An intelligent generation method for the CMIES daily scheduling scheme based on multi-task learning
By adopting a multi-task learning method in CMIES recently dispatch and combining multi-objective and single-objective mixed integer planning model, the problem of insufficient efficiency and effectiveness of CMIES recently dispatch problems in the existing technology is solved, and a rapid and effective scheduling plan generation is achieved to meet actual production needs and reduce operating costs and carbon emissions.
Patent Information
- Application Number
- CN202410324192.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-21
- Publication Date
- 2025-06-03
- Estimated Expiration
- 2044-03-21
AI Technical Summary
The existing technology is difficult to quickly and effectively solve the problem of the recent scheduling of multi-target mine integrated energy system (CMIES), resulting in a small number of feasible solutions, uneven front-line distribution and long running time.
Using a multi-task learning method, the multi-objective mixed integer programming model is used as the main task and the single-objective mixed integer programming model as the auxiliary task, and the multi-task framework is used to solve the optimal scheduling scheme set of the multi-objective mixed integer programming model.
It realizes the rapid generation of theoretically optimal scheduling schemes, with small calculation costs and short running time, meeting actual production needs, providing managers with diversified decision-making plans, and reducing enterprise operating costs and carbon emissions.
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Figure CN118153760B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of energy system scheduling, and particularly relates to an intelligent generation method for a CMIES day-ahead scheduling scheme based on multi-task learning. Background Art
[0002] The operation optimization problem of a Regional Integrated Energy System (RIES) is a research hotspot in the current energy and power field, especially reflected in the intelligent and rapid generation of diverse day-ahead scheduling schemes. Regarding the operation optimization problem of RIES, existing literature generally models it as a mixed-integer programming problem, and common solution methods include mathematical programming methods such as the Benders decomposition algorithm and the Cplex commercial solver. Based on the Benders decomposition method, Han Gao et al. effectively solved the steady-state dispatch problem of an integrated electricity-gas system in the literature "A Benders Decomposition Based Algorithm for Steady-State Dispatch Problem in an Integrated Electricity-Gas System" (IEEE Transactions on Power Systems, 2021, 36(4): 3817-3820); based on the Cplex commercial solver, Yongli Wang et al. solved the capacity planning and operation optimization problems of RIES in the literature "Planning and operation method of the regional integrated energy system considering economy and environment" (Energy, 2019, 171: 731-750). However, mathematical programming methods are not applicable to solving optimization problems with characteristics such as large scale, highly nonlinear terms, and multiple objectives.
[0003] Evolutionary optimization is a new type of population-based probabilistic search paradigm inspired by the intelligent behaviors of organisms in nature. It is a very effective approach for solving complex problems and has been successfully applied in many fields. Xiaonan Wu et al. used the MO-NSGA-II algorithm to solve the operation optimization problem of the RIES integrating geothermal energy, solar energy, and thermal storage devices in the literature "Multi-objective and multi-algorithm operation optimization of integrated energy system considering ground source energy and solar energy" (Electrical Power and Energy Systems, 2023, 144: 108529); Ting Wu et al. proposed an improved multi-objective and multi-factor evolutionary algorithm to solve the multi-objective day-ahead scheduling problem of the IES considering biogas-solar-wind renewable energies in the literature "Multitasking multi-objective operation optimization of integrated energy system considering biogas-solar-wind renewables" (Energy Conversion and Management, 2021, 229: 113736).
[0004] Compared with traditional RIES, the Coal Mine Integrated Energy System (CMIES) introduces a large number of mine-related derivative energies, making the physical laws of the energy link more complex and the energy flow between links having coupling characteristics. At the same time, the limited energy storage capacity and the rigid demand for different types of energy in production activities make the optimization variables need to meet complex and numerous constraints, including physical characteristics and safe operation conditions. In addition, an important function of CMIES is to timely absorb renewable energy and make full use of mine-derived energy, further introducing optimization objectives related to carbon emissions. Hejuan Hu et al. constructed a multi-objective mixed-integer programming model for the day-ahead scheduling problem of CMIES considering flexible loads in the literature "Enhanced evolutionary multiobjective optimization-based dispatch of coal mine integrated energy system with flexible load" (Applied Energy, 2021, 307: 118130), and used the NSGA-II algorithm and Cplex solver to obtain the scheduling scheme respectively. Yan Wang et al. established a unified operation optimization model suitable for various scenarios of CMIES in the literature "Unified operation optimization model of integrated coal mine energy systems and its solutions based on autonomous intelligence" (Applied Energy, 2022, 328: 120106) to reduce economic and carbon trading costs, and proposed an autonomous intelligent optimization strategy based on support vector machines. However, the above studies all have problems such as a small number of feasible solutions, uneven distribution of the PF front, and long running time. Therefore, it is particularly urgent to design an optimization method that can effectively and quickly solve the multi-objective CMIES day-ahead scheduling problem, which will provide diversified decisions for managers and help reduce enterprise operation costs and carbon emissions. Summary of the Invention
[0005] Objective of the Invention: Aiming at the above problems, the objective of the present invention is to provide an intelligent generation method for the day-ahead scheduling scheme of CMIES based on multi-task learning.
[0006] Technical Solution: An intelligent generation method for the day-ahead scheduling scheme of CMIES based on multi-task learning according to the present invention, the method includes:
[0007] For the selected integrated mine energy system, determine the actual production demand of CMIES;
[0008] Establish a multi-objective mixed-integer programming model for the day-ahead scheduling problem of CMIES according to the actual production demand, and determine the constraint conditions that need to be satisfied during the safe production of CMIES;
[0009] Construct a single-objective mixed-integer programming model for the day-ahead scheduling problem of CMIES based on the multi-objective mixed-integer programming model;
[0010] Take the multi-objective mixed-integer programming model as the main task and the single-objective mixed-integer programming model as the auxiliary task, and use the multi-task framework to solve the optimal scheduling plan set of the multi-objective mixed-integer programming model;
[0011] Generate the optimal scheduling plan according to the actual production status of CMIES.
[0012] Furthermore, establishing a multi-objective mixed-integer programming model for the day-ahead scheduling problem of CMIES according to the actual production demand includes:
[0013] Select the economic cost and the carbon trading cost as the two objective functions. The expression of the first objective function is:
[0014] Min f 1 =C trade +C ges +C cut ,
[0015] where, f 1 represents the economic cost, C trade represents the external energy trading cost, C ges represents the equipment operation cost, C cut represents the penalty cost for wind, light and associated energy abandonment;
[0016] The expression of the second objective function is:
[0017] Min f 2 =c i (E out -E all ),
[0018] where, f 2 represents the carbon trading cost, c i is the carbon trading market price on that day, E out represents the total CO 2 emissions, E all represents the CO 2 carbon emission quota.
