CN107067121A - A kind of improvement grey wolf optimized algorithm based on multiple target - Google Patents
A kind of improvement grey wolf optimized algorithm based on multiple target Download PDFInfo
- Publication number
- CN107067121A CN107067121A CN201710443537.9A CN201710443537A CN107067121A CN 107067121 A CN107067121 A CN 107067121A CN 201710443537 A CN201710443537 A CN 201710443537A CN 107067121 A CN107067121 A CN 107067121A
- Authority
- CN
- China
- Prior art keywords
- wolf
- mrow
- individual
- pack
- wolf pack
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
Abstract
The embodiment of the invention discloses a kind of improvement grey wolf optimized algorithm based on multiple target, the technical problem that convergence rate is slow, be easily trapped into the defects such as local optimum is there is when handling multi-objective optimization question for solving standard grey wolf algorithm of the prior art.Present invention method includes：S1, setting wolf pack initiation parameter and adjustment in direction probability, the position of random initializtion wolf individual；S2, the fitness value individual according to each wolf of target calculating is solved, and select three wolf individuals in the top；S3, optimization wolf pack wolf individual position, produce golden mean of the Confucian school wolf, and update wolf pack position；S4, the scale that adjustment in direction operation is performed to the wolf pack after renewal and participates in correcting dimension according to the wolf pack after the control renewal of adjustment in direction probability, the revised wolf pack position of acquisition；S5, judge whether iterations reaches default maximum iteration, if so, then exporting revised wolf pack position as final optimization pass result, otherwise, go to S3 and proceed iterative search.
Description
Technical field
The present invention relates to multi-objective optimization algorithm technical field, more particularly to a kind of improvement grey wolf optimization based on multiple target
Algorithm.
Background technology
As what the system engineering theory was studied reaches its maturity with the present computer technology in the continuous of multiple-objection optimization field
Development and application, various new methods and new technology also emerge in an endless stream.Common method is broadly divided into two major classes：One class is by many mesh
Mark is converted into single goal method, mainly there is Exchanger Efficiency with Weight Coefficient Method, membership function method etc..However, weight coefficient set reasonability and
Validity is the problem that Exchanger Efficiency with Weight Coefficient Method faces, and can not effectively handle the target with non-convex forward position；Membership function method
Then have and construct rational defect.Another kind of is that directly multi-objective problem is solved using heuritic approach, such as quick
Non-dominated sorted genetic algorithm (non-dominated sorting genetic algorithm, NSGA II), enhancing Pareto
Evolution algorithm (strength pareto evolutionary algorithm 2, SPEA2) etc..
The reasonability and validity that weight coefficient is set are problems that Exchanger Efficiency with Weight Coefficient Method faces, and can not effectively handle and have
The target in non-convex forward position；Membership function rule, which has, constructs rational defect.Another kind of is direct using heuritic approach
Multi-objective problem is solved, such as quick non-dominated sorted genetic algorithm (non-dominated sorting genetic
Algorithm, NSGA II), enhancing Pareto evolution algorithm (strength pareto evolutionary algorithm
2, SPEA2) etc..NSGA II is based on quick non-dominated ranking, external archival and selects the strategies such as male parent according to crowding distance, one
Determine to ensure that the diversity of population in degree and improve computational efficiency, but the algorithms of NSGA II by core of genetic algorithm are unavoidable
Inherit the defect that Premature Convergence easily occurs in genetic algorithm.SPEA2 algorithms just have an opportunity to find multiple in single run
Pareto optimal solutions, thus various multi-objective optimization questions are widely used in, but the algorithm excessively focuses on global search
Ability, but ignores local search ability, causes the algorithm to there is the deficiencies such as convergence rate is relatively low compared with slow, disaggregation precision.Especially
It is that, when facing the multi-modal optimization that there are a large amount of local best points, the problem of restraining less than global optimum is especially prominent.
Grey wolf algorithm (Grey Wolf Optimizer, GWO) be by Mirjalili et al. proposed in 2014 it is new
Type Swarm Intelligent Algorithm, the algorithm has that simple in construction, control parameter is few, easily operated, have stronger search capability etc.
Feature, in optimization field, is had been demonstrated to be superior to particle cluster algorithm in computational efficiency and solving precision, but the algorithm is being sought
The defect for being easily trapped into local optimum is still suffered from during excellent.In addition, current excellent for grey wolf algorithm solution multiple target both at home and abroad
The research of change problem still not yet deeply expansion.Only gloomy cyclopentadienyl of hairiness et al. solves power network carbon-can answer using multiple target grey wolf algorithm
Collaborate Optimal Scheduling, and obtain relatively good Pareto forward positions, but the algorithm is not directed in actual iteration mistake
Its part of wolf dimension that is dominant in journey in external archival is easily trapped into local optimum problem and is improved.
In the prior art, standard grey wolf algorithm still suffers from intrinsic convergence rate in processing multi-objective optimization question itself
Slowly the defects such as local optimum, are easily trapped into.
The content of the invention
The embodiments of the invention provide a kind of improvement grey wolf optimized algorithm based on multiple target, solve of the prior art
Standard grey wolf algorithm has that convergence rate is slow, be easily trapped into the defects such as local optimum when handling multi-objective optimization question
Technical problem.
A kind of improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention, including：
S1, the initiation parameter and adjustment in direction probability that wolf pack is set, each wolf individual of random initializtion in solution space
Position；
S2, calculate the fitness value of each wolf individual according to solving target, and select three wolves individual in the top according to
Secondary imparting Xα、Xβ、Xδ；
S3, according to Xα、Xβ、XδOptimize the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate the adaptation of golden mean of the Confucian school wolf
Angle value and renewal wolf pack position；
S4, to after renewal wolf pack perform adjustment in direction operation and according to adjustment in direction probability control update after wolf pack join
With the scale of amendment dimension, new golden mean of the Confucian school wolf is produced, and calculates the fitness value of new golden mean of the Confucian school wolf, revised wolf pack position is obtained
Put；
S5, judge whether iterations reaches default maximum iteration, make if so, then exporting revised wolf pack position
For final optimization pass result, otherwise, go to S3 and proceed iterative search.
Alternatively, S1 is specifically included：
Size M, maximum iteration max gen and the adjustment in direction Probability p of wolf pack are setv, it is random first in solution space
The position of each wolf individual of beginningization.
