yamane table and a 90% confidence level, approximately 196 samples were collected using a questionnaire to gather data. The results of this study are mainly presented through descriptive statistics, including percentages, means, and standard deviations, specifically for the Huay Ling Jone reservoir.

Overall, the majority of respondents from the Huay Ling Jone reservoir reported an increase in irrigation water demand (mean = 3.38). The increase was observed in January–February and October–December, when water demand rose by 20%. In May–July, and August–September, there were no significant increases or decreases in water demand. Further details can be found in “Figure 10”. As for domestic and livestock water requirements, there were no observed changes in demand compared to the current water demand level.

The efficiency of the obtained rule curves was evaluated by considering both the current water demand and the estimated water demand using the participation process.

Table 5. The situations of water shortage and excess water considering future inflow and current water demand from the Huay Ling Jone Reservoir.

Situations	Rule Curves	Frequency (Times/Year)	Volume (MCM.)		Time Period (Year)
			Average	Maximum	Average	Maximum
Shortage	Existing	0.792	4.917	12.000	3.8000	8.000
	GP Agripar-D	0.501	2.215	9.000	2.400	4.000
	GP Agripar-Dpar	0.633	3.135	10.000	5.000	6.000
Excess water	Existing	0.958	9.190	15.879	11.500	19.000
	GP Agripar-D	0.874	6.432	13.709	5.250	12.000
	GP Agripar-Dpar	1.000	9.395	13.800	5.500	12.000

presents the situations of water shortage and excess release when using the minimization of average water shortage as the objective function for both the current water demand and future inflow scenarios. These situations are presented in terms of frequency, magnitude, and duration.

The obtained rule curves (GP Agripar-D) showed a frequency of water shortages of 0.792 times/year, an average water shortage of 4.917 MCM/year, and an average shortage period of 3.800 years. Overall, the water shortage and overflow situations resulting from the use of the obtained rule curves (GP Agripar-D and GP Agripar-Dpar) were more efficient than the previous rule curves (existing).

Table 6. The situations of water shortage and excess water considering future inflow and water demand using participation from the Huay Ling Jone Reservoir.

Situations	Rule Curves	Frequency (Times/Year)	Volume (MCM.)		Time Period (Year)
			Average	Maximum	Average	Maximum
Shortage	Existing	0.474	0.789	2.000	2.250	3.000
	GP Agripar-D	0.346	0.643	2.400	2.035	4.000
	GP Agripar-Dpar	0.323	0.639	2.100	1.500	3.000
Excess water	Existing	1.000	10.303	20.834	18.000	19.000
	GP Agripar-D	1.000	9.963	20.832	18.000	19.000
	GP Agripar-Dpar	1.000	9.946	20.784	18.000	19.000

presents the situations of water shortage and excess release for the case of estimated water demand using the participation process and future inflow. The results indicate that the frequency of water shortages, the average water shortage per year, and the average shortage period of the obtained rule curves (GP Agripar-D) are 3.159 times/year, 16.000 MCM/year, and 3.500 years, respectively. The water shortage and overflow situations resulting from the use of rule curves GP Agripar-D and rule curves GP Agripar-Dpar were more efficient than the previous rule curves (existing).

The results of the study demonstrate that the newly obtained rule curves exhibit patterns similar to the existing rule curves, which can be attributed to the influence of seasonal inflow patterns. However, it was observed that the lower rule curves obtained through the GP Agripar-Dpar and GP Agripar-D techniques were lower than the existing rule curves. Furthermore, the study findings indicate that the newly obtained rule curves using the GP technique outperform the existing rule curves in mitigating situations of water shortage and excess water, considering both the current water demand and the estimated water demand derived from the participation process. This suggests that the GP technique offers improved performance in reservoir operations by better aligning the water supply with the required water demands.

6. Initial Condition of Reservoir Characteristic

Before commencing the search for optimal rule curves, several conditions of the simulation model were set. The impact of the initial reservoir capacity was considered by ranging from 10% of the capacity to the full capacity. The reservoir simulation model was integrated with an optimization technique to search for the optimal rule curves [81,82,83]. Following the optimization process, the obtained rule curves were subjected to an assessment to evaluate the occurrences of water shortage and excess release. This assessment involved comparing characteristics such as frequency, magnitude, and duration of these situations with those exhibited by the optimal curves [84,85,86]. By comparing these relevant metrics, the performance and effectiveness of the obtained rule curves in addressing water shortage and excess release situations were evaluated. The evaluation was performed employing a Monte Carlo re-enactment consideration, which included analyzing 500 tests of the produced month-to-month streams. The results were computed as intervals represented by the mean ± standard deviation for the assessment of the referred statistics. In the following sections, the assessment results for all cases regarding water deficit and excess release properties are presented [48].

