CN111861137A - Parallel Multi-objective Scheduling Method for Cascade Reservoir Groups - Google Patents

Abstract

The invention discloses a parallel multi-objective dispatching method for cascade reservoir groups, belonging to the hydropower station management technology, in particular to a hydropower energy optimization operation management method for cascade reservoir groups. The multi-objective bee colony algorithm based on Fork/Join parallel computing is used to solve the multi-objective scheduling model of cascade reservoir groups, and the heuristic constraint repair strategy is used to deal with the coupling constraints between various time periods in the process of reservoir group scheduling. This method can quickly generate a set of widely distributed and uniform multi-objective non-inferior dispatching scheme sets, which provides strong theoretical and technical support for multi-objective dispatching decision-making of cascade reservoir groups. This method combines multi-objective stochastic parallel optimization, multiple complex constraint heuristic correction and other efficient solution modes, and a set of non-inferior scheduling schemes that are widely and uniformly distributed in the multi-dimensional target domain space can be obtained in one solution, which provides a basis for the joint scheduling operation of cascade reservoir groups in the basin. Strong support.

Description

Parallel Multi-objective Scheduling Method for Cascade Reservoir Groups

technical field

The invention belongs to the hydropower station management technology, in particular to a hydropower energy optimization operation management method for cascade reservoir groups.

Background technique

The joint optimal dispatching of cascade reservoirs must comprehensively consider the competing and incommensurable dispatching objectives such as flood control, power generation, water supply, shipping, ecological water demand and power grid security. question. At present, there are classical mathematical modeling methods based on traditional operations research, which generally convert multi-objective problems into single-objective problems by introducing objective weight coefficients or objective constraints. The non-inferior scheduling solution set is difficult to fully reflect the competition and constraint relationship between scheduling objectives, especially when dealing with scheduling problems with non-convex and non-continuous multi-objective frontier characteristics, the non-inferior scheduling solution set calculated by the model cannot be very good. Reflects the actual non-inferior frontier characteristics. In addition, affected by many factors such as hydrometeorology, runoff process, power station dispatching mode, and dynamic characteristics of units, the joint optimal dispatching problem of cascade reservoir groups presents typical large-scale, strong coupling, multi-constrained, dynamic and discrete complex nonlinear characteristics. The classical mathematical modeling method based on traditional operations research is very difficult to solve such problems, and the algorithm execution efficiency is often not high due to the complexity of problem solving.

SUMMARY OF THE INVENTION

Aiming at the fact that the classical mathematical modeling method based on traditional operations research is difficult to meet the multi-objective scheduling problem of cascade reservoir groups in the basin under complex constraints, a parallel multi-objective scheduling solution method for cascade reservoir groups is proposed, which combines multi-objective stochastic parallel optimization, Efficient solution modes such as heuristic correction of multiple complex constraints can obtain a set of non-inferior scheduling schemes that are widely and uniformly distributed in the multi-dimensional target domain space in one solution, providing strong support for the joint scheduling operation of cascade reservoir groups in the basin.

The parallel multi-objective scheduling method for cascade reservoir groups, the specific steps are as follows:

S1, set the characteristic parameters of the hydropower station group and initialize the control parameters of the algorithm, including the EliteSet capacity NQ, the population size NP, the maximum evolution algebra G _max of the algorithm, and the number of scout bee starts Limit _abandon ; set the current evolution algebra of the algorithm g=1;

S2, construct and initialize NP population individuals, formula (1):

为个体编码；N为梯级水库个数；T为时段数；In the formula, x _r is the r-th individual;

is the individual code; N is the number of cascade reservoirs; T is the number of time periods;

S3, Reservoir scheduling constraint processing, the following formulas (2)-(7) are used to determine whether the individual satisfies the constraints. For the population individuals that do not meet the constraints, formulas (8) and (9) are used to pair the time periods of the hydropower station group in the individual one by one. Correct the water level;

① Cascade hydraulic connection formula (2):

为i-1水库在 t-τ_i-1时段弃水流量；R_i,t为i-1与i水库间区间入流；In the formula, I _i,t is the inflow flow of reservoir i at period t; τ _i-1 is the time delay of water flow between i-1 and reservoir i;

