A water resource allocation method based on multi-objective spiral grey wolf algorithm

Abstract

The application discloses a water resource allocation method based on a multi-target spiral grey wolf algorithm, and comprises the following steps: firstly, obtaining basic data of a water resource system; secondly, establishing a water resource optimal scheduling model; thirdly, improving a nonlinear convergence factor, a position updating weight coefficient and multiple position updating formulas based on the multi-target spiral grey wolf algorithm to obtain the multi-target spiral grey wolf algorithm; and finally, solving an optimal allocation scheme of the allocation model by using the multi-target spiral grey wolf algorithm. The application realizes global optimization, improves the calculation efficiency and meets the requirement of selecting a multi-target optimal scheduling scheme of the water resource system.

Description

Technical Field

[0001] This invention relates to the field of water resource allocation, and in particular to a water resource allocation method based on a multi-objective spiral gray wolf algorithm. Background Technology

[0002] Multi-objective optimization algorithms are frequently used in water resource allocation projects for the following reasons: 1. Multiple objective requirements: Water resource allocation problems typically involve multiple decision objectives, such as maximizing water resource utilization efficiency, minimizing costs, and minimizing environmental impact. These objectives are often contradictory, thus requiring multi-objective optimization to find trade-off solutions, forming Pareto fronts and providing decision-makers with multiple feasible solutions; 2. Complexity and uncertainty: Water resource allocation involves multiple factors, including hydrological and meteorological conditions, water demand, and water quality requirements, and these factors are often subject to uncertainty. Multi-objective optimization algorithms can help decision-makers find robust solutions in such complex and uncertain environments; 3. Decision-maker preferences: One characteristic of multi-objective optimization algorithms is their ability to generate Pareto fronts, from which decision-makers can choose the solution that best suits their preferences. This approach encourages decision-maker participation and subjective judgment, making decisions more aligned with actual needs; 4. Improved system performance: Through multi-objective optimization algorithms, equilibrium solutions can be found at different trade-off points, thereby improving the performance of the entire water resource system. For example, considering multiple objectives such as economic benefits, environmental sustainability, and social equity simultaneously helps to formulate more comprehensive water resource management solutions; 5. Sustainable Development: Multi-objective optimization algorithms help achieve sustainable water resource development. By balancing multiple objectives such as economic, social, and environmental goals, current needs can be better met while protecting future water resource supplies.

[0003] In general, the application of multi-objective optimization algorithms in water resource allocation engineering helps improve the overall benefits of the scheme, reduce decision-making uncertainty, increase decision-making flexibility, and promote sustainable development. Currently, most multi-objective water resource allocation research adopts traditional intelligent algorithms based on non-dominated sorting, such as NSGA-II and MOEA-D. However, most traditional intelligent algorithms are prone to getting trapped in local optima, meaning they cannot accurately approximate the true Pareto front, and their search regions are relatively small, which means they cannot achieve the goal of global optimization. Therefore, based on existing research on multi-objective water resource allocation, it is essential to seek an effective and reliable multi-objective algorithm. Summary of the Invention

[0004] Purpose of the invention: This invention aims to provide a water resource optimization allocation method based on the multi-objective spiral gray wolf algorithm, which has good global search capabilities and convergence.

[0005] Technical solution: The water resource allocation method based on the multi-objective spiral gray wolf algorithm described in this invention includes the following steps:

[0006] (1) Obtain basic data on the water resources system;

[0007] (2) Establish a multi-objective optimization scheduling mathematical model that takes into account the objective function of maximizing the comprehensive social, economic and ecological benefits, and takes into account the constraints of water balance, unit output and flow capacity.

[0008] (3) Improve the multi-objective gray wolf algorithm by introducing a nonlinear convergence factor. Add adaptive hunting dynamic weight coefficients to determine , , The position update formula of the wolf pack led by the wolf is used to obtain the multi-objective spiral gray wolf algorithm;

[0009] (4) The multi-objective spiral gray wolf algorithm is used to solve the optimization scheme of water resource scheduling and configuration model under different water conservancy year scenarios.

