Abstract
Aiming at the optimal allocation of irrigation water in a multi-water source project in a water resource shortage area, this study developed a water resource joint scheduling optimization model for the reservoir and the pumping station under deficit irrigation conditions. In the model, the maximum annual yield of the irrigation area was the objective function; the water supply, water spill of the reservoir and replenishment water of the pump station at each stage were the decision variables; and the total annual water supply of the system, the reservoir operation criteria, the water rights of the pumping station, and the water demand of the crop during the entire growth period were the constraint conditions. According to the characteristics of the model, a large system decomposition aggregation dynamic programming (DADP) method is proposed to transform the N + 1 dimensional dynamic programming problem into a N + 1 one-dimensional dynamic programming problem for solution. In addition, this study also uses the real-coded genetic algorithm (RGA) and DADP to compare the algorithms, and discusses the performance of the two algorithms from the optimization of the algorithm and the applicability of the algorithm.
HIGHLIGHTS
An optimization model for the joint operation of the reservoir and the pumping station in the water shortage area is established.
A new optimization method for a large-scale system model is proposed.
The complex nonlinear problem is transformed into a series of dynamic programming iterative operations.
Graphical Abstract
INTRODUCTION
In water-scarce areas, there has been much interest in research on the optimal allocation of irrigation water resources with the goal of increasing crop yields. Allocation methods involving irrigation water (Zhu et al. 2014; Yang et al. 2021), irrigation quota, irrigation timing, water demand characteristics of crops, growth stage, tillage methods (Anzai et al. 2014; Yamane et al. 2016), competition for water among different crops, and water deficit have all had an effect on optimal water supply decisions concerning irrigation.
Reservoirs, ponds, wells and pumping stations are common water source projects in irrigation areas. The joint operation of multiple water source projects can effectively ensure the irrigation task in dry years. The optimal operation model of the irrigation system with the joint operation of multiple reservoirs and multiple pumping stations is usually based on the minimum operation cost of the irrigation system (mainly the pumping cost of pumping stations) as the objective function. Yu et al. (1994) proposed a nonlinear model with the minimum cost of water replenishment as the objective function; Reca et al. (2014, 2015) proposed a linear model for the joint operation of reservoirs and pumping stations with the goal of minimizing the cost of water replenishment. However, the above studies did not consider the total amount of water replenishment from the perspective of agricultural water rights. With the gradual promotion of water price reform (Molle 2004; Heikkila 2015), regional water rights are strictly divided, and the total amount of water replenishment is limited. Therefore, the existing joint dispatching model needs to take into account the impact of water rights constraints on irrigation decisions.
The optimal operation of reservoir water resources can adopt linear programming (Yoo 2009), nonlinear programming (Cai et al. 2002), and dynamic programming (DP). However, for the optimal scheduling problem of complex irrigation systems characterized by high dimension and a large number of decision variables, the existence of the ‘curse of dimensionality’ (Cheng et al. 2012) is an unavoidable obstacle in classical algorithms. Heuristic algorithms, such as genetic algorithms (Yang et al. 2019) and genetic programming (Fallah-Mehdipour et al. 2013), particle swarm algorithms (Mousavi & Shourian, 2010), and simulated annealing algorithms (Teegavarapu & Simonovic, 2002), have also been widely used to optimize reservoirs. These heuristic algorithms with random search properties have significant advantages over classical algorithms in terms of the number of calculations that can be performed and their calculation time when solving problems that are highly dimensional and nonlinear and have multiple decision variables. However, such methods are difficult to apply to optimization problems with judgmental constraints, such as reservoir operational criteria. In addition, the treatment of equality constraints and the mathematical proof of global optimality using heuristic algorithms remains controversial (Samanipour & Jelovica 2020).
The decomposition coordination method and decomposition aggregation method are both called ‘two-level algorithms’, and the former has been widely used in the optimization of large system models (Li et al. 2014; Gong & Zhu 2022). For the optimal scheduling problem of high-dimensional and complex irrigation systems, the decomposition aggregation method (Litvinchev 1995) can give priority to the optimization of subsystems and replace independent variables with associated variables compared with the decomposition coordination method (Gong & Cheng 2018). In addition, the decomposition aggregation method can also ensure the connection between subsystems in the process of decomposition of the large system, so that the optimal solution of the large system model can be determined by the aggregation model.
In this study, taking the irrigation system consisting of the reservoirs and pumping stations as the research object, considering the water rights constraints, a water resources optimal allocation model for joint operation of water source projects under the condition of insufficient irrigation is established. According to the characteristics of the model, the decomposition aggregation dynamic programming (DADP) method is proposed to solve the problem. The DADP method can decompose the large system model into a series of subsystem models. The subsystem models are solved by using the one-dimensional dynamic programming method to ensure the optimality of each subsystem. Then, the associated variables are used as decision variables, and a series of subsystems is aggregated according to the recursive principle of DP. The aggregation model is also solved by using the DP method. The optimal solution of the aggregation model is used to check the optimal solution of each subsystem, Thus, the global optimal solution of the large scale system model is obtained. At the same time, the real-coded genetic algorithm (RGA) and the DADP method are used to compare and analyze the algorithms.
MODEL AND METHOD
System generalization
Schematic diagram of a single-reservoir and a single-pumping-station irrigation system.
Schematic diagram of a single-reservoir and a single-pumping-station irrigation system.
In Figure 1, i is the number of crop species in the irrigation area (i = 1,2); j is the crop growth stage number (j = 1,2,…,Mi); Xi,j is the water supply from the reservoir to crop i at growth stage j under deficit irrigation conditions, MCM; Yi,j is the volume of water replenishment from the pumping station at growth stage j of crop i, MCM; LSi,j is the inflow to the reservoir at growth stage j of crop i, MCM; PSi,j is the water spill by the reservoir at growth stage j of crop i, MCM; and EFi,j is the evaporation from the reservoir at growth stage j of crop i, MCM. (Note: MCM is million cubic meters.)
Model construction
Objective function
Constraint
Water supply constraints
- (2) Water supply restriction during the entire growth period of a single crop:where SK is the total annual water supply of the annual regulation reservoir, MCM; BZ is the water rights of the pumping station, that is, the maximum allowable water replenishment of the pumping station in a year, MCM; IWi is the upper limit of the water supply during the entire growth period of a single crop, MCM.
Scheduling criteria constraints
Pumping station constraints
Crop water demand constraints
Initial and boundary conditions
Model solution
Decomposition aggregation dynamic programming (DADP)
(a) is the schematic diagram of DP; (b) is the schematic diagram of DADP.
