A multi-objective optimization method for water resources allocation in arid regions

Abstract

The application discloses a water resource multi-objective optimization allocation method for arid regions, and comprises the following steps: collecting basic data of a research area and dividing units; constructing a unified network topology based on nodes and links; establishing a biophysical module for arid regions; establishing a multi-agent decision module for arid regions; constructing a multi-objective optimization model; and outputting a water resource multi-objective optimization result. Through multi-level unit division, the logical relationship among basic data, main decision and optimization variables is clarified. Through the construction of a unified network topology, the expression ability of the model to the scheduling rules of the multi-boundary and multi-agent of the arid region is improved. The double control target of groundwater and the supply capacity constraint are coupled to the optimization allocation process. A recommended allocation scheme is output through a Pareto scheme screening mechanism. The problem of joint regulation of multi-constraint, multi-objective and multi-agent in a complex arid region water system is solved, and a scientific basis is provided for water resource optimization allocation.

Description

Technical Field

[0001] This invention belongs to the field of water resource simulation and optimization regulation technology, and particularly relates to a multi-objective optimization allocation method for water resources in arid areas. Background Technology

[0002] Arid regions suffer from water scarcity and uneven spatial and temporal distribution. Ecosystems are highly sensitive to water quantity changes, making water resources a key factor restricting regional socio-economic development and ecological security. In typical inland arid regions, water resources are highly unevenly distributed in time and space. The regional water cycle is influenced by mountain precipitation, snowmelt, glacial meltwater, runoff from mountain outlets, water diversion and distribution in plain irrigation areas, and groundwater extraction. Regional development involves multiple water demands, including urban living, agricultural irrigation, industrial production, and ecological protection. Furthermore, differences in allocation rules, water supply priorities, and management boundaries exist between different watersheds and administrative units, resulting in a water resource system with significant multi-level, multi-objective, and multi-constraint coupling characteristics. Existing technologies employ two main approaches: one focuses on simulating hydrological and water resource processes, calculating changes in inflow, reservoir capacity, water level, or water demand, but often fails to reflect multi-agent decision-making, supply-demand feedback, and policy intervention effects; the other focuses on static optimization, generating phased water allocation schemes, but often lacks dynamic characterization of natural processes, engineering processes, and user response behaviors.

[0003] In existing technologies, the first type of method focuses on simulating hydrological and water resource processes. Although it can calculate changes in inflow, reservoir capacity, water level, or water demand, it is usually difficult to reflect the decision-making behavior of multiple stakeholders, dynamic feedback between supply and demand, and the real-time effects of policy intervention. The second type of method focuses on static optimization allocation. Although it can form phased water allocation plans, it often lacks a detailed characterization of natural runoff fluctuations, dynamic regulation of water conservancy projects, and user response behavior. Although some studies have attempted to use modular multi-agent modeling methods to characterize the physical and decision-making network through unified nodes, links, and mechanisms, and to reduce the complexity of groundwater coupling calculations using response matrices, existing solutions still have significant shortcomings in terms of specificity and integration. Specifically, existing publicly available solutions have not yet formed a dedicated technical solution for the entire integrated scenario of "snowmelt—joint scheduling of rivers, reservoirs, and canals—water allocation in oasis irrigation areas—groundwater pressure reduction—ecological water conveyance guarantee—reclaimed water substitution utilization" in arid areas, nor have they integrated dynamic coupling simulation and multi-objective optimization solutions into a closed-loop allocation mechanism. Especially when the watershed boundary is inconsistent with the administrative boundary, the rigid constraints of the ecological section are prominent, the dual control objectives of groundwater are clear, and the joint allocation of multiple water sources is complex, existing technologies are difficult to achieve water supply security, groundwater protection, ecological protection, cost control and fair allocation at the same time.

[0004] Therefore, it is necessary to propose a multi-objective optimization allocation method for water resources in arid regions to solve the problems of multi-constraint, multi-objective, and multi-entity joint regulation in complex arid water systems. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization allocation method for water resources in arid regions to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention discloses a multi-objective optimization allocation method for water resources in arid regions, the method comprising the following steps:

[0008] Step 1: Basic Data Collection and Unit Division of the Study Area: Collect basic data for the study area, including meteorological data, hydrological data, engineering data, socio-economic data, ecological data, and management rule data; divide the study area into watershed units, administrative units, irrigation district units, groundwater units, and end-user units;

[0009] Step 2: Construct a unified network topology based on nodes and links: Define a water resource allocation network, using nodes and links as basic components based on the node-link model, and institutions as non-spatial entities that make decisions on some nodes and links, thus forming a common topology for the physical network and the decision network; at the same time, construct mapping matrices to represent the affiliation or weight relationships of watershed-administrative region, administrative region-irrigation district, irrigation district-user, groundwater-user, node-user, and institution-object respectively.

[0010] Step 3: Establish biophysical modules for arid regions: Establish biophysical modules for arid regions, including watershed runoff generation and confluence modules, groundwater modules, reservoir and storage modules, water transmission and distribution modules, wastewater treatment and reuse modules, and crop water requirements modules; and summarize the outputs of each module into a closed-loop state vector;

[0011] Step 4: Establish a multi-agent decision-making module for arid regions: Based on the Agent-Based Model, a multi-agent decision-making module for arid regions is constructed. This module abstracts watershed management agents, administrative allocation agents, irrigation district management agents, water supply agents, groundwater control agents, ecological scheduling agents, and ecological end-user agents into agents with perception, state update, decision-making, and action capabilities, namely, watershed management agent, administrative allocation agent, irrigation district management agent, water supply agent, groundwater control agent, ecological scheduling agent, and end-user agent. Each type of agent is associated with nodes, links, institutions, and objects through a corresponding mapping matrix and coupled with the closed-loop state vector output in Step 3.

[0012] Step 5: Construct a multi-objective optimization model: In each scheduling period, surface water, groundwater, reclaimed water and inter-regional water transfer are taken as decision objects, and reservoir water release, link flow and planting area adjustment are taken as auxiliary decisions. Construct a multi-objective optimization model driven by Agent-Based Model and solve it to obtain the Pareto candidate scheme set for water resource allocation.

[0013] Step 6: Output the multi-objective optimization results of water resources: For each planning period, based on the optimization configuration results of each scheduling period, output the multi-objective optimization results of water resources, including water resources evaluation indicators, recommended configuration schemes, agent decision feedback results, and multi-objective optimization Pareto fronts; each non-dominated solution in the Pareto front corresponds to a set of candidate configuration schemes, which include one or more of the following for each scheduling period: surface water allocation, groundwater allocation, reclaimed water allocation, inter-regional water transfer, reservoir release, link flow, and planting area adjustment; each set of candidate configuration schemes satisfies user water supply and demand relationship, user achievable water supply capacity, minimum water supply guarantee, groundwater control, reservoir operation, ecological cross-section, reclaimed water utilization, link water conveyance capacity, planting structure, and administrative region allocable water constraints, and corresponds to a set of comprehensive water shortage rate, groundwater over-extraction, total system cost, ecological cross-section gap, and regional water supply fairness target values; based on the planning period evaluation indicators, management preferences, and agent decision feedback results, recommended configuration schemes are selected from the Pareto fronts.

[0014] Furthermore, the meteorological data in Step 1 includes daily or monthly precipitation, temperature, evaporation, wind speed, radiation, snow cover, and glacier area changes; the hydrological data includes flow rates at mountainous water inflow control sections, river cross-sections, reservoir inflow and outflow rates, and groundwater depth and level monitoring data; the engineering data includes reservoir characteristic curves, reservoir capacity-water level relationship, canal water conveyance capacity, pump station parameters, sewage treatment plant capacity, reclaimed water utilization facility capacity, and well capacity; the socio-economic data includes population, urbanization rate, residential water consumption, industrial added value, crop planting area, irrigation system, water price, and energy cost; the ecological data includes target flow rates at ecological cross-sections, wetland water replenishment demand, minimum water levels in key ecological zones, and ecological water conveyance cycles; and the management rule data includes administrative water allocation indicators, industry priorities, minimum living allowance coefficients for residents, groundwater dual control indicators, and reclaimed water priority utilization rules.

[0015] Watershed units are divided according to watersheds, mountain water inflow control sections, and river network confluence relationships; administrative units are divided according to the boundaries of counties, cities, farms, or management areas; irrigation district units are divided according to the canal system control range, canal heads, and branch canal outlets; groundwater units are divided according to aquifer structure, groundwater management zones, monitoring well control range, groundwater pressure extraction red lines, and prohibited / restricted extraction areas; end-user units are divided according to domestic, agricultural, industrial, and ecological water use functions.