[0010] Furthermore, in step (2), the multi-objective optimization scheduling mathematical model is as follows:

[0011]

[0012]

[0013] In the formula, n represents the number of objectives for the optimal scheduling of the water resources system, n = 1, 2, ..., N, where N represents the total number of objectives; F(x) is the set of objective functions; f(x) represents the objective function that maximizes the comprehensive social, economic and ecological benefits. Indicates the time interval for calculation; , Reservoirs The inflow and outflow of water from reservoirs, pumping stations, and sluice gates during the time period, in m³ / s; , These represent the water storage capacity of the reservoir, pumping station, and sluice gate at the end of time period t and time period t+1, respectively, in m³. express Loss amount during the time period, in m³; This represents the water level at the end of time period t, in meters (m). , These represent the minimum and maximum water levels allowed at the end of time period t, respectively. express The power generation flow rate during the time period, expressed in m³ / s; , These represent the minimum and maximum allowable discharge flow rates at the end of time period t, respectively, in m³ / s. Reservoir The power output of the hydropower station during the specified time period, expressed in kW. , Z represents the minimum and maximum power output allowed at the end of time period t of the hydropower station, in kW; Z and Z′ represent the initial and final water level limits of the reservoir, in meters.

[0014] Furthermore, in step (3), the nonlinear convergence factor for

[0015]

[0016] In the formula, ρ is the current iteration number. This represents the maximum number of iterations.

[0017] Furthermore, in step (3), the adaptive hunting dynamic weight coefficients are as follows:

[0018]

[0019]

[0020]

[0021] In the formula, This represents the position of the ordinary wolf ω after one iteration. , , It represents three ordinary wolves. In wolves , , The location to be updated under the guidance of M i These represent the inertia weight coefficients adopted by ordinary wolf packs. , They represent wolves , , The inertia weighting coefficient; wolf Current location; wolf Current location; wolf Current location.

[0022] Furthermore, regarding The updated positions of the wolf pack led by the wolf are as follows:

[0023]

[0024] In the formula, express The wolf's current location Represents ordinary wolf To the wolf The distance to run This represents the corresponding coefficient vector. Indicates control parameters, The mean is variance is The Gaussian random function.

[0025] Furthermore, control parameters for

[0026]

[0027] In the formula, This indicates that the logarithmic sigmoid transfer function in a neural network varies in value between [0,1]. This represents a random vector obtained within the interval [0,1].

[0028] Furthermore, regarding The updated positions of the wolf pack led by the wolf are as follows:

[0029]

[0030] In the formula, express The wolf's current location Represents ordinary wolf arrive The distance a wolf needs to run. This represents the corresponding coefficient vector. This represents a random parameter between [0,1].

[0031] Furthermore, regarding The updated positions of the wolf pack led by the wolf are as follows:

[0032]

[0033] In the formula, express The wolf's current location This represents the corresponding coefficient vector. , Represents ordinary wolf arrive , The distance a wolf (or its prey) needs to run.

[0034] Furthermore, the spiral update function for

[0035]

[0036] In the formula, This represents the spiral update function; The parameter is a spiral update parameter whose value varies between [-1, 1] depending on the number of iterations. This represents the logarithmic spiral shape constant.

[0037] Furthermore, in step (1), the basic data includes at least one of the following: pump, gate station and reservoir flow capacity values, initial and final storage capacity limits of lakes and reservoirs, normal water storage level of lakes and reservoirs, flood control limit water level, dead water level, reservoir capacity-water level relationship curve, downstream water level-discharge flow relationship curve of reservoir, inflow, irrigation area water demand and reservoir generator output constraint value.

[0038] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: 1. This invention uses a nonlinear convergence factor, which helps to expand the search range, improve global search capability, and strengthen convergence capability; 2. This invention incorporates adaptive hunting dynamic weight coefficients. , , 3. This invention solves the problem that existing multi-objective algorithms used for water resource allocation have small search areas and are prone to getting trapped in local optima. It introduces a spiral search method and dynamic hunting weight coefficient into the multi-objective gray wolf algorithm (MOGWO). The spiral search method expands the search area of ​​the multi-objective algorithm. Based on the original multi-objective gray wolf algorithm's Pareto curve, the upper left and lower right parts of the curve are extended. This means that decision-makers can choose better preferred solutions. The dynamic hunting weight coefficient effectively avoids local optima in the algorithm. This means that the solutions provided by the Pareto curve are more accurate. All of these contribute to the realization of multi-objective optimal scheduling of reservoirs. Attached Figure Description

[0039] Figure 1 This is a flowchart of the present invention;