Step 1: Large system decomposition. For the water-deficient irrigation areas of two main dry crops, the water competition relationship between the two dry crops under limited water resources is considered while studying the impact of water stress on the final yield of dry crops. The optimal allocation model of water resources of the reservoir and the pumping station irrigation system can be divided into two optimal allocation models for irrigation of a single a dry crop, as shown below:
The optimization solution process of the subsystem can refer to the relevant research (Wei et al. 2021). But it is worth emphasizing that the DP method adopted by Wei et al. (2021) in the research is only applicable to the solution of one-dimensional DP model. The DADP method proposed in this study is a solution method of the large system model, which can be applied to the dimensionality reduction of high-dimensional DO model.
Step 3: Subsystem aggregation. After the subsystem is solved, a series of corresponding relations of IWi ∼ fi(IWi) (i = 1,2) can be obtained, and then the subsystem models are aggregated according to the corresponding relations and the recursive idea of DP. The aggregation model is as follows:
Equations (14) and (15) form the aggregation model, which is also a typical one-dimensional mathematical model and can also be solved by DP. Where, state variable ξi is the sum of the total water supply of the large system, and the feasible area is [0, SK + BZ]; The decision variable IWi is the total water supply of the subsystem, and the feasible region is [0,ξi]。 The global optimal G* of the large system model and the optimal water supply IWi*(i = 1,2) corresponding to the optimal solution can be obtained after the solution is completed. Then, the optimal reservoir water supply process Xi,j*(i = 1,2; j = 1,2,…,Mi ), the optimal water replenishment process Yi,j*(i = 1,2; j = 1,2,…,Mi) of the pumping station, and the optimal reservoir water spill process PSi,j*(i = 1,2; j = 1,2,…,Mi) can be obtained by back checking the optimization results of the subsystem.
Real-coded genetic algorithm (RGA)
Wright (1991) proposed an RGA, which is a real-to-individual coding method that can achieve better optimization results than binary-coded genetic algorithms.
For a given optimization problem with m variables, the n initial solution sets are usually generated in a random manner when the RGA is used to solve the problem, where the process of population iteration, selection, crossover and mutation are adopted to ensure the evolution of the population. In this study, a roulette wheel was used for the selection operation, and the random single-point method was used for cross-operation. First, a sequence number t smaller than m was randomly generated, and then the sequence numbers corresponding to a pair of genes t to m were exchanged with each other to complete the crossover operation. For example: a pair of genomes
and
will become
and
through the cross-operation; The mutation operation was completed by random single-point mutation.
EXAMPLE APPLICATION
Study area
Experimental parameters of winter wheat
Growth period . | Seeding . | Returning green . | Jointing . | Heading . | Filling . | Mature . | |
---|---|---|---|---|---|---|---|
Sensitive index . | 0.2675 . | 0.0613 . | 0.3765 . | 0.5951 . | 0.5951 . | 0.2981 . | |
Crop water requirement (mm) | 50% probability | 97.3 | 17.3 | 30.4 | 92.1 | 110.7 | 105 |
75% probability | 107 | 19 | 33.4 | 101.3 | 121.8 | 115.5 |
Growth period . | Seeding . | Returning green . | Jointing . | Heading . | Filling . | Mature . | |
---|---|---|---|---|---|---|---|
Sensitive index . | 0.2675 . | 0.0613 . | 0.3765 . | 0.5951 . | 0.5951 . | 0.2981 . | |
Crop water requirement (mm) | 50% probability | 97.3 | 17.3 | 30.4 | 92.1 | 110.7 | 105 |
75% probability | 107 | 19 | 33.4 | 101.3 | 121.8 | 115.5 |
Experimental parameters of corn
Growth period . | Seeding . | Jointing . | Heading/filling . | Mature . | |
---|---|---|---|---|---|
Sensitive index . | 0.257 . | 0.2022 . | 0.3237 . | 0.2189 . | |
Crop water requirement(mm) | 50% probability | 81 | 90 | 77.4 | 109.8 |
75% probability | 92.4 | 91.8 | 85.2 | 115.8 |
Growth period . | Seeding . | Jointing . | Heading/filling . | Mature . | |
---|---|---|---|---|---|
Sensitive index . | 0.257 . | 0.2022 . | 0.3237 . | 0.2189 . | |
Crop water requirement(mm) | 50% probability | 81 | 90 | 77.4 | 109.8 |
75% probability | 92.4 | 91.8 | 85.2 | 115.8 |
The hydrological storage calculation period of traditional reservoirs is usually divided into daily, 10-day, and monthly periods. In this study, the regulation and storage calculation of the irrigation system is divided by crop growth period, which can be applied to the planning solution of the crop water production function for winter wheat and corn in the YB irrigation area. In addition, the incoming water process of the irrigation system was calculated statistically based on the total calendar time of each stage of growth. With reference to hydro-meteorological data from the local weather station, the inflow of the reservoir at each stage is shown in Table 3.
Inflow (104 m3)
Level year | 32 | 43 | 13 | 12 | 19 | 28 | 37 | 49 | 53 | 42 |
Dry year | 24 | 19 | 18 | 9 | 11 | 16 | 18 | 19 | 29 | 26 |
Level year | 32 | 43 | 13 | 12 | 19 | 28 | 37 | 49 | 53 | 42 |
Dry year | 24 | 19 | 18 | 9 | 11 | 16 | 18 | 19 | 29 | 26 |
YB irrigation area is located in hilly and mountainous areas. Relying on artesian water diversion alone can not ensure normal agricultural water use in the irrigation area, so water needs to be diverted for recharge while retaining surface water. The existing Haohu (HH) pumping station is used to divert and lift the water from the main canal to supplement the SD reservoir. The characteristic parameters of the pumping station are shown in Table 4.
Characteristics of pumping stations
Pumping station . | Design discharge (m3/h) . | Daily operation duration (h) . | Water rights (MCM) . |
---|---|---|---|
HH | 3,600 | 20 | 6 |
Pumping station . | Design discharge (m3/h) . | Daily operation duration (h) . | Water rights (MCM) . |
---|---|---|---|
HH | 3,600 | 20 | 6 |
The evaporation losses from irrigation reservoirs were determined based on the evaporation depth for the time period and the average reservoir water area, where the evaporation depth Ej was determined using measured evaporation data from an area near the study area (see Table 5) and corrected using the conversion factor wj. The water area was determined based on the reservoir area and storage volume relationship function provided by the reservoir manager. (With reference to the local water resources planning data, we can obtain that α = 2.117 × 10−3, β = 1.063.)