[0019] Furthermore, the constraint conditions that need to be satisfied during the safe production of CMIES include:
[0020] Load supply - demand balance constraint, ramp - up / down constraint of gas turbines, upper and lower limits of production equipment output, and actual energy storage constraints. The expression of the load supply - demand balance constraint is:
[0021]
[0022] Among them, \(P\) e,t represents the power purchased from the external power grid of the system at time \(t\), \(P\) g,t represents the output power of the gas turbine at time \(t\), \(P\) WT,t represents the output power of the wind turbine at time \(t\), \(P\) PV,t represents the output power of the photovoltaic at time \(t\), \(P\) Pac,t represents the input power of the electric chiller, and respectively represent the charging power and discharging power of the energy storage at time \(t\), and respectively represent the state variable of energy storage and the state variable of discharging of the energy storage device at time \(t\), \(H\) FW,t represents the output power of the waste - air oxidation device at time \(t\), \(H\) GB,t represents the output power of the gas - source heat pump at time \(t\), \(H\) SB,t represents the output power of the water - source heat pump at time \(t\), \(H\) DB.t represents the output power of the ground - source heat pump at time \(t\), \(H\) Hac,t represents the input power of the absorption chiller, and respectively represent the heat - storage power and heat - releasing power; \(P\) 0,t 、\(H\) 0,t and \(L\) 0,t respectively represent the electrical, thermal, and cooling loads required by the system at time \(t\); \(\nu\) 1 、\(\nu\) 2 、\(\nu\) 3 and \(\nu\) 4 respectively represent the efficiency coefficients of the waste - air oxidation device, gas - source heat pump, water - source heat pump, and ground - source heat pump; \(\eta\) 1 and \(\eta\) 2 respectively represent the electrical efficiency coefficient and thermal efficiency coefficient of the gas turbine; \(\omega\) 1 and \(\omega\) 2 respectively represent the refrigeration efficiency coefficient of the electric chiller and the refrigeration efficiency coefficient of the absorption chiller;
[0023] The expression of the ramp - up / down constraint of the gas turbine is: Among them, P gc and respectively represent the upper and lower limits of the ramp - up / down constraint of the gas turbine;
[0024] The expression of the upper and lower limits of the output of production equipment is:
[0025]
[0026] Among them, and respectively represent the predicted wind turbine output and photovoltaic output; and respectively represent the maximum grid power purchase and the maximum output power of the gas turbine; H FW and respectively represent the lower and upper limits of the output of the exhausted air oxidation device; H GB and respectively represent the lower and upper limits of the output of the air source heat pump; H SB and respectively represent the lower and upper limits of the output of the water source heat pump; H DB and respectively represent the lower and upper limits of the output of the ground source heat pump;
[0027] The actual energy storage constraints include the constraints of the electricity storage device and the heat storage device. The expression of the electricity storage device constraint is:
[0028]
[0029] Among them, and respectively represent the charging and discharging powers of the battery at time t; and respectively represent the maximum charging and discharging powers of the battery; η ES,in and η ES,out respectively represent the charging and discharging efficiencies; η ES,st represents the static energy efficiency of the battery; and respectively represent the charging and discharging state variables of the battery at time t; S OC,t represents the battery's charge capacity at time t; S OC,min and S OC,max respectively represent the upper and lower limits of the battery's charge capacity;
[0030] The expression of the heat storage device constraint is:
[0031]
[0032] Among them, and respectively represent the heat storage and heat release powers of the heat storage device at time t; and respectively represent the maximum heat storage and heat release powers of the heat storage device; η HS,st represents the heat dissipation rate; ηHS,in and η HS,out respectively represent the heat storage and release efficiencies of the heat storage device; and respectively represent the heat storage and release state variables of the heat storage device at time t; S HS,min represents the capacity of the heat storage device at time t; S HS,min and S HS,max respectively represent the upper and lower limits of the capacity of the heat storage device.
[0033] Furthermore, the process of constructing a single-objective mixed-integer programming model for the CMIES day-ahead scheduling problem based on the multi-objective mixed-integer programming model includes:
[0034] Introduce the objective weight λ, linearly weight the two objective functions in the multi-objective mixed-integer programming model using λ, and use the constraint conditions that need to be satisfied during the safe production of CMIES as the constraint conditions of the single-objective mixed-integer programming model. The mathematical expression of the single-objective mixed-integer programming model is: Minλ×f 1 +(1 - λ)×f 2 , and determine the non-dominated solution of the multi-objective mixed-integer programming model by solving the optimal solution of the single-objective mixed-integer programming model.
[0035] Furthermore, taking the multi-objective mixed-integer programming model as the main task and the single-objective mixed-integer programming model as the auxiliary task, the process of using the multi-task framework to solve the optimal scheduling scheme set of the multi-objective mixed-integer programming model includes:
[0036] Step 301: Set the auxiliary task startup frequency parameter α, individual repair ratio parameter γ, the maximum number of auxiliary tasks that can be started simultaneously NMT, neighborhood scale ST, and maximum number of iterations MaxGen; initialize the population P with an individual number of N, initialize the archive subsets A1, A2, and the temporary set AS as empty sets, and initialize the number of iterations Gen = 1;
[0037] Step 302: Determine whether to start the auxiliary task according to the current number of iterations. If Gen / α is an integer, start the auxiliary task, solve the optimal solution of the auxiliary task and save the optimal solution to the temporary set AS, and then add the elements in the temporary set AS to the archive subset A1; otherwise, do not start the auxiliary task and go to Step 303;
[0038] Step 303: Construct an adaptive multi-operator collaborative individual generation strategy to generate the offspring population O, and autonomously select appropriate individual update operators based on the feasible solution ratio;
[0039] Step 304: Combine the parent population P, offspring population O, archive subset A2, and temporary set AS, and select the parent population P for the next generation using non-dominated sorting and crowding distance;
[0040] Step 305: Randomly select γ%×N1 semi-feasible individuals from the parental population P and perform a rounding strategy to obtain feasible individuals, and store the obtained feasible individuals in the archive subset A2; where N1 represents the number of semi-feasible individuals in the current parental population P.
[0041] Step 306: Update the archive subset A2 using non-dominated sorting and crowding distance methods to make the archive subset A2 have the same scale as the parental population P.