[0040] Figure 2 This is a comparison chart of the nonlinear convergence factor in this invention and the convergence factor in the traditional multi-objective gray wolf algorithm;

[0041] Figure 3 spiral function Follow A graph of the changing function;

[0042] Figure 4 The spiral hunting graph is for the spiral gray wolf algorithm;

[0043] Figure 5 The bounding circle diagram is narrowed down from the original Grey Wolf algorithm;

[0044] Figure 6 The graph shows the performance of the multi-objective spiral gray wolf algorithm (AMOGWO) on the ZDT1 test function;

[0045] Figure 7 The graph shows the performance of the traditional multi-objective gray wolf algorithm (MOGWO) on the ZDT1 test function;

[0046] Figure 8 The graph shows the performance of the Multi-Objective Tubular Swarm Algorithm (MSSA) on the ZDT1 test function;

[0047] Figure 9 The graph shows the performance of the multi-objective spiral gray wolf algorithm (AMOGWO) on the ZDT2 test function;

[0048] Figure 10 The graph shows the performance of the traditional multi-objective gray wolf algorithm (MOGWO) on the ZDT2 test function;

[0049] Figure 11 The graph shows the performance of the Multi-Objective Tubular Swarm Algorithm (MSSA) on the ZDT2 test function;

[0050] Figure 12 The graph shows the performance of the multi-objective spiral gray wolf algorithm (AMOGWO) on the ZDT3 test function;

[0051] Figure 13 The graph shows the performance of the traditional multi-objective gray wolf algorithm (MOGWO) on the ZDT3 test function;

[0052] Figure 14 The graph shows the performance of the Multi-Objective Tubular Swarm Algorithm (MSSA) on the ZDT3 test function;

[0053] Figure 15 The graph shows the performance of the multi-objective spiral gray wolf algorithm (AMOGWO) on the ZDT6 test function;

[0054] Figure 16 The graph shows the performance of the traditional multi-objective gray wolf algorithm (MOGWO) on the ZDT6 test function;

[0055] Figure 17 The graph shows the performance of the Multi-Objective Tubular Swarm Algorithm (MSSA) on the ZDT6 test function;

[0056] Figure 18 Pareto curves obtained for the improved multi-objective gray wolf algorithm (AMOGWO). Detailed Implementation

[0057] The invention will now be further described with reference to the accompanying drawings.

[0058] The water resource allocation method based on the multi-objective spiral gray wolf algorithm described in this invention mainly includes the following four steps:

[0059] Step 1: Obtain basic data of the water resource system, including: the flow capacity q of pumps, sluice gates, and reservoirs; the initial and final storage capacity limits V of lakes and reservoirs; and the normal water level Z of lakes and reservoirs. 正 Flood control limit water level Z 防 Dead water level Z 死 The reservoir capacity-water level relationship curve S~Z, the downstream water level-discharge flow relationship curve Z~Q, the inflow W, the irrigation area water demand Y, and if the reservoir has power generation function, the power output constraint value E of the reservoir generator set also needs to be considered.

[0060] Step 2: Establish an objective function that maximizes the comprehensive benefits of society, economy and ecology, and a multi-objective optimization scheduling mathematical model that takes into account constraints such as water balance, unit output and flow capacity. This invention provides a relatively universal objective function and constraints in water resource systems. The objective function is shown in Equation (1), and the constraints are shown in Equation (2).

[0061]

[0062]

[0063] In equations (1) and (2), n represents the number of objectives for the optimal scheduling of the water resources system, n = 1, 2, ..., N; F(x) is the set of objective functions; f(x) represents the objective function that maximizes the comprehensive benefits considering social, economic and ecological factors. —Indicates the calculation period interval; , —Indicates a reservoir The inflow and outflow of units such as reservoirs, pumping stations, and sluices during the time period are expressed in m³ / s; , — This indicates the water storage capacity at the end of time period t and time period t+1 for units such as reservoirs, pumping stations, and sluices, in m³. -express The unit of loss during the period is m³. — indicates the reservoir water level at the end of time period t, in meters; , —Indicates the minimum and maximum water levels allowed at the end of time period t; -express The power generation flow rate during the time period, expressed in m³ / s; , —Indicates the minimum and maximum allowable discharge flow rates at the end of time period t, in m³ / s; —Indicates a reservoir The power output of the hydropower station during the specified time period, expressed in kW. , — represents the minimum and maximum power output allowed at the end of time period t of the hydropower station, in kW; Z, Z′ — represent the possible initial and final water level limits of the reservoir, in meters.