[0016] Furthermore, in step 2, nodes are defined as follows: mountain water inflow control sections, reservoirs, plain water storage units, river control nodes, irrigation canal heads, branch canal outlets, well groups, sewage treatment plants, reclaimed water utilization points, urban water supply areas, industrial parks, ecological water conveyance control sections, and groundwater management zones are represented as nodes; links are defined as follows: river water conveyance, canal water conveyance, pipeline water conveyance, inter-regional water transfer, reclaimed water reuse, and groundwater extraction and replenishment are represented as links; institutions are defined as follows: basin management institutions, administrative allocation institutions, irrigation district management institutions, water supply units, groundwater control institutions, and ecological scheduling institutions are represented as institutions; objects are defined as: objects that can be managed, scheduled, constrained, or evaluated by institutions, including basin units, administrative district units, irrigation district units, groundwater units, and end-user units, in the form of one or more of nodes and links;

[0017] The elements of the mapping matrix can be 0 or 1, or can be area ratio, population ratio, canal system control ratio, or water supply weight.

[0018] Furthermore, step 3 involves establishing the following modules: The watershed runoff generation and inflow module uses SWAT water balance relationships for watershed simulation to calculate inflow at mountainous control sections; the groundwater module simulates changes in groundwater level, depth, and exploitable groundwater capacity, while preprocessing the numerical groundwater model into a response matrix; the reservoir and storage module simulates inflow, storage, evaporation loss, leakage loss, discharge, and wastewater disposal processes in reservoirs and plain storage units; the water transmission and distribution routing module performs water conservation calculations in rivers, canals, pipe networks, inter-regional water transfer links, and reclaimed water reuse links; the wastewater treatment and reuse module calculates the amount of wastewater generated by urban users, treated effluent, and reclaimed water allocation; and the crop water requirement module calculates water requirements for domestic, industrial, agricultural, and ecological use.

[0019] Furthermore, the closed-loop state vector in step 4 Represented as:

[0020] (15)

[0021] in, For the mountainous water inflow status of watershed unit b, The reservoir or regulating unit v represents the storage capacity status. Let k represent the groundwater level status of groundwater unit k. Let k be the upper limit of exploitable groundwater unit k. For the water conveyance capacity of link l, The amount of reclaimable water from wastewater treatment plant w. For user u's water demand, This refers to the ecological water demand or ecological deficit status of ecological section e. Let represent the memory state of Agent i in the previous scheduling period.

[0022] Furthermore, the specific process of constructing a multi-objective optimization model driven by an Agent-Based Model in step 5 to obtain the Pareto candidate solution set for water resource allocation is as follows:

[0023] The set of optimized input parameters for the agent is represented as follows:

[0024]

[0025] In the formula, Input the set of Agent decision parameters for the multi-objective optimization model for the scheduling period t; Action variables generated for the i-th type of Agent; Prioritize the overall water supply for user u; The minimum water supply guarantee factor for user u; The dynamic weights of the m-th optimization objective; The allocable water supply for administrative region r; The total water demand of administrative region r; Input the groundwater exploitability constraint for user u; The available water supply capacity for user u; The state of the object perceived by the management agency's agent;

[0026] To incorporate agent behavior into the optimization model, the user's overall water supply priority Π(u,t)\Pi(u,t)Π(u,t) is converted into water shortage target weights:

[0027] (39)

[0028] In the formula, The water shortage penalty weight for user u during scheduling period t; The baseline water shortage weight for user u; This is the coefficient representing the influence of water supply priority on the weight of water shortage penalty.

[0029] The decision variable vector is represented as follows:

[0030]

[0031]

[0032] In the formula, The amount of surface water allocated from water supply node n to user u; The amount of groundwater allocated from groundwater unit k to user u; The amount of reclaimed water allocated by wastewater treatment plant w to user u; For administrative region r to administrative region Inter-regional water transfer volume; The amount of water released from the reservoir or regulating unit v; For link The inbound traffic; The planting area of ​​crop c in irrigation district a For user u, the water shortage relaxation variable; Let e ​​be the ecological gap slack variable for ecological cross section e;

[0033] The total water supply for user u during scheduling period t is expressed as:

[0034] (41)

[0035] The amount of water ultimately allocated to user u through inter-regional water transfer is represented as follows:

[0036] (42)

[0037] In the formula, The total water supply for user u; The amount of water ultimately allocated to user u through inter-regional water transfer; The comprehensive mapping coefficient between administrative region r and user u;

[0038] The objective function includes five terms: minimizing the overall water shortage rate, minimizing groundwater over-extraction, minimizing the total system cost, minimizing the ecological cross-section gap, and optimizing regional water supply equity.

[0039] The overall objective function is expressed as:

[0040]

[0041] And satisfy:

[0042]

[0043] In the formula, Let m be the objective function of the m-th item; The m-th target weight is dynamically updated for each Agent based on the operational deviation of the previous scheduling period;

[0044] The constraints include: user water supply and demand relationship constraints, user achievable water supply capacity constraints, minimum water supply guarantee constraints, groundwater control constraints, reservoir operation constraints, ecological section constraints, reclaimed water utilization constraints, water conveyance capacity constraints, planting structure constraints, and administrative region allocable water volume constraints.

[0045] Node conservation is performed according to the node conservation relationship of the water transmission and distribution routing module, and reservoir mass conservation is performed according to the reservoir and storage module's capacity update relationship; after solving the optimization model, the Pareto candidate scheme set for water resource allocation in scheduling period t is obtained:

[0046] (74)

[0047] In the formula, The optimized configuration result for scheduling time period t is given, where This represents the normalized objective function value;

[0048] After solving the multi-objective optimization model, the optimization configuration results are mapped to the corresponding nodes, links, reservoirs, groundwater units, and ecological sections. Consistency checks are performed on node water conservation, link water conveyance capacity, reservoir operating boundaries, groundwater extraction constraints, and ecological section compliance. The check results are used to update the system state and serve as historical memory input for various agents in the next scheduling period.

[0049]

[0050] In the formula, This represents the memory state of Agent i after the scheduling period t is updated. (·) is the Agent memory update function; For users' water shortage rate; This is due to groundwater over-extraction deviation; This represents an ecological gap; This is due to a bias in fairness.

[0051] Furthermore, the water resource evaluation indicators in step 6 include one or more of the following: surface water supply during the planning period, groundwater supply, reclaimed water utilization, comprehensive water shortage rate, groundwater level decline, water supply vulnerability indicators, longest continuous water shortage duration, ecological section compliance rate, total system cost, and regional water supply equity indicators.

[0052] The beneficial effects of this invention are reflected in the following aspects: First, by connecting watershed units, administrative region units, irrigation district units, groundwater units, and end-user units through multi-level unit division and mapping matrices, the logical relationships between basic data, network topology, subject decision-making, and optimization variables are clarified. Second, by simultaneously representing the physical water flow network and management decision-making network through a unified network topology of nodes, links, and institutions, the model's ability to express multi-boundary, multi-subject scheduling rules in arid regions is improved. Third, the dual control objectives of groundwater and water supply capacity constraints are coupled to the optimization allocation process. Fourth, by introducing reclaimed water substitution, minimum flow hard constraints at ecological sections, and Pareto scheme screening mechanisms, an interpretable compromise can be formed between water supply security, ecological protection, groundwater protection, and cost control. This invention solves the problem of multi-constraint, multi-objective, and multi-subject joint regulation in complex arid region water systems, providing a scientific basis for the optimal allocation of water resources.

[0053] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the method flow described in this invention;

[0055] Figure 2 A diagram illustrating a unified network topology;

[0056] Figure 3 A schematic diagram illustrating the calculation process for the multi-objective optimal allocation of water resources;

[0057] Figure 4 A schematic diagram of the Pareto front for multi-objective optimization output. Detailed Implementation

[0058] This invention discloses a multi-objective optimization allocation method for water resources in arid regions, such as... Figures 1-3 As shown, the method includes the following steps:

[0059] Step 1: Collection of basic data and division of units in the study area: Collect basic data of the study area, including meteorological data, hydrological data, engineering data, socio-economic data, ecological data, and management rule data.