Figure 11 and Figure 12 delineate the patterns of the rule curves for the two reservoirs, which generally display assertion. This may be attributed to the regular impacts on store inflows and the considered water demands [48]. In addition, it was observed that the optimal rule curves obtained utilizing distinctive starting capacities did not show critical differences. These optimal rule curves were assessed to evaluate the events of water shortage and excess discharge. A Monte Carlo simulation study was conducted for this purpose, which permitted a comprehensive examination of the execution of the rule curves under different scenarios and random varieties of input parameters. By utilizing the Monte Carlo simulation, the impact and likelihood of water shortage and excess release events could be analyzed in a probabilistic manner, providing valuable insights into the robustness and reliability of the optimal rule curves obtained.

Table 7. The situations of water shortage and excess water considering future inflow and current demand [48].

Initial Capacity of Reservoir (%)	Frequency		Magnitude (MCM/Year)		Duration (Year)
	(Times/Year)		Average	Maximum	Average	Maximum
10	μ	0.113	20	300	1.9	2.7
	σ	0.071	17	207	0.9	1.6
20	μ	0.114	20	306	1.9	2.7
	σ	0.072	18	204	0.9	1.8
30	μ	0.114	21	314	1.9	2.8
	σ	0.073	18	220	0.9	1.6
40	μ	0.118	21	316	1.9	2.8
	σ	0.072	18	227	0.9	1.6
50	μ	0.136	23	326	2.0	3.1
	σ	0.077	18	220	1.0	1.7
60	μ	0.126	22	313	1.9	2.9
	σ	0.072	18	206	0.8	1.5
70	μ	0.102	19	309	1.8	2.5
	σ	0.067	17	220	1.0	1.5
80	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7
90	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7
100	μ	0.137	24	323	2.0	3.1
	σ	0.076	18	206	1.0	1.7

Note: μ = mean, σ = standard deviation.

and

Table 8. Frequency, magnitude, and successive period of excess release water for all initial reservoir capacities [48].

Initial Capacity of Reservoir (%)	Frequency		Magnitude (MCM/Year)		Duration (Year)
	(Times/Year)		Average	Maximum	Average	Maximum
10	μ	0.812	1113	4579	7.0	15.1
	σ	0.080	195	1918	3.2	5.6
20	μ	0.812	1117	4574	7.0	15.1
	σ	0.079	197	1908	3.2	5.7
30	μ	0.812	1124	4637	7.0	15.1
	σ	0.079	203	1893	3.3	5.9
40	μ	0.816	1132	4532	7.2	15.4
	σ	0.079	202	1836	3.2	5.7
50	μ	0.819	1114	4497	7.4	15.7
	σ	0.080	196	1883	3.5	6.1
60	μ	0.815	1102	4477	7.1	15.2
	σ	0.079	195	1879	3.3	5.8
70	μ	0.817	1121	4558	7.4	15.7
	σ	0.080	205	1828	3.5	6.1
80	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9
90	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9
100	μ	0.816	1108	4545	7.2	15.3
	σ	0.079	198	1862	3.3	5.9

Note: μ = mean, σ = standard deviation.

present the assessment intervals for water shortage and excess release characteristics, including frequency, magnitude, and duration, considering different initial reservoir capacities [48]. The results indicate that the rule curves obtained using different initial capacities do not exhibit significant differences in terms of water shortage and excess release situations. This implies that the performance of the rule curves remains consistent across various initial capacities, indicating robustness in addressing water scarcity and excess water events. Furthermore, Figure 13 depicts the relationship between the average water shortage and initial reservoir capacity. It shows that the average water shortages are similar across different initial capacities, indicating that the initial reservoir capacity has a limited influence on the average water shortage. This information is valuable for reservoir operators and planners in understanding the expected water shortage levels in relation to the initial reservoir capacity, allowing for better management and decision-making in water resource allocation.

Traditionally, simulations of reservoir operations have been conducted with the initial reservoir capacity set at full capacity [15,87,88]. However, the findings of this study suggest that the simulation model can generate rule curves that do not significantly differ, regardless of the initial reservoir capacity. Additionally, the water deficit and excess release situations observed using the obtained rule curves are not significantly different. Based on these results, it is concluded that the minimum initial capacity for the simulation model should be set at 10% of the reservoir capacity [89,90].

