CN105719091B - A kind of parallel Multiobjective Optimal Operation method of Hydropower Stations - Google Patents
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Abstract
A kind of parallel Multiobjective Optimal Operation method of Hydropower Stations, ensure the relative independentability of small-scale sub- population using Populations evolution strategy, and it is coupled into Pareto disaggregation elite individual annular migration mechanism between population during evolution, it realizes the information transmitting and mutually feedback between sub- population, guarantees the diversity of individual and the guiding performance of disaggregation;It realizes that the synchronous of each sub- population is evolved using multi-core parallel concurrent computing technique, evades the computing resource waste phenomenon under serial computing mode, the calculating of implementation method accelerates.The present invention can further expansion Optimal operation of cascade hydropower stations can calculation scale, while being supplied to the scheduling scheme collection of policymaker's reasonable, guarantee computational efficiency, is a kind of practicable method for realizing extensive Hydropower Stations Multiobjective Optimal Operation.
Description
Technical field
The present invention relates to hydroelectric system power generation dispatching field, in particular to a kind of parallel multiple-objection optimization of Hydropower Stations
Dispatching method.
Technical background
HYDROELECTRIC ENERGY is needed as the highest renewable and clean energy resource of accounting in electric system at this stage in Optimized Operation mistake
It is balanced in journey to consider generated energy and guarantee two momentum indicators of power output.Generated energy maximum model can maximally utilise water energy money
Electricity power enterprise's maximizing the benefits is realized in source;Minimum load maximum model can then promote hydroelectric system and guarantee power output, and enhancing water power is rich
Withered regulating and compensating role.The power generation of GROUP OF HYDROPOWER STATIONS is instructed using the Optimized Operation scheme for taking into account generated energy and guarantee power output,
The negative influence that runoff spatial and temporal distributions unevenness can effectively be weakened promotes the power supply reliability and the market competitiveness of hydroelectric system, has
Conducive to the safe and stable operation of electric system.The conventional methods such as Non-Linear Programming, Dynamic Programming concentrate on single-object problem,
It needs to convert single-objective problem for multi-objective problem using the methods of leash law or the method for weighting and solve, it is difficult to obtain for determining
The reasonable plan collection of plan person's reference, and the problems such as face dyscalculia in large-scale hydropower systems Optimized Operation, to a certain degree
On limit its application in engineering in practice.In recent years, it can get the multi-objective Evolutionary Algorithm etc. of non-bad scheduling scheme set
Powerful vitality is gradually shown, wherein with multi-objective genetic algorithm (Multi-Objective Genetic
Algorithm, MOGA) it is Typical Representative.
However, Hydropower Stations Multi-Objective Scheduling is a higher-dimension, nonlinear multiobjective Dynamic Optimization problem,
It solves difficulty and expands and sharply increase with system scale;It is multiple that increasingly sophisticated water conservancy, power communication have been further exacerbated by calculating
It is difficult to increase optimization for polygamy;Higher requirements are also raised to optimization method for Precise control of the traffic department to each power station.
Above-mentioned several respects reason causes to be limited using the multi-objective Evolutionary Algorithm of serial computing mode at present, no matter solution efficiency
Or computational accuracy.At the same time, with the fast development of computer industry, multi-core processor and parallel computation frame, platform
Deng the standard configuration for almost having become PC, work station, it is greatly promoted the development and application of parallel computation, is allowed to
The effective means of boosting algorithm performance is had become, and has gradually extended to water power scheduling field practical work.However, by mesh
Before, parallel computation focuses mostly in the improvement of single goal dispatching method, and the research in multi-objective optimization scheduling and practice are reported
Road is still rare.