[0064] Steps 3 and 4: Improve and implement the multi-objective spiral gray wolf algorithm, mainly including the following steps:

[0065] (1) Determine the water resource scheduling cycle period T by taking the water storage volume (final water level) S at the end of the water resource project period, the discharge flow u or the project flow q and the pumping volume Q as decision variables; and establish an objective function that maximizes the comprehensive benefits of society, economy and ecology.

[0066] (2) Running the multi-objective spiral gray wolf algorithm: The preceding content of this section has described the data, constraints, and objective function required for the water resource optimization allocation problem. Based on the basic research on water resource optimization allocation, the multi-objective spiral gray wolf algorithm is used to solve the water resource optimization allocation model under various constraints.

[0067] The Multi-Objective Grey Wolf Optimization (MOGWO) algorithm is a novel metaheuristic optimization algorithm developed by Mirjalili et al. at Griffith University, Australia. Inspired by nature, MOGWO mimics the leadership hierarchy and hunting mechanisms of grey wolves. It involves four types of grey wolves to simulate the leadership hierarchy, namely a three-alpha wolf. , , Compared to ordinary wolves Furthermore, it realizes the three main steps of hunting: surrounding the prey, chasing the prey, and attacking the prey. Its mathematical model is shown in formulas (3) and (4):

[0068]

[0069]

[0070] In equation (3) and equation (4), Indicates the number of iterations. Let represent the position vector of the prey. In MOGWO, we consider the position vectors of the three alpha wolves to be the position vectors of the prey, which is reflected in equation (7). This represents the position vector of the gray wolf. express The number of iterations represents the position vector of the gray wolf. and Let be the coefficient vector, defined as shown in formulas (5) and (6):

[0071]

[0072]

[0073] In equations (5) and (6), and For the coefficient vector, and It is a variable randomly selected within the interval [0,1]. The convergence factor decreases linearly from 2 to 0 as the number of iterations increases.

[0074] In the MOGWO algorithm, there are three alpha wolves. , , The wolf pack, led by the wolf, approaches the prey from different directions, forming an encirclement to trap the prey and achieve the goal of hunting. This encirclement behavior is shown in formulas (7), (8), and (9):

[0075]

[0076]

[0077]

[0078] In equations (7), (8), and (9), , , Representatives respectively , , Leading ordinary wolves arrive , , (That is, the distance the prey) needs to run; and , , and express , , and The wolf's current location; , , and , , The coefficient vector represents the corresponding position of a three-headed wolf pack. , , It represents three ordinary wolves. exist , , Under guidance, the location is updated; This indicates that after the iterative process of equations (7) and (8), the position of all ordinary wolves in the wolf pack is updated in equation (9), which serves as the last updated position of all ordinary wolves in one iteration.

[0079] Based on this, an improvement has been made to the traditional MOGWO algorithm. This invention proposes a multi-objective spiral gray wolf algorithm (AMOGWO). In the traditional MOGWO, the convergence factor decreases linearly from 2 to 0 with the increase of the number of iterations. Inspired by the complex behavior of gray wolves hunting prey in the real world, a new nonlinearly varying convergence factor is proposed. As shown in formula (10), this improvement helps to expand the search range of the algorithm and enhance its convergence ability.

[0080]

[0081] In equation (10), Let ρ be the new convergence factor, and ρ be the current iteration number. This is a constant, an algorithm parameter that represents the maximum number of iterations the algorithm can achieve during the optimization process.

[0082] In traditional MOGWO The wolf's position update formula, i.e., equation (7), is derived from the received... , , The three ordinary wolves that led the way The leadership of the three alpha wolves is determined by the average value of the alpha group, meaning they have equal leadership weight. This does not conform to the real-world hierarchy of wolf packs. To mimic the real-world hierarchy, the leadership of the wolf alpha is strengthened. To assess the alpha position of wolves, an adaptive dynamic hunting weight coefficient is proposed, as shown in formulas (11), (12), and (13).

[0083]

[0084]

[0085]

[0086] In formula (11) They represent , , Their respective inertia weight coefficients, in equation (13) M1 represents the last updated position of the ordinary wolf in one iteration, while M2 and M3 represent the inertia weight coefficients adopted by the ordinary wolf pack. The calculation method is given by equation (12).

