CN105719091A - Parallel multi-objective optimized scheduling method for cascaded hydropower station group - Google Patents

Abstract

The invention relates to a parallel multi-objective optimized scheduling method for a cascaded hydropower station group. A multi-population evolution strategy is used to ensure the relative independence of small-scale subpopulations, elite individuals of a Pareto solution set are coupled to an inter-population annular migration mechanism in the evolution process, information is transmitted and back fed mutually among the subpopulations, and the individual diversity and guidance quality of the solution set are ensured; and a multi-core parallel calculation technology is used to realize synchronized evolution of the subpopulations, waste of calculation resources under in the serial calculation mode is avoided, and calculation is accelerated. According to the invention, the calculable scale of optimized scheduling of the cascaded hydropower station group is further enlarged, a reasonable and feasible scheduling scheme set is provided for a decision maker, the calculation efficiency is ensured, and the method of the invention is a feasible method to realize multi-objective optimized scheduling for the cascaded hydropower station group.

Description

A kind of parallel Multiobjective Optimal Operation method of Hydropower Stations

Technical field

The present invention relates to hydroelectric system power generation dispatching field, particularly to a kind of parallel Multiobjective Optimal Operation method of Hydropower Stations.

Technical background

HYDROELECTRIC ENERGY is as the highest renewable and clean energy resource of accounting in present stage power system, it is necessary to balanced in Optimized Operation process consider that generated energy and guarantee are exerted oneself two momentum indicators.Energy Maximization model can maximally utilise hydraulic power potentials, it is achieved electricity power enterprise's maximizing the benefits；The maximum model of minimum load then can promote hydroelectric system and ensure to exert oneself, and strengthens the rich withered regulating and compensating role of water power.Adopt and take into account generated energy and ensure that the Optimized Operation scheme exerted oneself instructs the power generation of GROUP OF HYDROPOWER STATIONS, can effectively weaken the negative influence that runoff spatial and temporal distributions is uneven, promote power supply reliability and the market competitiveness of hydroelectric system, be conducive to the safe and stable operation of power system.The traditional method such as Non-Linear Programming, dynamic programming concentrates on single-object problem, need to utilize the method such as leash law or the method for weighting that multi-objective problem is converted into single-objective problem to solve, it is difficult to obtain the reasonable plan collection for policymaker's reference, and face the problems such as dyscalculia in large-scale hydropower systems Optimized Operation, limit its application in engineering reality to a certain extent.In recent years, the multi-objective Evolutionary Algorithm etc. that can obtain non-bad scheduling scheme set progressively shows powerful vitality, wherein with multi-objective genetic algorithm (Multi-ObjectiveGeneticAlgorithm, MOGA) for Typical Representative.

But, Hydropower Stations Multi-Objective Scheduling is a higher-dimension, nonlinear multiobjective Dynamic Optimization problem, and it solves difficulty and sharply increases with system scale expansion；Increasingly sophisticated water conservancy, power communication have been further exacerbated by computational complexity, increase optimization difficulty；Optimization method be it is also proposed higher requirement by the Precise control in each power station by traffic department.Above-mentioned several respects reason causes adopting the multi-objective Evolutionary Algorithm of serial computing pattern to receive limitation at present, no matter solution efficiency or computational accuracy.Meanwhile, fast development with computer industry, polycaryon processor and parallel computation frame, platform etc. almost have become as the standard configuration of PC, work station, it is greatly promoted development and the application of parallel computation, so as to be increasingly becoming the effective means of boosting algorithm performance, and progressively extend to water power scheduling field practical work.But, so far, parallel computation focuses mostly in the improvement of single goal dispatching method, and the research in multi-objective optimization scheduling is still rare with practice report.