R _i,t is the inflow between the i _- 1 and i reservoirs;

②Reservoir water balance constraint (3): V _i,t =V _i,t-1 +(I _i,t -Q _i,t -S _i,t )·Δt;

In the formula, Vi _,t is the storage capacity of reservoir i at the end of period t;

③Water level/flow/output constraint (4):

与Z_i,t 、

与Q_i,t 、

与P_i,t 分别为i水库t时段水位、 出库和出力边界；In the formula, P _i,t is the output of reservoir i in period t;

with Z _i,t ,

with Q _i,t ,

and P _i,t are the water level, outgoing and outgoing boundaries of reservoir i at time t, respectively;

④Water level/flow/output variable amplitude constraint formula (5):

In the formula, ΔZ _i , ΔQ _i , and ΔP _i are the limits of the water level, flow, and output variation of reservoir i, respectively;

⑤ Reservoir operating head constraint (6):

H_i,t分别为水库稳定运行水头上下限；In the formula, H _i,t is the water head of reservoir i during t period,

H _{i, t} are the upper and lower limits of the water head for stable operation of the reservoir, respectively;

⑥ Reservoir water level control constraint formula (7) at the beginning and end of the period:

和

为i水库调度期初、期末水位及其控制值；In the formula, Z _i,0 , Z _i,T ,

and

is the water level and its control value at the beginning and end of the dispatching period of the i reservoir;

⑦The generation method of the water level constraint corridor is formula (8):

⑧ Generation method of water level constraint corridor (9):

和

分别为t时段末库容和初库容计算函数；

和

为下泄流量和出力特征值，其设定为流量和出力的上下边界值；In the formula,

and

are the calculation functions of the storage capacity at the end of the period t and the initial storage capacity, respectively;

and

is the characteristic value of discharge flow and output, which is set as the upper and lower boundary values of flow and output;

S4: Calculate the target fitness values of individuals of different populations, normalize the target fitness values, and perform non-dominated sorting on the population individuals based on the individual target fitness values; add all non-dominated individuals in the first level of the population to EliteSet ;

The individual fitness takes the maximum total power generation of cascade reservoirs and the minimum total ecological water shortage of each cascade downstream river as the scheduling objective. The objective functions are described as equations (10) and (11) respectively:

Formula (10):

Formula (11):

为i水库t时段下泄流量与其下游河道适宜生态需求流量的差值；

为t时段i电站下游河道 的适宜生态流量；In the formula, E is the total power generation of cascade reservoirs; P _i,t , Qi _,t , H _i,t are the power generation output, discharge flow and average water head of reservoir i in t period respectively; N is the number of cascade reservoirs; T, ΔT is the number of periods and the length of the period, respectively; W is the cascade ecological water shortage;

is the difference between the discharge flow of the i reservoir and the suitable ecological demand flow of the downstream river channel during t period;

is the suitable ecological flow of the river downstream of the i power station in period t;

Equation (10) and Equation (11) have different dimensions between the objective functions, which are normalized to make it a dimensionless function value; the normalization of the scheduling objective is calculated according to Equation (12):

Formula (12):

和

分别表示种群中所有个体年发电量和缺水量最大值和最小值；In the formula, x _r is the r-th individual in the evolutionary population; Er and W _r are the annual power generation and water shortage of individual r, respectively; E ^max and E ^min ,

and

represent the maximum and minimum annual power generation and water shortage of all individuals in the population, respectively;

S5, population evolution, including the evolution of the employed bee stage, the observation bee stage and the scout bee stage;

①Employment bee stage: The hired bee stage searches for new nectar sources through the "search mechanism" of formulas (13)-(16), and uses formulas (8) and (9) to constrain the newly generated individuals; Based on the pros and cons of the individual and the original individual, the greedy strategy is used to select excellent individuals into the next generation population; the EliteSet is updated and maintained, and the elite candidate individuals are added to the EliteSet;

Formula (13):