[0042] Step 307: Determine whether the iteration termination condition is satisfied. If not, return to Step 302 and the iteration count Gen = Gen + 1; if satisfied, output the optimal solution set in the parental population P.
[0043] Furthermore, the process of starting an auxiliary task, solving the optimal solution of the auxiliary task, and saving the optimal solution to the temporary set AS in Step 302 includes:
[0044] First, calculate the proportion fr of feasible solutions and the number n of sparse regions in the current population 2 , and then calculate the scale of the auxiliary task to be started through the following formula: NT = max(n 1 , n 2 ), where the parameter
[0045] Then, determine the form of the auxiliary task to be started according to the relative sizes of n 1 , n 2 : When n 1 > n 2 , obtain n 1 auxiliary tasks by randomly generating n 1 weights λ; when n 2 ≥ n 1 , calculate the distance d i,j between adjacent neighborhoods i and j, sort the sparse regions in descending order according to this distance value, select the first n 2 sparse regions and introduce a new weight λ' according to the following formula: where λ i represents the weight corresponding to individual i in the archive subset A1, and λ j represents the weight corresponding to individual j in the archive subset A1;
[0046] Finally, use the Gurobi solver to calculate the optimal solution of the auxiliary task and save it to the temporary set AS.
[0047] Furthermore, the calculation process of the number n 2 of sparse regions is as follows:
[0048] Determine the neighborhood B(i) of each element i in the archived subset A1 in sequence, that is, select the T individuals closest to the element i from the current population P according to the objective function value; then calculate the minimum distance d between the adjacent neighborhoods B(i) and B(j). i,j , if d i,j > θ, it indicates that the area between the neighborhood B(i) and the neighborhood B(j) is a sparse area, and update n 2 = n 2 + 1; where the calculation formulas for the minimum distance d i,j and the threshold θ are respectively:
[0049]
[0050]
[0051] Among them, the minimum distance d i,j is used to measure the sparsity of the area; f 1,min , f 1,max , f 2,min and f 2,max are respectively the minimum and maximum values of the two objective functions, f 1 (k1) represents the first objective function value of the individual k1, f 1 (k2) represents the first objective function value of the individual k2, f 2 (k1) represents the second objective function value of the individual k1, f 2 (k2) represents the second objective function value of the individual k2.
[0052] Furthermore, step 303 specifically includes:
[0053] Construct two individual update operator methods. The first method is to introduce an individual update operator guided by the optimal solution of an auxiliary task, and the update formula is as follows: x i (t + 1) = x i (t) + rand × (x * - x i (t)), where x i (t + 1) represents the newly generated offspring individual, x i (t) represents the parent individual, x * represents the individual randomly selected from the archived subset A1; rand is a random number in the interval [0, 1];
[0054] The second method is to use the GA operator as the individual update operator in the main task, and the update formula is:
[0055]
[0056] Among them, and denote two newly generated offspring individuals and denote two parent individuals selected for mating; the parameter β is related to the distribution factor η and is dynamically and randomly determined by the following formula:
[0057]
[0058] If the proportion of feasible solutions in the current population is low, select the first method to update the operator; if the proportion of feasible solutions in the population is high, select the second method to update the operator.
[0059] Beneficial effects: Compared with the prior art, the significant advantages of the present invention are:
[0060] The present invention establishes a multi-objective mixed-integer programming model and a single-objective mixed-integer programming model for the CMIES day-ahead scheduling problem according to actual production requirements. The multi-objective mixed-integer programming model is used as the main task, and the single-objective mixed-integer programming model is used as the auxiliary task. The multi-task framework is used to solve the optimal scheduling plan set of the multi-objective mixed-integer programming model, and a set of theoretically optimal scheduling plans can be obtained; the present invention has a small calculation cost and a short running time during the calculation process, better meets the actual production requirements, and provides a real-time decision-making plan for managers; the present invention can ensure the distribution of the obtained scheduling plans and has the ability to provide diversified decision-making plans for managers. Description of the drawings
[0061] Figure 1 is a flowchart for solving the optimal scheduling plan set of the multi-objective mixed-integer programming model using the multi-task framework in the embodiment;
[0062] Figure 2 is a comparison chart of the objective function value results obtained by using two different methods in the embodiment;
[0063] Figure 3 is a power load supply-demand matching balance chart obtained by using the method in the embodiment;
[0064] Figure 4 is a heat load supply-demand matching balance chart obtained by using the method in the embodiment;
[0065] Figure 5 is a cold load supply-demand matching balance chart obtained by using the method in the embodiment. Detailed implementation manners
[0066] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments.
[0067] An intelligent generation method for the CMIES daily scheduling scheme based on multi-task learning according to this embodiment, the method includes:
[0068] For the selected mine integrated energy system, determine the actual production demand of CMIES;
[0069] Establish a multi-objective mixed-integer programming model for the CMIES daily scheduling problem according to the actual production demand, and determine the constraint conditions that need to be satisfied during the safe production of CMIES;
[0070] Construct a single-objective mixed-integer programming model for the CMIES daily scheduling problem according to the multi-objective mixed-integer programming model;
[0071] Take the multi-objective mixed-integer programming model as the main task and the single-objective mixed-integer programming model as the auxiliary task, and use the multi-task framework to solve the optimal scheduling scheme set of the multi-objective mixed-integer programming model;
[0072] Generate an optimal scheduling scheme according to the actual production status of CMIES.
[0073] In this example, a typical mine integrated energy system (CMIES) is selected, and the energy types, production equipment, decision variables, optimization objectives, system physical characteristics, and safe operation conditions of CMIES are obtained. Determine the actual production demand of CMIES to establish a multi-objective mixed-integer programming model for the CMIES daily scheduling problem. CMIES uses internal and external energy to meet the rigid demand for the three loads of electricity, heat, and cold required for its own safe production. Among them, the internal energy type refers to mine-derived energy, such as exhausted air, air heat, mine wastewater, and geothermal energy. The external energy types include two renewable energy sources, wind energy and solar energy, as well as electricity purchased from the grid and gas purchased through pipelines. The production equipment in CMIES includes fans, photovoltaics, gas turbines, heat collection equipment, exhausted air oxidation devices, heat pumps, electric chillers, absorption chillers, heat storage equipment, and electricity storage equipment. The decision variables include the purchased power, gas turbine output power, fan output, photovoltaic output, electric chiller output, absorption chiller output, electricity storage equipment discharge power, electricity storage equipment charge power, heat storage equipment heat dissipation power, heat storage equipment heat storage power, exhausted air oxidation device output, water source heat pump output, gas source heat pump output, ground source heat pump output, current electricity of the electricity storage equipment, current heat of the heat storage equipment, charge state of the electricity storage equipment, discharge state of the electricity storage equipment, heat storage state of the heat storage equipment, and heat dissipation state of the heat storage equipment; the system physical characteristics and safe operation conditions include: cold, heat, and electricity load supply and demand balance constraints, gas turbine ramp constraints, equipment output upper and lower limit constraints, and actual energy storage constraints.