Therefore, for further expansion Optimal operation of cascade hydropower stations can calculation scale, be supplied to policymaker's reasonable
Scheduling scheme collection while, guarantee computational efficiency, achievement of the present invention proposes a kind of parallel multiple-objection optimization of Hydropower Stations
Dispatching method.The achievement relies on 12 science and technology branch of the great international cooperation (51210014) of state natural sciences fund committee and country
It supports planning item (2013BAB06B04), is back with Lancang River Watershed Hydropower Stations multiple target joint optimal operation problem
Scape has invented one kind and has been very practical and high using middle and lower reaches " two library Pyatyis " Hydropower Stations as main study subject
Effect property, convenient for the parallel Multiobjective Optimal Operation method of Hydropower Stations being widely used to promote.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of parallel Multiobjective Optimal Operation methods of Hydropower Stations, divide
Safety pin proposes solution to main problem present in standard multi-objective genetic algorithm engineer application.Standard multi-objective Genetic is calculated
Method is with non-dominated sorted genetic algorithm (Non-dominated Sorting Genetic Algorithm II, NSGA-II)
Typical Representative has been used widely in scientific research and engineering practice because multiple target solves advantage, but has been still had at present
Two aspect disadvantage below: (1) after the evolution of certain algebra, individual convergence is gradually highlighted, and population diversity constantly loses
It loses, easily obtains the pseudo- Pareto optimal solution of former problem;(2) conventional method uses serial computing mode, larger in population scale
When, it faces and calculates the disadvantages such as time-consuming, operation efficiency is low.In view of the above-mentioned problems, the present invention takes multi-core parallel concurrent computing technique real
Existing Populations evolution strategy guarantees that the calculating of the diversity and implementation method of individual accelerates, has good distribution with acquisition and dissipate
The optimal forward position approximate Pareto of cloth.
The technical solution of the present invention is as follows: present invention discloses a kind of parallel Multiobjective Optimal Operation sides of Hydropower Stations
Method, (1)-(8) complete the parallel Multiobjective Optimal Operation process of Hydropower Stations as steps described below:
(1) algorithm calculating parameter is set: including mutation probability Pm, crossover probability Pc, population at individual sum F, nucleus number in calculating
G, maximum number of iterations kmax, migration algebra kmAnd individual amount n etc.;
(2) individual is encoded using individual real number tandem coding method, and calculates the sub- population at individual scale of acquisition and is
F/G;
(3) carry out parallel computation using Fork/Join frame: main thread opens up shared memory space to store each power station
Water level-storage capacity, the basic characteristics data such as water level-letdown flow, the systems such as runoff reach input condition and water level limitation,
The constraint conditions such as power limit out, while generating the thread pool with G thread;
(4) each sub- population is initialized using chaos intialization strategy, enables each sub- population iterative calculation number kg=1, simultaneously
External elite set is setAnd it is added each sub- Evolution of Population as thread in thread pool;
(5) k is enabledg=kg+ 1, NSGA-II method is respectively adopted to the sub- population of unfinished evolutional operation and implements intersection, variation
Equal genetic manipulations, and be dominant elite set omega outside new mechanism using constraint ParetogWith store algorithm search obtain it is non-
Inferior solution;
(6) determine whether each sub- population reaches to need to carry out migration operation, if being unsatisfactory for transition condition, be transferred to step
(7);Otherwise use circumferential topological migration mechanism by the outer of n individual migration in elite set outside this population to next sub- population
Portion's elite set, and move into some individuals of a sub- population;
(7) the external elite set of each sub- population, two generation populations being then combined with before and after each sub- Evolution of Population are updated, and are pressed
New Advanced group species are obtained according to NSGA-II method;
(8) judge whether all sub- populations reach termination condition, if not satisfied, step (5) are then gone to, it is corresponding to complete
Sub- Evolution of Population operation;Otherwise, main thread is returned, the external elite set of all sub- populations is merged, and exports Noninferior Solution Set institute
Corresponding scheduling result.