为第r个变异个体的第l个分量；r1，r2，r3，r4为[0,NP] 内互异的随机整数，NP为种群个数；gc为算法进化代数；F_r∈(0,1)为变异因子；In the formula, e _q,d is the lth component of the elite individual q randomly selected from the elite archive set EliteSet (the elite individuals in the EliteSet are gradually updated with the evolution of the population);

is the l-th component of the r-th mutant individual; r1, r2, r3, r4 are mutually different random integers in [0, NP], NP is the population number; gc is the algorithm evolution algebra; F _r ∈ (0, 1) is the variation factor;

Formula (14):

为均值为0、标准差为σ_r的高斯随机变量；Γ[e_q]_distance为精英个体q在 EliteSet中的拥挤距离，Γ_max为EliteSet中个体的最大拥挤距离；In the formula,

is a Gaussian random variable with a mean of 0 and a standard deviation of σ _r ; Γ[e _q ] _distance is the crowding distance of the elite individual q in the EliteSet, and Γ _max is the maximum crowding distance of the individual in the EliteSet;

Formula (15):

Formula (16):

为第r个原始个体的第l个分量；rnd(r)是[0,1]的随机数；rndr(l) 为{0,1,...,NP}内随机产生的整数；CR∈(0,1)为交叉因子，CR_ini取值为0.15；In formulas (15) and (16),

is the l-th component of the r-th original individual; rnd(r) is a random number in [0,1]; rndr(l) is a randomly generated integer in {0,1,...,NP}; CR∈ (0,1) is the crossover factor, and the value of CR _ini is 0.15;

Equations (15) and (16) are to improve the diversity of the population and avoid the algorithm falling into local optimum, and perform crossover operations on individuals after mutation and before mutation to generate new individuals;

与

中的较优个体进入下一代种群，并对 精英档案集EliteSet进行更新维护；After mutation and crossover operations are completed, a greedy strategy is used to select

and

The better individuals in the group enter the next generation population, and update and maintain the elite archive set EliteSet;

② In the observation bee stage, use the formula (17) to calculate the probability value of the recruited bees corresponding to the selected nectar source, use the roulette selection method to determine the following target, and use the same method as the hired bee to perform neighborhood search; update and maintain the EliteSet calculation process In the Fork/Join parallel computing mode, the main tasks of individual constraint processing, fitness calculation, and elite individual update are decomposed and merged;

Formula (17):

In the formula, p _r is the probability that the rth hired bee in the population is selected; Voilation _j is the constraint destruction depth of the jth hired bee; ε is the feasible margin for evaluating the constraint destruction depth; Nv is the infeasible solution. The number (when the individual constraint destruction depth of the employed bee is greater than ε, the individual is judged as an infeasible solution); Nd is the number of feasible solutions;

③ Scout bee stage: If a hired bee fails to be updated within Limit _abandon , the hired bee will be turned into a scouting bee, and a new solution will be found through random search.

S6: If g<G _max , let g=g+1, go to S5; otherwise, the solution is completed, and the EliteSet is output as the Pareto optimal frontier of the multi-objective scheduling problem.

In the method of the present invention, when applying the multi-objective bee colony algorithm to solve the multi-objective scheduling model of the cascade reservoir group in the watershed, the water level in front of the reservoir dam is selected as the decision variable for individual coding. Initialize NP individuals. In the process of model solution, the simulation calculation of "determining electricity by water" is carried out according to the water level process, and the water level and discharge flow process of the hydropower station in each period are determined. Reservoir output and water level storage and discharge process control need to comprehensively consider factors such as natural water conditions, upstream discharge conditions, its own operation mode, power system demand, etc., and complex constraints are intertwined between time periods and time periods, which is very difficult to deal with. In order to solve this problem, a heuristic strategy based on constraint corridors is used to deal with various inter-period coupling constraints faced in the process of reservoir group scheduling. and take the intersection with the characteristic water level of the reservoir during the dispatch period to form a water level constraint corridor. In the optimization process, when the individual decision variable of the population exceeds the boundary of the water level corridor, it is directly corrected to the boundary value to ensure the feasibility of the individual population and effectively improve the optimization efficiency of the algorithm.