Alternatively, S2 is specifically included：
According to the fitness value for solving target and calculating each wolf individual, and according to quick noninferior solution sorting operation, it is crowded away from
X is assigned successively from the three wolves individual calculated, the selection of elite retention strategy is in the topα、Xβ、Xδ。
Alternatively, quick noninferior solution sorting operation is specifically included：
The non-dominant disaggregation in wolf pack is found, by non-dominant disaggregation labeled as the first non-dominant layer F1 and by non-dominant disaggregation
In all wolves individual assign the first non-dominant sequence value, and by all wolves individual reject；
Found out in wolf pack after rejecting next layer of non-dominant disaggregation go forward side by side line flag, non-dominant sequence value assign operation and pick
Division operation；
It is lasting successively to carry out that the layering of wolf pack progress non-dominant disaggregation, mark, non-dominant sequence value are assigned operating and rejecting to grasp
Make, until whole wolf pack is layered and causes the wolf individual in same non-dominant layer to have identical non-dominant sequence value completely.
Alternatively, crowding distance is calculated and specifically included：
The distance of the wolf individual in same non-dominant layer is initialized, wolf individual i crowding distance L [i] is madedFor 0；
Wolf individual in same non-dominant layer carries out sort ascending by m-th of desired value；
Two wolves individual on given edge assigns number Inf one big, two wolf individuals is had absolute selective advantage；
The crowding distance of wolf individual sequence in the middle of is sought the wolf individual in the middle of sequence according to formula eight, and formula eight is specific
For：
Wherein, NobjFor number of targets,Respectively m-th of fitness value of i+1 and the i-th -1 wolf individual,The maximum and minimum value of m-th of fitness value respectively in Noninferior Solution Set.
Alternatively, S3 is specifically included：
According to Xα、Xβ、XδThe position of each wolf individual of the step of being caught with wolf pack optimization wolf pack is surrounded by wolf pack, is produced
Golden mean of the Confucian school wolf, and calculate the fitness value of golden mean of the Confucian school wolf and retain plan according to quick noninferior solution sorting operation, crowding distance calculating, elite
Omit selective updating wolf pack position.
Alternatively, also include between S3 and S4：
Individual to all wolves of the wolf pack after renewal is every one-dimensional by the execution normalization operation of formula nine, and formula nine is specific
For：
Wherein, D is dimension,For wolfD dimension variable,ForCorresponding scalar after normalization,
Max (d), min (d) are respectively the bound of d dimension variables in wolf pack.
Alternatively, S4 is specifically included：
Adjustment in direction operation is performed to the wolf pack after renewal and controls the wolf pack after updating to participate according to adjustment in direction probability
The scale of dimension is corrected, new golden mean of the Confucian school wolf is produced, and calculates the fitness value of new golden mean of the Confucian school wolf, is sorted and grasped according to quick noninferior solution
Make, crowding distance is calculated, elite retention strategy preferentially retains wolf body position, and the individual ranking of the wolf in wolf pack, by wolf
Group is divided into Xα、Xβ、Xδ、Xω, obtain revised wolf pack position.
Alternatively, adjustment in direction operation is performed to the wolf pack after renewal to specifically include：
Adjustment in direction is performed by the wolf pack after ten pairs of renewals of formula to operate, formula ten is specially：
Wherein, d1,d2∈ (1, D), r are 0 to 1 random number,For the individual scalar of golden mean of the Confucian school wolfD1Dimension；
Renormalization operation is carried out to every one-dimensional formula 11 that passes through of the golden mean of the Confucian school wolf individual scalar of generation, formula 11 has
Body is：
Wherein,For golden mean of the Confucian school wolfD dimension.
Alternatively, S5 is specifically included：
Judge whether iterations reaches default maximum iteration, if so, then exporting the conduct of revised wolf pack position
Final optimization pass result, and the optimal compromise solution of fuzzy Decision Making Method selection is combined, otherwise, go to S3 and proceed iterative search.
As can be seen from the above technical solutions, the embodiment of the present invention has advantages below：
The embodiments of the invention provide a kind of improvement grey wolf optimized algorithm based on multiple target, including：S1, wolf pack is set
Initiation parameter and adjustment in direction probability, the position of each wolf individual of random initializtion in solution space；S2, according to solve target
The fitness value of each wolf individual is calculated, and selects three wolves individual in the top to assign X successivelyα、Xβ、Xδ；S3, according to Xα、
Xβ、XδOptimize the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate the fitness value of golden mean of the Confucian school wolf and update wolf pack position；
S4, to after renewal wolf pack perform adjustment in direction operation and according to adjustment in direction probability control update after wolf pack participate in amendment dimension
Scale, produce new golden mean of the Confucian school wolf, and calculate the fitness value of new golden mean of the Confucian school wolf, obtain revised wolf pack position；S5, judgement
Whether iterations reaches default maximum iteration, if so, revised wolf pack position is then exported as final optimization pass result,
Otherwise, go to S3 and proceed iterative search.By using crossed longitudinally operation in crossover algorithm in length and breadth in the embodiment of the present invention
Process part ties up the exclusive advantage for being easily trapped into local optimum problem, on the basis of standard grey wolf algorithm, incorporates adjustment in direction behaviour
Make (crossed longitudinally operation) there is provided a kind of new wolf pack location updating method, broken away from the dimension for helping part to be absorbed in local optimum
Current quagmire, corrects the direction of advance of wolf pack, strengthens the global convergence of algorithm, solves standard grey wolf of the prior art and calculates
Method has the technical problem that convergence rate is slow, be easily trapped into the defects such as local optimum when handling multi-objective optimization question.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, without having to pay creative labor, may be used also
To obtain other accompanying drawings according to these accompanying drawings.
Fig. 1 is specific wolf pack Social Grading and major responsibility schematic diagram in grey wolf algorithm provided in an embodiment of the present invention；
Fig. 2 is the wolf pack position updating process schematic diagram of grey wolf algorithm provided in an embodiment of the present invention；
Fig. 3 is a kind of one embodiment of the improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention
Schematic flow sheet；
Fig. 4 is a kind of another embodiment of the improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention
Schematic flow sheet；
Fig. 5 is that a kind of meter provided in an embodiment of the present invention and thermal power plant's consumption characteristic curve with ignoring valve point effect are contrasted
Figure；
Fig. 6 is the coupled thermomechanics relation schematic diagram of cogeneration units provided in an embodiment of the present invention；
Fig. 7 is the various optimal forward position contrast schematic diagrams of the optimal Pareto of algorithm provided in an embodiment of the present invention.
Embodiment
The embodiments of the invention provide a kind of improvement grey wolf optimized algorithm based on multiple target, for solving in the prior art
Standard grey wolf algorithm exist that convergence rate is slow, be easily trapped into the defects such as local optimum when handling multi-objective optimization question
Technical problem.