The present invention compares the prior art and has the advantages that: a kind of parallel multiple-objection optimization of Hydropower Stations of the present invention
Dispatching method, the relative independentability of small-scale sub- population is ensured using Populations evolution strategy, and is coupled into during evolution
Pareto disaggregation elite individual annular migration mechanism between population is realized that the information between sub- population is transmitted and mutually presented, is guaranteed a
The diversity of body and the guiding performance of disaggregation;It realizes that the synchronous of each sub- population is evolved using multi-core parallel concurrent computing technique, evades serial
The calculating of computing resource waste phenomenon under calculating mode, implementation method accelerates.The prior art is compared, the present invention is by realizing simultaneously
Row Multiobjective Optimal Operation method effectively carries out the production of Hydropower Stations Multiobjective Optimal Operation scheme, and simultaneously by multicore
Row computing technique significantly improves computational efficiency, provides a kind of feasible efficient calculating for Hydropower Stations Multiobjective Optimal Operation
Method.
Detailed description of the invention
Fig. 1 is that the method for the present invention totally solves frame;
Fig. 2 (a) is the non-bad dispatching party of the method for the present invention and the acquisition of standard multi-objective genetic algorithm under the conditions of 10% water
Case collection comparison diagram;
Fig. 2 (b) is the non-bad dispatching party of the method for the present invention and the acquisition of standard multi-objective genetic algorithm under the conditions of 50% water
Case collection comparison diagram;
Fig. 3 (a) is accumulation of energy process comparison diagram obtained by three kinds of typical scenarios;
Fig. 3 (b) is process comparison diagram of contributing obtained by three kinds of typical scenarios.
Specific embodiment
The invention will be further described with reference to the accompanying drawings and examples.
On addressed standard multi-objective genetic algorithm main problem present in search process, for these problems, this
Inventive method is respectively adopted following strategies and is pocessed: (1) ensuring the opposite of small-scale sub- population using Populations evolution strategy
Independence, and be coupled into Pareto disaggregation elite individual annular migration mechanism between population during evolution, realize sub- population it
Between information transmitting with mutually feedback, guarantee individual diversity and disaggregation guiding performance;(2) it is realized using multi-core parallel concurrent computing technique
The synchronous of each sub- population is evolved, and the computing resource waste phenomenon under serial computing mode is evaded, and the calculating of implementation method accelerates.It is logical
Populations evolution strategy is realized in the introduction for crossing multicore parallel computing, and introduces circumferential topological migration mechanism during evolution
The information communication for promoting population to see, overcomes standard multi-objective genetic algorithm to solve Hydropower Stations Multiobjective Optimal Operation with this
The problem of.
In the present invention, Hydropower Stations Multiobjective Optimal Operation, which generally requires, to be taken into account generated energy and guarantees that power output two refer to
Mark, to realize the two-win of hydroelectric system reliability and economy.Model is described in detail below:
(1) objective function 1: generated energy is maximum
(2) objective function 2: minimum load is maximum
In formula, E is step gross capability, kWh;F is that step guarantees power output, kW;N indicates power station number;I is reservoir sequence
Number;T indicates fixed number;J is period serial number;Pi,jIndicate power output of the power station i in period j, kW;tjFor in the hour of period j
Number, h.
The main method introduced in solution procedure has:
(a) multigroup parallel evolution strategy:
Using the parallel frame of Fork/Join, the evolutional operation of anyon population is considered as a subtask, all sub- populations
Evolutional operation be considered as general assignment, general assignment is decomposed into everywhither reason device using task parallel computation mode and carries out synchronous calculate;
Using Thread Pool Technology United Dispatching management, to realize the reasonable disposition of resource and organic equilibrium of load, and then resource is improved
Utilization rate.The method of the present invention is consigned to thread pool combined dispatching, each sub- population difference is voluntarily after initializing each sub- population
Carry out genetic evolutionary operations;Carry out the information exchange between population under certain conditions simultaneously, until meeting termination condition;Most
Main thread merges the external elite aggregated result of each sub- population afterwards, and compares and obtain final Pareto disaggregation.