[0060] The meteorological data includes daily or monthly precipitation, temperature, evaporation, wind speed, radiation, snow cover, and glacier area changes; the hydrological data includes flow rates at mountainous water control sections, river cross-sections, reservoir inflow and outflow, and groundwater depth and level monitoring data; the engineering data includes reservoir characteristic curves, reservoir capacity-water level relationship, canal water conveyance capacity, pump station parameters, sewage treatment plant capacity, reclaimed water utilization facility capacity, and well capacity; the socio-economic data includes population, urbanization rate, residential water consumption, industrial added value, crop planting area, irrigation system, water price, and energy cost; the ecological data includes target flow rates at ecological cross-sections, wetland water replenishment demand, minimum water levels in key ecological zones, and ecological water conveyance cycles; and the management rules data includes administrative water allocation indicators, industry priorities, minimum living allowance coefficients for residents, groundwater dual control indicators, and rules for priority utilization of reclaimed water.

[0061] Watershed units are divided according to watersheds, mountain inflow control sections, and river network confluence relationships; administrative units are divided according to the boundaries of counties, cities, farms, or management areas; irrigation district units are divided according to the canal system control range, canal heads, and branch canal outlets; groundwater units are divided according to aquifer structure, groundwater management zones, monitoring well control range, groundwater pressure extraction red lines, and prohibited / restricted extraction areas; end-user units are divided according to domestic, agricultural, industrial, ecological, and other water use functions.

[0062] Step 2: Construct a unified network topology based on nodes and links: Define a water resource allocation network, based on the node-link model with nodes and links as basic components, and institutions as non-spatial entities that make decisions on some nodes and links, thereby forming a common topology for the physical network and the decision network.

[0063] Node definition: Mountain water inflow control sections, reservoirs, plain water storage units, river control nodes, irrigation canal heads, branch canal outlets, well groups, sewage treatment plants, reclaimed water utilization points, urban water supply areas, industrial parks, ecological water conveyance control sections, and groundwater management zones are represented as nodes.

[0064] Link definition: Water conveyance through rivers, canals, pipelines, inter-regional water transfer, reclaimed water reuse, and groundwater extraction and replenishment are represented as links.

[0065] Institutional definition: River basin management agencies, administrative allocation agencies, irrigation district management agencies, water supply units, groundwater control agencies, and ecological dispatch agencies are referred to as institutions.

[0066] Object definition: An object refers to an object that can be managed, scheduled, constrained or evaluated by an organization, including watershed units, administrative units, irrigation district units, groundwater units, end-user units divided in step 1, as well as one or more of the nodes and links defined in this step.

[0067] To clarify the transitive relationships between steps, mapping matrices M_BR, M_RA, M_AU, M_KU, M_NU, and M_OR are constructed to represent the attribution or weight relationships between watershed and administrative region, administrative region and irrigation district, irrigation district and user, groundwater and user, node and user, and institution and object, respectively. The elements of the mapping matrices can be 0 or 1, or they can represent area proportions, population proportions, canal system control proportions, or water supply weights.

[0068] Step 3: Establish biophysical modules for arid regions, including watershed runoff generation and confluence modules, groundwater modules, reservoir and storage modules, water transmission and distribution modules, wastewater treatment and reuse modules, and crop water requirements modules.

[0069] 1) Establishing a watershed runoff generation and inflow module: The watershed runoff generation and inflow module uses SWAT water balance relationships for watershed simulation to calculate the inflow at the control section of the mountainous area. Its form is as follows:

[0070]

[0071] In the formula, This represents the soil moisture content at the end of the time period. This represents the initial soil moisture content. This refers to precipitation. Surface runoff; For evaporation; This indicates deep leakage; It is the base current.

[0072] The inflow into the mountainous areas of arid regions is output by a calibrated runoff generation and confluence model, with explicit overlay of rainfall runoff, snowmelt, glacier melt, and baseflow components:

[0073]

[0074] In the formula, For watershed unit b, the total inflow during time period t. To generate runoff from rainfall, Water from melting snow. Water from glacial meltwater The base flow rate.

[0075] The amount of water flowing from snowmelt is expressed as: ;

[0076] The amount of water flowing from glacial melt is expressed as: ;

[0077] In the formula, As a factor for snow cover duration; The glacier diurnal factor; Let be the snow cover area of ​​watershed unit b during time period t; Let be the glacier area of ​​watershed unit b during time period t; The average temperature of watershed unit b during time period t; This refers to the snow melting threshold temperature. This refers to the glacier melting threshold temperature. This represents the length of the scheduling period.

[0078] 2) Establishing a groundwater module: The groundwater module is used to simulate changes in groundwater level, groundwater depth, and groundwater exploitability. Simultaneously, the numerical groundwater model is preprocessed into a response matrix, and its basic governing equations can be written as:

[0079]

[0080] in, Let g be the water storage coefficient of the groundwater unit; The groundwater head or water level of groundwater unit g at the end of the scheduling period t; This refers to the groundwater head or water level at the end of the previous scheduling period; The coefficient of conductivity; The comprehensive stress term includes equivalent terms such as mining, replenishment, lateral inflow and outflow, and river seepage replenishment; Δt is the length of the scheduling period.

[0081] To avoid repeatedly running the complete numerical groundwater model during each scheduling period, the numerical groundwater model is preprocessed into a response matrix. This is then applied to groundwater extraction units. Applying a unit pulse of pumping, the groundwater management unit k is obtained in the lag... Descent response coefficient after a scheduling period The groundwater drawdown at any time t is expressed as:

[0082]

[0083] In the formula, Let K be the drawdown of groundwater unit k at time t; K is the set of groundwater units. This represents the maximum response lag period. For mining units Lag The unit extraction drawdown response coefficient generated for groundwater unit k after a certain time period; For groundwater unit k' in time period Total mining volume.

[0084] Furthermore, the groundwater level can be written as:

[0085]

[0086] In the formula, Let K be the groundwater level of groundwater unit k in time period t; Let k be the simulated initial groundwater level for groundwater unit k. This refers to the equivalent rise in water level caused by natural replenishment, irrigation return, and artificial recharge.

[0087] The upper limit of groundwater extraction is expressed as:

[0088]

[0089] Among them, the output attenuation coefficient Represented as:

[0090]

[0091] In the formula, This represents the upper limit of exploitable groundwater unit k in time period t; This represents the initial maximum output of the well group under normal groundwater level conditions. The output attenuation coefficient of the well group; This represents the upper threshold water level for the normal operation of the well group in groundwater unit k; This is the lower threshold water level at which well groups in groundwater unit k cease operation or face severe extraction restrictions.

[0092] 3) Establish reservoir and regulation module: The reservoir and regulation module is used to simulate the inflow, storage, evaporation loss, seepage loss, water release and wastewater disposal processes of reservoirs and plain regulation units.

[0093] For any reservoir or regulating unit v, the reservoir capacity is updated using the mass conservation law. First, the temporary reservoir capacity during the scheduling period t is calculated:

[0094]

[0095] When the storage capacity exceeds the Xingli storage capacity limit At this time, the overflow can be expressed as: ;

[0096] The reservoir or regulating unit's capacity is updated at the end of the scheduling period t as follows:

[0097] (9)

[0098] At the same time, dead storage capacity constraints should be met: ;

[0099] In the formula, The temporary storage capacity of a reservoir or regulating unit v during the scheduling period t; The reservoir or regulating unit v has a capacity at the end of the scheduling period t; This refers to the storage capacity at the end of the previous scheduling period; This refers to the local inbound volume; This refers to the amount of water transferred from external sources. The amount of water released from a reservoir or regulating unit; Losses due to evaporation from the water surface; For leakage or other losses; This refers to water discharge or overflow. Minimum operating capacity; This is the maximum operating capacity.

[0100] 4) Establish a water transmission and distribution routing module: The water transmission and distribution routing module is used to perform water conservation calculations in rivers, canals, pipe networks, inter-regional water transfer links, and reclaimed water reuse links.

[0101] For any water transport link l, define For ingress traffic of the link, To calculate the flow rate arriving at the link outlet after deducting water transmission and distribution losses, we have:

[0102]

[0103] And meet the water transport capacity constraints of the link: ;

[0104] In the formula, For link The water transmission and distribution loss coefficient during the scheduling period t; For link The upper limit of water conveyance capacity during the scheduling period t.

[0105] For any non-reservoir node n, the water conservation relationship is expressed as:

[0106]

[0107] In the formula, The set of links leading to node n; Let n be the set of links flowing out from node n; For node n, the external inflow during scheduling period t; The amount of water to be taken from node n for local users or ecological sections; This refers to unused discharges, abandoned water, or verification slack.

[0108] 5) Establish a wastewater treatment and reuse module: The wastewater treatment and reuse module is used to calculate the amount of wastewater generated by urban users, the amount of treated effluent, and the amount of reclaimed water to be prepared.