Ej and wj of each period
Period . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . |
---|---|---|---|---|---|---|---|---|---|---|
Ej | 92.8 | 102 | 44.2 | 51.6 | 107.6 | 94.6 | 126.3 | 134.4 | 118.6 | 96.5 |
Wj | 1.04 | 1.11 | 1.03 | 0.96 | 0.93 | 0.92 | 0.94 | 0.96 | 0.97 | 1.01 |
Period . | 1 . | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | 8 . | 9 . | 10 . |
---|---|---|---|---|---|---|---|---|---|---|
Ej | 92.8 | 102 | 44.2 | 51.6 | 107.6 | 94.6 | 126.3 | 134.4 | 118.6 | 96.5 |
Wj | 1.04 | 1.11 | 1.03 | 0.96 | 0.93 | 0.92 | 0.94 | 0.96 | 0.97 | 1.01 |
Solution results of the DADP method
According to the information provided by the reservoir manager, the initial boundaries V0 of reservoir storage in a level year (50% probability) and in a dry year (75% probability) were 3.18 MCM and 2.86 MCM, respectively, for the SD reservoir. The water supply of winter wheat in the YB irrigation area was discretized in the interval [4.48 MCM, 7.0 MCM] and [4.51 MCM, 5.18 MCM] at 50% probability and 75% probability. The corn water supply at 50% probability and 75% probability is discretized within the interval [0.82 MCM, 3.36 MCM] and [1.27 MCM, 1.94 MCM], and the optimization solution results of the subsystem are shown in Tables 6 and 7:
IWi∼ fi(IWi) ∼ (X*,Y*,PS*) correspondence table in a level year (50% probability)
IW1 (104m3) . | f1(IW1) . | Xj(j = 1,2,…,6) . | Yj(j = 1,2,…,6) . | PSj(j = 1,2,…,6) . | IW2 (104m3) . | f2(IW2) . | Xj(j = 1,2,3,4) . | Yj(j = 1,2,3,4) . | PSj(j = 1,2,3,4) . |
---|---|---|---|---|---|---|---|---|---|
448 | 0.221 | 82 19 30 105 116 96 | 0 0 0 65 113 82 | 0 0 0 0 0 0 | 334 | 1.000 | 70 66 31 144 | 52 19 53 216 | 0 0 0 0 |
453 | 0.231 | 82 19 35 105 116 96 | 0 0 0 70 113 82 | 0 0 0 0 0 0 | 329 | 1.000 | 70 66 31 144 | 52 19 48 216 | 0 0 0 0 |
458 | 0.240 | 82 19 40 105 116 96 | 0 0 0 75 113 82 | 0 0 0 0 0 0 | 324 | 1.000 | 70 66 31 144 | 52 19 43 216 | 0 0 0 0 |
463 | 0.249 | 82 19 45 105 116 96 | 0 0 0 80 113 82 | 0 0 0 0 0 0 | 319 | 1.000 | 70 66 31 144 | 52 19 38 216 | 0 0 0 0 |
468 | 0.257 | 82 19 50 105 116 96 | 0 0 0 85 113 82 | 0 0 0 0 0 0 | 314 | 1.000 | 70 66 31 144 | 52 19 33 216 | 0 0 0 0 |
473 | 0.265 | 82 19 55 105 116 96 | 0 0 0 90 113 82 | 0 0 0 0 0 0 | 309 | 0.998 | 70 66 31 142 | 52 19 28 216 | 0 0 0 0 |
478 | 0.272 | 82 19 60 105 116 96 | 0 0 0 95 113 82 | 0 0 0 0 0 0 | 304 | 0.993 | 70 66 31 137 | 52 19 23 216 | 0 0 0 0 |
483 | 0.279 | 82 19 65 105 116 96 | 0 0 0 100 113 82 | 0 0 0 0 0 0 | 299 | 0.988 | 70 66 31 132 | 52 19 18 216 | 0 0 0 0 |
… | … | … | … | … | … | … | … | … | … |
540 | 0.355 | 82 19 69 144 130 96 | 0 0 3 140 127 82 | 0 0 0 0 0 0 | 242 | 0.923 | 70 45 31 96 | 52 0 0 144 | 0 0 0 0 |
545 | 0.362 | 82 19 69 146 133 96 | 0 0 3 142 130 82 | 0 0 0 0 0 0 | 237 | 0.917 | 70 42 31 94 | 52 0 0 139 | 0 0 0 0 |
550 | 0.368 | 82 19 69 149 135 96 | 0 0 3 145 132 82 | 0 0 0 0 0 0 | 232 | 0.911 | 70 40 31 91 | 52 0 0 134 | 0 0 0 0 |
555 | 0.375 | 82 19 69 152 137 96 | 0 0 3 147 135 82 | 0 0 0 0 0 0 | 227 | 0.905 | 70 37 31 89 | 52 0 0 129 | 0 0 0 0 |
560 | 0.382 | 82 19 69 154 140 96 | 0 0 3 150 137 82 | 0 0 0 0 0 0 | 222 | 0.899 | 70 35 31 86 | 52 0 0 124 | 0 0 0 0 |
565 | 0.388 | 82 19 69 157 142 96 | 0 0 3 152 140 82 | 0 0 0 0 0 0 | 217 | 0.893 | 70 32 31 84 | 52 0 0 119 | 0 0 0 0 |
570 | 0.395 | 82 19 69 159 145 96 | 0 0 3 155 142 82 | 0 0 0 0 0 0 | 212 | 0.886 | 70 30 31 81 | 52 0 0 114 | 0 0 0 0 |
… | … | … | … | … | … | … | … | … | … |
650 | 0.505 | 82 19 69 199 185 96 | 0 0 3 195 182 82 | 0 0 0 0 0 0 | 132 | 0.778 | 53 0 31 48 | 6 0 0 32 | 0 0 0 0 |
655 | 0.512 | 82 19 69 202 187 96 | 0 0 3 198 184 82 | 0 0 0 0 0 0 | 127 | 0.771 | 50 0 31 46 | 6 0 0 37 | 0 0 0 0 |