(b) circumferential topological migration mechanism:
For anyon population, every fixed algebra of evolving, which is just concentrated from its external elite, randomly chooses n elite
The external elite that body moves into adjacent sub- population concentrates, and then is moved to sub- population, concentrates individual to dominate according to its external elite and closes
System increases noninferior solution and rejects inferior solution.By above-mentioned circumferential topological migration mechanism, on the one hand can preferably realize sub- population it
Between information isolation, on the other hand can also be effectively ensured elite individual in population stablize propagate and diffusion.Setting son kind
The number of group is G, by taking g (g=1,2 ..., G) a sub- population as an example, sets its original external elite collection and is combined into Jg, from JgIn
Move out n individual and constitute setSet is moved into from g-1 sub- populations simultaneouslyTo form new external elite collection
It closesThen corresponding mathematical expression formula is as follows:
In formula, Jg,fIndicate JgIn f-th of noninferior solution;|Jg| indicate set JgRadix;[x] indicates bracket function;riTable
Show equally distributed random number in [0,1] section, ri∈ [1, | Jg|]。
(c) individual real number tandem coding method:
Each power station is taken as state variable and decision variable in the water level and storage outflow of different scheduling slots respectively, uses
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
Body X is the chromosome with special characteristic, contains the potential step power station combined dispatching method of operation, such as following formula institute
Show.
X=(Xk)NT×1=[Z1,1,Z1,2,…,Z1,T,Z2,1,Z2,2,…,Z2,T,…,ZN, 1,ZN, 2,…,ZN,T]T
In formula, XkIndicate power stationIn period (k-N) water level;Indicate the smallest positive integral for being not less than x.
(d) chaos intialization strategy:
The generting machanism of initial population has very the diversity that individual is distributed in solution space with convergence
Important influence.Chaos phenomenon is prevalent in nature, has exquisite immanent structure, can effectively go through in a certain range
Through all potentially possible states.Therefore, the method for the present invention is all made of Logistic mapping development Chaos Search to each sub- population, with
The quality of initial population is promoted, detail formula is as follows:
In formula, xm,kIndicate value of the kth dimension variable in the m times iteration, xm,k∈[0,1];Xm,kIndicate xm,kOriginal
Mapping value in variable search space; X kRespectively indicate kth dimension variable XkUpper and lower limit.
(e) constraint Pareto is dominant mechanism:
Model for Cascade Hydroelectric Stations is related to the operation constraint of a series of complex, generallys use in single object optimization scheduling
Constraint is destroyed item and is included in objective function by Means of Penalty Function Methods, constitutes superiority and inferiority of the individual adaptation degree functional value to assess individual.So
And in multi-objective optimization question, since the mechanism identification that needs to be dominant using Pareto dominates individual, traditional penalty side
Method is difficult to effectively distinguish infeasible solutions and feasible solution, easily occur infeasible solutions dominate Evolution of Population phenomenon, finally converge to it is non-can
The forward position row Pareto.For this purpose, constraint is destroyed item by the method for the present invention is included in individual goal attribute, it is dominant machine using constraint Pareto
Dominance relation between system processing any two body guides group orderly to evolve simultaneously conscientiously to ensure that feasible solution dominates infeasible solutions
Converge to feasible Pareto optimal solution forward position.Individual XiObject vector calculation method it is as follows:
F1(Xi)=F (Xi)∪Δ(Xi)=[f1(Xi),f2(Xi)]T∪Δ(Xi)
In formula, XiTo indicate i-th of individual;F1(Xi) indicate individual XiExtension object vector;F(Xi) indicate individual Xi's
Original object vector;Δ(Xi) it is to indicate individual XiConstraint destroy the sum of item, be nonnegative value;If Δ (Xi)=0, then XiFor can
Row solution;Otherwise, XiFor infeasible solutions.