[0109] For any wastewater treatment plant w, its influent flow rate is expressed as:

[0110]

[0111] Its reclaimable water volume is expressed as follows:

[0112]

[0113] In the formula, The influent volume of wastewater treatment plant w during the scheduling period t; For the set of users connected to wastewater treatment plant w; The proportion of water used by user u that is converted into wastewater recirculation is a non-consumption ratio. The total water supply obtained by user u during the scheduling period t; The amount of reclaimable water from wastewater treatment plant w during the scheduling period t; The effluent treatment rate of wastewater treatment plant w; This represents the upper limit of the treatment capacity of the wastewater treatment plant w.

[0114] The reclaimed water configuration should simultaneously meet the treatment plant's effluent volume constraints and the user's acceptable proportion constraints: and ;

[0115] In the formula, The amount of reclaimed water allocated by wastewater treatment plant w to user u; The maximum acceptable proportion of reclaimed water for user u; Let t be the water demand of user u during the scheduling period t.

[0116] 6) Establish a crop water requirement module:

[0117] The crop water requirement module is used to calculate water requirements for domestic, industrial, agricultural, and ecological purposes.

[0118] User u's domestic water requirement is expressed as: ;

[0119] The industrial water demand of user u is expressed as: ;

[0120] The net irrigation quota for crop c in irrigation district a is expressed as follows: ;

[0121] The gross agricultural water requirement of irrigation district a is expressed as follows: ;

[0122] The ecological water replenishment requirement of ecological section e is expressed as follows: ;

[0123] In the formula, This refers to the water demand of user u during the scheduling period t. The population corresponding to user u; The benchmark per capita domestic water consumption quota; Climate correction factor; This is a correction factor for water price or water conservation response; The industrial water demand of user u during the scheduling period t; For industrial added value; Water consumption intensity per unit of industrial added value; For water conservation or internal reuse ratio; The net irrigation quota for crop c in irrigation district a during the scheduling period t; Let be the crop water requirement coefficient of crop c during the scheduling period t; The reference crop evapotranspiration for irrigation district a during the scheduling period t; The effective precipitation in irrigation district a during the scheduling period t; The gross agricultural water demand of irrigation district a during the scheduling period t; Let be the planting area of ​​crop c in irrigation district a; Let be the irrigation water use efficiency of irrigation district a during the scheduling period t; The ecological water replenishment needs of ecological section e during the scheduling period t; The target flow rate for ecological section e; The natural inflow volume of ecological section e during the scheduling period t; This represents the length of the scheduling period.

[0124] After completing the calculations for the above six types of biophysical modules, the key outputs of each module during the scheduling period t are summarized into a closed-loop state vector, which serves as the environmental state input for subsequent steps.

[0125] Step 4: Establish a multi-agent decision-making module for arid regions: Based on the Agent-Based Model, construct a multi-agent decision-making module for water resource allocation in arid regions. This module abstracts the watershed management agent (watershed management entity), administrative allocation agent (administrative allocation entity), irrigation district management agent (irrigation district management entity), water supply agent (water supply entity), groundwater control agent (groundwater management entity), ecological scheduling agent (ecological scheduling entity), and end-user agent as agents with perception, state update, decision-making, and action capabilities. Each agent is associated with nodes, links, management agencies, and managed objects through a corresponding mapping matrix and coupled with the closed-loop state vector output in Step 3.

[0126] Where the closed-loop state vector It can be represented as:

[0127] (14)

[0128] in, For the mountainous water inflow status of watershed unit b, The reservoir or regulating unit v represents the storage capacity status. Let k represent the groundwater level status of groundwater unit k. Let k be the upper limit of exploitable groundwater unit k. For the water conveyance capacity of link l, The amount of reclaimable water from wastewater treatment plant w. For user u's water demand, This refers to the ecological water demand or ecological deficit status of ecological section e. Let represent the memory state of Agent i in the previous scheduling period.

[0129] The mapping matrix includes a watershed-administrative region mapping matrix. Administrative Region-Irrigation District Mapping Matrix Irrigation District-User Mapping Matrix Groundwater Unit-User Mapping Matrix Node-User Mapping Matrix and the mechanism-object mapping matrix Where B represents the set of watershed units, R represents the set of administrative district units, A represents the set of irrigation district units, K represents the set of groundwater units, N represents the set of water supply nodes, U represents the set of end-user units, O represents the set of management agencies, and Y represents the set of managed objects.

[0130]

[0131]

[0132] (15)

[0133]

[0134]

[0135]

[0136] In the formula, This indicates the affiliation or allocation weight between watershed unit b and administrative region r; This indicates the management or water supply control weight between administrative region r and irrigation district a; This represents the service or water supply weight between irrigation district a and user u; This represents the mining association weight between groundwater unit k and user u; This represents the water supply association weight between water supply node n and user u; This represents the management, scheduling, or constraint weight of the management organization o on the managed object y.

[0137] The agent-based model consists of an environmental state, an agent set, a perception function, internal states, decision rules, action variables, and feedback update rules. The environmental state is represented by the closed-loop state vector Ω(t) output in step 3; the agent set includes watershed management agents, administrative allocation agents, irrigation district management agents, water supply agents, groundwater management agents, ecological scheduling agents, and end-user agents; the perception function is represented by a mapping matrix. , , , , and The internal state is defined by the environmental state perceived by the agent, target preferences, management rules, scheduling rules or behavioral rules followed, and its memory of the results of the previous scheduling period; decision rules are used to generate water supply priority, minimum guarantee coefficient, groundwater extraction restrictions, ecological protection weight and multi-objective optimization weight; action variables serve as parameter inputs for the multi-objective optimization model in step 5.

[0138] The Agent set can be represented as:

[0139] (16)

[0140] In the formula, For the Agent set; A watershed management agent; For administrative allocation of agents; Agent for irrigation district management; Water supply agent; Groundwater management agent; As an ecological scheduling agent; Agent for end users.

[0141] Step 3: The output closed-loop state vector, as the environment state, can be represented as: ;

[0142] in, The environmental state during scheduling period t; This includes inflow status, reservoir capacity status, groundwater level status, upper limit of groundwater exploitability, water transmission capacity of the pipeline, available reclaimed water, user water demand, water shortage status in the previous period, and target weight in the previous period.

[0143] To enable different agents to extract relevant information from environmental states, a perception mapping operator is constructed: ;

[0144] In the formula, Let i be the local environmental state perceived by the i-th Agent during the scheduling period t; (·) represents the perception function of the i-th Agent. This perception function is used to convert the global hydrological, engineering, groundwater, reclaimed water, and water demand states into local states that the Agent can recognize.

[0145] Watershed Management Agent uses a watershed-administrative region mapping matrix Perceive the available water supply for the administrative region:

[0146]

[0147] In the formula, The identifiable and allocable water volume for administrative region r during the scheduling period t; The mapping coefficient between watershed unit b and administrative region r; Let be the inflow of watershed unit b during scheduling period t.

[0148] Watershed Management Agent via Institution-Object Mapping Matrix Perceive the running status of its corresponding scheduling object:

[0149] (18)

[0150] In the formula, This refers to the comprehensive status of watershed scheduling objects perceived by the watershed management agent during scheduling period t. An index of the organization corresponding to the watershed management agent; This refers to the running status, demand status, or rule status of object y during scheduling period t; The scheduling weight of object y for the watershed management agent.

[0151] The action variables of the watershed management agent are represented as follows: ;

[0152] In the formula, The set of action variables output by the watershed management agent during scheduling period t; The recommended amount of water to be transferred between administrative regions r and r'.

[0153] Administrative allocation agent through administrative region-irrigation district mapping matrix Irrigation District-User Mapping Matrix Sensing the water needs of users within the administrative region.

[0154] The administrative region-user integrated mapping matrix is ​​represented as follows: ;

[0155] The total water demand of administrative region r during the scheduling period t is expressed as: ;

[0156] In the formula, The total water demand of administrative region r during the scheduling period t; The water demand of user u during the scheduling period t; This is the comprehensive mapping coefficient between user u and administrative region r.

[0157] The administrative allocation agent perceives the operational status of its corresponding administrative allocation object through the agency-object mapping matrix (MoR):

[0158] (19)

[0159] In the formula, The overall status of the administrative allocation object perceived by the administrative allocation agent during the scheduling period t; For the organizational index corresponding to the administrative allocation agent; The allocation weight of the administrative allocation agent on object y.