660 | 0.519 | 82 19 69 204 190 96 | 0 0 3 200 187 82 | 0 0 0 0 0 0 | 122 | 0.764 | 47 0 31 44 | 6 0 0 42 | 0 0 0 0 |
665 | 0.526 | 82 19 69 207 192 96 | 0 0 3 203 189 82 | 0 0 0 0 0 0 | 117 | 0.757 | 44 0 31 42 | 6 0 0 47 | 0 0 0 0 |
670 | 0.533 | 82 19 69 209 195 96 | 0 0 3 205 192 82 | 0 0 0 0 0 0 | 112 | 0.750 | 42 0 31 39 | 6 0 0 52 | 0 0 0 0 |
675 | 0.540 | 82 19 69 212 197 96 | 0 0 3 208 194 82 | 0 0 0 0 0 0 | 107 | 0.742 | 39 0 31 37 | 6 0 0 57 | 0 0 0 0 |
680 | 0.547 | 82 20 69 213 200 96 | 0 0 4 209 197 82 | 0 0 0 0 0 0 | 102 | 0.735 | 35 0 31 36 | 6 0 0 62 | 0 0 0 0 |
685 | 0.554 | 82 20 69 216 202 96 | 0 0 4 212 199 82 | 0 0 0 0 0 0 | 97 | 0.727 | 31 0 30 36 | 6 0 0 67 | 0 0 0 0 |
690 | 0.561 | 82 20 69 219 204 96 | 0 0 4 215 201 82 | 0 0 0 0 0 0 | 92 | 0.720 | 29 0 27 36 | 6 0 0 72 | 0 0 0 0 |
695 | 0.568 | 82 20 69 220 208 96 | 0 0 4 216 205 82 | 0 0 0 0 0 0 | 87 | 0.712 | 26 0 25 38 | 6 0 0 77 | 0 0 0 0 |
700 | 0.575 | 82 21 69 220 212 96 | 0 0 5 216 209 82 | 0 0 0 0 0 0 | 82 | 0.704 | 24 0 22 36 | 6 0 0 82 | 0 0 0 0 |
IW1 (104m3) . | f1(IW1) . | Xj(j = 1,2,…,6) . | Yj(j = 1,2,…,6) . | PSj(j = 1,2,…,6) . | IW2 (104m3) . | f2(IW2) . | Xj(j = 1,2,3,4) . | Yj(j = 1,2,3,4) . | PSj(j = 1,2,3,4) . |
---|---|---|---|---|---|---|---|---|---|
448 | 0.221 | 82 19 30 105 116 96 | 0 0 0 65 113 82 | 0 0 0 0 0 0 | 334 | 1.000 | 70 66 31 144 | 52 19 53 216 | 0 0 0 0 |
453 | 0.231 | 82 19 35 105 116 96 | 0 0 0 70 113 82 | 0 0 0 0 0 0 | 329 | 1.000 | 70 66 31 144 | 52 19 48 216 | 0 0 0 0 |
458 | 0.240 | 82 19 40 105 116 96 | 0 0 0 75 113 82 | 0 0 0 0 0 0 | 324 | 1.000 | 70 66 31 144 | 52 19 43 216 | 0 0 0 0 |
463 | 0.249 | 82 19 45 105 116 96 | 0 0 0 80 113 82 | 0 0 0 0 0 0 | 319 | 1.000 | 70 66 31 144 | 52 19 38 216 | 0 0 0 0 |
468 | 0.257 | 82 19 50 105 116 96 | 0 0 0 85 113 82 | 0 0 0 0 0 0 | 314 | 1.000 | 70 66 31 144 | 52 19 33 216 | 0 0 0 0 |
473 | 0.265 | 82 19 55 105 116 96 | 0 0 0 90 113 82 | 0 0 0 0 0 0 | 309 | 0.998 | 70 66 31 142 | 52 19 28 216 | 0 0 0 0 |
478 | 0.272 | 82 19 60 105 116 96 | 0 0 0 95 113 82 | 0 0 0 0 0 0 | 304 | 0.993 | 70 66 31 137 | 52 19 23 216 | 0 0 0 0 |
483 | 0.279 | 82 19 65 105 116 96 | 0 0 0 100 113 82 | 0 0 0 0 0 0 | 299 | 0.988 | 70 66 31 132 | 52 19 18 216 | 0 0 0 0 |
… | … | … | … | … | … | … | … | … | … |
540 | 0.355 | 82 19 69 144 130 96 | 0 0 3 140 127 82 | 0 0 0 0 0 0 | 242 | 0.923 | 70 45 31 96 | 52 0 0 144 | 0 0 0 0 |
545 | 0.362 | 82 19 69 146 133 96 | 0 0 3 142 130 82 | 0 0 0 0 0 0 | 237 | 0.917 | 70 42 31 94 | 52 0 0 139 | 0 0 0 0 |
550 | 0.368 | 82 19 69 149 135 96 | 0 0 3 145 132 82 | 0 0 0 0 0 0 | 232 | 0.911 | 70 40 31 91 | 52 0 0 134 | 0 0 0 0 |
555 | 0.375 | 82 19 69 152 137 96 | 0 0 3 147 135 82 | 0 0 0 0 0 0 | 227 | 0.905 | 70 37 31 89 | 52 0 0 129 | 0 0 0 0 |
560 | 0.382 | 82 19 69 154 140 96 | 0 0 3 150 137 82 | 0 0 0 0 0 0 | 222 | 0.899 | 70 35 31 86 | 52 0 0 124 | 0 0 0 0 |
565 | 0.388 | 82 19 69 157 142 96 | 0 0 3 152 140 82 | 0 0 0 0 0 0 | 217 | 0.893 | 70 32 31 84 | 52 0 0 119 | 0 0 0 0 |
570 | 0.395 | 82 19 69 159 145 96 | 0 0 3 155 142 82 | 0 0 0 0 0 0 | 212 | 0.886 | 70 30 31 81 | 52 0 0 114 | 0 0 0 0 |
… | … | … | … | … | … | … | … | … | … |
650 | 0.505 | 82 19 69 199 185 96 | 0 0 3 195 182 82 | 0 0 0 0 0 0 | 132 | 0.778 | 53 0 31 48 | 6 0 0 32 | 0 0 0 0 |
655 | 0.512 | 82 19 69 202 187 96 | 0 0 3 198 184 82 | 0 0 0 0 0 0 | 127 | 0.771 | 50 0 31 46 | 6 0 0 37 | 0 0 0 0 |
660 | 0.519 | 82 19 69 204 190 96 | 0 0 3 200 187 82 | 0 0 0 0 0 0 | 122 | 0.764 | 47 0 31 44 | 6 0 0 42 | 0 0 0 0 |
665 | 0.526 | 82 19 69 207 192 96 | 0 0 3 203 189 82 | 0 0 0 0 0 0 | 117 | 0.757 | 44 0 31 42 | 6 0 0 47 | 0 0 0 0 |