Set two individual X of any selectioniWith XjParticipation is compared, specific operating procedure are as follows:
(1) if XiWith XjIt is feasible solution, then determines dominance relation according to individual goal functional value;
(2) if XiFor feasible solution, XjFor infeasible solutions, then feasible solution XiDominate infeasible solutions Xj;
(3) if XiWith XjIt is infeasible solutions, and the two constraint extent of the destruction is identical, then is determined according to individual goal functional value
Dominance relation;Otherwise, the small individual of constraint extent of the destruction is dominant.
It needs to meet following constraint condition during Optimization Solution:
(1) water balance equation
Vi,j+1=Vi,j+3600×(Ii,j-Oi,j)tj
Oi,j=Qi,j+Si,j
In formula, Vi,jStorage capacity for power station i in period j, m3;Ii,j、Oi,jRespectively power station i period j reservoir inflow,
Outbound
Flow, m3/s;qi,j、Si,j、Qi,jRespectively power station i period j section flow, abandon water flow and generating flow,
m3/s;miFor m-th of power station i power station immediately upstream;ΩiFor the reservoir set immediately upstream of power station i.
(2) reservoir storage constrains
In formula, V i,jStorage capacity upper and lower limit of the respectively power station i in period j.
(3) generating flow constrains
In formula, Q i,jGenerating flow upper and lower limit of the respectively power station i in period j.
(4) letdown flow constrains
In formula, O i,jStorage outflow upper and lower limit of the respectively power station i in period j.
(5) output of power station constrains
In formula, P i,jPower output upper and lower limit of the respectively power station i in period j.
According to above-mentioned introduction, the parallel Multiobjective Optimal Operation process of primary complete Hydropower Stations, according to following steps
Suddenly (1)-(8) are achieved:
(1) algorithm calculating parameter is set: including mutation probability Pm, crossover probability Pc, population at individual sum F, nucleus number in calculating
G, maximum number of iterations kmax, migration algebra kmAnd individual amount n etc.;
(2) individual is encoded using individual real number tandem coding method, and calculates the sub- population at individual scale of acquisition and is
F/G;
(3) carry out parallel computation using Fork/Join frame: main thread opens up shared memory space to store each power station
Water level-storage capacity, the basic characteristics data such as water level-letdown flow, the systems such as runoff reach input condition and water level limitation,
The constraint conditions such as power limit out, while generating the thread pool with G thread;
(4) each sub- population is initialized using chaos intialization strategy, enables each sub- population iterative calculation number kg=1, simultaneously
External elite set is setAnd it is added each sub- Evolution of Population as thread in thread pool;
(5) k is enabledg=kg+ 1, NSGA-II method is respectively adopted to the sub- population of unfinished evolutional operation and implements intersection, variation
Equal genetic manipulations, and be dominant elite set omega outside new mechanism using constraint ParetogWith store algorithm search obtain it is non-
Inferior solution;
(6) determine whether each sub- population reaches to need to carry out migration operation, if being unsatisfactory for transition condition, be transferred to step
(7);Otherwise use circumferential topological migration mechanism by the outer of n individual migration in elite set outside this population to next sub- population
Portion's elite set, and move into some individuals of a sub- population;
(7) the external elite set of each sub- population, two generation populations being then combined with before and after each sub- Evolution of Population are updated, and are pressed
New Advanced group species are obtained according to NSGA-II method;
(8) judge whether all sub- populations reach termination condition, if not satisfied, step (5) are then gone to, it is corresponding to complete
Sub- Evolution of Population operation;Otherwise, main thread is returned, the external elite set of all sub- populations is merged, and exports Noninferior Solution Set institute
Corresponding scheduling result.