[0160] The action variables of the administrative allocation agent are represented as follows:

[0161] (20)

[0162] In the formula, The set of action variables output by the administrative allocation agent during the scheduling period t; The priority of water supply to users is determined by the administrative allocation agent; The minimum water supply guarantee coefficient for users formed by the administrative allocation agent.

[0163] Irrigation District Management Agent uses an administrative district-irrigation district mapping matrix. Irrigation District-User Mapping Matrix Node-User Mapping Matrix and the mechanism-object mapping matrix The system senses the achievable water supply capacity of the irrigation district, agricultural water demand, crop water consumption intensity, irrigation efficiency, and water shortage status in the previous scheduling period, and generates revised agricultural water demand, crop planting structure adjustment suggestions, and irrigation water allocation priorities for the irrigation district. The achievable water supply capacity of irrigation district a in scheduling period t is expressed as:

[0164] (twenty one)

[0165] In the formula, The achievable water supply capacity of irrigation district a during the scheduling period t, as perceived by the irrigation district management agent; The water supply service mapping coefficient between irrigation district a and user u; The water supply mapping coefficient between water supply node n and user u; Let represent the water supply capacity of water supply node n during the scheduling period t.

[0166] The agricultural water demand of irrigation district a during the scheduling period t is expressed as: ;

[0167] In the formula, Let 'a' represent the agricultural water demand of irrigation district a during the scheduling period 't'. Let t be the water demand of user u during the scheduling period t.

[0168] The supply and demand status of irrigation district a is represented as follows: ;

[0169] In the formula, Let t be the supply and demand guarantee coefficient of irrigation district a during the scheduling period t; To avoid tiny positive numbers with a denominator of zero.

[0170] Irrigation district management agent through an organization-object mapping matrix Perceive the operational status of the corresponding irrigation area object:

[0171] (twenty two)

[0172] In the formula, The comprehensive status of irrigation area objects perceived by the irrigation area management agent during the scheduling period t; For the organization index corresponding to the irrigation district management agent; The management or scheduling weight of object y by the irrigation district management agent.

[0173] The action variables of the irrigation district management agent are represented as follows:

[0174] (twenty three)

[0175] In the formula, The set of action variables output by the irrigation district management agent during the scheduling period t; The agricultural water demand correction generated by the irrigation district management agent; Recommended amount for adjusting the planting structure of crop c in irrigation district a; The priority of irrigation water allocation for crop c in irrigation district a.

[0176] Groundwater Management Agent uses a groundwater unit-user mapping matrix. Sensing the user's corresponding groundwater status and exploitable limitations:

[0177]

[0178]

[0179] In the formula, The groundwater level status corresponding to user u; Input the groundwater exploitability constraint for user u; Let k be the groundwater level of groundwater unit k. This represents the upper limit of exploitable groundwater unit k.

[0180] Groundwater management agents perceive the operational status of their corresponding groundwater management objects through the Institution-Object Mapping (MoR) matrix:

[0181] (26)

[0182] In the formula, The overall status of the groundwater management object perceived by the groundwater management agent during the scheduling period t; An index of organizations corresponding to groundwater management agents; The control weight of object y for the groundwater control agent.

[0183] The action variables of the groundwater management agent are represented as follows:

[0184] (27)

[0185] In the formula, This refers to the set of action variables output by the groundwater management agent during the scheduling period t. These are the extraction control parameters for groundwater unit k; This represents the pressure extraction intensity or groundwater protection weight of groundwater unit k.

[0186] Water supply agent via node-user mapping matrix Perceived user-accessible water supply capacity:

[0187]

[0188] In the formula, The achievable water supply capacity for user u during the scheduling period t; Let n be the water supply capacity of water supply node n during the scheduling period t. This is the water supply mapping coefficient between water supply node n and user u.

[0189] The water supply agent perceives the operational status of its corresponding water supply object through the institution-object mapping matrix (MoR):

[0190] (29)

[0191] In the formula, This refers to the overall status of the water supply objects perceived by the water supply agent during the scheduling period t. The index of the organization corresponding to the water supply agent; The water supply or scheduling weight for object y by the water supply agent.

[0192] The action variables of the water supply agent are represented as follows: ;

[0193] In the formula, This refers to the set of action variables output by the water supply agent during the scheduling period t. The water source combination preference formed by the water supply agent for user u; This is a set of cost parameters for surface water, groundwater, reclaimed water, and inter-regional water transfer generated by the water supply agent.

[0194] The ecological scheduling agent is used to sense the target flow of the ecological cross-section, the natural arrival water volume, the ecological gap in the previous scheduling period, and the ecological water conveyance cycle. The ecological water replenishment demand of ecological cross-section e in scheduling period t is expressed as:

[0195] (30)

[0196] In the formula, The ecological water replenishment demand of ecological section e during the scheduling period t; The target flow rate for ecological section e during scheduling period t; The natural arrival flow at ecological section e during the scheduling period t; This represents the length of the scheduling period.

[0197] The achievable ecological water replenishment capacity of ecological end-user u is represented as:

[0198] (31)

[0199] In the formula, The achievable ecological water replenishment capacity for ecological end-user u during the scheduling period t; This is the water supply mapping coefficient between water supply node n and ecological end-user u.

[0200] The ecological scheduling agent perceives the operational status of its corresponding ecological scheduling object through the institution-object mapping matrix MoR:

[0201] (32)

[0202] In the formula, This refers to the comprehensive status of the ecological scheduling objects perceived by the ecological scheduling agent during the scheduling period t. For the organization index corresponding to the ecological scheduling agent; The ecological scheduling or ecological protection weights of the ecological scheduling agent for object y.

[0203] The action variables of the ecological scheduling agent are represented as follows:

[0204] (33)

[0205] In the formula, This refers to the set of action variables output by the ecological scheduling agent during the scheduling period t. The ecological protection weight of ecological section e; Prioritize ecological water replenishment for ecological cross section e or ecological end-user u.

[0206] The end-user agent uses a watershed-user mapping matrix. Groundwater Unit - User Mapping Matrix And node-user mapping matrix It can sense its own water demand status, available water supply capacity, groundwater correlation status, irrigation district service relationship, water shortage status in the previous scheduling period, and the availability of alternative water sources.

[0207] The overall achievable water supply capacity of end user u is expressed as: ;

[0208] The groundwater association status of end user u is represented as follows: ;

[0209] The irrigation district service relationship for end user u is represented as follows: ;

[0210] In the formula, The overall achievable water supply capacity for end user u; The groundwater association status for end user u; The strength of the association between end user u and the service area of ​​the irrigation district.

[0211] The action variables of the end-user agent are represented as follows:

[0212] (34)

[0213] In the formula, The set of action variables output by the end-user agent during the scheduling period t; The water demand after the end-user agent responds; The percentage of reclaimed water accepted by the end user (u); The minimum water supply guarantee factor for end user u; This represents the water shortage status of end user u in the previous scheduling period.

[0214] The internal state of the i-th Agent during scheduling period t can be represented as:

[0215]

[0216] In the formula, Let i be the internal state of the i-th Agent; This refers to the environmental state perceived by the Agent; This refers to the target preferences of the Agent; The management rules, scheduling rules, or behavioral rules that this Agent follows; This is the Agent's memory of the results of the previous scheduling period, including the water shortage rate, groundwater over-extraction bias, ecological gap, and fairness bias of the previous period.

[0217] The decision-making behavior of the i-th agent can be represented as:

[0218] (36)

[0219] In the formula, The action variables generated by the i-th Agent during the scheduling period t; Let be the decision function of the i-th Agent.

[0220] The set of action variables output by various agents during scheduling period t is represented as follows:

[0221] (37)

[0222] In the formula, The action variable sets output by the watershed management agent, administrative allocation agent, irrigation district management agent, water supply agent, groundwater control agent, ecological scheduling agent, and end-user agent during the scheduling period t are synchronously output to step 5.

[0223] Step 5: Construct a multi-objective optimization model: In each scheduling period t, surface water, groundwater, reclaimed water, and inter-regional water transfer are used as decision objects, and reservoir water release, link flow, and planting area adjustment are used as auxiliary decisions. A multi-objective optimization model driven by an Agent-Based Model is constructed. The set of Agent optimization input parameters is represented as follows:

[0224]

[0225] In the formula, Input the set of Agent decision parameters for the multi-objective optimization model for the scheduling period t; Action variables generated for the i-th type of Agent; Prioritize the overall water supply for user u; The minimum water supply guarantee factor for user u; The dynamic weights of the m-th optimization objective; The allocable water supply for administrative region r; The total water demand of administrative region r; Input the groundwater exploitability constraint for user u; The available water supply capacity for user u; The state of the object as perceived by the management agency's agent.