Therefore, can calculating scale for expanding Optimal operation of cascade hydropower stations further, it is provided that while the scheduling scheme collection of policymaker's reasonable, it is ensured that computational efficiency, achievement of the present invention proposes a kind of parallel Multiobjective Optimal Operation method of Hydropower Stations.This achievement relies on the state natural sciences fund great international cooperation of committee (51210014) and country's 12 science and technology supporting project projects (2013BAB06B04), with Lancang River Watershed Hydropower Stations multiple target joint optimal operation problem for background, with middle and lower reaches " two storehouse Pyatyis " Hydropower Stations for main study subject, invent one to be very practical and high efficiency, it is simple to be widely popularized the parallel Multiobjective Optimal Operation method of Hydropower Stations of use.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of parallel Multiobjective Optimal Operation method of Hydropower Stations, is respectively directed to the subject matter proposition solution of existence in standard multi-objective genetic algorithm engineer applied.Standard multi-objective genetic algorithm is with non-dominated sorted genetic algorithm (Non-dominatedSortingGeneticAlgorithmII, NSGA-II) for Typical Representative, it is used widely because multiple target solves advantage in scientific research and engineering practice, but remain shortcoming in following two at present: (1) is after the evolution of certain algebraically, individual convergence highlights gradually, population diversity is constantly lost, and very easily obtains the pseudo-Pareto optimal solution of former problem；(2) traditional method adopts serial computing pattern, when population scale is bigger, faces the shortcomings such as calculating length consuming time, operation efficiency are low.For the problems referred to above, the present invention takes multi-core parallel concurrent computing technique to realize Populations evolution strategy, it is ensured that individual multiformity also realizes the calculating of method and accelerates, and has approximate Pareto optimum forward position that is well distributed and that spread to obtain.

The technical scheme is that and present invention is disclosed a kind of parallel Multiobjective Optimal Operation method of Hydropower Stations, (1)-(8) complete the parallel Multiobjective Optimal Operation process of Hydropower Stations as steps described below:

(1) algorithm is set and calculates parameter: comprise mutation probability P_m, crossover probability P_c, population at individual sum F, calculate in check figure G, maximum iteration time k_max, migrate algebraically k_mAnd individual amount n etc.；

(2) adopt individual real number tandem coding method that individuality is encoded, and to calculate the sub-population at individual scale of acquisition be F/G；

(3) Fork/Join framework is utilized to carry out parallel computation: main thread opens up shared memory space to store the basic characteristic data such as the water level-storage capacity in each power station, water level-letdown flow, the system initial conditions such as runoff reach, and water level restriction, the constraintss such as restriction of exerting oneself, it is simultaneously generated the thread pool with G thread；

(4) adopt chaos intialization strategy to initialize each sub-population, make each sub-population iterative computation number of times k_g=1, outside elite set is set simultaneouslyAnd each sub-Evolution of Population is added in thread pool as thread；

(5) k is made_g=k_g+ 1, the sub-population being not fully complete evolutional operation is respectively adopted NSGA-II method and implements the genetic manipulation such as intersections, variation, and adopt constraint Pareto to be dominant elite set omega outside new mechanism_gTo store the noninferior solution that algorithm search obtains；

(6) judging whether each sub-population arrives to need to carry out migration operation, if being unsatisfactory for transition condition, then proceeding to step (7)；Otherwise adopt hoop topology migration mechanism that n individuality in outside for this population elite set migrates to the outside elite set of next son population the some individuals of a upper sub-population of moving into；

(7) update the outside elite set of each sub-population, be then combined with two generation populations before and after each sub-Evolution of Population, and obtain new Advanced group species according to NSGA-II method；

(8) judging whether all sub-populations arrive end condition, if being unsatisfactory for, then going to step (5), to complete the operation of corresponding sub-Evolution of Population；Otherwise, return main thread, merge the outside elite set of all sub-populations, and export the scheduling result corresponding to Noninferior Solution Set.

The present invention contrasts prior art and has the advantages that: the parallel Multiobjective Optimal Operation method of one Hydropower Stations of the present invention, Populations evolution strategy is adopted to guarantee the relative independentability of sub-population on a small scale, and it is coupled into the individual annular migration mechanism between population of Pareto disaggregation elite during evolution, realize the information transmission between sub-population and feedback mutually, it is ensured that the multiformity of individuality and the guidance quality of disaggregation；Adopt the synchronization that multi-core parallel concurrent computing technique realizes each sub-population to evolve, evade the computing resource waste phenomenon under serial computing pattern, it is achieved the calculating of method is accelerated.Contrast prior art, the present invention is by realizing parallel Multiobjective Optimal Operation method, effectively carry out Hydropower Stations Multiobjective Optimal Operation scheme to make, and significantly improve computational efficiency by multi-core parallel concurrent computing technique, provide a kind of feasible efficient computational methods for Hydropower Stations Multiobjective Optimal Operation.