[0074] Establishing a multi-objective mixed-integer programming model for the CMIES daily scheduling problem according to the actual production demand includes:
[0075] Select the economic cost and carbon trading cost as the two objective functions. The expression of the first objective function is:
[0076] Min f 1 =C trade +C ges +C cut ,
[0077] where f 1 represents the economic cost, C trade represents the external energy trading cost, C ges represents the equipment operation cost, C cut represents the penalty cost for curtailment of wind, solar and associated energy;
[0078] The expression of the second objective function is:
[0079] Min f 2 =c i (E out -E all ),
[0080] where f 2 represents the carbon trading cost, c i is the carbon trading market price on the day, E out represents the total CO 2 emissions, E all represents the CO 2 carbon emission quota. If f 2 is positive, it means that the carbon emissions exceed the quota, and carbon emission allowances must be purchased; if f 2 is negative, it means that carbon emission allowances are sold to obtain benefits.
[0081] Specifically, the external energy trading cost C trade refers to the cost of purchasing electricity from outside the CMIES system and the cost of purchasing fuel. The calculation expression is:
[0082]
[0083] where t represents the scheduling interval, which is 1 hour in this example, T represents the scheduling period, which is 24 hours in this example, c e,t is the unit price of electricity purchase; c g,t is the unit calorific value price of natural gas; P e,t is the power of purchasing electricity from the external power grid of the system; P g,t is the output power of the gas turbine;
[0084] The calculation expression of the equipment operation cost C ges is:
[0085]
[0086] Among them, P WT,t 、P PV,t 、H FW,t 、H GB,t 、H SB,t 、H DB,t 、 are the wind turbine output, photovoltaic output, exhausted air oxidation device output, gas source heat pump output, water source heat pump output, ground source heat pump output, heat storage and release power, and electricity storage and release power at time t respectively; c WT,om 、c PV,om 、c FW,om 、c GB,om 、c SB,om 、c DB,om 、c H 、c E represent the operation and maintenance costs per unit power per unit time of the corresponding equipment (wind turbine, photovoltaic, exhausted air oxidation device, gas source heat pump, water source heat pump, ground source heat pump, heat storage equipment, and electricity storage equipment) respectively; is the heat storage and release state variable of the heat storage equipment at time t; is the electricity storage and release state variable of the electricity storage equipment at time t;
[0087] The penalty cost C cut for wind, photovoltaic, and associated energy curtailment is calculated as follows:
[0088]
[0089] Among them, represent the predicted output of the wind turbine, the predicted output of the photovoltaic, and the output of the exhausted air, gas source, water source, and ground source heat pumps at time t respectively; λ 1 、λ 2 、λ 3 、λ 4 and λ 5 represent the penalty coefficients for renewable energy curtailment, exhausted air, air heat, mine wastewater, and geothermal energy respectively.
[0090] The second objective function refers to constraining carbon emissions through market trading means during the carbon emission trading process, guiding enterprises to incorporate carbon emissions into the optimization indicators, and thus promoting the enthusiasm of enterprises to develop clean and low-carbon electricity. Specifically, it is manifested as follows: ① When the actual carbon emissions are less than the carbon emission allocation quota, the remaining quota can be sold on the market at the real-time trading price to obtain benefits; ② When the actual carbon emissions are greater than the carbon emission allocation quota, the insufficient part of the quota needs to be purchased on the market or the corresponding over-emission fine needs to be paid. The carbon emissions of CMIES occur in the production, transportation, and use processes of various energy sources. Therefore, the carbon emissions should be equal to the sum of the carbon emissions in these two processes, and the calculation formula is:
[0091]
[0092] Among them, are the carbon emission coefficients corresponding to the energy production and transportation stages of the fan output, photovoltaic output, power grid, energy storage device, gas turbine, and exhausted air oxidation device, with the unit g / (kW·h); are the carbon emission coefficients corresponding to the energy usage stages of the fan output, photovoltaic output, power grid, energy storage device, gas turbine, and exhausted air oxidation device, with the unit g / (kW·h).
[0093] The constraint conditions that need to be satisfied during the safe production of CMIES include:
[0094] Load supply-demand balance constraint, gas turbine ramp constraint, output upper and lower limit constraints of production equipment, and actual energy storage constraint. Among them, the expression of the load supply-demand balance constraint is:
[0095]
[0096] Among them, P e,t represents the purchased power from the external power grid of the system at time t, P g,t represents the output power of the gas turbine at time t, P WT,t represents the output power of the fan at time t, P PV,t represents the output power of the photovoltaic at time t, P Pac,t represents the input power of the electric chiller, and represent the stored power and discharge power of the energy storage at time t respectively, and represent the state variable of stored power and the state variable of discharge of the energy storage device at time t respectively, H FW,t represents the output power of the exhausted air oxidation device at time t, H GB,t represents the output power of the gas source heat pump at time t, H SB,t represents the output power of the water source heat pump at time t, H DB.t represents the output power of the ground source heat pump at time t, H Hac,t represents the input power of the absorption chiller, and represent the stored heat power and the released heat power respectively; P 0,t 、H 0,t and L 0,t represent the electrical, thermal, and cooling loads required by the system at time t respectively; ν 1 、ν 2 、ν 3 and ν 4 represent the efficiency coefficients of the exhausted air oxidation device, gas source heat pump, water source heat pump, and ground source heat pump respectively; η 1 and η 2 represent the electrical efficiency coefficient and thermal efficiency coefficient of the gas turbine respectively; ω 1 and ω2 respectively represent the refrigeration efficiency coefficient of the electric refrigerator and the absorption refrigerator;
[0097] The ramp constraint expression of the gas turbine is: where, P gc and respectively represent the upper and lower limits of the ramp constraint of the gas turbine;
[0098] The upper and lower limit constraint expressions of the production equipment output are:
[0099]
[0100] where, and respectively represent the predicted fan output and PV output; and respectively represent the maximum grid power purchase and the maximum output power of the gas turbine; H FW and respectively represent the lower and upper limits of the output of the waste gas oxidation device; H GB and respectively represent the lower and upper limits of the output of the air source heat pump; H SB and respectively represent the lower and upper limits of the output of the water source heat pump; H DB and respectively represent the lower and upper limits of the output of the ground source heat pump;
[0101] The actual energy storage constraints include the electricity storage equipment constraint and the heat storage equipment constraint. The electricity storage equipment constraint expression is:
[0102]
[0103] where, and respectively represent the charging and discharging powers of the storage battery at time t; and respectively represent the maximum charging and discharging powers of the storage battery; η ES,in and η ES,out respectively represent the charging and discharging efficiencies; η ES,st represents the static energy efficiency of the storage battery; and respectively represent the charging and discharging state variables of the storage battery at time t; S OC,t represents the electricity storage capacity of the storage battery at time t; S OC,min and S OC,max respectively represent the upper and lower limits of the electricity storage capacity of the storage battery;
[0104] The constraint expression of the heat storage device is as follows:
[0105]
[0106] Among them, and respectively represent the heat storage and heat release powers of the heat storage device at time t; and respectively represent the maximum heat storage and heat release powers of the heat storage device; η HS,st represents the heat dissipation rate; η HS,in and η HS,out respectively represent the heat storage and heat release efficiencies of the heat storage device; and respectively represent the heat storage and heat release state variables of the heat storage device at time t; S HS,min represents the capacity of the heat storage device at time t; S HS,min and S HS,max respectively represent the upper and lower limits of the capacity of the heat storage device.