To enable goal of the invention, feature, the advantage of the present invention more obvious and understandable, below in conjunction with the present invention
Accompanying drawing in embodiment, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that disclosed below
Embodiment be only a part of embodiment of the invention, and not all embodiment.Based on the embodiment in the present invention, this area
All other embodiment that those of ordinary skill is obtained under the premise of creative work is not made, belongs to protection of the present invention
Scope.
In order to make it easy to understand, the following general principle that will simply introduce grey wolf algorithm.
As Canidae class animal, grey wolf is located at the top of food chain in nature, is often considered as top and hunts trencherman.It is given birth to
Mode living likes gregarious mostly, and each wolf pack generally averagely has 5~12 wolves, in daily life, especially goes out to hunt,
They follow extremely strict Social Grading and task division of labor system, and such as in grey wolf algorithm, grade highest is referred to as a wolf
And α is designated as, it is main to be responsible for the whole wolf pack of leader, and decision-making is formulated in hunting process, β wolves are in the second stratum of wolf pack, and it is made
With to assist α to make a policy, δ wolves are then the third class of wolf pack, main the task such as to be responsible for investigate, guard against, encircling and hunting down, guarding, surplus
Remaining wolf pack is ω, positioned at the whole wolf pack bottom, submits to the order of other high-level wolves, and the group related according to development is indicated
Body, which is hunted, takes action.Specific wolf pack Social Grading and major responsibility are as shown in Figure 1.
In each iteration, the optimal individual of fitness is endowed Xα, suboptimum individual is endowed Xβ, third is individual to be determined
Justice is Xδ, remaining individual is set to Xω.GWO algorithm bionic wolf pack hunting processes are broadly divided into three steps, that is, surround, catch and attack
Hit, it is comprised the following steps that.
1st, surround
Wolf pack surrounds, the mathematical modeling of the process is represented by prey first when performing hunting task:
In formula, t is current wolf pack algebraically,For the distance between wolf and prey vector；WithTo swing factor vector,For prey current location (global optimum's solution vector),For wolf position (potential solution vector).WithValue by public affairs
Formula (3), (4) calculate and obtained：
In formula,The random vector that span is [0,1] is characterized,The value a of vector is linearly passed with iterations by 2
Reduce to 0.
2nd, catch
After prey is surrounded, execution is caught action by wolf pack, is the position for searching prey more directionally, this action
Typically guided by α, β, δ, other ω wolves then update their own position according to α, β, δ instruction.It is specific to update table
It is up to formula：
In formula,Respectively the distance between ω wolves and α, β, δ vector,For the wolf position after renewal,
Position updating process is as shown in Figure 2.
3rd, attack
What wolf pack was hunted will finally enter phase of the attack, the main task of the stage wolf pack is to complete to arrest prey this mesh
Mark, i.e. grey wolf algorithm obtain globally optimal solution.The implementation of the process is mainly：With in formula (3)Value linearly passed from 2
0 is reduced to, correspondingly,Value will also obtain Arbitrary Digit in [- 2a, 2a].WhenWhen, wolf pack is in concentrate and attacked
The state of prey, and work asWhen, wolf pack will gradually scatter from the position where prey, cause grey wolf algorithm to lose
Optimal solution position, and then go during being transferred to the other locally optimal solutions of searching, this is also that grey wolf algorithm is easily trapped into part
Optimal solution, and convergence time it is tediously long the problem of where.
It is the brief description to the general principle of grey wolf algorithm above, below will be to a kind of base provided in an embodiment of the present invention
It is described in detail in one embodiment of the improvement grey wolf optimized algorithm of multiple target.
Referring to Fig. 3, a kind of improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention, including：
S1, the initiation parameter and adjustment in direction probability that wolf pack is set, each wolf individual of random initializtion in solution space
Position；
First, initiation parameter (size of such as wolf pack and the maximum iteration of algorithm) and the side of wolf pack are set
To amendment probability, and the individual position of each wolf of random initializtion in the solution space for solving target.
S2, calculate the fitness value of each wolf individual according to solving target, and select three wolves individual in the top according to
Secondary imparting Xα、Xβ、Xδ；
Set wolf pack initiation parameter and adjustment in direction probability, and in solution space random initializtion finish it is each
After the position of wolf individual, the fitness value of each wolf individual is calculated according to target is solved, and select three wolves in the top
Individual assigns X successivelyα、Xβ、Xδ。
S3, according to Xα、Xβ、XδOptimize the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate the adaptation of golden mean of the Confucian school wolf
Angle value and renewal wolf pack position；
After three wolves in the top are obtained, according to Xα、Xβ、XδThe each wolf of wolf pack is optimized by above-mentioned formula (1-7)
The position of individual, produces golden mean of the Confucian school wolf, and calculates the fitness value of golden mean of the Confucian school wolf and update wolf pack position, that is, perform wolf pack encirclement and
Catch behavior.
S4, to after renewal wolf pack perform adjustment in direction operation and according to adjustment in direction probability control update after wolf pack join
With the scale of amendment dimension, new golden mean of the Confucian school wolf is produced, and calculates the fitness value of new golden mean of the Confucian school wolf, revised wolf pack position is obtained
Put；
After generating golden mean of the Confucian school wolf and updating wolf pack position, adjustment in direction operation and basis are performed to the wolf pack after renewal
Wolf pack after the control of adjustment in direction probability updates participates in the scale that amendment is tieed up, and produces new golden mean of the Confucian school wolf, and calculate new golden mean of the Confucian school wolf
Fitness value, obtain revised wolf pack position.
S5, judge whether iterations reaches default maximum iteration, make if so, then exporting revised wolf pack position
For final optimization pass result, otherwise, go to S3 and proceed iterative search.
Finally, judge whether the iterations for improving grey wolf algorithm reaches default maximum iteration, if so, then output is repaiied
Otherwise wolf pack position after just, goes to S3 and proceeds iterative search as final optimization pass result.