Accompanying drawing explanation

Fig. 1 is that the inventive method totally solves framework；

Fig. 2 (a) is the 10% non-bad scheduling scheme collection comparison diagram coming that under water condition, the inventive method and standard multi-objective genetic algorithm obtain；

Fig. 2 (b) is the 50% non-bad scheduling scheme collection comparison diagram coming that under water condition, the inventive method and standard multi-objective genetic algorithm obtain；

Fig. 3 (a) is three kinds of typical scenario gained accumulation of energy process comparison diagrams；

Fig. 3 (b) is that three kinds of typical scenario gained are exerted oneself process comparison diagram.

Detailed description of the invention

Below in conjunction with drawings and Examples, the invention will be further described.

The subject matter that upper already described and standard multi-objective genetic algorithm exists in search procedure, for these problems, the inventive method is respectively adopted following strategy and is acted upon: (1) adopts Populations evolution strategy to guarantee the relative independentability of sub-population on a small scale, and it is coupled into the individual annular migration mechanism between population of Pareto disaggregation elite during evolution, realize the information transmission between sub-population and feedback mutually, it is ensured that the multiformity of individuality and the guidance quality of disaggregation；(2) adopt the synchronization that multi-core parallel concurrent computing technique realizes each sub-population to evolve, evade the computing resource waste phenomenon under serial computing pattern, it is achieved the calculating of method is accelerated.Populations evolution strategy is realized by the introduction of multi-core parallel concurrent computing technique, and introduce the information communication that hoop topology migration mechanism promotes population to see during evolution, overcome standard multi-objective genetic algorithm to solve Problems existing in Hydropower Stations Multiobjective Optimal Operation with this.

In the present invention, Hydropower Stations Multiobjective Optimal Operation is it is generally required to take into account generated energy and guarantee is exerted oneself two indices, to realize the doulbe-sides' victory of hydroelectric system reliability and economy.Model is described in detail below:

(1) object function 1: Energy Maximization

$f_1=max\left(E\right)=max\left(\underset{i=1}{\overset{N}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}{P}_{i,j}{t}_j\right)$

(2) object function 2: minimum load is maximum

$f_2=max\left(F\right)=max\left(\underset{1\≤j\≤T}{min}\right(\underset{i=1}{\overset{N}{\Σ}}{P}_{i,j}\left)\right)$

In formula, E is step gross capability, kW h；F is that step ensures to exert oneself, kW；N represents power station number；I is reservoir sequence number；T represents fixed number；J is period sequence number；P_i,jRepresent power station i exerting oneself at period j, kW；T_jFor the hourage at period j, h.

The main method introduced in solution procedure has:

(a) multigroup parallel evolution strategy:

Adopting the parallel framework of Fork/Join, the evolutional operation of anyon population is considered as a subtask, the evolutional operation of all sub-populations is considered as general assignment, utilizes tasks in parallel computation schema that general assignment decomposes to each processor and carries out synchronization calculating；Adopt the management of Thread Pool Technology United Dispatching, organic equilibrium of reasonable disposition and load to realize resource, and then improve resource utilization.The inventive method, after initializing each sub-population, is consigned to thread pool combined dispatching, and each sub-population carries out genetic evolutionary operations respectively voluntarily；The information between population of simultaneously carrying out under meeting specified conditions is mutual, until meeting end condition；Last main thread merges the outside elite aggregated result of each sub-population, and compares the Pareto disaggregation that acquisition is final.

(b) hoop topology migration mechanism:

For anyon population, fixing algebraically of often evolving just is concentrated from its outside elite and is randomly choosed n elite individuality and move into the outside elite concentration of adjacent sub-population, and then it is moved to sub-population, concentrate individual dominance relation increase noninferior solution and reject inferior solution according to its outside elite.By above-mentioned hoop topology migration mechanism, the information isolation between sub-population can be realized on the one hand preferably, the stable propagation in population of the elite individuality and diffusion can also be effectively ensured on the other hand.Set the number of sub-population as G, with g (g=1,2 ..., G) individual sub-population is example, sets its original outside elite set as J_g, from J_gIn move out n individual and constitute setMove into set from g-1 sub-population simultaneouslyTo form new outside elite setThen corresponding mathematical expression formula is as follows:

$J_g^1={\tilde{J}}_{g-1}\∪\{J_g-{\tilde{J}}_g\}=\left\{{\tilde{J}}_{g-1,\[r_1\·\left|J_{g-1}\right|\]},{\tilde{J}}_{g-1,\[r_2\·\left|J_{g-1}\right|\]},...,{\tilde{J}}_{g-1,\[r_n\·\left|J_{g-1}\right|\]},J_{g-1,\[r_{n+1}\·\left|J_g\right|\]},J_{g,\[r_{n+2}\·\left|J_g\right|\]},J_{g,\[r_{\left|J_g\right|}\·\left|J_g\right|\]}\right\}$

In formula, J_g,fRepresent J_gIn the f noninferior solution；| J_g| represent set J_gRadix；[x] represents bracket function；R_iRepresent [0,1] interval interior equally distributed random number, r_i∈ [1, | J_g|]。

(c) individual real number tandem coding method:

Each power station is taken as state variable and decision variable at the water level of different scheduling slots respectively with storage outflow, adopts the decimal floating point type data each state variable of tandem coding step by step, to reduce the consumption of code length and EMS memory occupation.Any individual X is the chromosome with special characteristic, contains the potential step power station combined dispatching method of operation, is shown below.

X=(X_k)_NT×1=[Z_1,1,Z_1,2,…,Z_1,T,Z_2,1,Z_2,2,…,Z_2,T,…,Z_{N, 1},Z_{N, 2},…,Z_N,T]^T

In formula, X_kRepresent power stationAt period (k-N) water level；Represent the smallest positive integral being not less than x.

(d) chaos intialization strategy:

The multiformity that individuality is distributed by the generting machanism of initial population in solution space and convergence have highly important impact.Chaos phenomenon is prevalent in nature, has the immanent structure of exquisiteness, it is possible to effectively go through all potentially possible states within the specific limits.Therefore, each sub-population is all adopted Logistic mapping to carry out Chaos Search by the inventive method, and to promote the quality of initial population, detail formula is as follows:

$\left\{\begin{array}{c}{x}_{m,k}=4x_{m,k-1}\left(1-x_{m,k-1}\right)\\ X_{m,k}=\underset{\‾}{X}+x_{m,k}\left({\stackrel{\‾}{X}}_k-{\underset{\‾}{X}}_k\right)\end{array}\right.$

In formula, x_m,kRepresent the kth dimension variable value when the m time iteration, x_m,k∈ [0,1]；X_m,kRepresent x_m,kMapping value in original variable search volume； X _kRepresent kth dimension variable X respectively_kUpper and lower limit.

E () constraint Pareto is dominant mechanism:

Model for Cascade Hydroelectric Stations relates to the operation constraint of series of complex, generally adopts Means of Penalty Function Methods that constraint is destroyed item and include object function in single object optimization is dispatched, and constitutes ideal adaptation degree functional value in order to assess the quality of individuality.But, in multi-objective optimization question, owing to needs adopt Pareto to be dominant mechanism identification domination individuality, traditional penalty functional method is difficult to distinguish infeasible solutions and feasible solution, easily occur that infeasible solutions dominates Evolution of Population phenomenon, finally converge to non-feasible Pareto forward position.For this, constraint is destroyed item and includes individual goal attribute in by the inventive method, adopt the constraint Pareto mechanism of being dominant to process dominance relation between any two body, to guarantee feasible solution domination infeasible solutions, conscientiously guide colony evolve in order and converge to feasible Pareto optimal solution forward position.Individual X_iObject vector computational methods as follows:

F₁(X_i)=F (X_i)∪Δ(X_i)=[f₁(X_i),f₂(X_i)]^T∪Δ(X_i)

In formula, X_iFor representing that i-th is individual；F₁(X_i) represent individual X_iExtended target vector；F (X_i) represent individual X_iOriginal object vector；Δ (X_i) for representing individual X_iConstraint destroy item sum, for nonnegative value；If Δ (X_i)=0, then X_iFor feasible solution；Otherwise, X_iFor infeasible solutions.