Now using hydraulic power potentials Lancang River Watershed Hydropower Stations abundant as engineering practice object, using present invention side
Method carries out the parallel power generation dispatching of multiple target, makes year scheduling scheme.Lancang River Watershed is one of big Hydropower Base in China 13, is opened
Hair task is and to have the comprehensive benefits such as tourism, environmental protection concurrently based on generating electricity, and has particularly important promotion to Western Economic
Effect.5 power stations for selecting Lancang River downstream to put into operation as computing object, each power station is respectively voe, Man Wan, make a pilgrimage to a temple on a famous mountain greatly,
Waxy common wheat and Jinghong all have season adjusting and the above regulation performance, wherein voe and waxy common wheat storage capacity are larger, have and adjust for many years
Save performance.The part that table 1 lists each power station calculates information, and table 2 lists the method for the present invention and standard multi-objective genetic algorithm
(MOGA) computational efficiency comparative information.Under the conditions of Fig. 2 shows different waters, the method for the present invention and MOGA noninferior solution obtained
Collect distribution map.It selects three kinds of typical scenarios in Noninferior Solution Set to compare, Fig. 3 shows that the year of three kinds of typical scenarios dispatched
Journey.Analyzed by table 2 it is found that the method for the present invention calculating acceleration effect is very significant: population scale gradually increases to 4000 by 1000,
System operations amount also increases with it, and serial computing time-consuming is increased rapidly by 3.6min to 16.3min, and the big reduction of a fraction of PMOGA under 8 nuclear environments
31s and 135s are not needed, significantly reduces and calculates the time;Under identical population scale, with the interior nucleus number for participating in parallel computation
Mesh increases, and the degree of concurrence of total calculating task is higher, and the speed-up ratio of the method for the present invention also increases with it, in 4000 individuals and 8 cores
Under scene, speed-up ratio 1.84, parallel efficiency has reached 0.92;, by Fig. 2 analysis known to the method for the present invention can obtain non-bad
The scheduling scheme set that forward position is evenly distributed, range is wider;By Fig. 3 analysis it is found that the accumulation of energy of each scheduling scheme of the method for the present invention
It remains basically stable with power output process in flood season, and differs greatly in dry season.In 1~August, water is relatively fewer, and step is to supply water
Based on, each scheme stresses difference to economic benefit, leads to that there are larger differences;And in water more rich 9~October,
System is based on water storage, and difference scheduling scene lower step GROUP OF HYDROPOWER STATIONS maintains maximum accumulation of energy substantially, therefore system is contributed and accumulation of energy
Process shows good synchronism.To sum up, with MOGA method compare, the method for the present invention can active balance system economy
Property and reliability, the organic coordination both realized, it is withered water power can be effectively ensured while improving GROUP OF HYDROPOWER STATIONS generated energy
Phase peak modulation capacity;There is good computational efficiency simultaneously, can guarantee to complete Hydropower Stations multiple target within a short period of time
Optimal Scheduling provides strong technical support for hydroelectric project practice, is that a kind of more efficient Hydropower Stations are more
Objective optimization dispatching method.
Table 1
Table 2
Claims (1)
1. a kind of parallel Multiobjective Optimal Operation method of Hydropower Stations, feature include the following steps:
(1) algorithm calculating parameter is set: including mutation probability Pm, crossover probability Pc, population at individual sum F, nucleus number G in calculating, most
Big the number of iterations kmax, migration algebra kmAnd individual amount n;
(2) individual is encoded using individual real number tandem coding method, and calculates and obtains sub- population at individual scale as 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 in the water level and storage outflow of different scheduling slots respectively, use ten into
Real-coded GA processed each state variable of tandem coding step by step, to reduce the consumption of code length and EMS memory occupation;Any individual X is equal
For the chromosome with special characteristic, the potential step power station combined dispatching method of operation is contained, is shown below:
X=(Xk)NT×1=[Z1,1,Z1,2,…,Z1,T,Z2,1,Z2,2,…,Z2,T,…,ZN, 1,ZN, 2,…,ZN,T]T