The embodiments of the invention provide a kind of improvement grey wolf optimized algorithm based on multiple target, including：S1, wolf pack is set
Initiation parameter and adjustment in direction probability, the position of each wolf individual of random initializtion in solution space；S2, according to solve target
The fitness value of each wolf individual is calculated, and selects three wolves individual in the top to assign X successivelyα、Xβ、Xδ；S3, according to Xα、
Xβ、XδOptimize the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate the fitness value of golden mean of the Confucian school wolf and update wolf pack position；
S4, to after renewal wolf pack perform adjustment in direction operation and according to adjustment in direction probability control update after wolf pack participate in amendment dimension
Scale, produce new golden mean of the Confucian school wolf, and calculate the fitness value of new golden mean of the Confucian school wolf, obtain revised wolf pack position；S5, judgement
Whether iterations reaches default maximum iteration, if so, revised wolf pack position is then exported as final optimization pass result,
Otherwise, go to S3 and proceed iterative search.By using crossed longitudinally operation in crossover algorithm in length and breadth in the embodiment of the present invention
Process part ties up the exclusive advantage for being easily trapped into local optimum problem, on the basis of standard grey wolf algorithm, incorporates adjustment in direction behaviour
Make (crossed longitudinally operation) there is provided a kind of new wolf pack location updating method, broken away from the dimension for helping part to be absorbed in local optimum
Current quagmire, corrects the direction of advance of wolf pack, strengthens the global convergence of algorithm, solves standard grey wolf of the prior art and calculates
Method has the technical problem that convergence rate is slow, be easily trapped into the defects such as local optimum when handling multi-objective optimization question.
It is to a kind of implementation of the improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention above
The detailed description of example, below by a kind of the another of improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention
Individual embodiment is described in detail.
Referring to Fig. 4, another of a kind of improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention
Embodiment, including：
The 201st, size M, maximum iteration max gen and the adjustment in direction Probability p of wolf pack be setv, in solution space with
Machine initializes the position of each wolf individual；
First, initiation parameter (the size M of such as wolf pack and the maximum iteration max gen of algorithm of wolf pack are set
Deng) and adjustment in direction Probability pv, and the individual position of each wolf of random initializtion in the solution space for solving target.
202nd, according to the fitness value for solving target and calculating each wolf individual, and according to quick noninferior solution sorting operation, gather around
Squeeze three wolves individual that distance is calculated, the selection of elite retention strategy is in the top and assign X successivelyα、Xβ、Xδ；
Set wolf pack initiation parameter and adjustment in direction probability, and in solution space random initializtion finish it is each
After the position of wolf individual, the fitness value of each wolf individual is calculated according to target is solved, and grasp according to the sequence of quick noninferior solution
Make, crowding distance is calculated, elite retention strategy selects three wolves individual in the top to assign X successivelyα、Xβ、Xδ。
Specifically, following will be carried out in detail to quick noninferior solution sorting operation, crowding distance calculating, elite retention strategy
Illustrate.
Quick non-dominated ranking operation：Advance for guiding wolf pack location updating towards Pareto optimal solution sets direction, must be to wolf
Group carries out quick non-dominated ranking operation, and the operation is the fitness delaminating process of a circulation.Specially：Wolf pack is found out first
In non-dominant disaggregation, be designated as the first non-dominant layer F1, secondly, by the solution concentrate all wolves individual assign non-dominant sequences (in formula,
irankCharacterize individual i non-dominant sequence value), and rejected from whole wolf pack；Continue thereafter with and next layer is found out from remaining wolf pack
Non-dominant disaggregation, is similarly designated as the second non-dominant layer F2, and wolf individual is endowed non-dominant sequence irank=2, and removed from wolf pack；According to
It is secondary to analogize, until whole wolf pack is layered, there is identical non-dominant sequence i with the wolf individual in layerrank.Following steps can be divided
Carry out：The non-dominant disaggregation in wolf pack is found, non-dominant disaggregation labeled as the first non-dominant layer F1 and is concentrated non-domination solution
All wolves individual assign the first non-dominant sequence value, and by all wolves individual reject；Next layer is found out in wolf pack after rejecting
Non-dominant disaggregation go forward side by side line flag, non-dominant sequence value assign operation and reject operation；It is lasting successively to carry out carrying out non-branch to wolf pack
Operation is assigned with disaggregation layering, mark, non-dominant sequence value and operation is rejected, until whole wolf pack is layered and caused same completely
Wolf individual in non-dominant layer has identical non-dominant sequence value.
Individual crowding distance is calculated：Selectivity can not be carried out to same layer non-dominant disaggregation for the operation of quick non-dominated ranking
Sequencing problem, introduces individual crowding distance and calculates operation.Wolf individual crowding distance refers to adjacent with individual i on object space
Two wolves individual the distance between i-1 and i+1, are comprised the following steps that：
1. the distance of same layer wolf individual is initialized, even wolf individual i crowding distance L [i]dFor 0；
2. sort ascending is carried out by m-th of desired value with layer wolf individual；
3. give two wolves individual on edge and assign number Inf one big, make it have absolute selective advantage；
4. its crowding distance is asked according to formula (8) to the wolf individual in the middle of sequence：
In formula：NobjFor number of targets,Respectively m-th of fitness value of i+1 and the i-th -1 wolf individual,The maximum and minimum value of m-th of fitness value respectively in the Noninferior Solution Set.
5. similarly, to different target function, repeat step 2.~4., you can obtain gathering around for wolf individual i in the Noninferior Solution Set
Squeeze distance.
Elite retention strategy：In the stage of hunting, to assign wolf individual a certain degree of independence, in wolf pack location updating
When, will be according to the evolution laws of " survival of the fittest, the survival of the fittest ", the only more preferable wolf in position, that is, the wolf physical efficiency guarantor of M before arranging
Stay, as the wolf DS that is dominant, and participate in next iteration.
As can be seen here, wolf itself of the position of ω wolves except in addition to the guide according to α, β, δ wolf, will also retain a part
Greediness, is selectively updated the position of oneself, therefore, while whole wolf pack approaches towards prey, will be protected all the time
Hold that whole wolf pack position is optimal, this has further speeded up the search speed of wolf pack.
203rd, according to Xα、Xβ、XδThe position of each wolf individual of the step of being caught with wolf pack optimization wolf pack is surrounded by wolf pack,
Produce golden mean of the Confucian school wolf, and calculate golden mean of the Confucian school wolf fitness value and according to quick noninferior solution sorting operation, crowding distance calculate, Jing Yingbao
Policy selection is stayed to update wolf pack position；
After three wolves in the top are obtained, according to Xα、Xβ、XδThe step of being caught with wolf pack is surrounded by wolf pack excellent
Change the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate the fitness value of golden mean of the Confucian school wolf and sorted according to quick noninferior solution
Operation, crowding distance are calculated, elite retention strategy selective updating wolf pack position.
204th, every one-dimensional the pass through formula nine individual to all wolves of the wolf pack after renewal performs normalization operation；
Directly carrying out arithmetic crossover for the different dimensional variable for different dimensions and different bounds can not directly be calculated
The problem of art is intersected, needed before performing adjustment in direction operation it is unified to the wolf pack after renewal in the every of all wolves individuals one-dimensional hold
Row normalization operation：
Wherein, D is dimension,For wolfD dimension variable,ForCorresponding scalar after normalization,
Max (d), min (d) are respectively the bound of d dimension variables in wolf pack.