[0226] in, This includes the regional allocable water volume formed by the watershed management agent, the water allocation weight formed by the administrative allocation agent, the planting structure adjustment boundary formed by the irrigation district management agent, the water source combination preference formed by the water supply agent, the groundwater extraction restrictions formed by the groundwater control agent, the ecological security priority formed by the ecological scheduling agent, and the water demand response and acceptance of alternative water sources formed by the end-user agent.

[0227] To incorporate agent behavior into the optimization model, the user's overall water supply priority Π(u,t)\Pi(u,t)Π(u,t) is converted into water shortage target weights:

[0228] (39)

[0229] In the formula, The water shortage penalty weight for user u during scheduling period t; The baseline water shortage weight for user u; This is the influence coefficient of water supply priority on the water shortage penalty weight. This formula indicates that the priority objects determined by the agent will receive a higher water shortage penalty weight in the optimization model.

[0230] The decision variable vector is represented as follows:

[0231]

[0232]

[0233] In the formula, The amount of surface water allocated from water supply node n to user u; The amount of groundwater allocated from groundwater unit k to user u; The amount of reclaimed water allocated by wastewater treatment plant w to user u; For administrative region r to administrative region Inter-regional water transfer volume; The amount of water released from the reservoir or regulating unit v; For link The inbound traffic; The planting area of ​​crop c in irrigation district a For user u, the water shortage relaxation variable; Let e ​​be the ecological gap slack variable for ecological cross section e.

[0234] The total water supply for user u during scheduling period t is expressed as:

[0235] (41)

[0236] The amount of water ultimately allocated to user u through inter-regional water transfer is represented as follows:

[0237] (42)

[0238] In the formula, The total water supply for user u; The amount of water ultimately allocated to user u through inter-regional water transfer; The comprehensive mapping coefficient between administrative region r and user u.

[0239] The objective function should include at least the following five items:

[0240] Objective 1: Minimize the overall water shortage rate: The overall water shortage objective is expressed as:

[0241]

[0242] In the formula, To achieve the comprehensive water shortage target; Water supply priority is determined by the agent. The converted user water shortage penalty weight; To avoid tiny positive numbers with a denominator of zero, this objective reflects the Agent's priority protection role for residential, ecological, continuously water-scarce, and key users.

[0243] Objective 2: Minimize groundwater over-extraction: The total extraction volume of groundwater unit k is expressed as:

[0244] (44)

[0245] The target for groundwater over-extraction is represented as:

[0246]

[0247] In the formula, The target is groundwater over-extraction; This refers to the safe extraction volume or phased control index for groundwater unit k. The groundwater management agent uses over-extraction penalty weights based on groundwater level decline, extraction reduction targets, and historical over-extraction deviations. When the over-extraction risk of a groundwater unit is high... Increase the size of the unit, thereby enhancing its protection strength in the optimization model.

[0248] Objective 3: Minimize total system cost.

[0249]

[0250] in:

[0251]

[0252]

[0253]

[0254]

[0255]

[0256] In the formula, c , , and These are the unit costs of surface water, groundwater, reclaimed water, inter-regional water transfer, and reservoir operation, respectively, after adjustments by agents such as the water supply agent and the groundwater management agent. The adjusted unit costs simultaneously reflect economic costs, energy costs, policy constraint costs, ecological risk costs, and groundwater extraction reduction costs.

[0257] Objective 4: Minimize the ecological section gap: The ecological section gap objective is represented as follows:

[0258]

[0259] In the formula, To address the ecological gap target; The ecological protection weights for the ecological scheduling agent are determined based on the ecological gap, the importance of ecological sections, and the ecological water conveyance cycle of the previous scheduling period. Let e ​​be the ecological gap slack variable for ecological section e; Target flow for ecological cross-sections; This represents the length of the scheduling period.

[0260] Objective 5: Optimal regional water supply equity: The total water supply of administrative region r is expressed as:

[0261]

[0262] The per capita water supply of administrative region r is expressed as:

[0263]

[0264] The average per capita water supply for each administrative region is expressed as follows:

[0265] (55)

[0266] The regional water supply equity objective is expressed as:

[0267] (56)

[0268] In the formula, The total water supply for administrative region r; The population of administrative region r; The per capita water supply for administrative region r; This represents the average per capita water supply in each administrative region. The number of administrative districts.

[0269] The overall objective function is expressed as:

[0270]

[0271] And satisfy:

[0272]

[0273] In the formula, The weights of the m-th objective are dynamically updated for each agent based on the operational deviation from the previous scheduling period. By employing methods such as multi-objective genetic algorithms and multi-objective particle swarm optimization, a Pareto solution set for multi-objective optimization can be obtained.

[0274] The constraints include the following.

[0275] Constraints on the relationship between user water supply and demand:

[0276]

[0277] User-accessible water supply capacity constraints:

[0278]

[0279] In the formula, The water supply agent obtains the user's reachable water supply capacity through the node-user mapping matrix.

[0280] Minimum water supply guarantee constraints:

[0281]

[0282] In the formula, This is the minimum water supply guarantee coefficient formed by the combined action of the end-user agent, administrative allocation agent, and ecological scheduling agent in step S4.

[0283] Groundwater control constraints:

[0284] (62)

[0285]

[0286] in:

[0287]

[0288] In the formula, This represents the actual upper limit of extraction for groundwater unit k during the scheduling period t. The upper limit of the extraction limit is the water level constraint calculated by the groundwater response module; The upper limit for extraction is set by the dual control or management indicators for groundwater. Groundwater management agents define extraction restrictions based on extraction targets, historical over-extraction status, and groundwater level thresholds.

[0289] Reservoir operation constraints:

[0290]

[0291]

[0292] In the formula, The dead storage capacity or minimum operating storage capacity of the reservoir or regulating unit v; Maximum operating capacity; This represents the maximum discharge capacity.

[0293] Ecological cross-section constraints:

[0294]

[0295]

[0296] In the formula, The amount of water reaching the ecological section e is calculated by the water transmission and distribution routing module. This is a slack variable for ecological gaps.

[0297] Constraints on the use of reclaimed water:

[0298] (69)

[0299]

[0300] In the formula, The amount of reclaimable water from the wastewater treatment plant (w); This represents the maximum acceptable proportion of reclaimed water for the end-user agent, which can be dynamically adjusted based on water quality suitability, industry type, and the usage of alternative water sources in the previous period.

[0301] Water conveyance capacity constraints:

[0302]

[0303] In the formula, For the ingress traffic of link ℓ\ellℓ; This represents the upper limit of the water transmission capacity of the link.

[0304] Planting structure constraints:

[0305]

[0306] In the formula, and These are the lower and upper limits of crop planting area determined by the irrigation district management agent based on crop yield, water use intensity, policy constraints, and expected water availability.

[0307] Water allocation constraints for administrative regions:

[0308] (73)

[0309] In the formula, The watershed management agent perceives the allocable water inflow of an administrative region (r) through a watershed-administrative region mapping matrix. This constraint integrates watershed inflow, administrative region boundaries, and inter-regional water transfer behavior into the optimization model. All variables follow non-negativity constraints.

[0310] Node conservation is performed according to the node conservation relationship of the water transmission and distribution routing module in step 3, and reservoir mass conservation is performed according to the reservoir and regulation module's capacity update relationship in step 3. After solving the optimization model, the Pareto candidate scheme set for water resource allocation during scheduling period t is obtained:

[0311] (74)

[0312] In the formula, The optimized configuration result for scheduling time period t is given, where This represents the normalized objective function value.

[0313] After solving the multi-objective optimization model, the optimization configuration results are mapped to the corresponding nodes, links, reservoirs, groundwater units, and ecological sections. Consistency checks are performed on node water conservation, link water conveyance capacity, reservoir operating boundaries, groundwater extraction constraints, and ecological section compliance. The check results are used to update the system state and serve as historical memory input for various agents in the next scheduling period.

[0314]

[0315] In the formula, This represents the memory state of Agent i after the scheduling period t is updated. (·) is the Agent memory update function; For users' water shortage rate; This is due to groundwater over-extraction deviation; This represents an ecological gap; This is due to a bias in fairness.