[0107] The process of constructing a single-objective mixed-integer programming model for the CMIES day-ahead scheduling problem based on the multi-objective mixed-integer programming model includes:
[0108] Introduce the objective weight λ, and use λ to perform a linear weighted operation on the two objective functions in the multi-objective mixed-integer programming model. At the same time, the constraint conditions that need to be satisfied during the safe production of CMIES are used as the constraint conditions of the single-objective mixed-integer programming model. The mathematical expression of the single-objective mixed-integer programming model is: Min λ×f 1 +(1 - λ)×f 2 , and determine the non-dominated solution of the multi-objective mixed-integer programming model by solving the optimal solution of the single-objective mixed-integer programming model.
[0109] Take the multi-objective mixed-integer programming model of the CMIES day-ahead scheduling problem as the main task, and take the single-objective mixed-integer programming model of the CMIES day-ahead scheduling problem as the auxiliary task. The parameter λ is the objective weight. It can be seen that the constraint conditions of the main task and the auxiliary task are the same, that is, the feasible regions of the main and auxiliary problems are the same. The objective functions and constraint conditions in the main task are all linear. By performing a linear weighting on the two objective functions in the main task, it can be converted into multiple standard mixed-integer linear programming problems, and the mathematical programming method can quickly obtain the optimal solution of this type of problem. The verification is carried out through the following process, and the global optimal solution of the auxiliary task is a non-dominated solution of the main task.
[0110] Verification conclusion: If the main task is a multi-objective mixed-integer linear programming problem, and the auxiliary task is a single-objective mixed-integer linear programming problem obtained by linearly weighting the multiple objective functions in the main task, then the optimal solution of the auxiliary task must be a non-dominated solution Pareto of the main task.
[0111] Verification process: Given that the optimal solution of the auxiliary task is The objective function value is z = λ × f 1 +(1 - λ) × f 2 , where f 1 and f 2 are two objective function values. Assume that os is not a non-dominated solution of the original problem. Then there must be at least one solution whose objective function value is such that os * is dominated by it, that is, or Therefore, at this time, it must satisfy Also, because the feasible regions of the primary and auxiliary tasks are the same, so os must not be the optimal solution of the auxiliary task. In summary, the original hypothesis is not valid, that is, os must be a non-dominated solution of the original problem.
[0112] As Figure 1 shown in the flowchart, taking the multi-objective mixed integer programming model as the primary task and the single-objective mixed integer programming model as the auxiliary task, the process of using the multi-task framework to solve the optimal scheduling scheme set of the multi-objective mixed integer programming model includes the following steps:
[0113] Step 301: Set the auxiliary task startup frequency parameter α, the individual repair ratio parameter γ, the maximum number of simultaneously startable auxiliary tasks NMT, the neighborhood scale ST, and the maximum number of iterations MaxGen; Initialize the population P with an individual number of N, initialize the archive subsets A1, A2, and the temporary set AS as empty sets, and initialize the iteration number Gen = 1;
[0114] Step 302: Determine whether to start the auxiliary task according to the current iteration number. If Gen / α is an integer, start the auxiliary task, solve the optimal solution of the auxiliary task and save the optimal solution to the temporary set AS, and then add the elements in the temporary set AS to the archive subset A1; Otherwise, do not start the auxiliary task and go to Step 303;
[0115] Step 303: Construct an adaptive multi-operator collaborative individual generation strategy to generate the offspring population O, and autonomously select appropriate individual update operators based on the feasible solution ratio;
[0116] Step 304: Combine the parent population P, the offspring population O, the archive subset A2, and the temporary set AS, and use non-dominated sorting and crowding distance to select the parent population P for the next generation;
[0117] Step 305: Randomly select γ%×N1 semi-feasible individuals from the parental population P and perform a rounding strategy to obtain feasible individuals, and store the obtained feasible individuals in the archive subset A2; where N1 represents the number of semi-feasible individuals in the current parental population P.
[0118] Step 306: Update the archive subset A2 using non-dominated sorting and crowding distance methods to make the archive subset A2 have the same scale as the parental population P.
[0119] Step 307: Determine whether the iteration termination condition is satisfied. If not, return to Step 302 and the iteration count Gen = Gen + 1; if satisfied, output the optimal solution set in the parental population P.
[0120] Specifically, the process of starting an auxiliary task, solving the optimal solution of the auxiliary task, and saving the optimal solution to the temporary set AS in Step 302 includes:
[0121] First, calculate the proportion fr of feasible solutions and the number n of sparse regions in the current population 2 , and then calculate the scale of the started auxiliary task through the following formula: NT = max(n 1 , n 2 ), where the parameter
[0122] Then, determine the form of the started auxiliary task according to the relative sizes of n 1 and n 2 : When n 1 > n 2 , obtain n 1 auxiliary tasks by randomly generating n 1 weights λ; when n 2 ≥ n 1 , calculate the distance d i,j between adjacent neighborhoods i and j, sort the sparse regions in descending order according to this distance value, select the first n 2 sparse regions and introduce a new weight λ' according to the following formula: where λ i represents the weight corresponding to individual i in the archive subset A1, and λ j represents the weight corresponding to individual j in the archive subset A1; when different weights λ correspond to the same objective function value, only retain the smallest weight λ value.