[0087] In traditional MOGWO , , That is, three ordinary wolves exist , , The formulas for position updates under the leadership are all given by equation (8), which is inconsistent with the phenomenon of specific division of labor when wolves search for prey in the real world. In the wolf pack hierarchy mechanism When hunting, a wolf pack typically scouts the perimeter of its prey for other large predators and patrols the area to prevent the prey from escaping. The formula for updating the position of a wolf pack led by a wolf is... An improvement is proposed: its new position update formula is given by equation (14).

[0088]

[0089] In equation (14) express The wolf's current location This represents the corresponding coefficient vector. Represents ordinary wolf arrive The distance a wolf (or its prey) needs to run. The expression for the control parameter is given by equation (15). The mean is variance is The Gaussian random function.

[0090]

[0091] In formula (15) The logarithmic sigmoid transfer function in a neural network has a value that varies between [0,1]. It is a variable randomly selected within the interval [0,1]. This represents the current iteration number. This is a constant, an algorithm parameter that represents the maximum number of iterations that the algorithm can achieve during the optimization process.

[0092] In the real world, wolf packs employ diverse hunting methods, adapting to the size of their prey. When hunting small animals, they gradually encircle the prey, forming a square shape as shown in equation (8). When hunting large animals, they often use a spiral encirclement, surrounding the prey in a circular pattern and attacking it from within the circle until the prey is exhausted, at which point they deliver the fatal blow. Inspired by this behavior, [further details about wolf behavior are needed]. The wolf pack, led by the wolf, proposed improvements: making... A wolf pack led by wolves may employ a square-shaped, gradually shrinking encirclement, or it may use a spiral attack within a circular encirclement. The new position update formula is given by equations (16) and (17):

[0093]

[0094]

[0095] In equations (16) and (17) For spiral update function, The update parameter for the spiral changes in value between [-1, 1] depending on the number of iterations. The shape constant of the logarithmic spiral, express The wolf's current location This represents the corresponding coefficient vector. Represents ordinary wolf arrive The distance a wolf (or its prey) needs to run. The parameter is random and its value varies between [0,1].

[0096] In the real world, when a wolf pack surrounds and attacks its prey, the alpha wolf ( Wolves have absolute leadership, while When a wolf pack, led by a wolf, attacks large prey, it often obeys the alpha wolf. The wolf's command, inspired by this behavior, led to... The wolf pack, led by the wolf, proposed: A wolf pack led by a wolf may employ a square-shaped, gradually shrinking encirclement, or it may move towards the wolf alpha within a circular encirclement. Unlike the wolf pack led by the alpha wolf that spirals around its prey from the front, the wolf pack approaches and launches a spiral attack. The wolf pack, led by wolves, spirals around its prey from behind, and , The wolf pack, led by a wolf, moves in opposite directions, which helps to make the encirclement more complex and makes it difficult for the prey to escape. The new position update formula is given by equations (18) and (19).

[0097]

[0098]

[0099] In equations (18) and (19), For spiral update function, The update parameter for the spiral changes in value between [-1, 1] depending on the number of iterations. is the logarithmic spiral shape constant. express The wolf's current location This represents the corresponding coefficient vector. , Represents ordinary wolf arrive , The distance a wolf (or its prey) needs to run. The parameter is random and its value varies between [0,1].

[0100] Taking the multi-objective optimized water resource scheduling of Yuetang Reservoir in Yizheng City, Jiangsu Province as an example, this paper illustrates the effectiveness and rationality of the invented method. Yuetang Reservoir is located on the upper reaches of the Xupu River within Yuetang Town, Yizheng City, Yangzhou City, Jiangsu Province, in a hilly and mountainous area. Construction of the reservoir began in 1958; originally named Yazuiqiao Reservoir, it was completed and renamed Yuetang Reservoir in 1966. In 2005, Yuetang Reservoir was designated as a key medium-sized reservoir for national flood control, and its reinforcement project was completed in June 2009. The scheduling of Yuetang Reservoir prioritizes the safety of the reservoir project and regional flood control, while also considering downstream flood control, urban domestic water supply, industrial and agricultural water supply, and aquaculture. Water storage and supply scheduling are subordinate to flood control and emergency scheduling. Under the premise of ensuring dam safety, the relationship between flood control and flood resource utilization is coordinated to fully utilize the reservoir's flood control and water storage functions and comprehensive social benefits. Yuetang Reservoir primarily functions as a water pumping station. It contains four electric pumping stations with six sets of generating units, totaling 570 kW in capacity and a pumping flow rate of 2.5 m³ / s. 3 The water supply is 1,000 cubic meters per second, irrigating an area of ​​27,000 mu (approximately 1,800 hectares), with a gravity-fed irrigation area of ​​5,000 mu (approximately 333 hectares), resulting in an actual irrigated area of ​​32,000 mu (approximately 2,800 hectares). The Yuetang Reservoir is geographically very important, 2 223,000 people, 2,000 hectares 2 Farmland. This invention generalizes the Yuetang Reservoir and its surrounding replenishment pumping stations and lifting pumping stations into a one-reservoir-two-station system.