In formula, XkIndicate power stationIn the periodWater level;Indicate the smallest positive integral for being not less than x;
(3) carry out parallel computation using Fork/Join frame: main thread opens up shared memory space to store the base in each power station
Plinth performance data, system input condition, constraint condition, while generating the thread pool with G thread;
(4) each sub- population is initialized using chaos intialization strategy, enables each sub- population iterative calculation number kg=1, while being arranged outer
Portion's elite setAnd it is added each sub- Evolution of Population as thread in thread pool;Wherein, chaos intialization strategy according to
Following steps operation:
Logistic mapping is all made of to each sub- population and carries out Chaos Search, to promote the quality of initial population, detail formula is such as
Under:
In formula, xm,kIndicate value of the kth dimension variable in the m times iteration, xm,k∈[0,1];Xm,kIndicate xm,kIn original variable
Mapping value in search space; X kRespectively indicate kth dimension variable XkUpper and lower limit;
(5) k is enabledg=kg+ 1, NSGA-II method is respectively adopted to the sub- population of unfinished evolutional operation and implements genetic manipulation, and is adopted
It is dominant elite set omega outside new mechanism with constraint ParetogTo store the noninferior solution that algorithm search obtains;Wherein, Pareto
The mechanism that is dominant judgment step is as follows:
Individual XiObject vector calculation method it is as follows:
F1(Xi)=F (Xi)∪Δ(Xi)=[f1(Xi),f2(Xi)]T∪Δ(Xi)
In formula, XiTo indicate i-th of individual;F1(Xi) indicate individual XiExtension object vector;F(Xi) indicate individual XiIt is original
Object vector;Δ(Xi) it is to indicate individual XiConstraint destroy the sum of item, be nonnegative value;If Δ (Xi)=0, then XiFor feasible solution;
Otherwise, XiFor infeasible solutions;
Set two individual X of any selectioniWith XjParticipation is compared, specific operating procedure are as follows:
1. if XiWith XjIt is feasible solution, then determines dominance relation according to individual goal functional value;
2. if XiFor feasible solution, XjFor infeasible solutions, then feasible solution XiDominate infeasible solutions Xj;
3. if XiWith XjIt is infeasible solutions, and the two constraint extent of the destruction is identical, then determines to dominate according to individual goal functional value and close
System;Otherwise, the small individual of constraint extent of the destruction is dominant;
(6) determine whether each sub- population reaches to need to carry out migration operation, if being unsatisfactory for transition condition, be transferred to step (7);It is no
Then use circumferential topological migration mechanism by n individual migration in elite set outside this population to the external elite of next sub- population
Set, and move into some individuals of a sub- population;Wherein, circumferential topological migration mechanism executes in accordance with the following steps:
For anyon population, every fixed algebra of evolving just concentrates n elite individual of random selection to move from its external elite
The external elite for entering adjacent sub- population concentrates, and then is moved to sub- population, concentrates individual dominance relation to increase according to its external elite
Add noninferior solution and rejects inferior solution;By above-mentioned circumferential topological migration mechanism, the information isolation between sub- population is on the one hand realized, separately
On the one hand guarantee that elite individual stablizing in population is propagated and diffusion;The number of sub- population is set as G, with g (g=1,
2 ..., G) a sub- population, it sets its original external elite collection and is combined into Jg, from JgIn move out n individual and constitute setTogether
G-1 sub- populations of Shi Cong move into setTo form new external elite setThen corresponding mathematical expression formula is such as
Under:
In formula, Jg,fIndicate JgIn f-th of noninferior solution;|Jg| indicate set JgRadix;[x] indicates bracket function;riIndicate [0,
1] equally distributed random number, r in sectioni∈ [1, | Jg|];
(7) the external elite set of each sub- population of update, two generation populations being then combined with before and after each sub- Evolution of Population, and according to
NSGA-II method obtains new Advanced group species;
(8) judge whether all sub- populations reach termination condition, if not satisfied, going to step (5), then to complete corresponding son kind
Group's evolutional operation;Otherwise, main thread is returned, the external elite set of all sub- populations is merged, and is exported corresponding to Noninferior Solution Set
Scheduling result.
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