Set and arbitrarily select two individual X_iWith X_jParticipation is compared, and concrete operating procedure is:

(1) if X_iWith X_jIt is feasible solution, then determines dominance relation according to individual goal functional value；

(2) if X_iFor feasible solution, X_jFor infeasible solutions, then feasible solution X_iDomination infeasible solutions X_j；

(3) if X_iWith X_jIt is infeasible solutions, and the two constraint destructiveness is identical, then determine dominance relation according to individual goal functional value；Otherwise, the individuality that constraint destructiveness is little is dominant.

Optimization Solution process needs meet following constraints:

(1) water balance equation

V_i,j+1=V_i,j+3600×(I_i,j-O_i,j)t_j

$I_{i,j}=q_{i,j}+\underset{m_i\∈{\mathrm{\Ω}}_i}{\Σ}(Q_{m_i,j}+S_{m_i,j})$

O_i,j=Q_i,j+S_i,j

In formula, V_i,jFor the power station i storage capacity at period j, m³；I_i,j、O_i,jRespectively power station i is in the reservoir inflow of period j, outbound

Flow, m³/ s；Q_i,j、S_i,j、Q_i,jRespectively power station i period j interval flow, abandon discharge and generating flow,

m³/ s；M_iM-th power station immediately upstream for power station i；Ω_iReservoir set immediately upstream for power station i.

(2) reservoir storage constraint

${\underset{\‾}{V}}_{i,j}\≤V_{i,j}\≤{\stackrel{\‾}{V}}_{i,j}$

In formula, V _i,jRespectively power station i is at the storage capacity upper and lower limit of period j.

(3) generating flow constraint

${\underset{\‾}{Q}}_{i,j}\≤Q_{i,j}\≤{\stackrel{\‾}{Q}}_{i,j}$

In formula, Q _i,jRespectively power station i is at the generating flow upper and lower limit of period j.

(4) letdown flow constraint

${\underset{\‾}{O}}_{i,j}\≤O_{i,j}\≤{\stackrel{\‾}{O}}_{i,j}$

In formula, O _i,jRespectively power station i is at the storage outflow upper and lower limit of period j.

(5) output of power station constraint

${\underset{\‾}{P}}_{i,j}\≤P_{i,j}\≤{\stackrel{\‾}{P}}_{i,j}$

In formula, P _i,jRespectively power station i is at the upper and lower limit of exerting oneself of period j.

According to above-mentioned introduction, the parallel Multiobjective Optimal Operation process of once complete Hydropower Stations, (1)-(8) are achieved as steps described below:

(1) algorithm is set and calculates parameter: comprise mutation probability P_m, crossover probability P_c, population at individual sum F, calculate in check figure G, maximum iteration time k_max, migrate algebraically k_mAnd individual amount n etc.；

(2) adopt individual real number tandem coding method that individuality is encoded, and to calculate the sub-population at individual scale of acquisition be F/G；

(3) Fork/Join framework is utilized to carry out parallel computation: main thread opens up shared memory space to store the basic characteristic data such as the water level-storage capacity in each power station, water level-letdown flow, the system initial conditions such as runoff reach, and water level restriction, the constraintss such as restriction of exerting oneself, it is simultaneously generated the thread pool with G thread；

(4) adopt chaos intialization strategy to initialize each sub-population, make each sub-population iterative computation number of times k_g=1, outside elite set is set simultaneouslyAnd each sub-Evolution of Population is added in thread pool as thread；

(5) k is made_g=k_g+ 1, the sub-population being not fully complete evolutional operation is respectively adopted NSGA-II method and implements the genetic manipulation such as intersections, variation, and adopt constraint Pareto to be dominant elite set omega outside new mechanism_gTo store the noninferior solution that algorithm search obtains；

(6) judging whether each sub-population arrives to need to carry out migration operation, if being unsatisfactory for transition condition, then proceeding to step (7)；Otherwise adopt hoop topology migration mechanism that n individuality in outside for this population elite set migrates to the outside elite set of next son population the some individuals of a upper sub-population of moving into；

(7) update the outside elite set of each sub-population, be then combined with two generation populations before and after each sub-Evolution of Population, and obtain new Advanced group species according to NSGA-II method；

(8) judging whether all sub-populations arrive end condition, if being unsatisfactory for, then going to step (5), to complete the operation of corresponding sub-Evolution of Population；Otherwise, return main thread, merge the outside elite set of all sub-populations, and export the scheduling result corresponding to Noninferior Solution Set.