和

取流量和出力的上下边界值进行逐时段正反推计算时，可获得水库在不 同运行工况下的水位边界

与

逐时段将

与

求取交集，即可生成决策变量约束廊道

此外，在模型求解过程中，为避免算法陷入局部最优，在推求不同 种群个体水位约束廊道时，可令

其中a,b∈(0,1)，使种群个体所反 映的调度方案能覆盖整个解空间，以提高种群多样性。in will

and

When the upper and lower boundary values of flow and output are used for forward and reverse calculation period by period, the water level boundary of the reservoir under different operating conditions can be obtained.

and

Period by period will be

and

By finding the intersection, the decision variable constraint corridor can be generated

In addition, in the process of model solving, in order to avoid the algorithm falling into local optimum, when estimating the individual water level constraint corridors of different populations, the

Among them, a,b∈(0,1), so that the scheduling scheme reflected by the individual population can cover the entire solution space, so as to improve the diversity of the population.

In the technical scheme, the multi-objective bee colony algorithm is used to solve the multi-objective optimization scheduling modeling problem of cascade reservoir groups, and strategies such as EliteSet and adaptive dynamic parameter control are introduced into the algorithm optimization process, so that new individuals can be transformed from elite individuals into the optimization process. And other individuals absorb more information, effectively improve the diversity of the population, and enhance the global search ability of the algorithm. During the calculation process, the hired bees search for the nectar source in the neighborhood, and realize the mutation operation by introducing random disturbances on the basis of elite individuals. Usually, the value of _Fr will affect the convergence speed of the algorithm. In order to improve the convergence ability of the algorithm, a Gaussian random variable can be used for adaptive dynamic control of _Fr. At the same time, in order to improve the diversity of the population and avoid the algorithm falling into local optimum, new individuals are generated by the crossover operation between the individuals after mutation and those before mutation. In the multi-objective bee colony algorithm hiring bee stage and observation bee stage, the constraint processing and fitness calculation of a single individual in the population can be regarded as an independent calculation process. The decomposed subpopulation constraint processing and fitness operations are added as threads to the thread pool for parallel processing. In the process of solving the multi-objective scheduling problem of cascade reservoir groups, a thread pool with M threads (the number of threads is preferably equal to the number of computer logical threads) can be generated, and a memory space is opened in each thread to store NP/M (NP is Multi-objective bee colony algorithm population number) individuals and their intermediate calculation results.

Compared with the prior art, the invention has the following advantages and beneficial effects:

1. The present invention improves the solution mode of the multi-objective scheduling model of cascade reservoir groups through the multi-objective bee colony algorithm based on the Fork/Join parallel framework, and adopts the multi-thread parallel computing method to effectively improve the execution efficiency of the algorithm; for multi-objective scheduling of cascade reservoir groups The spatio-temporal coupling correlation characteristics and multiple complex constraints are designed, and an adaptive optimization mechanism and a corresponding heuristic constraint repair strategy are designed to improve the search performance and robustness of the algorithm, effectively ensure the quality of the optimization results, and make the algorithm have good practicability and reliability. Engineering operability.

2. The parallel multi-objective scheduling solution method proposed by the present invention has fast calculation speed and high calculation efficiency, and a set of non-inferior scheduling schemes that are uniformly distributed and widely distributed in the solution space can be obtained in one solution. The quality is far superior to traditional operations research-based modeling methods.

Description of drawings

Fig. 1 is the flow chart of solving the multi-objective dispatching model of cascade reservoir groups.

FIG. 2 is a front view of a non-inferior solution of multi-objective scheduling in Embodiment 1. FIG.

Detailed ways

Example 1: Multi-objective power generation-ecological dispatch simulation was carried out by taking the cascade power station in the Nam Ou River basin in Laos as an example.