670 | 0.533 | 82 19 69 209 195 96 | 0 0 3 205 192 82 | 0 0 0 0 0 0 | 112 | 0.750 | 42 0 31 39 | 6 0 0 52 | 0 0 0 0 |
675 | 0.540 | 82 19 69 212 197 96 | 0 0 3 208 194 82 | 0 0 0 0 0 0 | 107 | 0.742 | 39 0 31 37 | 6 0 0 57 | 0 0 0 0 |
680 | 0.547 | 82 20 69 213 200 96 | 0 0 4 209 197 82 | 0 0 0 0 0 0 | 102 | 0.735 | 35 0 31 36 | 6 0 0 62 | 0 0 0 0 |
685 | 0.554 | 82 20 69 216 202 96 | 0 0 4 212 199 82 | 0 0 0 0 0 0 | 97 | 0.727 | 31 0 30 36 | 6 0 0 67 | 0 0 0 0 |
690 | 0.561 | 82 20 69 219 204 96 | 0 0 4 215 201 82 | 0 0 0 0 0 0 | 92 | 0.720 | 29 0 27 36 | 6 0 0 72 | 0 0 0 0 |
695 | 0.568 | 82 20 69 220 208 96 | 0 0 4 216 205 82 | 0 0 0 0 0 0 | 87 | 0.712 | 26 0 25 38 | 6 0 0 77 | 0 0 0 0 |
700 | 0.575 | 82 21 69 220 212 96 | 0 0 5 216 209 82 | 0 0 0 0 0 0 | 82 | 0.704 | 24 0 22 36 | 6 0 0 82 | 0 0 0 0 |
IWi∼ fi(IWi) ∼ (X*,Y*,PS*) correspondence table in a dry year (75% probability)
IW1 (104m3) . | f1(IW1) . | Xj(j = 1,2,…,6) . | Yj(j = 1,2,…,6) . | PSj(j = 1,2,…,6) . | IW2 (104m3) . | f2(IW2) . | Xj(j = 1,2,3,4) . | Yj(j = 1,2,3,4) . | PSj(j = 1,2,3,4) . |
---|---|---|---|---|---|---|---|---|---|
451 | 0.219 | 85 8 21 106 126 105 | 0 0 5 105 131 103 | 0 0 0 0 0 0 | 194 | 0.607 | 48 28 60 58 | 49 29 49 129 | 0 0 0 0 |
454 | 0.224 | 85 8 24 106 126 105 | 0 0 8 105 131 103 | 0 0 0 0 0 0 | 191 | 0.603 | 47 28 58 58 | 48 29 47 129 | 0 0 0 0 |
457 | 0.23 | 85 8 27 106 126 105 | 0 0 11 105 131 103 | 0 0 0 0 0 0 | 188 | 0.599 | 45 28 57 58 | 47 29 45 129 | 0 0 0 0 |
460 | 0.235 | 85 8 30 106 126 105 | 0 0 14 105 131 103 | 0 0 0 0 0 0 | 185 | 0.594 | 44 28 55 58 | 45 29 44 129 | 0 0 0 0 |
463 | 0.24 | 85 8 33 106 126 105 | 0 0 17 105 131 103 | 0 0 0 0 0 0 | 182 | 0.59 | 43 28 53 58 | 44 29 42 129 | 0 0 0 0 |
466 | 0.244 | 85 8 36 106 126 105 | 0 0 20 105 131 103 | 0 0 0 0 0 0 | 179 | 0.585 | 41 28 52 58 | 42 29 41 129 | 0 0 0 0 |
469 | 0.249 | 85 8 39 106 126 105 | 0 0 23 105 131 103 | 0 0 0 0 0 0 | 176 | 0.581 | 40 28 50 58 | 41 29 39 129 | 0 0 0 0 |
472 | 0.253 | 85 8 42 106 126 105 | 0 0 26 105 131 103 | 0 0 0 0 0 0 | 173 | 0.576 | 39 28 48 58 | 40 29 37 129 | 0 0 0 0 |
475 | 0.258 | 85 8 45 106 126 105 | 0 0 29 105 131 103 | 0 0 0 0 0 0 | 170 | 0.572 | 37 28 47 58 | 38 29 36 129 | 0 0 0 0 |
478 | 0.262 | 85 8 48 106 126 105 | 0 0 32 105 131 103 | 0 0 0 0 0 0 | 167 | 0.567 | 36 28 45 58 | 37 29 34 129 | 0 0 0 0 |
481 | 0.266 | 85 8 51 106 126 105 | 0 0 35 105 131 103 | 0 0 0 0 0 0 | 164 | 0.562 | 35 28 43 58 | 36 29 32 129 | 0 0 0 0 |
484 | 0.27 | 85 8 54 106 126 105 | 0 0 38 105 131 103 | 0 0 0 0 0 0 | 161 | 0.558 | 33 28 42 58 | 34 29 31 129 | 0 0 0 0 |
487 | 0.274 | 85 8 57 106 126 105 | 0 0 41 105 131 103 | 0 0 0 0 0 0 | 158 | 0.553 | 33 28 39 58 | 34 29 28 129 | 0 0 0 0 |
490 | 0.278 | 85 8 60 106 126 105 | 0 0 44 105 131 103 | 0 0 0 0 0 0 | 155 | 0.548 | 33 28 36 58 | 34 29 25 129 | 0 0 0 0 |
493 | 0.282 | 85 8 62 107 126 105 | 0 0 46 106 131 103 | 0 0 0 0 0 0 | 152 | 0.544 | 33 28 33 58 | 34 29 22 129 | 0 0 0 0 |
496 | 0.285 | 85 8 63 109 126 105 | 0 0 47 108 131 103 | 0 0 0 0 0 0 | 149 | 0.539 | 33 28 30 58 | 34 29 19 129 | 0 0 0 0 |
499 | 0.289 | 85 8 64 111 126 105 | 0 0 48 110 131 103 | 0 0 0 0 0 0 | 146 | 0.534 | 33 28 27 58 | 34 29 16 129 | 0 0 0 0 |
502 | 0.293 | 85 8 65 113 126 105 | 0 0 49 112 131 103 | 0 0 0 0 0 0 | 143 | 0.528 | 33 28 24 58 | 34 29 13 129 | 0 0 0 0 |
505 | 0.297 | 85 8 65 116 126 105 | 0 0 49 115 131 103 | 0 0 0 0 0 0 | 140 | 0.523 | 33 28 21 58 | 34 29 10 129 | 0 0 0 0 |
508 | 0.3 | 85 8 65 119 126 105 | 0 0 49 118 131 103 | 0 0 0 0 0 0 | 137 | 0.518 | 33 28 18 58 | 34 29 7 129 | 0 0 0 0 |
511 | 0.304 | 85 8 65 122 126 105 | 0 0 49 121 131 103 | 0 0 0 0 0 0 | 134 | 0.512 | 33 28 15 58 | 34 29 4 129 | 0 0 0 0 |