The study also investigated the impact of initial reservoir capacity on the search for rule curves using the simulation model integrated with the GA technique. The results indicate that the rule curves obtained using initial capacities exceeding 10% of the full capacity do not exhibit significant differences. Furthermore, the evaluation of each set of obtained rule curves using Monte Carlo simulation revealed no significant disparities in water deficit and excess release situations. Consequently, it can be concluded that setting the minimum initial capacity for the simulation model at 10% of the reservoir capacity is sufficient for obtaining reliable and consistent rule curves.

7. Evaluation Scenarios

The optimal rule curves, generated by connecting a reservoir simulation model with an optimization technique, were used to evaluate different scenarios. These scenarios were classified based on the characteristics of inflow data, including historic inflow data, dry year duration data, wet year duration data, and a synthesis of historic data and future inflow data. The results of the evaluations were presented in terms of water shortage and excess situations. In a previous study, both the constrictor congregational search (CCS) algorithm and the cooperative particle swarm optimization (CPSO) algorithm were utilized in conjunction with a reservoir operation model to search for optimal rule curves. The evaluation of the algorithms was carried out using three different scenarios: historic inflow data, dry year inflow data, wet year inflow data, and synthetic inflow data. These scenarios allowed for a comprehensive assessment of the performance of the algorithms under different hydrological conditions, providing insights into their effectiveness in finding optimal rule curves for reservoir operations [34].

The results from the three cases (normal year, dry year, and wet year inflows) indicated that rule curves produced using normal yearly inflow data had the fewest water shortages and excess occurrences. Therefore, normal yearly inflow data were deemed suitable for use when searching for optimal rule curves using search optimization techniques [34]. Normal year inflow rule curves demonstrate better mitigation of shortage and water excess situations compared to the rule curves based on dry-year and wet-year inflows, both in dry-year and long-term scenarios. Thus, normal year inflow data is recommended for determining optimal rule curves using any search optimization technique. Incorporating historic inflow data is necessary in the search process [91].

For future situations, the newly generated rule curves from the GA connected to the reservoir simulation model were evaluated using historic inflow data and future inflows. The results are presented in

Table 9. Simulations of water shortage and excess release of systems under the historic streamflow scenario [11].

Situation	Rule Curve		Frequency (Times/Year)	Magnitude (MCM/Year)		Duration (Years)
				Average	Maximum	Average	Maximum
Water shortage	RC1	μ	0.180	21.024	340.800	2.2	3.3
		σ	0.052	9.149	116.722	0.6	1.1
	RC2-A2	μ	0.260	32.475	398.000	2.4	3.9
		σ	0.062	10.138	115.097	0.6	1.3
	RC2-B2	μ	0.284	33.440	394.770	2.4	4.3
		σ	0.066	10.024	121.184	0.6	1.5
	RC3	μ	0.512	113.104	597.560	2.8	6.4
		σ	0.052	13.484	93.274	0.5	2.0
Excess release	RC1	μ	0.878	990.632	4204.398	9.3	19.3
		σ	0.041	17.546	781.166	3.3	6.7
	RC2-A2	μ	0.881	1004.786	4196.273	8.9	19.5
		σ	0.036	18.213	804.820	2.8	7.0
	RC2-B2	μ	0.875	1001.375	4201.483	8.6	18.7
		σ	0.038	18.565	832.729	2.9	6.5
	RC3	μ	0.957	1098.163	4337.941	20.7	30.9
		σ	0.026	21.655	828.049	13.1	11.1

Note: μ = average, σ = standard deviation.

,

Table 10. Simulations of water shortage and excess release of systems under the A2 scenario [11].

Situation	Rule Curve	Frequency (Times/Year)	Magnitude (MCM/Year)		Duration (Years)
			Average	Maximum	Average	Maximum
Water shortage	RC1	0.320	33.740	223.000	1.6	3.0
	RC2-A2	0.200	5.780	154.000	1.3	2.0
	RC2-B2	0.060	5.980	167.000	1.5	2.0
	RC3	0.260	37.980	475.000	1.3	2.0
Excess release	RC1	0.940	1533.717	7000.341	11.8	33.0
	RC2-A2	0.940	1508.881	7000.341	11.8	26.0
	RC2-B2	0.940	1504.936	7026.783	11.8	26.0
	RC3	0.940	1558.373	7000.341	11.8	26.0

and

Table 11. Simulations of water shortage and excess release of systems under the B2 scenario [11].