Selecting 98% frequency inflow water, that is, extremely dry inflow water, as listed in Table 1 as the model input, the proposed MOBCO algorithm is used to solve the multi-objective optimal scheduling model of the reservoir group power generation. The algorithm parameters are set as follows, and the calculation results of the cascade power station are scheduling scheme set;

Population size NP=100;

Elite file set capacity NQ=30;

The maximum evolutionary generation G _max = 600;

Honey source abandonment timer Limit _abandon = 10;

LS maximum number of iterations km _max =20;

Table 1 98% frequency of water inflow for each cascade power station in the Nanou River Basin

power station January February March April May June July August September October November December Level 7 22.2 18.0 15.3 13.6 14.1 23.0 70.2 97.9 81.9 50.6 35.6 27.5 Level 6 11.8 9.5 8.1 7.2 7.4 12.2 37.1 51.8 43.3 26.8 18.8 14.5 Level 5 24.4 19.8 16.8 14.9 15.4 25.2 77.0 107.3 89.8 55.5 39.0 30.1

The hydrological method is used to determine the suitable ecological flow of the river channel. According to the natural flow data at the dam site for many years, the series of multi-year monthly runoff at the dam site of the cascade power station in the Nanou River Basin are sorted from large to small, and the second maximum and second minimum are selected from the sequence. , forming the annual maximum and second-minimum ecological runoff process, as the basis for multi-objective ecological water scarcity assessment, as listed in Table 2. In this embodiment, the lower limit of the suitable ecological flow interval is taken as the minimum control value of each month's ecological flow;

Table 2 The suitable ecological flow range of the Nan Ou River cascade calculated by the hydrological method

The embodiment calculates to obtain a set of non-inferior cascaded scheduling schemes, and compares and analyzes the scheduling results. The specific steps are as follows:

Step 1: Set the characteristic parameters of the hydropower station group, and initialize the control parameters of the algorithm: the EliteSet capacity NQ is 30, the population size NP is 100, the maximum evolution algebra of the algorithm G _max is 600, and the number of scout bee starts Limit _abandon is 10; The current evolutionary algebra of the algorithm is g=1.

Step 2: Use formula (1) to construct and initialize NP population individuals; use the reservoir scheduling constraints involved in formulas (2)-(7) to determine whether the individual satisfies the constraints, and apply formula (8) to the population individuals that do not meet the constraints , Equation (9) "Hydropower Station Constraint Processing Strategy Based on Constraint Corridor", the water level of the hydropower station group in the individual is corrected one by one.

Step 3: Apply equations (10) and (11) to calculate the individual target fitness values of different populations, the total power generation f ₁ and the ecological water shortage f ₂ , and normalize the target fitness values through equation (12). processing, and based on the individual target fitness value, the non-dominated individuals of the population are sorted; all non-dominated individuals in the first level of the population are added to the EliteSet.

Step 4: Population evolution, including the evolution of the employed bee stage, the observation bee stage and the scout bee stage;

①Employment bee stage: The hired bee stage searches for new nectar sources through the "search mechanism" of formulas (13)-(16), and uses formulas (8) and (9) to constrain the newly generated individuals; Based on the pros and cons of the individual and the original individual, the greedy strategy is used to select excellent individuals into the next generation population; the EliteSet is updated and maintained, and the elite candidate individuals are added to the EliteSet; the probability that the honey source corresponding to the employed bee is selected is calculated by formula (17). ; In the calculation process, the Fork/Join parallel computing mode is used to decompose and merge the main tasks of individual constraint processing, fitness calculation, and elite individual update to improve the execution efficiency of the algorithm.

②Observation bee stage: According to the aforementioned nectar source selection probability, the observation bee uses the roulette selection method to determine the following target, and uses the same method as the employed bee to conduct neighborhood search; Update and maintain the EliteSet; In the calculation process, use Fork/Join parallelism The calculation mode decomposes and merges the main tasks of individual constraint processing, applicability calculation, and elite individual update to improve the efficiency of algorithm execution;

③ Scouting bee stage: If a hired bee fails to be updated within Limit _abandon = 10, the hired bee will become a scouting bee, and a new solution will be found through random search.

Step 5: If g<G _max , let g=g+1, go to step 4; otherwise, the solution is completed, and the EliteSet is used as the Pareto optimal frontier output of the multi-objective scheduling problem.

After the calculation of the above steps, the spatial distribution results of the non-inferior dispatching scheme set of the cascade reservoir group in the Nanoujiang River Basin are shown in Figure 2, and the specific dispatching index results are shown in Table 3.