514 | 0.306 | 85 8 65 125 126 105 | 0 0 49 124 131 103 | 0 0 0 0 0 0 | 131 | 0.507 | 33 28 12 58 | 34 29 1 129 | 0 0 0 0 |
517 | 0.311 | 85 8 65 128 126 105 | 0 0 49 127 131 103 | 0 0 0 0 0 0 | 128 | 0.511 | 33 28 9 58 | 34 29 0 127 | 0 0 0 0 |
IW1 (104m3) . | f1(IW1) . | Xj(j = 1,2,…,6) . | Yj(j = 1,2,…,6) . | PSj(j = 1,2,…,6) . | IW2 (104m3) . | f2(IW2) . | Xj(j = 1,2,3,4) . | Yj(j = 1,2,3,4) . | PSj(j = 1,2,3,4) . |
---|---|---|---|---|---|---|---|---|---|
451 | 0.219 | 85 8 21 106 126 105 | 0 0 5 105 131 103 | 0 0 0 0 0 0 | 194 | 0.607 | 48 28 60 58 | 49 29 49 129 | 0 0 0 0 |
454 | 0.224 | 85 8 24 106 126 105 | 0 0 8 105 131 103 | 0 0 0 0 0 0 | 191 | 0.603 | 47 28 58 58 | 48 29 47 129 | 0 0 0 0 |
457 | 0.23 | 85 8 27 106 126 105 | 0 0 11 105 131 103 | 0 0 0 0 0 0 | 188 | 0.599 | 45 28 57 58 | 47 29 45 129 | 0 0 0 0 |
460 | 0.235 | 85 8 30 106 126 105 | 0 0 14 105 131 103 | 0 0 0 0 0 0 | 185 | 0.594 | 44 28 55 58 | 45 29 44 129 | 0 0 0 0 |
463 | 0.24 | 85 8 33 106 126 105 | 0 0 17 105 131 103 | 0 0 0 0 0 0 | 182 | 0.59 | 43 28 53 58 | 44 29 42 129 | 0 0 0 0 |
466 | 0.244 | 85 8 36 106 126 105 | 0 0 20 105 131 103 | 0 0 0 0 0 0 | 179 | 0.585 | 41 28 52 58 | 42 29 41 129 | 0 0 0 0 |
469 | 0.249 | 85 8 39 106 126 105 | 0 0 23 105 131 103 | 0 0 0 0 0 0 | 176 | 0.581 | 40 28 50 58 | 41 29 39 129 | 0 0 0 0 |
472 | 0.253 | 85 8 42 106 126 105 | 0 0 26 105 131 103 | 0 0 0 0 0 0 | 173 | 0.576 | 39 28 48 58 | 40 29 37 129 | 0 0 0 0 |
475 | 0.258 | 85 8 45 106 126 105 | 0 0 29 105 131 103 | 0 0 0 0 0 0 | 170 | 0.572 | 37 28 47 58 | 38 29 36 129 | 0 0 0 0 |
478 | 0.262 | 85 8 48 106 126 105 | 0 0 32 105 131 103 | 0 0 0 0 0 0 | 167 | 0.567 | 36 28 45 58 | 37 29 34 129 | 0 0 0 0 |
481 | 0.266 | 85 8 51 106 126 105 | 0 0 35 105 131 103 | 0 0 0 0 0 0 | 164 | 0.562 | 35 28 43 58 | 36 29 32 129 | 0 0 0 0 |
484 | 0.27 | 85 8 54 106 126 105 | 0 0 38 105 131 103 | 0 0 0 0 0 0 | 161 | 0.558 | 33 28 42 58 | 34 29 31 129 | 0 0 0 0 |
487 | 0.274 | 85 8 57 106 126 105 | 0 0 41 105 131 103 | 0 0 0 0 0 0 | 158 | 0.553 | 33 28 39 58 | 34 29 28 129 | 0 0 0 0 |
490 | 0.278 | 85 8 60 106 126 105 | 0 0 44 105 131 103 | 0 0 0 0 0 0 | 155 | 0.548 | 33 28 36 58 | 34 29 25 129 | 0 0 0 0 |
493 | 0.282 | 85 8 62 107 126 105 | 0 0 46 106 131 103 | 0 0 0 0 0 0 | 152 | 0.544 | 33 28 33 58 | 34 29 22 129 | 0 0 0 0 |
496 | 0.285 | 85 8 63 109 126 105 | 0 0 47 108 131 103 | 0 0 0 0 0 0 | 149 | 0.539 | 33 28 30 58 | 34 29 19 129 | 0 0 0 0 |
499 | 0.289 | 85 8 64 111 126 105 | 0 0 48 110 131 103 | 0 0 0 0 0 0 | 146 | 0.534 | 33 28 27 58 | 34 29 16 129 | 0 0 0 0 |
502 | 0.293 | 85 8 65 113 126 105 | 0 0 49 112 131 103 | 0 0 0 0 0 0 | 143 | 0.528 | 33 28 24 58 | 34 29 13 129 | 0 0 0 0 |
505 | 0.297 | 85 8 65 116 126 105 | 0 0 49 115 131 103 | 0 0 0 0 0 0 | 140 | 0.523 | 33 28 21 58 | 34 29 10 129 | 0 0 0 0 |
508 | 0.3 | 85 8 65 119 126 105 | 0 0 49 118 131 103 | 0 0 0 0 0 0 | 137 | 0.518 | 33 28 18 58 | 34 29 7 129 | 0 0 0 0 |
511 | 0.304 | 85 8 65 122 126 105 | 0 0 49 121 131 103 | 0 0 0 0 0 0 | 134 | 0.512 | 33 28 15 58 | 34 29 4 129 | 0 0 0 0 |
514 | 0.306 | 85 8 65 125 126 105 | 0 0 49 124 131 103 | 0 0 0 0 0 0 | 131 | 0.507 | 33 28 12 58 | 34 29 1 129 | 0 0 0 0 |
517 | 0.311 | 85 8 65 128 126 105 | 0 0 49 127 131 103 | 0 0 0 0 0 0 | 128 | 0.511 | 33 28 9 58 | 34 29 0 127 | 0 0 0 0 |
The optimal irrigation water volume of winter wheat and corn in the entire growth period obtained by the large system can be checked back in Tables 6 and 7, and the optimal water supply and spill processes of the reservoirs, and the optimal water replenishment of the pumping stations in different periods of the irrigation system can be obtained.