Now using the abundant Lancang River Watershed Hydropower Stations of hydraulic power potentials as engineering practice object, adopt the inventive method to carry out the parallel power generation dispatching of multiple target, make year scheduling scheme.Lancang River Watershed is one of big Hydropower Base of China 13, and its development task is based on generating, and has the comprehensive benefits such as tourism, environmental protection concurrently, and Western Economic has particularly important facilitation.Select 5 power stations having put into operation, downstream, the Lancang River as calculating object, each power station respectively voe, Man Wan, make a pilgrimage to a temple on a famous mountain greatly, waxy common wheat and Jinghong, be respectively provided with and season regulate and regulate performance above, wherein, voe and waxy common wheat storage capacity are relatively big, possess many years regulation performance.Table 1 is listed the part in each power station and is calculated information, and table 2 lists the inventive method and standard multi-objective genetic algorithm (MOGA) computational efficiency comparative information.Fig. 2 shows that difference is come under water condition, the Noninferior Solution Set scattergram that the inventive method and MOGA obtain.Selecting three kinds of typical scenarios in Noninferior Solution Set to contrast, Fig. 3 shows the year scheduling process of three kinds of typical scenarios.Analyzed from table 2, it is very notable that the inventive method calculates acceleration effect: population scale is progressively increased to 4000 by 1000, system operations amount also increases therewith, serial computing is consuming time to be increased rapidly to 16.3min by 3.6min, and PMOGA is about respectively necessary for 31s and 135s under 8 nuclear environments, significantly reduce the calculating time；Under identical population scale, along with the number of cores participating in parallel computation increases, the degree of concurrence of total calculating task is more high, and the speed-up ratio of the inventive method also increases therewith, and under 4000 individualities and 8 core sights, speed-up ratio is 1.84, and parallel efficiency has reached 0.92；, analyzed the scheduling scheme set that known the inventive method can obtain being evenly distributed, scope is wider in non-bad forward position by Fig. 2；Analyzed by Fig. 3 it can be seen that the accumulation of energy of each scheduling scheme of the inventive method remains basically stable in flood season with the process of exerting oneself, and differ greatly in dry season.In 1～August, water is relatively fewer, and step is to supply water, and economic benefit is stressed difference to some extent by each scheme, causes there is larger difference；And in water more rich 9～October, system is based on water-retention, different scheduling sight lower step GROUP OF HYDROPOWER STATIONS maintain maximum accumulation of energy all substantially, therefore system is exerted oneself and accumulation of energy process presents good synchronicity.To sum up, contrasting with MOGA method, the inventive method can the economy of active balance system and reliability, it is achieved that the organic coordination of the two, it is possible to be effectively ensured the withered phase peak modulation capacity of water power while improving GROUP OF HYDROPOWER STATIONS generated energy；There is good computational efficiency, it is possible to ensure to complete Hydropower Stations multi-objective optimization scheduling within a short period of time simultaneously, provide strong technical support for hydroelectric project practice, be the more efficient Hydropower Stations Multiobjective Optimal Operation method of one.

Table 1

Table 2

Claims (1)

1. the parallel Multiobjective Optimal Operation method of Hydropower Stations, its feature comprises the steps:

(1) algorithm is set and calculates parameter: comprise mutation probability P_m, crossover probability P_c, population at individual sum F, calculate in check figure G, maximum iteration time k_max, migrate algebraically k_mAnd individual amount n；

(2) adopt individual real number tandem coding method that individuality is encoded, and to calculate the sub-population at individual scale of acquisition be F/G；Wherein, individual real number tandem coding method operates in accordance with the following steps:

Each power station is taken as state variable and decision variable at the water level of different scheduling slots respectively with storage outflow, adopts the decimal floating point type data each state variable of tandem coding step by step, to reduce the consumption of code length and EMS memory occupation；Any individual X is the chromosome with special characteristic, contains the potential step power station combined dispatching method of operation, is shown below:

X=(X_k)_NT×1=[Z_1,1,Z_1,2,…,Z_1,T,Z_2,1,Z_2,2,…,Z_2,T,…,Z_{N, 1},Z_{N, 2},…,Z_N,T]^T

In formula, X_kRepresent power stationIn the periodWater level；Represent the smallest positive integral being not less than x；

(3) Fork/Join framework is utilized to carry out parallel computation: main thread opens up shared memory space to store the basic characteristic data in each power station, system initial conditions, constraints, is simultaneously generated the thread pool with G thread；