It can be seen from Fig. 2 that the proposed MOBCO algorithm has obvious application effect in solving the multi-objective power generation-ecological scheduling problem, and obtains a good non-inferior frontier distribution, and the non-inferior solution front has good convergence and non-inferior solution. The leading edge is overall continuous and smooth. Further analysis based on the frontier characteristics of the non-inferior solution shows that when the Nanoujiang cascade hydropower stations are jointly dispatched, the constraints and conflicts between the power generation of the cascade hydropower stations and the ecological benefits are very obvious. ) increases accordingly. The difference between the schemes is mainly reflected in the dry season, and the impact on the ecology in the dry period is mainly reflected in the water shortage. The plan with the greatest ecological benefit increases the drainage during the dry season to quickly reduce the water level, which reduces the ecological water shortage in the dry season, thereby increasing the ecological benefit, but it also causes the hydropower station to operate at a lower water level throughout the dry season, reducing the power generation benefit.

Table 3 lists the Nanou River cascade power generation-ecological multi-objective dispatch scheme set under the condition of 98% frequency of water inflow. The 30 schemes in the elite file set NQ in the table are all feasible dispatch schemes.

Table 3 Cascade power generation in the Nanou River under the condition of 98% frequency inflow—ecological multi-objective dispatching scheme set

Claims (1)

1. The parallel multi-target scheduling method of the cascade reservoir group is characterized by comprising the following specific steps:

s1, setting characteristic parameters of hydropower station group and control parameters of initialization algorithm, including Eliteset capacity NQ, group size NP, algorithm maximum evolution algebra G_maxAnd number of scout bee starts Limit_abandon(ii) a Setting the current evolution algebra g of the algorithm as 1;

s2, constructing and initializing NP population individuals, wherein the expression is as follows:

in the formula, x_rIs the r-th oneA body;

encoding the individual; n is the number of step reservoirs; t is the number of time segments;

s3, reservoir dispatching constraint processing, namely judging whether the individual meets the constraint by adopting the following formulas (2) to (7), and correcting the hydropower station group time-segment water level in the individual one by using the formulas (8) and (9) for the population individual which does not meet the constraint;

step hydraulic connection formula (2):

in the formula I_i,tThe flow rate of the reservoir is i; tau is_i-1Is the water flow time lag between the reservoir i-1 and the reservoir i;

reservoir at t-tau for i-1 _i-1Water abandon flow in time intervals; r_i,tInflow between the reservoir i-1 and the reservoir i;

reservoir water balance constraint (3): v_i,t＝V_i,t-1+(I_i,t-Q_i,t-S_i,t)·Δt；

In the formula, V_i,tThe storage capacity at the end of time t of the reservoir i;

water level/flow/output constraint formula (4):

in the formula, P_i,tOutputting force for the reservoir at the time t;

and _i,tZ、

and _i,tQ、

and _i,tPthe water level, the ex-warehouse and the output boundary of the reservoir at the time interval t are respectively shown;

fourthly, the water level/flow/output amplitude constraint formula (5):

in the formula,. DELTA.Z_i、ΔQ_i、ΔP_iI reservoir water level, flow and output amplitude limit respectively;

reservoir operation water head constraint formula (6):

in the formula, H_i,tFor the water head of the reservoir at the time t,

_i,tHrespectively the upper limit and the lower limit of a stable operation water head of the reservoir;

sixthly, controlling the water level at the beginning and end of the reservoir stage according to a restraint formula (7):

in the formula, Z_i,0、Z_i,T、

And

dispatching initial stage water level, final stage water level and control values of the water level for the reservoir;

seventhly, a water level constraint corridor generation method is represented by the formula (8):

the method for generating the water level constraint corridor is characterized by the following formula (9):

wherein f (V'_i,t-1,I_i,t,P_i ^BRep) And g (V'_i,t,I_i,t,P_i ^BRep) Calculating functions of the end storage capacity and the initial storage capacity in the t time period respectively;

and P_i ^BRepThe characteristic values of the lower leakage flow and the output are set as the upper and lower boundary values of the flow and the output;

s4, calculating target fitness values of different population individuals, carrying out target fitness value normalization processing, and carrying out non-dominated sorting on the population individuals based on the individual target fitness values; adding all non-dominant individuals at a first level in the population into the Eliteset;