[0123] Finally, the Gurobi solver is used to calculate the optimal solution of the auxiliary task and save it to the temporary set AS. The elements in the obtained temporary set AS are added to the archive subset A1. It should be noted that when calling the Gurobi solver to solve the auxiliary task, the feasible solutions obtained from the population in the main task are selected as the initial solutions of the auxiliary task for the following reasons: the objective values of the feasible solutions in the main task provide a good upper bound for the objective value of the auxiliary task, which helps to reduce the number of algorithm iterations and accelerate the problem-solving process.
[0124] Specifically, the number n of sparse regions 2 is calculated as follows:
[0125] The neighborhood B(i) of each element i in the archive subset A1 is determined in turn, that is, T individuals closest to element i are selected from the current population P according to the objective function value; then the minimum distance d between adjacent neighborhoods B(i) and B(j) is calculated i,j , if d i,j > θ, it indicates that the region between the neighborhood B(i) and the neighborhood B(j) is a sparse region, and n 2 is updated as n 2 = n i,j + 1; where the calculation formulas for d
[0126]
[0127]
[0128] where the minimum distance d i,j is used to measure the sparsity of the region; f 1,min , f 1,max , f 2,min and f 2,max are the minimum and maximum values of the two objective functions respectively, f 1 (k1), f 1 (k2) represent the first objective function values of individuals k1 and k2 respectively, and f 2 (k1), f 2 (k2) represent the second objective function values of individuals k1 and k2 respectively. Each element in the archive subset A1 corresponds to an optimal solution of an auxiliary task, that is, a non-dominated solution in the main task. Based on the known non-dominated solutions in the archive subset A1 and the current population state, the sparse regions in the PF distribution can be dynamically determined. Further, by adjusting the auxiliary task to explore these sparse regions, it helps to improve the uniformity of the PF distribution.
[0129] Step 303 specifically includes:
[0130] Construct two individual update operator methods. The first method is to introduce an individual update operator guided by the optimal solution of an auxiliary task, and the update formula is as follows: x i (t + 1) = x i (t) + rand × (x * - x i (t)), where x i (t + 1) represents the newly generated offspring individual, x i (t) represents the parent individual, and x * represents an individual randomly selected from the archive subset A1; rand is a random number in the interval [0, 1];
[0131] The second method is to use the GA operator as the individual update operator in the main task, and the update formula is:
[0132]
[0133] where, and represent two newly generated offspring individuals, and represent two parent individuals selected for mating; the parameter β is related to the distribution factor η and is dynamically and randomly determined by the following formula:
[0134]
[0135] If the proportion of feasible solutions in the current population is low, select the first method to update the operator; if the proportion of feasible solutions in the population is high, select the second method to update the operator.
[0136] In the above step 304, non-dominated sorting is a sorting algorithm that divides the population individuals into different levels, and the crowding distance is used to measure the quality of individuals at the same level. Combining the two is used to ensure the convergence and diversity of the population.
[0137] In step 305, for the semi-feasible solution x i of the relaxation problem and the feasible solution x i ' obtained after implementing the rounding strategy, their relationship is shown in the following verification process, and it can be seen that the archive subset A2 can effectively balance the convergence and feasibility of individuals in the population.
[0138] Verification conclusion: For the multi-objective mixed-integer linear programming problem, the semi-feasible solution x i of the relaxation problem must dominate the feasible solution x' i obtained after implementing the rounding strategy.
[0139] Verification process: Without loss of generality, assume x' iis the optimal solution for the auxiliary task corresponding to the weight parameter λ, and the objective function value is z1 = λ × f 1 (x′ i )+(1 - λ)×f 2 (x′ i ). According to the basic properties of the mixed-integer programming problem, the following formula holds:
[0140] z = λ × f 1 (x i )+(1 - λ)×f 2 (x i ) < z1 = λ × f 1 (x′ i )+(1 - λ)×f 2 (x′ i )
[0141] At this time, there are the following two possible cases for the relationship between (f 1 (x i ), f 2 (x i )) and (f 1 (x′ i ), f 2 (x′ i )):
[0142] Case 1: f 1 (x i ) < f 1 (x′ i ), f 2 (x i ) ≤ f 2 (x′ i ) or f 1 (x i ) ≤ f 1 (x′ i ), f 2 (x i ) < f 2 (x′ i ). At this time, the semi-feasible solution x i dominates the optimal solution x′ i of the auxiliary task;
[0143] Case 2: f 1 (x i ) < f 1 (x′ i ), f 2 (x i ) ≥ f 2 (x′ i ) or f 1 (x i ) ≥ f 1 (x′i ),f 2 (x i ) < f 2 (x') i ), at this time, the semi-feasible solution x i and the optimal solution x' of the auxiliary task i are in a non-dominating relationship with each other. Therefore, the semi-feasible solution x i must be the optimal solution of the auxiliary task corresponding to a certain weight λ'. Then, the semi-feasible solution x i must be a feasible solution that satisfies the integer constraint, which does not conform to the known conditions. Therefore, case two does not exist.
[0144] In summary, the conclusion can be drawn: The semi-feasible solution x of the relaxation problem i must dominate the feasible solution x' obtained after implementing the rounding strategy i .
[0145] In an example, the on-site manager can select one of the scheduling schemes as the final day-ahead scheduling scheme of CMIES according to the actual production status or preference information. For example, if the manager tends to reduce the economic cost, the solution corresponding to the minimum value of the objective function f1 is selected as the scheduling scheme; if the manager tends to reduce carbon emissions, the solution corresponding to the minimum value of the objective function f2 is selected as the scheduling scheme. In addition, the manager can also consider the economic cost and carbon emissions in a balanced manner, and then the solution corresponding to the minimum value of the objective function 0.5*f1 + 0.5*f2 is selected as the scheduling scheme.
[0146] Next, the following example is used to conduct a specific experimental analysis on the intelligent generation method for the day-ahead scheduling scheme of CMIES based on multi-task learning described in the present invention.