[0101] This invention uses the water replenishment volume of the reservoir replenishment pumping station and the water lifting volume of the pumping station as decision variables, and employs the AMOGWO algorithm for optimal scheduling to achieve the two main objectives of minimizing the sum of squares of water shortage and minimizing the sum of squares of water lifting volume. This establishes an objective function that maximizes both social and economic benefits. The spatial distribution of the scheduling scheme set is as follows: Figure 18 As shown: by Figure 18 As can be seen, the scheduling schemes are widely and evenly distributed. The two objectives—minimizing the sum of squares of water extraction and minimizing the sum of squares of water shortage—are mutually restrictive and conflicting, exhibiting a clear inverse relationship. Therefore, the water resource scheduling scheme set solved by AMOGWO is reasonable and effective. Furthermore, AMOGWO has a large and evenly distributed distribution in the upper left, lower right, and middle regions of the Pareto solution set graph, which are of interest to decision-makers. This ensures that AMOGWO can provide good feasible solutions regardless of the decision-maker's preferences, thus achieving the invention's objective of overcoming the limitations of small search areas and local optima. Table 1 shows a solution selected from the upper left portion of the Pareto curve (preferring minimum water shortage) to demonstrate AMOGWO's good global search capability.

[0102] Table 1. Results of Optimal Allocation of Water Resources in Normal Years (Unit: 10,000 m³)

[0103] 10 72.00 304.42 0.00 0 49.29 49.6 0.00 0 11 304.42 473.37 0.00 0 48.00 48 0.00 0 12 473.37 522.41 0.00 0 49.60 49.6 0.00 0 1 522.41 600.58 0.00 0 48.79 49.6 0.00 0 2 600.58 690.87 0.00 0 43.84 44.8 0.00 0 3 690.87 795.68 0.00 0 48.34 49.6 0.00 0 4 795.68 924.30 0.00 0 47.63 48 0.00 0 5 924.30 873.98 6.90 6.9 93.1 93.1 0.00 49.6 0.00 0 6 on 873.98 813.87 4.50 4.5 61.2 61.2 0.00 16 0.00 0 6 813.87 661.78 13.50 13.5 183.5 183.5 0.00 16 0.00 0 6th 661.78 549.57 13.50 13.5 183.5 183.5 15.76 16 0.00 0 7 on 549.57 398.87 15.80 15.8 212.91 214.1 15.92 16 -1.15 0 7 398.87 684.94 0.00 0 0 0 16.00 16 0.00 0 7th 684.94 785.12 0.00 0 0 0 17.60 17.6 0.00 0 8 785.12 603.42 17.86 18.1 244.6 244.6 0.00 16 -0.24 0 8 603.42 479.39 18.10 18.1 244.14 244.6 16.00 16 -0.46 0 8th 479.39 605.31 0.00 0 0 0 17.60 17.6 0.00 0 9 on 605.31 383.34 18.10 18.1 244.6 244.6 15.51 16 0.00 0 9 383.34 336.81 8.94 9 122.3 122.3 15.77 16 -0.11 0 9th 336.81 181.91 13.46 13.5 183.5 183.5 15.85 16 0.00 0

[0104] Table 1 shows that AMOGWO has strong global search capabilities. When the decision-maker's preference is to minimize water shortage, AMOGWO can provide a high-quality feasible solution. Figure 18 It can be seen that if the decision-maker prefers to minimize water extraction, AMOGWO can provide diverse and excellent feasible solutions when the decision-maker requires minimizing water extraction, because of its excellent convergence and resistance to getting trapped in local optima. If the decision-maker prefers a compromise solution, the excellent distribution of AMOGWO's solution set can also provide a compromise solution for the decision-maker.