The individual fitness takes the maximum total power generation of the cascade reservoir group and the minimum total ecological water shortage of each cascade downstream river as a scheduling target, and the objective functions are respectively described as an expression (10) and an expression (11):

formula (10):

formula (11):

in the formula, E is the total generating capacity of the cascade reservoir group; p_i,t、Q_i,t、H_i,tGenerating output, discharging flow and average water head for the i reservoir at the t time period respectively; n is the number of step reservoirs; t and Delta T are respectively equal toThe number of segments and the time period are long; w is the step ecological water shortage;

the difference value of the discharge flow of the reservoir at the time t and the suitable ecological demand flow of the downstream river channel is shown as the I;

the suitable ecological flow of the downstream river of the power station i in the period t;

the target functions of the formula (10) and the formula (11) have different dimensions, and are normalized to form a dimensionless function value; the scheduling objective normalization is calculated as equation (12):

formula (12):

in the formula, x _r Is the r individual in the evolved population; er, W_rThe annual energy production and the water shortage of the No. r individual are respectively determined; e^maxAnd E^min、

And

respectively representing the maximum value and the minimum value of annual power generation and water shortage of all individuals in the population;

s5, population evolution, including the evolution of a bee hiring stage, a bee observing stage and a bee reconnaissance stage;

hiring bee stage: in the stage of employing bees, new honey sources are searched through the formulas (13) to (16) of a search mechanism, and newly generated individuals are subjected to constraint processing by utilizing the formulas (8) and (9); comparing the advantages and disadvantages of the newly generated individuals and the original individuals, and selecting the excellent individuals to the next generation of population by adopting a greedy strategy; updating and maintaining the EliteSet, and adding the EliteSet candidate individuals into the EliteSet;

Formula (13):

in the formula, e_q,dThe l-th component of elite individual q randomly selected from the elite archive set EliteSet (elite individuals in EliteSet are gradually updated with population evolution);

the l component of the r variant individual; r1, r2, r3 and r4 are [0, NP]Random integers with different contents, NP is the number of the population; gc is an algorithm evolution algebra; f_rE (0,1) is a variation factor;

formula (14):

in the formula (I), the compound is shown in the specification,

is a mean value of 0 and a standard deviation of sigma_r(ii) a gaussian random variable; [ e ] a_q]_distanceFor the crowding distance of elite individual q in the EliteSet,_maxmaximum crowding distance for an individual in EliteSet;

formula (15):

formula (16):

in the formulae (15) and (16),

is the l component of the r original individual; rnd (r) is [0,1]The random number of (2); rndr (l) is a randomly generated integer within {0, 1.., NP }; CR is a cross factor of the CR epsilon (0,1)_iniThe value is 0.15;

the formulas (15) and (16) are used for improving the diversity of the population, avoiding the algorithm from falling into local optimum, and performing cross operation on the individuals after mutation and before mutation to generate new individuals;

after the variation and the cross operation are finished, greedy strategy selection is adopted

And

the better individual in the group enters the next generation of population, and updates and maintains Eliteset;

in the bee observation stage, calculating the probability value of the selected honey source corresponding to the employed bee by using the formula (17), determining a following target by using a wheel disc selection method, and performing neighborhood search by using the same method as the employed bee; in the process of updating and maintaining the Eliteset, decomposing and merging the main tasks of individual constraint processing, fitness calculation and elite individual updating by adopting a Fork/Join parallel calculation mode;

Formula (17):

in the formula, p_rProbability of being selected for the r-th hiring bee in the population; voiling_jDepth of constraint damage for hired bees # j; a feasible margin for judging the constraint damage depth; nv is the number of impossible solutions (when the breaking depth of the individual constraint of the employed bee is greater than, the individual is judged as an impossible solution); nd is the number of feasible solutions;

③ detecting bees: if a certain employed bee is in Limit_abandonIf the hiring bee is not updated, the hiring bee is changed into a scout beeNew solutions are sought by random search.

S6: if G < G_maxLet g be g +1, go to S5; otherwise, the solution is completed, and the Eliteset is used as the Pareto optimal front edge of the multi-objective scheduling problem to be output.

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