[0147] A coal mine enterprise located in Shanxi Province is selected as the research object, which has all the production equipment and energy type characteristics in the CMIES system, including renewable energy and mine-derived energy. All the relevant parameters of the proposed multi-objective CMIES day-ahead scheduling model can be obtained from the papers published by Hejuan Hu et al., "Enhanced evolutionary multi-objective optimization-based dispatch of coal mine integrated energy system with flexible load" (Applied Energy, 2021, 307: 118130), and Yan Wang et al., "Unified operation optimization model of integrated coal mine energy systems and its solutions based on autonomous intelligence" (Applied Energy, 2022, 328: 120106). The scheduling period T of the established multi-objective mixed integer programming model is 24h, the scheduling interval t is 1h, the number of decision variables is 20 * 24 = 480, and the number of constraint conditions is 22 * 24 = 528. To verify the effectiveness of the method described in this embodiment, C-MOEA\D in the paper published by H. Jain and K. Deb, "An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part II: Handling constraints and extending to an adaptive approach" (IEEE Transactions on Evolutionary Computation, 2014, 18(4): 602-622) is selected as the comparison algorithm. Further, four indicators, namely the proportion of feasible solutions, the number of non-dominated solutions, the HV value, and the running time, are selected to comprehensively measure the performance of the method MD-EAMP proposed in this embodiment and the comparison algorithm C-MOEA\D. The detailed experimental results are shown in Table 1 and Figure 2 .
[0148] Table 1 Comparison results of multi-objective CMIES day-ahead scheduling schemes [mean (standard deviation)]
[0149]
[0150] As can be seen from Table 1: (1) The C-MOEA\D algorithm can only obtain a small number of scheduling schemes with poor convergence and distribution, and this conclusion can also be directly drawn from Figure 2 ; while the MD-EAMP method proposed in the present invention can obtain a set of PF fronts with good convergence and uniform distribution, and the scheduling schemes obtained by MD-EAMP Pareto-dominate the scheduling schemes obtained by the CMOEA\D algorithm, which can provide diversified scheduling schemes for on-site managers. (2) Regarding the algorithm running time index, the MD-EAMP proposed in the present invention is significantly superior to C-MOEA\D, and the running time is much less than the scheduling interval (1 h) of the CMIES day-ahead scheduling problem, which further proves the superiority of the MD-EAMP described in this embodiment.
[0151] In addition, to analyze the supply-demand balance relationship of the electrical, thermal, and cooling loads of the scheduling scheme obtained by the MD-EAMP method proposed in the present invention, one of the scheduling schemes is randomly selected, and the specific output of each device is shown in Figure 3 、 4 and 5. Among them, Figure 3 、 Figure 4 and Figure 5 are the supply-demand matching balance diagrams of the electrical, thermal, and cooling loads respectively. From Figures 3 - 5 analysis, it can be known that the electrical, thermal, and cooling loads of the obtained scheduling scheme satisfy the supply-demand matching balance relationship. Therefore, the scheduling scheme obtained by the method of the present invention can effectively meet various energy supply demands, and at the same time can effectively utilize renewable energy and mine-derived energy.
Claims
1. A method for intelligently generating a CMIES day-ahead scheduling scheme based on multi-task learning, characterized in that: The method includes: Determine the actual production requirements of CMIES for the selected mine integrated energy system; Establish a multi-objective mixed integer programming model for the CMIES day-ahead scheduling problem based on actual production demand, and determine the constraints that need to be met for CMIES safe production; Based on the multi-objective mixed integer programming model, a single-objective mixed integer programming model for the CMIES day-ahead scheduling problem is constructed; The multi-objective mixed integer programming model is used as the main task, the single-objective mixed integer programming model is used as the auxiliary task, and the optimal scheduling solution set of the multi-objective mixed integer programming model is solved using the multi-task framework; Generate the optimal scheduling plan based on the actual production status of CMIES; Among them, the multi-objective mixed integer programming model for the CMIES day-ahead scheduling problem is established based on actual production demand, including: Economic cost and carbon trading cost are selected as two objective functions. The first objective function expression is: Min f1=C trade +C ges +C cut , Among them, f1 represents the economic cost, C trade represents the external energy transaction cost, C ges Indicates the equipment operating cost, C cut It represents the penalty cost for abandoning wind, solar and associated energy; The second objective function expression is: My f2=c i (E out -E all ), Among them, f2 represents the carbon trading cost, c i is the carbon trading market price on that day, E out Indicates the total CO2 emissions, E all Represents CO2 carbon emission quota; The constraints that CMIES needs to meet during safe production include: Load supply and demand balance constraints, gas turbine ramp constraints, upper and lower output limits of production equipment, and actual energy storage constraints. The expression of load supply and demand balance constraints is: Among them, P e,t represents the power purchased from the external power grid at time t, P g,t represents the output power of the gas turbine at time t, P WT,t represents the fan output power at time t, P PV,t represents the photovoltaic output power at time t, P Pac,t represents the input power of the electric refrigerator, and They represent the storage power and discharge power at time t respectively, and They represent the storage state variable and discharge state variable of the storage device at time t, respectively. FW,t It represents the output power of the air-deficient oxidation device at time t, H GB,t represents the output power of the air source heat pump at time t, H SB,t represents the output power of the water source heat pump at time t, H DB.t represents the output power of the ground source heat pump at time t, H Hac,t represents the input power of the absorption chiller, and Represent heat storage power and heat release power respectively; P 0,t , H 0,t and L 0,t They represent the electricity, heat and cooling loads required by the system at time t respectively; ν1, ν2, ν3 and ν4 represent the efficiency coefficients of the exhaust air oxidation device, the air source heat pump, the water source heat pump and the ground source heat pump respectively; η1 and η2 represent the electrical efficiency coefficient and thermal efficiency coefficient of the gas turbine respectively; ω1 and ω2 represent the refrigeration efficiency coefficients of the electric chiller and the absorption chiller respectively; The ramp constraint expression of the gas turbine is: in, P gc and They represent the upper and lower limits of the gas turbine ramp constraint respectively; The upper and lower limit constraint expressions of the output of production equipment are: in, and represent the predicted wind turbine output and photovoltaic output respectively; and They represent the maximum power purchased by the power grid and the maximum output power of the gas turbine respectively; H FW and They represent the lower and upper limits of the output of the lack of air oxidation device respectively; H GB and They represent the lower and upper limits of the output of the air source heat pump respectively; H SB and They represent the lower and upper limits of the water source heat pump output respectively; H DB and They represent the lower and upper limits of the ground source heat pump output respectively; The actual energy storage constraints include power storage equipment constraints and heat storage equipment constraints. The power storage equipment constraint expression is: in, and Respectively represent the storage and discharge power of the battery at time t; and Respectively represent the maximum storage and discharge power of the battery; η ES,in and η ES,out Respectively represent the storage and discharge efficiency; η ES,st Indicates the static energy efficiency of the battery; and They represent the storage and discharge state variables of the battery at time t respectively; S OC,t Represents the battery storage capacity at time t; S OC,min and S OC,max Respectively represent the upper and lower limits of the battery storage capacity; The constraint expression of heat storage equipment is: in, and They represent the heat storage and release power of the heat storage device at time t respectively; and Respectively represent the maximum heat storage and heat release power of the heat storage equipment; η HS,st Indicates the heat dissipation rate; η HS,in and η HS,out They represent the heat storage and release efficiency of the heat storage equipment respectively; and They represent the heat storage and heat release state variables of the heat storage device at time t; S HS,min represents the capacity of the heat storage device at time t; S HS,min and S HS,max Respectively represent the upper and lower limits of the capacity of the heat storage equipment; The process of constructing a single-objective mixed integer programming model for the CMIES day-ahead scheduling problem based on the multi-objective mixed integer programming model includes: The objective weight λ is introduced, and λ is used to perform linear weighted operation on the two objective functions in the multi-objective mixed integer programming model. The constraints that need to be met during CMIES safe production are also used as constraints of the single-objective mixed integer programming model. The mathematical expression of the single-objective mixed integer programming model is: Minλ×f1+(1-λ)×f2. The non-inferior solution of the multi-objective mixed integer programming model is determined by solving the optimal solution of the single-objective mixed integer programming model.