(4) adopt chaos intialization strategy to initialize each sub-population, make each sub-population iterative computation number of times k_g=1, outside elite set is set simultaneouslyAnd each sub-Evolution of Population is added in thread pool as thread；Wherein, chaos intialization strategy operates in accordance with the following steps:

Each sub-population all adopting Logistic map and carries out Chaos Search, to promote the quality of initial population, detail formula is as follows:

$\left\{\begin{array}{c}{x}_{m,k}=4x_{m,k-1}\left(1-x_{m,k-1}\right)\\ X_{m,k}=\underset{\‾}{X}+x_{m,k}\left({\stackrel{\‾}{X}}_k-{\underset{\‾}{X}}_k\right)\end{array}\right.$

In formula, x_m,kRepresent the kth dimension variable value when the m time iteration, x_m,k∈ [0,1]；X_m,kRepresent x_m,kMapping value in original variable search volume； X _kRepresent kth dimension variable X respectively_kUpper and lower limit；

(5) k is made_g=k_g+ 1, the sub-population being not fully complete evolutional operation is respectively adopted NSGA-II method and implements genetic manipulation, and adopt constraint Pareto to be dominant the outside elite set omega of new mechanism_gTo store the noninferior solution that algorithm search obtains；Wherein, the Pareto mechanism of being dominant judges that step is as follows:

Individual X_iObject vector computational methods as follows:

F₁(X_i)=F (X_i)∪Δ(X_i)=[f₁(X_i),f₂(X_i)]^T∪Δ(X_i)

In formula, X_iFor representing that i-th is individual；F₁(X_i) represent individual X_iExtended target vector；F (X_i) represent individual X_iOriginal object vector；Δ (X_i) for representing individual X_iConstraint destroy item sum, for nonnegative value；If Δ (X_i)=0, then X_iFor feasible solution；Otherwise, X_iFor infeasible solutions.

Set and arbitrarily select two individual X_iWith X_jParticipation is compared, and concrete operating procedure is:

If 1. X_iWith X_jIt is feasible solution, then determines dominance relation according to individual goal functional value；

If 2. X_iFor feasible solution, X_jFor infeasible solutions, then feasible solution X_iDomination infeasible solutions X_j；

If 3. X_iWith X_jIt is infeasible solutions, and the two constraint destructiveness is identical, then determine dominance relation according to individual goal functional value；Otherwise, the individuality that constraint destructiveness is little is dominant；

(6) judging whether each sub-population arrives to need to carry out migration operation, if being unsatisfactory for transition condition, then proceeding to step (7)；Otherwise adopt hoop topology migration mechanism that n individuality in outside for this population elite set migrates to the outside elite set of next son population the some individuals of a upper sub-population of moving into；Wherein, hoop topology migration mechanism performs in accordance with the following steps:

For anyon population, fixing algebraically of often evolving just is concentrated from its outside elite and is randomly choosed n elite individuality and move into the outside elite concentration of adjacent sub-population, and then it is moved to sub-population, concentrate individual dominance relation increase noninferior solution and reject inferior solution according to its outside elite；By above-mentioned hoop topology migration mechanism, realize the information isolation between sub-population on the one hand, ensure the stable propagation in population of the elite individuality and diffusion on the other hand；Set the number of sub-population as G, with g (g=1,2 ..., G) individual sub-population, set its original outside elite set as J_g, from J_gIn move out n individual and constitute setMove into set from g-1 sub-population simultaneouslyTo form new outside elite setThen corresponding mathematical expression formula is as follows:

In formula, J_g,fRepresent J_gIn the f noninferior solution；| J_g| represent set J_gRadix；[x] represents bracket function；R_iRepresent [0,1] interval interior equally distributed random number, r_i∈ [1, | J_g|]；

(7) update the outside elite set of each sub-population, be then combined with two generation populations before and after each sub-Evolution of Population, and obtain new Advanced group species according to NSGA-II method；

(8) judging whether all sub-populations arrive end condition, if being unsatisfactory for, then going to step (5), to complete the operation of corresponding sub-Evolution of Population；Otherwise, return main thread, merge the outside elite set of all sub-populations, and export the scheduling result corresponding to Noninferior Solution Set.