[0316] Perform simulation—optimize closed-loop solution:

[0317] Using months as the time step, calculate cyclically in the following order:

[0318] (1) Input meteorological, water inflow, population, industry and policy parameters for time period t;

[0319] (2) Calculate the water inflow in mountainous areas using the watershed module;

[0320] (3) Update reservoir capacity via the reservoir module;

[0321] (4) The water requirement module for crops and the update needs of residential and industrial agents;

[0322] (5) The groundwater level and the upper limit of well output are updated by the groundwater module;

[0323] (6) Establish and solve a multi-objective optimization model for time period t;

[0324] (7) Input the optimized configuration results into the routing module to calculate the node water supply and distribution;

[0325] (8) The wastewater module calculates the amount of reclaimed water and updates the available resources for the next time period;

[0326] (9) Output the water shortage rate, groundwater depth, ecological compliance rate, fairness indicators and system cost for time period t;

[0327] (10) The transition period is t+1.

[0328] This coupled model progresses on a monthly scale and in a transient manner, with biophysical conditions influencing human decisions, which in turn feed back to the physical module.

[0329] Multi-objective optimization is represented as:

[0330]

[0331] Equation (76) shows that the multi-objective optimization model in step 5 is not an independent solver, but a closed-loop optimization link embedded in the Agent-Based Model. In step 4, each Agent forms decision parameters based on the environmental state. In step 5, the water resource optimization allocation scheme is solved based on the decision parameters, and the allocation results are written back to the node-link unified network topology to perform constraint verification on water transmission, engineering operation, groundwater extraction and ecological section compliance. The verification results further update the system operation status and serve as the input for Agent perception, memory update and decision adjustment in the next scheduling period.

[0332] Step 6: Output multi-objective optimization results for water resources: For each planning period, based on the optimization allocation results of each scheduling period, output multi-objective optimization results for water resources, including water resource evaluation indicators, recommended allocation schemes, agent decision feedback results, and the Pareto front for multi-objective optimization. The water resource evaluation indicators include one or more of the following: surface water supply during the planning period, groundwater supply, reclaimed water utilization, comprehensive water shortage rate, groundwater level decline, water supply vulnerability indicators, longest continuous water shortage duration, ecological section compliance rate, total system cost, and regional water supply equity indicators.

[0333] The output of multi-objective optimization can be represented using the Pareto front, such as... Figure 4 As shown, each non-dominated solution in the Pareto front corresponds to a set of candidate configuration schemes. These candidate configuration schemes include one or more of the following for each scheduling period: surface water allocation, groundwater allocation, reclaimed water allocation, inter-regional water transfer, reservoir release, link flow, and planting area adjustment. Each set of candidate configuration schemes satisfies constraints such as user water supply and demand relationship, user achievable water supply capacity, minimum water supply guarantee, groundwater control, reservoir operation, ecological cross-sections, reclaimed water utilization, link water conveyance capacity, planting structure, and administrative region allocable water volume. It also corresponds to a set of comprehensive water shortage rate, groundwater over-extraction, total system cost, ecological cross-section gap, and regional water supply equity target values. Based on the planning period evaluation indicators, management preferences, and agent decision feedback results, recommended configuration schemes are selected from the Pareto front.

[0334] Let T be the set of scheduling periods during the planning period, and T be the period at the end of the planning period. e The surface water supply during the planning period is expressed as follows:

[0335] (77)

[0336] In the formula, This refers to the surface water supply during the planning period. Let N be the amount of surface water allocated by water supply node n to user u during scheduling period t; N is the set of water supply nodes; and U is the set of users.

[0337] The amount of reclaimed water used during the planning period is expressed as follows:

[0338] (78)

[0339] In the formula, This refers to the amount of reclaimed water utilized during the planning period; W represents the amount of reclaimed water allocated by wastewater treatment plant w to user u during the scheduling period t; W is the set of wastewater treatment plants.

[0340] Replenish groundwater supply:

[0341] (79)

[0342] In the formula, This refers to the planned groundwater supply. Let W be the amount of groundwater allocated to user u by groundwater unit k during the scheduling period t; W is the set of groundwater units.

[0343] The degree of water level decline in groundwater unit k during the planning period is expressed as follows:

[0344]

[0345] In the formula, This represents the degree of water level decay in groundwater unit k at the end of the planning period relative to the start of the simulation. Let k be the simulated initial groundwater level for groundwater unit k. For groundwater unit k at the end of the planning period The groundwater level. If A value >0 indicates a drop in the groundwater level; if DG(k)≤0, it indicates that the groundwater level has not dropped or has recovered somewhat.

[0346] The overall water shortage rate during the planning period is expressed as follows:

[0347] (81)

[0348] In the formula, The overall water shortage rate during the planning period; The water demand of user u during the scheduling period t; The total water supply for user u during the scheduling period t; To avoid tiny positive numbers with a denominator of zero.

[0349] Vulnerability indicators are expressed as follows:

[0350]

[0351] In the formula, This is a vulnerability indicator for water supply during the planning period, representing the percentage of the population whose water supply ratio is below the minimum guarantee threshold. Let u be the population corresponding to the scheduling period t; is the minimum water supply guarantee coefficient for user u during the scheduling period t; 1[·] is an indicator function, which takes the value of 1 when the condition in parentheses is true, and takes the value of 0 otherwise.

[0352] The longest continuous water shortage duration for user u is represented as:

[0353]

[0354] In the formula, [t1, t2] represents the longest continuous water shortage duration for user u within the planning period; [t1, t2] represents any continuous scheduling interval within the planning period T. This indicator is used to identify vulnerable users or vulnerable areas that are in a state of low security for a long period of time.

[0355] The compliance rate of ecological sections is expressed as follows:

[0356] (84)

[0357] In the formula, ER represents the ecological section compliance rate during the planning period; Let e ​​be the ecological gap slack variable for ecological cross section e during scheduling period t; The ecological target flow for ecological section e during scheduling period t; E represents the length of the scheduling period; E represents the set of ecological cross sections.

[0358] The total system cost during the planning period is expressed as follows:

[0359] (85)

[0360] In the formula, TC represents the total system cost during the planning period; Let t be the system cost objective function value for the scheduling period t.

[0361] The fairness of regional water supply during the planning period can be represented by the average of the fairness targets for each scheduling period:

[0362] (86)

[0363] In the formula, Indicators for regional water supply equity during the planning period; Let |T| be the objective function value for regional water supply fairness during the scheduling period t; |T| is the number of scheduling periods within the planning period.

[0364] Finally, it should be noted that the above description is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A multi-objective optimization allocation method for water resources in arid regions, characterized in that, The method includes the following steps: Step 1: Basic Data Collection and Unit Division of the Study Area: Collect basic data for the study area, including meteorological data, hydrological data, engineering data, socio-economic data, ecological data, and management rule data; divide the study area into watershed units, administrative units, irrigation district units, groundwater units, and end-user units; Step 2: Construct a unified network topology based on nodes and links: Define a water resource allocation network, using nodes and links as basic components based on the node-link model, and institutions as non-spatial entities that make decisions on some nodes and links, thus forming a common topology for the physical network and the decision network; at the same time, construct mapping matrices to represent the affiliation or weight relationships of watershed-administrative region, administrative region-irrigation district, irrigation district-user, groundwater-user, node-user, and institution-object respectively. Step 3: Establish biophysical modules for arid regions: Establish biophysical modules for arid regions, including watershed runoff generation and confluence modules, groundwater modules, reservoir and storage modules, water transmission and distribution modules, wastewater treatment and reuse modules, and crop water requirements modules; and summarize the outputs of each module into a closed-loop state vector; Step 4: Establish a multi-agent decision-making module for arid regions: Based on the Agent-Based Model, a multi-agent decision-making module for arid regions is constructed. This module abstracts watershed management agents, administrative allocation agents, irrigation district management agents, water supply agents, groundwater control agents, ecological scheduling agents, and ecological end-user agents into agents with perception, state update, decision-making, and action capabilities, namely, watershed management agent, administrative allocation agent, irrigation district management agent, water supply agent, groundwater control agent, ecological scheduling agent, and end-user agent. Each type of agent is associated with nodes, links, institutions, and objects through a corresponding mapping matrix and coupled with the closed-loop state vector output in Step 3. Step 5: Construct a multi-objective optimization model: In each scheduling period, surface water, groundwater, reclaimed water and inter-regional water transfer are taken as decision objects, and reservoir water release, link flow and planting area adjustment are taken as auxiliary decisions. Construct a multi-objective optimization model driven by Agent-Based Model and solve it to obtain the Pareto candidate scheme set for water resource allocation. Step 6: Output the multi-objective optimization results of water resources: For each planning period, based on the optimization configuration results of each scheduling period, output the multi-objective optimization results of water resources, including water resources evaluation indicators, recommended configuration schemes, agent decision feedback results, and multi-objective optimization Pareto fronts; each non-dominated solution in the Pareto front corresponds to a set of candidate configuration schemes, which include one or more of the following for each scheduling period: surface water allocation, groundwater allocation, reclaimed water allocation, inter-regional water transfer, reservoir release, link flow, and planting area adjustment; each set of candidate configuration schemes satisfies user water supply and demand relationship, user achievable water supply capacity, minimum water supply guarantee, groundwater control, reservoir operation, ecological cross-section, reclaimed water utilization, link water conveyance capacity, planting structure, and administrative region allocable water constraints, and corresponds to a set of comprehensive water shortage rate, groundwater over-extraction, total system cost, ecological cross-section gap, and regional water supply fairness target values; based on the planning period evaluation indicators, management preferences, and agent decision feedback results, recommended configuration schemes are selected from the Pareto fronts.

2. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, The meteorological data in Step 1 includes daily or monthly precipitation, temperature, evaporation, wind speed, radiation, snow cover, and glacier area changes; the hydrological data includes flow rates at mountainous water inflow control sections, river cross-sections, reservoir inflow and outflow, and groundwater depth and level monitoring data; the engineering data includes reservoir characteristic curves, reservoir capacity-water level relationship, canal water conveyance capacity, pump station parameters, sewage treatment plant capacity, reclaimed water utilization facility capacity, and well capacity; the socio-economic data includes population, urbanization rate, residential water consumption, industrial added value, crop planting area, irrigation system, water price, and energy cost; the ecological data includes target flow rates at ecological cross-sections, wetland water replenishment demand, minimum water levels in key ecological zones, and ecological water conveyance cycles; and the management rule data includes administrative water allocation indicators, industry priorities, minimum living allowance coefficients for residents, groundwater dual control indicators, and reclaimed water priority utilization rules. Watershed units are divided according to watersheds, mountain water inflow control sections, and river network confluence relationships; administrative units are divided according to the boundaries of counties, cities, farms, or management areas; irrigation district units are divided according to the canal system control range, canal heads, and branch canal outlets; groundwater units are divided according to aquifer structure, groundwater management zones, monitoring well control range, groundwater pressure extraction red lines, and prohibited / restricted extraction areas; end-user units are divided according to domestic, agricultural, industrial, and ecological water use functions.

3. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, In step 2, nodes are defined as follows: mountain water inflow control sections, reservoirs, plain water storage units, river control nodes, irrigation canal heads, branch canal outlets, well groups, sewage treatment plants, reclaimed water utilization points, urban water supply areas, industrial parks, ecological water conveyance control sections, and groundwater management zones are represented as nodes; links are defined as follows: river water conveyance, canal water conveyance, pipeline water conveyance, inter-regional water transfer, reclaimed water reuse, and groundwater extraction and replenishment are represented as links; institutions are defined as follows: watershed management institutions, administrative allocation institutions, irrigation district management institutions, water supply units, groundwater control institutions, and ecological scheduling institutions are represented as institutions; objects are defined as: objects that can be managed, scheduled, constrained, or evaluated by institutions, including watershed units, administrative district units, irrigation district units, groundwater units, and end-user units, represented by one or more of nodes and links; The elements of the mapping matrix can be 0 or 1, or can be area ratio, population ratio, canal system control ratio, or water supply weight.

4. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, Step 3 involves establishing the following modules: The watershed runoff generation and inflow module uses SWAT water balance relationships for watershed simulation to calculate inflow at mountainous control sections; the groundwater module simulates changes in groundwater level, depth, and exploitable groundwater capacity, and preprocesses the numerical groundwater model into a response matrix; the reservoir and storage module simulates inflow, storage, evaporation loss, leakage loss, discharge, and wastewater disposal processes in reservoirs and plain storage units; the water transmission and distribution routing module performs water conservation calculations in rivers, canals, pipe networks, inter-regional water transfer links, and reclaimed water reuse links; the wastewater treatment and reuse module calculates the amount of wastewater generated by urban users, treated effluent, and reclaimed water allocation; and the crop water requirement module calculates water requirements for domestic, industrial, agricultural, and ecological use.

5. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, Closed-loop state vector in step 4 Represented as: （15） in, For the mountainous water inflow status of watershed unit b, The reservoir or regulating unit v represents the storage capacity status. Let k represent the groundwater level status of groundwater unit k. Let k be the upper limit of exploitable groundwater unit k. For the water conveyance capacity of link l, The amount of reclaimable water from wastewater treatment plant w. For user u's water demand, This refers to the ecological water demand or ecological deficit status of ecological section e. Let represent the memory state of Agent i in the previous scheduling period.

6. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, The specific process in step 5 of constructing a multi-objective optimization model driven by an Agent-Based Model and solving for the Pareto candidate solution set for water resource allocation is as follows: The set of optimized input parameters for the agent is represented as follows: In the formula, Input the set of Agent decision parameters for the multi-objective optimization model for the scheduling period t; Action variables generated for the i-th type of Agent; Prioritize the overall water supply for user u; The minimum water supply guarantee factor for user u; The dynamic weights of the m-th optimization objective; The allocable water supply for administrative region r; The total water demand of administrative region r; Input the groundwater exploitability constraint for user u; The available water supply capacity for user u; The state of the object perceived by the management agency's agent; To incorporate agent behavior into the optimization model, the user's overall water supply priority Π(u,t)\Pi(u,t)Π(u,t) is converted into water shortage target weights: (39) In the formula, The water shortage penalty weight for user u during scheduling period t; The baseline water shortage weight for user u; This is the coefficient representing the influence of water supply priority on the weight of water shortage penalty. The decision variable vector is represented as follows: In the formula, The amount of surface water allocated from water supply node n to user u; The amount of groundwater allocated from groundwater unit k to user u; The amount of reclaimed water allocated by wastewater treatment plant w to user u; For administrative region r to administrative region Inter-regional water transfer volume; The amount of water released from the reservoir or regulating unit v; For link The inbound traffic; The planting area of ​​crop c in irrigation district a For user u, the water shortage relaxation variable; Let e ​​be the ecological gap slack variable for ecological cross section e; The total water supply for user u during scheduling period t is expressed as: (41) The amount of water ultimately allocated to user u through inter-regional water transfer is represented as follows: (42) In the formula, The total water supply for user u; The amount of water ultimately allocated to user u through inter-regional water transfer; The comprehensive mapping coefficient between administrative region r and user u; The objective function includes five terms: minimizing the overall water shortage rate, minimizing groundwater over-extraction, minimizing the total system cost, minimizing the ecological cross-section gap, and optimizing regional water supply equity. The overall objective function is expressed as: And satisfy: In the formula, Let m be the objective function of the m-th item; The m-th target weight is dynamically updated for each Agent based on the operational deviation of the previous scheduling period; The constraints include: user water supply and demand relationship constraints, user achievable water supply capacity constraints, minimum water supply guarantee constraints, groundwater control constraints, reservoir operation constraints, ecological section constraints, reclaimed water utilization constraints, water conveyance capacity constraints, planting structure constraints, and administrative region allocable water volume constraints. Node conservation is performed according to the node conservation relationship of the water transmission and distribution routing module, and reservoir mass conservation is performed according to the reservoir and storage module's capacity update relationship; after solving the optimization model, the Pareto candidate scheme set for water resource allocation in scheduling period t is obtained: (74) In the formula, The optimized configuration result for scheduling time period t is given, where This represents the normalized objective function value; After solving the multi-objective optimization model, the optimization configuration results are mapped to the corresponding nodes, links, reservoirs, groundwater units, and ecological sections. Consistency checks are performed on node water conservation, link water conveyance capacity, reservoir operating boundaries, groundwater extraction constraints, and ecological section compliance. The check results are used to update the system state and serve as historical memory input for various agents in the next scheduling period. In the formula, This represents the memory state of Agent i after the scheduling period t is updated. (·) is the Agent memory update function; For users' water shortage rate; This is due to groundwater over-extraction deviation; This represents an ecological gap; This is due to a bias in fairness.

7. The multi-objective optimization allocation method for water resources in arid regions according to claim 1, characterized in that, The water resources evaluation indicators in step 6 include one or more of the following: surface water supply during the planning period, groundwater supply, reclaimed water utilization, comprehensive water shortage rate, groundwater level decline, water supply vulnerability indicators, longest continuous water shortage duration, ecological section compliance rate, total system cost, and regional water supply equity indicators.

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