205th, adjustment in direction operation is performed to the wolf pack after renewal and the wolf pack after updating is controlled according to adjustment in direction probability
The scale of amendment dimension is participated in, new golden mean of the Confucian school wolf is produced, and calculates the fitness value of new golden mean of the Confucian school wolf, is sorted according to quick noninferior solution
Operation, crowding distance are calculated, elite retention strategy preferentially retains wolf body position, and the individual ranking of the wolf in wolf pack, will
Wolf pack is divided into Xα、Xβ、Xδ、Xω, obtain revised wolf pack position；
The phenomenon of local optimum is absorbed in for being likely to occur part dimension in wolf pack, adjustment in direction operation is repaiied using a direction
Positive Probability pvTo control the scale that amendment dimension is participated in current wolf pack, and correct only produce one-dimensional filial generation every time, this is conducive to
Assist part dimension to avoid damage to normal dimension while breaking away from dimension local optimum, effectively correct the direction of wolf pack.The mould of the process
Type is built：
It is assumed that wolf individual scalar in wolf packD1,d2Dimension is respectivelyWithAdjustment in direction then is performed to them
Operation produces the d of golden mean of the Confucian school wolf1Dimension is represented by：
In formula:d1,d2∈ (1, D), r are 0 to 1 random number,For the individual scalar of golden mean of the Confucian school wolfD1Dimension.
After adjustment in direction operation has been performed, one-dimensional renormalization behaviour must be carried out to the every of the individual scalar of produced golden mean of the Confucian school wolf
Make：
In formula,For golden mean of the Confucian school wolfD dimension.
In addition, for convenience of to the wolf pack DS and produced golden mean of the Confucian school wolf pack X that is dominantt+1/ MS is effectively sorted, and it must be entered
Row merges, the merging wolf pack CM that generation number of individuals is 2M.
206th, judge whether iterations reaches default maximum iteration, if so, then exporting revised wolf pack position
As final optimization pass result, and the optimal compromise solution of fuzzy Decision Making Method selection is combined, otherwise, go to 203 and proceed iteration and search
Rope.
Finally, judge whether iterations reaches default maximum iteration, if so, then exporting revised wolf pack position
As final optimization pass result, and the optimal compromise solution of fuzzy Decision Making Method selection is combined, otherwise, go to S3 and proceed iteration and search
Rope.
In actual motion, general final embodiment only has one.Therefore, be assist policymaker before Pareto is optimal
An optimal compromise solution is chosen in, can be determined according to fuzzy set theory.Wherein, each Pareto solves each desired value correspondence
Satisfaction can be represented by fuzzy membership function, be defined as follows：
In formula：m∈(1,Nobj),i∈(1,M)fm(xi) be noninferior solution i m-th of target function value.
Therefore, the standardization satisfaction that each noninferior solution in Pareto forward positions can be tried to achieve by formula (13) is：
Eventually through comparing, the solution of Maximum Satisfaction is solved as optimal compromise in selection Pareto forward positions.
It is to a kind of another reality of the improvement grey wolf optimized algorithm based on multiple target provided in an embodiment of the present invention above
Apply the detailed description of example, below with reference to a specific example checking improve grey wolf algorithm processing with multiple constraint, it is non-linear,
Validity when non-differentiability and multi-objective optimization question comprising a large amount of local best points.
Grey wolf algorithm is improved for checking handling with multiple constraint, non-linear, non-differentiability and including a large amount of local best points
Multi-objective optimization question validity, grey wolf algorithm and grey wolf algorithm will be improved and be respectively applied to containing 4 pure generating thermoelectricitys
Unit, the cogeneration of heat and power power system of 2 cogeneration units and 1 pure heating unit carry out simulation analysis, and the system considers
The valve point effect of the pure generating set of thermoelectricity, via net loss, electrically and thermally balance and the constraint etc. that generates electricity of generating heat, electricity, thermal load demands
Respectively 700MW and 150MWth.Example carries out programming language using MATLAB R2010b；Computer running environment is
Inter (R) CPU G5400,2.49GHz, it is interior save as 3.40GB, operating system is Windows XP Professional.Together
When, to ensure the reasonability of test result and effectively checking adjustment in direction operates influence to standard grey wolf algorithm, therefore, except changing
Enter the exclusive amendment Probability p of grey wolf algorithmvBe set to outside 0.4, improve grey wolf algorithm and grey wolf algorithm using identical Population Size 50,
Maximum iteration 500, tested at 100 times in use identical initialization population, and select respective optimal solution as final
The optimal forward positions of Pareto.
In order to make it easy to understand, following will carry out detailed explanation to the economic and environment-friendly Problems of Optimal Dispatch model of cogeneration of heat and power.
The core of the economic and environment-friendly Problems of Optimal Dispatch of cogeneration of heat and power is to meet thermoelectricity yield balancing the load and various constraints
Under the conditions of, fuel cost and the two environmentally friendly targets are optimized simultaneously, to obtain more satisfied optimal compromise dispatching party
Case.Its mathematical modeling can be expressed as follows.
Object function：
(1) fuel cost function
The system includes the pure generating set of common thermoelectricity, cogeneration units and pure heating unit.Therefore, its total fuel
Expense such as formula (14)
In formula：CtotalFor overall-fuel cost；Np、Nc、NhThe respectively pure generating set of thermoelectricity, cogeneration units, pure heating
The number of units of unit；Cpi(Pi) it is the pure generating set fuel cost of i-th thermoelectricity；Cci(Oi,Hi) fired for i-th cogeneration units
Material expense；Chi(Ti) it is i-th pure heating unit fuel cost；PiFor the exerting oneself of i-th pure generating set of thermoelectricity, Oi、HiRespectively
For the generated energy and caloric value of i-th cogeneration units；TiFor the caloric value of i-th pure heating unit；
In the economic and environment-friendly scheduling problem of actual cogeneration of heat and power, it usually needs (counted and with ignoring valve point effect in view of such as Fig. 5
The thermal power plant's consumption characteristic curve comparison diagram answered) shown in the pure generating set of thermoelectricity in steam turbine intake valve when opening suddenly
Existing hot candied phenomenon --- valve point effect, the phenomenon to be superimposed on the secondary consumption characteristic curve of the pure generating set of original thermoelectricity
One sinuous pulsation function, therefore while more accurate progress problem solving, also cause a large amount of parts of the problem abruptly increase
Optimum point, adds the solution difficulty of problem.It is specifically stated such as formula (15).