2. According to claim 1, a method for intelligently generating a CMIES day-ahead scheduling scheme based on multi-task learning is characterized in that: The process of using the multi-objective mixed integer programming model as the main task and the single-objective mixed integer programming model as the auxiliary task to solve the optimal scheduling solution set of the multi-objective mixed integer programming model using the multi-task framework includes: Step 301: Set the auxiliary task start frequency parameter α, the individual repair ratio parameter γ, the maximum number of auxiliary tasks that can be started simultaneously NMT, the neighborhood size ST, and the maximum number of iterations MaxGen; initialize the population P with N individuals, initialize the archive subset A1, archive subset A2, and temporary set AS to empty sets, and initialize the number of iterations Gen=1; Step 302: Determine whether to start the auxiliary task according to the current number of iterations. If Gen / α is an integer, start the auxiliary task, find the optimal solution of the auxiliary task and save the optimal solution to the temporary set AS, and then add the elements in the temporary set AS to the archive subset A1; otherwise, do not start the auxiliary task and go to step 303; Step 303: construct an adaptive multi-operator collaborative individual generation strategy to generate a sub-population O, and autonomously select a suitable individual update operator based on the proportion of feasible solutions; Step 304: merge the parent population P, the child population O, the archived subset A2, and the temporary set AS, and select the parent population P to enter the next generation by using the non-dominated sorting and crowding distance method; Step 305: Randomly select γ%×N1 semi-feasible individuals in the parent population P and execute the rounding strategy to obtain feasible individuals, and store the obtained feasible individuals in the archive subset A2; wherein N1 represents the number of semi-feasible individuals in the parent generation P of the current population; Step 306: Update the archive subset A2 using non-dominated sorting and crowding distance, so that the archive subset A2 has the same size as the parent population P; Step 307: Determine whether the iteration termination condition is met. If not, return to step 302, and the number of iterations Gen = Gen + 1; if satisfied, output the optimal solution set in the parent population P.
3. According to claim 2, a method for intelligently generating a CMIES day-ahead scheduling scheme based on multi-task learning is characterized in that: In step 302, the auxiliary task needs to be started, and the process of solving the optimal solution of the auxiliary task and saving the optimal solution to the temporary set AS includes: First, calculate the proportion of feasible solutions fr and the number of sparse regions n2 in the current population, and then calculate the scale of the auxiliary task to be started by the following formula: NT = max(n1,n2), where the parameters Then, the form of starting the auxiliary task is determined according to the relative size of n1 and n2: when n1>n2, n1 auxiliary tasks are obtained by randomly generating n1 weights λ; when n2≥n1, the distance d between adjacent neighborhoods i and j is calculated. i,j , sort the sparse regions in descending order according to the distance value, select the first n2 sparse regions and introduce a new weight λ' based on the following formula: Among them, λ i represents the weight corresponding to individual i in the archive subset A1, λ j represents the weight corresponding to individual j in the archive subset A1; Finally, the Gurobi solver is used to calculate the optimal solution of the auxiliary task and save it in the temporary set AS.
4. According to claim 3, a method for intelligently generating a CMIES day-ahead scheduling scheme based on multi-task learning is characterized in that: The calculation process of the number of sparse regions n2 is as follows: Determine the neighborhood B(i) of each element i in the archive subset A1 in turn, that is, select the T individuals closest to element i from the current population P according to the objective function value; then calculate the minimum distance d between adjacent neighborhoods B(i) and B(j) i,j , if d i,j >θ, it indicates that the area between neighborhood B(i) and neighborhood B(j) is a sparse area, and n2=n2+1 is updated; where the minimum distance d i,j The calculation formulas for and threshold θ are: Among them, the minimum distance d i,j Used to measure the sparsity of the region; f 1,min 、f 1,max 、f 2,min and f 2,max are the minimum and maximum values of the two objective functions respectively, f1(k1) represents the first objective function value of individual k1, f1(k2) represents the first objective function value of individual k2, f2(k1) represents the second objective function value of individual k1, and f2(k2) represents the second objective function value of individual k2.
5. According to claim 4, a method for intelligently generating a CMIES day-ahead scheduling scheme based on multi-task learning is characterized in that: Step 303 specifically includes: Two individual update operator methods are constructed. The first method is to introduce an individual update operator guided by the optimal solution of the auxiliary task. The update formula is as follows: i (t+1)=x i (t)+rand×(x * -x i (t)), where x i (t+1) represents the newly generated offspring individual, x i (t) represents the parent individual, x * represents an individual randomly selected from the archive subset A1; rand is a random number in the interval [0,1]; The second method is to use the GA operator as the individual update operator in the main task. The update formula is: in, and represents the two newly generated offspring individuals, and represents the two parent individuals selected for mating; the parameter β is related to the distribution factor η and is dynamically and randomly determined by the following formula: If the proportion of feasible solutions in the current population is low, choose the first method to update the operator. If the proportion of feasible solutions in the population is high, choose the second method to update the operator.
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