Claims

1. A water resource allocation method based on a multi-objective spiral gray wolf algorithm, characterized in that, Includes the following steps: (1) Obtain basic data on the water resources system; (2) Establish a multi-objective optimization scheduling mathematical model that takes into account the objective function of maximizing social, economic and ecological comprehensive benefits and the constraints of water balance, unit output and flow capacity; (3) Improve the multi-objective gray wolf algorithm by introducing a nonlinear convergence factor. Add adaptive hunting dynamic weight coefficients to determine , , The position update formula of the wolf pack led by the wolf is used to obtain the multi-objective spiral gray wolf algorithm; (4) The multi-objective spiral gray wolf algorithm is used to solve the optimization scheme of water resource scheduling and allocation model under different water conservancy year scenarios; right Updated position of the wolf pack led by the wolf as follows: In the formula, express The wolf's current location Represents ordinary wolf To the wolf The distance to run This represents the corresponding coefficient vector. Indicates control parameters, The mean is variance is Gaussian random function; right Updated position of the wolf pack led by the wolf as follows: In the formula, express The wolf's current location Represents ordinary wolf arrive The distance a wolf needs to run. This represents the corresponding coefficient vector. This represents a random parameter between [0,1]. For spiral update function; right Updated position of the wolf pack led by the wolf as follows: In the formula, express The wolf's current location This represents the corresponding coefficient vector. , Represents ordinary wolf arrive , The distance a wolf needs to run.

2. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to claim 1, characterized in that, In step (2), the multi-objective optimization scheduling mathematical model is as follows: In the formula, n represents the number of objectives for the optimal scheduling of the water resources system, n = 1, 2, ..., N, where N represents the total number of objectives; F(x) is the set of objective functions; f(x) represents the objective function that maximizes the comprehensive social, economic and ecological benefits. Indicates the time interval for calculation; , Reservoirs The inflow and outflow of water from reservoirs, pumping stations, and sluice gates during the time period, in m³ / s; , These represent the water storage capacity of the reservoir, pumping station, and sluice gate at the end of time period t and time period t+1, respectively, in m³. express Loss amount during the time period, in m³; This represents the water level at the end of time period t, in meters (m). , These represent the minimum and maximum water levels allowed at the end of time period t, respectively. express The power generation flow rate during the time period, expressed in m³ / s; , These represent the minimum and maximum allowable discharge flow rates at the end of time period t, respectively, in m³ / s. Reservoir The power output of the hydropower station during the specified time period, expressed in kW. , This represents the minimum and maximum power output allowed at the end of time period t at a hydropower station, in kW. Z and Z′ represent the initial and final water level limits of the reservoir, in meters (m).

3. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to claim 2, characterized in that, In step (3), the nonlinear convergence factor for In the formula, ρ is the current iteration number. This represents the maximum number of iterations.

4. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to claim 3, characterized in that, In step (3), the adaptive hunting dynamic weight coefficients are as follows: In the formula, For ordinary wolves The position updated after one iteration; , , It represents three ordinary wolves. In wolves , , The location to be updated under the guidance of M i This represents the inertia weighting coefficient adopted by ordinary wolf packs. , They represent wolves , , The inertia weighting coefficient; wolf Current location; wolf Current location; wolf Current location.

5. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to claim 3, characterized in that, Control parameters for In the formula, This indicates that the logarithmic sigmoid transfer function in a neural network varies in value between [0,1]. This represents a random vector obtained within the interval [0,1].

6. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to claim 1, characterized in that, Spiral update function for In the formula, This represents the spiral update function; The parameter is a spiral update parameter whose value varies between [-1, 1] depending on the number of iterations. This represents the logarithmic spiral shape constant.

7. The water resource allocation method based on the multi-objective spiral gray wolf algorithm according to any one of claims 1-6, characterized in that, In step (1), the basic data includes at least one of the following: pump, gate station and reservoir flow capacity values, initial and final storage capacity limits of lakes and reservoirs, normal water storage level of lakes and reservoirs, flood control limit water level, dead water level, reservoir capacity-water level relationship curve, downstream water level-discharge flow relationship curve of reservoir, inflow, irrigation area water demand and reservoir generator output constraint value.

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