Situation	Rule Curve	Frequency (Times/Year)	Magnitude (MCM/Year)		Duration (Years)
			Average	Maximum	Average	Maximum
Water shortage	RC1	0.300	38.860	277.000	1.3	2.0
	RC2-A2	0.060	9.840	408.000	1.5	2.0
	RC2-B2	0.060	9.240	352.000	1.5	2.0
	RC3	0.140	23.200	660.000	1.2	2.0
Excess release	RC1	0.980	2084.397	4699.003	24.5	27.0
	RC2-A2	0.980	2054.251	4681.015	24.5	27.0
	RC2-B2	1.000	2048.272	4690.969	50.0	50.0
	RC3	0.980	2085.463	4711.864	24.5	27.0

. Table 9 presents the water shortage and excess release characteristics of the systems under the historic inflow scenario (RC1). The results indicate that the utilization of the historic inflow rule curves resulted in the lowest occurrences of water shortages and excess releases. The frequency of water shortages was found to be 0.018 ± 0.052 times per year. Furthermore, the average and maximum water shortages were observed to be 21.024 ± 9.149 million cubic meters (MCM) per year and 340.800 ± 116.722 MCM per year, respectively [11].

In the A2 scenario (Table 10), the new rule curves (RC2-A2) demonstrated the best performance in terms of water shortage characteristics. The frequency of water shortages was found to be 0.200 times per year. Additionally, the average and maximum magnitudes of water shortages were observed to be 5.700 and 154.000 million cubic meters (MCM) per year, respectively. The average and maximum durations of water shortages were 1.3 and 2.0 years, respectively [11]. Similarly, in the B2 scenario (Table 11), the results using RC2-B2 indicated the lowest occurrences of water shortages compared to other rule curves. The frequency of water shortages was 0.060 times per year, with the average and maximum magnitudes of water shortages at 9.240 and 352.000 MCM per year, respectively. The findings suggest that the future rule curves (RC2-A2 and RC2-B2) are more suitable for addressing climate and land use changes compared to the current and historic rule curves. Therefore, it can be concluded that rule curves developed based on specific inflow periods will be the most appropriate for managing reservoir operations under changing conditions.

8. Reservoir Size

The size of the reservoir is one factor investigated in the reservoir simulation model connected to optimization techniques for searching optimal rule curves [92,93]. The study focused on reservoirs in Thailand, which are classified into three levels based on water retention volume criteria: small, medium, and large reservoirs [94]. A small reservoir refers to one that can be constructed within one year. A medium-sized reservoir has a storage capacity of less than 100 million cubic meters (MCM), while a large reservoir has a capacity of 100 MCM or more. The conditions and details related to reservoir size are incorporated into the simulation model of the reservoir system. When applying the simulation model of the reservoir system to various optimization techniques, it needs to be adjusted based on the information specific to each basin. Regardless of the reservoir size, modifications were made to the data, as shown in previous studies. The results of reservoir rule curves did not depend on the reservoir size, but rather on the monthly runoff data flowing into the reservoir each month [79,80,95,96].

Therefore, the size factors of small, medium, and large reservoirs will not affect the rule curves obtained through the simulation of the reservoir system connected to the applied optimization technique. The physical data of each reservoir already provides the fundamental information required for reservoir operations. The shape trend of the rule curves is directly linked to the trend of monthly runoff data in the reservoir, which holds true for all reservoirs [97,98].

9. Conclusions

The development of advanced optimization techniques coupled with reservoir system simulation models is indeed crucial for optimizing operating rule curves. Several factors need to be considered in this process: (1) The objective function: The average water scarcity value should be chosen as the objective function, ensuring its practical applicability. (2) Conditional equations: It has been observed that using the trend function as the conditional equation results in smoother rule curves compared to using the moving average. (3) Length of runoff data: Selecting the appropriate timing of the runoff data is essential for obtaining suitable rule curves. This involves utilizing historical runoff data from the beginning of recording until the latest available data. (4) Incorporating stakeholder participation: Updating downstream water demand with stakeholder participation is a suitable approach for integrating it into reservoir simulation models connected with any optimization techniques. (5) Initial conditions of reservoir operation: Different determinations of initial water content may lead to slight variations in the obtained rule curves. However, the performance of each set of rule curves does not show significant differences. (6) Historical and future inflow data: The synthesis of historical inflow data and future inflow data is appropriate for evaluating optimal rule curves. It is important to consider these two types of data separately. (7) Reservoir size: The size of the reservoir does not have a significant effect on the obtained rule curves. This is because the physical data of each reservoir already provides the basic information required for reservoir operation. Finally, considering these factors and incorporating them into the optimization process will contribute to the development of more effective and practical rule curves for reservoir management.