DISCUSSION AND ANALYSIS
Algorithm optimality
In order to compare the performance of the algorithms of DADP and RGA, the optimization of the algorithm is analyzed from four aspects: the optimization of the objective function value, the stability of the algorithm, the convergence of the algorithm and the solving speed of the algorithm.
To compare the optimality of the objective function, the sensitivity analysis of the two algorithms is required first. As shown in Table 8, for DADP, in a level year (50% probability), the optimal value of the objective function is (1.86E + 07) RMB, and in the dry year (75% probability), the optimal value of the objective function is (1.38E + 07) RMB. There is no parameter demand calibration in the solution process.
Sensitivity analysis of DADP and RGA
Level year (50% probability) | DADP | Objective function | |||||
1.86E + 07 | |||||||
RGA | Population size | Objective function | Crossover pm | Objective function | Mutation pe | Objective function | |
20 | 1.68E + 07 | 0.3 | 1.57E + 07 | 0.1 | 1.66E + 07 | ||
40 | 1.71E + 07 | 0.4 | 1.63E + 07 | 0.2 | 1.82E + 07 | ||
60 | 1.55E + 07 | 0.5 | 1.68E + 07 | 0.3 | 1.69E + 07 | ||
80 | 1.63E + 07 | 0.6 | 1.82E + 07 | 0.4 | 1.74E + 07 | ||
100 | 1.82E + 07 | 0.7 | 1.76E + 07 | 0.5 | 1.80E + 07 | ||
Dry year (75% probability) | DADP | Objective function | |||||
1.38E + 07 | |||||||
RGA | Population size | Objective function | Crossover pm | Objective function | Mutation pe | Objective function | |
20 | 1.25E + 07 | 0.3 | 1.31E + 07 | 0.1 | 1.31E + 07 | ||
40 | 1.33E + 07 | 0.4 | 1.22E + 07 | 0.2 | 1.29E + 07 | ||
60 | 1.29E + 07 | 0.5 | 1.37E + 07 | 0.3 | 1.36E + 07 | ||
80 | 1.37E + 07 | 0.6 | 1.34E + 07 | 0.4 | 1.37E + 07 | ||
100 | 1.35E + 07 | 0.7 | 1.24E + 07 | 0.5 | 1.35E + 07 |
Level year (50% probability) | DADP | Objective function | |||||
1.86E + 07 | |||||||
RGA | Population size | Objective function | Crossover pm | Objective function | Mutation pe | Objective function | |
20 | 1.68E + 07 | 0.3 | 1.57E + 07 | 0.1 | 1.66E + 07 | ||
40 | 1.71E + 07 | 0.4 | 1.63E + 07 | 0.2 | 1.82E + 07 | ||
60 | 1.55E + 07 | 0.5 | 1.68E + 07 | 0.3 | 1.69E + 07 | ||
80 | 1.63E + 07 | 0.6 | 1.82E + 07 | 0.4 | 1.74E + 07 | ||
100 | 1.82E + 07 | 0.7 | 1.76E + 07 | 0.5 | 1.80E + 07 | ||
Dry year (75% probability) | DADP | Objective function | |||||
1.38E + 07 | |||||||
RGA | Population size | Objective function | Crossover pm | Objective function | Mutation pe | Objective function | |
20 | 1.25E + 07 | 0.3 | 1.31E + 07 | 0.1 | 1.31E + 07 | ||
40 | 1.33E + 07 | 0.4 | 1.22E + 07 | 0.2 | 1.29E + 07 | ||
60 | 1.29E + 07 | 0.5 | 1.37E + 07 | 0.3 | 1.36E + 07 | ||
80 | 1.37E + 07 | 0.6 | 1.34E + 07 | 0.4 | 1.37E + 07 | ||
100 | 1.35E + 07 | 0.7 | 1.24E + 07 | 0.5 | 1.35E + 07 |
For the RGA, in a level year (50% probability), the optimal value of the objective function is (1.82E + 07) RMB, when the population size is 100, the crossover rate pm is 0.6, and the variation rate pe is 0.2; In a dry year (75% probability), the optimal value of the objective function is (1.37E + 07) RMB. At this time, the population size is 80, the crossover rate pm is 0.5, and the variation rate pe is 0.4. Although the objective function values of the above two algorithms are close, the DADP proposed in this study is still slightly better than RGA. At the same time, DADP does not need calibration parameters in the solution process, while RGA has three parameters that need sensitivity analysis. The essence of the DADP algorithm is to decompose the high-dimensional DP model into multiple one-dimensional DP models. The solution results are not affected by additional parameters and have better algorithm operability.
According to the parameters specified in Table 8, DADP and RGA were run 10 times to verify the stability of each algorithm. As shown in Table 9, the objective function value obtained by DADP is the best in the 10 times of operation results. Compared with the best solution, the worst solution, the average and the standard deviation, DADP is still better than RGA. Therefore, the above results show that the proposed DADP has better algorithm stability.