In formula：ai、bi、ciThe fuel cost coefficient of the respectively i-th pure generating set of thermoelectricity；ei、fiGenerated electricity for thermoelectricity is pure
Unit i valve point effect coefficient；Minimum technology for the pure generating set i of thermoelectricity is exerted oneself.Secondly, cogeneration of heat and power and pure heating
Unit fuel cost function is respectively as shown in formula (16) and formula (17).
In formula：αi、βi、γi、δi、εi、ξiFor cogeneration units i fuel cost coefficient；ψi、ηi、λiFor pure hypertherm
Group i fuel cost coefficient.
(2) dusty gas discharge function
Operationally produced pollution gas is mainly for the pure generating set of thermoelectricity, cogeneration units and pure heating unit
SO2, NOx and CO2 etc., its discharge capacity depend primarily on unit generation and caloric value, and concrete mathematical model is：
In formula：EtotalDischarged for gross contamination thing；Epi(Pi) be the pure generating set i of thermoelectricity discharge capacity；Eci(Oi) it is thermoelectricity
Coproduction unit i discharge capacity；
Ehi(Ti) for pure heating unit i discharge capacity；μi、ki、πi、σi、θiFor pure generating set i emission factor；τiFor
Cogeneration units i emission factor；ρiFor pure heating unit i emission factor；
Constraints：
(1) system optimized distributionl equilibrium constraint
Heat, electricity production and the consumption that electric energy and heat energy are difficult in Mass storage requirement system possess simultaneity, therefore palpus
Heat, electricity productioin in guarantee system meet workload demand balance, specific as follows shown.
In formula：PD、PLThe respectively electrical load requirement and via net loss of system；HDFor the thermal load demands of system.
Pure generating set units limits condition
In formula：Exerted oneself the upper limit for pure generating set.
Cogeneration units operation constraint
Fig. 6 illustrates the coupled thermomechanics relation of cogeneration units, and the closed area surrounded by pinpointing ABCDEF is heat
The unit safety operation region that Electricity Federation production unit is allowed.Along the boundary sections BC in region, unit output is passed with caloric value
Increase and be gradually reduced, and then successively decrease along line segment CD player group caloric value.
In formula：Respectively cogeneration units i generated output bound；
Respectively cogeneration units i caloric value upper and lower limit.
Pure heating Unit commitment
In formula：The caloric value upper and lower limit of respectively pure heating unit.
, below will be to two kinds above for the economic and environment-friendly Problems of Optimal Dispatch model of cogeneration of heat and power is discussed in detail
The optimum results of algorithm are analyzed.
Optimum results are analyzed：
Fig. 7 illustrates the improvement grey wolf algorithm carried in the algorithms of NSGA II, SPEA2 algorithms, grey wolf algorithm and the present invention
The optimal forward positions of optimal Pareto that 100 independent operatings are obtained.Table 1 lists RCGA algorithm single object optimization minimum fuel expenses
With and discharge, go out side by side grey wolf algorithm and improve grey wolf algorithm the optimal forward position end points of Pareto at target function value.For checking
The validity of solution, table 2 provides the optimal compromise solution and its corresponding scheduling scheme of each algorithm.
Learnt by each algorithm single goal extremums of table 1-2, compromise solution contrast, each scheduling scheme either pure generator of thermoelectricity
Group is exerted oneself, cogeneration units generated energy and caloric value or pure heating unit caloric value strictly meet various complicated constraints
Condition, and heat, electricity also preferably meet balancing the load demand, and this optimum results indicate grey wolf algorithm and improve grey wolf and calculate
The correctness for the optimal solution set that method is tried to achieve.It can be found by table 1 simultaneously, although improving grey wolf algorithm incoming direction amendment operation makes
Obtain CPU run times and add 18.54% compared to grey wolf algorithm, but improve the Pareto economic goals that grey wolf algorithm is obtained
Extremum is 10069.38 $, reduces by 8.85% expense than grey wolf algorithm, while reducing by 6.01%, and its environmental protection than RCGA algorithm
Target extremum is 14.0443kg, than the discharge that grey wolf reduces 16.03%, or even 17% row is also reduced than NSGA II
Put.Therefore, when improving the economic and environment-friendly Problems of Optimal Dispatch of grey wolf Algorithm for Solving multiple constraint, non-linear, non-differentiability cogeneration of heat and power
The optimal forward positions of the wider array of Pareto of scope can be obtained within the relatively reasonable calculating time, this, which also show the algorithm, has more
Strong ability of searching optimum.Secondly, each unit relevant parameter is combined by table 2, it is seen that, improve the folding obtained by grey wolf algorithm
Middle solution holds water, and either fuel cost or discharge value are small compared with other algorithms, and this further illustrates improve grey wolf
Superiority of the algorithm in scheduling decision.Finally, with the algorithms of NSGA II, SPEA2 algorithms, Pareto obtained by grey wolf algorithm it is optimal before
Along comparing, the optimal forward positions of Pareto that improvement grey wolf algorithm is obtained are evenly distributed in solution space, and scope is wider, closer to entirely
Office's optimal solution.Because grey wolf algorithm is improved not only while multiple-objection optimization expansion is carried out to grey wolf algorithm, introduction
NSGA II quick noninferior solution sequence and crowding distance calculate processing multicriterion scheduling problem, effectively maintain particle various
Property, improve the computational efficiency of algorithm.And merged adjustment in direction operation process part dimension be absorbed in the only of local optimum problem
It is advantageous, it is effectively prevented from Premature Convergence occur.This series shows that the multiple target grey wolf optimized algorithm after improvement has
Preferable global convergence, adaptability.
Each algorithm extremum of table 1 and its scheduling scheme contrast
The optimal compromise solution contrast of each algorithm of table 2
The notable of improvement grey wolf optimized algorithm provided in an embodiment of the present invention based on multiple target is advantageous in that：
1) the crossed longitudinally operation in crossover algorithm in length and breadth is incorporated in grey wolf algorithm to help part to be absorbed in local optimum
Dimension break away from current quagmire, correct the direction of advance of wolf pack, strengthen the global convergence of algorithm.
2) NSGA II sequence of quick noninferior solution, crowding distance calculative strategy is quoted, assistance is ranked up to wolf individual, and
The diversity of particle is maintained to a certain extent.
3) in wolf pack location updating, using elite retention strategy, assign wolf pack certain independence, this wolf pack is all the time
Wolf pack total optimization position is kept, whole convergence of algorithm speed is effectively accelerated.
4) the cogeneration of heat and power electric power of 4 pure generating sets of thermoelectricity, 2 cogeneration units and 1 pure heating unit is included
Improvement grey wolf algorithm proposed in the system Example Verification embodiment of the present invention, as a result indicating improvement grey wolf algorithm has
Stronger global convergence, adaptability.
It is apparent to those skilled in the art that, for convenience and simplicity of description, the system of foregoing description,
The specific work process of device and unit, may be referred to the corresponding process in preceding method embodiment, will not be repeated here.
In several embodiments provided herein, it should be understood that disclosed system, apparatus and method can be with
Realize by another way.For example, device embodiment described above is only schematical, for example, the unit
Divide, only a kind of division of logic function there can be other dividing mode when actually realizing, such as multiple units or component
Another system can be combined or be desirably integrated into, or some features can be ignored, or do not perform.It is another, it is shown or
The coupling each other discussed or direct-coupling or communication connection can be the indirect couplings of device or unit by some interfaces
Close or communicate to connect, can be electrical, machinery or other forms.
The unit illustrated as separating component can be or may not be it is physically separate, it is aobvious as unit
The part shown can be or may not be physical location, you can with positioned at a place, or can also be distributed to multiple
On NE.Some or all of unit therein can be selected to realize the mesh of this embodiment scheme according to the actual needs
's.
In addition, each functional unit in each embodiment of the invention can be integrated in a processing unit, can also
That unit is individually physically present, can also two or more units it is integrated in a unit.Above-mentioned integrated list
Member can both be realized in the form of hardware, it would however also be possible to employ the form of SFU software functional unit is realized.
If the integrated unit is realized using in the form of SFU software functional unit and as independent production marketing or used
When, it can be stored in a computer read/write memory medium.Understood based on such, technical scheme is substantially
The part contributed in other words to prior art or all or part of the technical scheme can be in the form of software products
Embody, the computer software product is stored in a storage medium, including some instructions are to cause a computer
Equipment (can be personal computer, server, or network equipment etc.) performs the complete of each embodiment methods described of the invention
Portion or part steps.And foregoing storage medium includes：USB flash disk, mobile hard disk, read-only storage (ROM, Read-Only
Memory), random access memory (RAM, Random Access Memory), magnetic disc or CD etc. are various can store journey
The medium of sequence code.
Described above, the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to before
Embodiment is stated the present invention is described in detail, it will be understood by those within the art that：It still can be to preceding
State the technical scheme described in each embodiment to modify, or equivalent substitution is carried out to which part technical characteristic；And these
Modification is replaced, and the essence of appropriate technical solution is departed from the spirit and scope of various embodiments of the present invention technical scheme.
Claims (10)
1. a kind of improvement grey wolf optimized algorithm based on multiple target, it is characterised in that including：
S1, the initiation parameter and adjustment in direction probability that wolf pack is set, the position of each wolf individual of random initializtion in solution space
Put；
S2, calculate the fitness value of each wolf individual according to solving target, and select three wolves individual in the top according to
Secondary imparting Xα、Xβ、Xδ；
S3, according to the Xα, the Xβ, the XδOptimize the position of each wolf individual of wolf pack, produce golden mean of the Confucian school wolf, and calculate
The fitness value of the golden mean of the Confucian school wolf and renewal wolf pack position；
S4, adjustment in direction operation is performed to the wolf pack after renewal and the wolf after the renewal is controlled according to the adjustment in direction probability
Group participates in the scale of amendment dimension, produces new golden mean of the Confucian school wolf, and calculates the fitness value of the new golden mean of the Confucian school wolf, obtains revised
Wolf pack position；
S5, judge whether iterations reaches default maximum iteration, if so, then exporting revised wolf pack position as most
Whole optimum results, otherwise, go to S3 and proceed iterative search.
2. the improvement grey wolf optimized algorithm according to claim 1 based on multiple target, it is characterised in that the S1 is specifically wrapped
Include：
Size M, maximum iteration maxgen and the adjustment in direction Probability p of wolf pack are setv, random initializtion is every in solution space
The position of individual wolf individual.
3. the improvement grey wolf optimized algorithm according to claim 1 based on multiple target, it is characterised in that the S2 is specifically wrapped
Include：
According to the fitness value for solving target and calculating each wolf individual, and according to quick noninferior solution sorting operation, it is crowded away from
X is assigned successively from the three wolves individual calculated, the selection of elite retention strategy is in the topα、Xβ、Xδ。
4. the improvement grey wolf optimized algorithm according to claim 3 based on multiple target, it is characterised in that described quick non-bad
Solution sorting operation is specifically included：
The non-dominant disaggregation in wolf pack is found, by the non-dominant disaggregation labeled as the first non-dominant layer F1 and by the non-dominant
Solve all wolves individual concentrated and assign the first non-dominant sequence value, and all wolf individuals are rejected；
Found out in wolf pack after rejecting next layer of non-dominant disaggregation go forward side by side line flag, non-dominant sequence value assign operation and reject behaviour
Make；
It is lasting successively to carry out that the layering of wolf pack progress non-dominant disaggregation, mark, non-dominant sequence value are assigned operating and rejecting to operate, directly
It is layered completely to whole wolf pack and causes the wolf individual in same non-dominant layer that there is identical non-dominant sequence value.
5. the improvement grey wolf optimized algorithm according to claim 4 based on multiple target, it is characterised in that the crowding distance
Calculating is specifically included：
The distance of the wolf individual in same non-dominant layer is initialized, wolf individual i crowding distance L [i] is madedFor 0；
Wolf individual in the same non-dominant layer carries out sort ascending by m-th of desired value；
Two wolves individual on given edge assigns number Inf one big, two wolves individual is had absolute selective advantage；
The crowding distance of the wolf individual sequence in the middle of is sought the wolf individual in the middle of sequence according to formula eight, and the formula eight has
Body is：
<mrow>
<mi>L</mi>
<msub>
<mrow>
<mo>&lsqb;</mo>
<mi>i</mi>
<mo>&rsqb;</mo>
</mrow>
<mi>d</mi>
</msub>
<mo>=</mo>
<mi>L</mi>
<msub>
<mrow>
<mo>&lsqb;</mo>
<mi>i</mi>
<mo>&rsqb;</mo>
</mrow>
<mi>d</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>m</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>f</mi>
<mi>m</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>f</mi>
<mi>m</mi>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>f</mi>
<mi>m</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>m</mi>
<mo>&Element;</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>o</mi>
<mi>b</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, NobjFor number of targets,Respectively m-th of fitness value of i+1 and the i-th -1 wolf individual,The maximum and minimum value of m-th of fitness value respectively in Noninferior Solution Set.