Results of ten runs of DADP and RGA
Run . | Level year (50% probability) . | Dry year (75% probability) . | ||
---|---|---|---|---|
DADP . | RGA . | DADP . | RGA . | |
1 | 1.86E + 07 | 1.66E + 07 | 1.38E + 07 | 1.31E + 07 |
2 | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.22E + 07 |
3 | 1.86E + 07 | 1.69E + 07 | 1.38E + 07 | 1.37E + 07 |
4 | 1.86E + 07 | 1.74E + 07 | 1.38E + 07 | 1.34E + 07 |
5 | 1.86E + 07 | 1.80E + 07 | 1.38E + 07 | 1.24E + 07 |
6 | 1.86E + 07 | 1.68E + 07 | 1.38E + 07 | 1.31E + 07 |
7 | 1.86E + 07 | 1.71E + 07 | 1.38E + 07 | 1.29E + 07 |
8 | 1.86E + 07 | 1.55E + 07 | 1.38E + 07 | 1.36E + 07 |
9 | 1.86E + 07 | 1.63E + 07 | 1.38E + 07 | 1.37E + 07 |
10 | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.35E + 07 |
Best | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.37E + 07 |
Worst | 1.86E + 07 | 1.55E + 07 | 1.38E + 07 | 1.22E + 07 |
Average | 1.86E + 07 | 1.71E + 07 | 1.38E + 07 | 1.32E + 07 |
Standard deviation | 0 | 8.31E + 05 | 0 | 5.04E + 05 |
Run . | Level year (50% probability) . | Dry year (75% probability) . | ||
---|---|---|---|---|
DADP . | RGA . | DADP . | RGA . | |
1 | 1.86E + 07 | 1.66E + 07 | 1.38E + 07 | 1.31E + 07 |
2 | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.22E + 07 |
3 | 1.86E + 07 | 1.69E + 07 | 1.38E + 07 | 1.37E + 07 |
4 | 1.86E + 07 | 1.74E + 07 | 1.38E + 07 | 1.34E + 07 |
5 | 1.86E + 07 | 1.80E + 07 | 1.38E + 07 | 1.24E + 07 |
6 | 1.86E + 07 | 1.68E + 07 | 1.38E + 07 | 1.31E + 07 |
7 | 1.86E + 07 | 1.71E + 07 | 1.38E + 07 | 1.29E + 07 |
8 | 1.86E + 07 | 1.55E + 07 | 1.38E + 07 | 1.36E + 07 |
9 | 1.86E + 07 | 1.63E + 07 | 1.38E + 07 | 1.37E + 07 |
10 | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.35E + 07 |
Best | 1.86E + 07 | 1.82E + 07 | 1.38E + 07 | 1.37E + 07 |
Worst | 1.86E + 07 | 1.55E + 07 | 1.38E + 07 | 1.22E + 07 |
Average | 1.86E + 07 | 1.71E + 07 | 1.38E + 07 | 1.32E + 07 |
Standard deviation | 0 | 8.31E + 05 | 0 | 5.04E + 05 |
(a) is the convergence trend of the algorithm; (b) is the solution time of the algorithm.
(a) is the convergence trend of the algorithm; (b) is the solution time of the algorithm.
In general, compared with RGA, DADP has outstanding performance in optimization of the objective function, algorithm stability, algorithm convergence and algorithm solving time, and has better algorithm optimization.
Algorithm applicability
The applicability of DADP and RGA is compared and analyzed. This study considers the scheduling process and results of the irrigation system. For the water source project, the most common dispatching method is the standard operation policy (SOP) (Faber & Stedinger 2001; Ngo et al. 2007). Therefore, in order to analyze the dispatching effect of the optimization algorithm, the dispatching process and results of SOP, DADP and RGA are comprehensively compared and analyzed.
(a) Reservoir water supply process under 50% probability; (b) reservoir water supply process under 75% probability.
(a) Reservoir water supply process under 50% probability; (b) reservoir water supply process under 75% probability.
It can be seen from Table 10 that in a level year (50% probability), the total output value of the irrigation area obtained by DADP and RGA is 8.4% and 5.8% higher than that of SOP respectively; In a dry year (75% probability), it increased by 4.5% and 3.8% respectively. In terms of irrigation water volume, compared with SOP and RGA, DADP increases the water supply to 0.15 MCM and 0.3 MCM respectively in a level year (50% probability) and 0.22 MCM and 0.43 MCM, respectively, in a dry year (75% probability). The operation results of the above irrigation system show that the scheduling results of the irrigation system can be optimized using DADP and RGA. In addition, compared with RGA, DADP can also increase the total water supply of the irrigation system, reduce water shortage, effectively improve the utilization rate of water resources in the water shortage irrigation area, and alleviate the water conflict in the irrigation area on the basis of improving the output value of the irrigation area.
Irrigation system operation results (MCM)
Method . | Probability . | Supply . | Replenishment . | Spill . | Evaporation . | Shortage . | Total value (107 RMB) . |
---|---|---|---|---|---|---|---|
SOP | 50% | 767 | 600 | 0 | 161 | 585 | 1.72 |
75% | 623 | 600 | 0 | 166 | 991 | 1.32 | |
DADP | 50% | 782 | 600 | 0 | 146 | 570 | 1.86 |
75% | 645 | 600 | 0 | 144 | 969 | 1.38 | |
RGA | 50% | 752 | 600 | 0 | 146 | 600 | 1.82 |
75% | 602 | 600 | 0 | 143 | 1,012 | 1.37 |
Method . | Probability . | Supply . | Replenishment . | Spill . | Evaporation . | Shortage . | Total value (107 RMB) . |
---|---|---|---|---|---|---|---|
SOP | 50% | 767 | 600 | 0 | 161 | 585 | 1.72 |
75% | 623 | 600 | 0 | 166 | 991 | 1.32 | |
DADP | 50% | 782 | 600 | 0 | 146 | 570 | 1.86 |
75% | 645 | 600 | 0 | 144 | 969 | 1.38 | |
RGA | 50% | 752 | 600 | 0 | 146 | 600 | 1.82 |
75% | 602 | 600 | 0 | 143 | 1,012 | 1.37 |
In general, the analysis of the scheduling process and results of the irrigation system show that DADP has better algorithm applicability than RGA, and is more suitable for planning and solving the optimal allocation of water resources in such a joint scheduling model.
CONCLUSION
On the basis of considering regional water rights restrictions, this study establishes a water resources optimal operation model for joint irrigation of reservoirs and pumping stations. The model is solved using the DADP method. Aiming at the more difficult judgment constraints such as the operation criteria, it is coupled with the recursive process of DP to simultaneously solve the optimal water supply, water spill process of the irrigation system and the optimal water replenishment process of the pumping station, and formulate an effective joint operation strategy of reservoir and pumping station. The analysis results of the optimization and applicability of the algorithm show that the optimization model and solution method established in this paper can not only realize the optimal allocation of water resources in complex irrigation systems, but also improve the agricultural output value of irrigation areas, and provide a theoretical basis for the formulation of similar irrigation system operation schemes, while ensuring the sustainable development of a regional economy. In addition, the insufficient irrigation model and the solution method of large systems established in this paper have certain reference significance for future research on the optimal operation of the ‘Reservoir (group) and Pumping station (group)’ joint irrigation with more complex topology.
ACKNOWLEDGEMENTS
This work was supported by the National Natural Science Foundation of China (NSFC) [grant number 52079119].
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.