6. the improvement grey wolf optimized algorithm according to claim 3 based on multiple target, it is characterised in that the S3 is specifically wrapped
Include：
According to the Xα, the Xβ, the XδThe each wolf individual of the step of being caught with wolf pack optimization wolf pack is surrounded by wolf pack
Position, produce golden mean of the Confucian school wolf, and calculate the fitness value of the golden mean of the Confucian school wolf and according to quick noninferior solution sorting operation, crowding distance
Calculating, elite retention strategy selective updating wolf pack position.
7. the improvement grey wolf optimized algorithm according to claim 6 based on multiple target, it is characterised in that the S3 and S4 it
Between also include：
Individual to all wolves of the wolf pack after renewal is every one-dimensional by the execution normalization operation of formula nine, and the formula nine is specific
For：
<mrow>
<mover>
<mi>N</mi>
<mo>&RightArrow;</mo>
</mover>
<mrow>
<mo>(</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<msup>
<mover>
<mi>X</mi>
<mo>&RightArrow;</mo>
</mover>
<mi>t</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>max</mi>
<mrow>
<mo>(</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<mi>d</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
<mi>d</mi>
<mo>&Element;</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>,</mo>
<mi>D</mi>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, D is dimension,For wolfD dimension variable,ForCorresponding scalar, max after normalization
(d), min (d) is respectively the bound of d dimension variables in wolf pack.
8. the improvement grey wolf optimized algorithm according to claim 7 based on multiple target, it is characterised in that the S4 is specifically wrapped
Include：
Adjustment in direction operation is performed to the wolf pack after renewal and the wolf pack after the renewal is controlled according to the adjustment in direction probability
The scale of amendment dimension is participated in, new golden mean of the Confucian school wolf is produced, and calculates the fitness value of the new golden mean of the Confucian school wolf, according to quick noninferior solution
Sorting operation, crowding distance are calculated, elite retention strategy preferentially retains wolf body position, and the wolf individual row in wolf pack
Name, X is divided into by wolf packα、Xβ、Xδ、Xω, obtain revised wolf pack position.
9. the improvement grey wolf optimized algorithm according to claim 8 based on multiple target, it is characterised in that after described pair updates
Wolf pack perform adjustment in direction operation specifically include：
Adjustment in direction is performed by the wolf pack after ten pairs of renewals of formula to operate, the formula ten is specially：
<mrow>
<mover>
<mi>M</mi>
<mo>&RightArrow;</mo>
</mover>
<mi>N</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>r</mi>
<mo>&CenterDot;</mo>
<mover>
<mi>N</mi>
<mo>&RightArrow;</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mover>
<mi>N</mi>
<mo>&RightArrow;</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, d1,d2∈ (1, D), r are 0 to 1 random number,For the individual scalar of golden mean of the Confucian school wolfD1Dimension；
Renormalization operation is carried out to every one-dimensional formula 11 that passes through of the golden mean of the Confucian school wolf individual scalar of generation, the formula 11 has
Body is：
Wherein,For golden mean of the Confucian school wolfD dimension.
10. the improvement grey wolf optimized algorithm according to claim 9 based on multiple target, it is characterised in that the S5 is specific
Including：
Judge whether iterations reaches default maximum iteration, if so, then exporting revised wolf pack position as final
Optimum results, and the optimal compromise solution of fuzzy Decision Making Method selection is combined, otherwise, go to S3 and proceed iterative search.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710443537.9A CN107067121A (en) | 2017-06-13 | 2017-06-13 | A kind of improvement grey wolf optimized algorithm based on multiple target |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710443537.9A CN107067121A (en) | 2017-06-13 | 2017-06-13 | A kind of improvement grey wolf optimized algorithm based on multiple target |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107067121A true CN107067121A (en) | 2017-08-18 |
Family
ID=59593903
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710443537.9A Pending CN107067121A (en) | 2017-06-13 | 2017-06-13 | A kind of improvement grey wolf optimized algorithm based on multiple target |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107067121A (en) |
Cited By (24)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106896716A (en) * | 2017-04-17 | 2017-06-27 | 华北电力大学（保定） | Micro-capacitance sensor alternating current-direct current section transverter pid parameter optimization method based on grey wolf algorithm |
| CN107832830A (en) * | 2017-11-17 | 2018-03-23 | 湖北工业大学 | Intruding detection system feature selection approach based on modified grey wolf optimized algorithm |
| CN108429633A (en) * | 2018-01-18 | 2018-08-21 | 西南交通大学 | Virtual network function dispositions method based on grey wolf algorithm |
| CN108646560A (en) * | 2018-05-11 | 2018-10-12 | 河北工业大学 | Power of fan model parameter optimization method based on grey wolf algorithm improvement |
| CN108829036A (en) * | 2018-06-12 | 2018-11-16 | 昆明理工大学 | A kind of Optimization Scheduling of metal slab shaping by stock removal process |
| CN109408905A (en) * | 2018-09-30 | 2019-03-01 | 湘潭大学 | A kind of Alpha guiding grey wolf algorithm and its application in two-stage calculation amplifier design |
| CN109657885A (en) * | 2019-02-25 | 2019-04-19 | 华南理工大学 | A kind of electric-thermal net coordinated operation optimization method based on more searcher algorithms |
| CN109669423A (en) * | 2019-01-07 | 2019-04-23 | 福州大学 | The method that part processes optimal scheduling scheme is obtained based on multiple target grey wolf algorithm is improved |
| CN109670639A (en) * | 2018-12-17 | 2019-04-23 | 邓茂云 | Regional complex energy resource system real-time optimization method based on multiple target grey wolf algorithm |
| CN109858739A (en) * | 2018-12-20 | 2019-06-07 | 电子科技大学中山学院 | logistics transportation scheduling method, computer storage medium and electronic equipment |
| CN109993270A (en) * | 2019-03-27 | 2019-07-09 | 东北大学 | Lithium ion battery residual life prediction technique based on grey wolf pack optimization LSTM network |
| CN110145432A (en) * | 2019-03-29 | 2019-08-20 | 广东工业大学 | A kind of wave-power device Poewr control method based on fourier analysis and improvement grey wolf algorithm |
| CN110322692A (en) * | 2019-07-09 | 2019-10-11 | 广东工业大学 | A kind of detection method, device and equipment repeating traffic flow data |
| CN111539508A (en) * | 2020-04-01 | 2020-08-14 | 国家电网公司华东分部 | Generator excitation system parameter identification algorithm based on improved wolf algorithm |
| CN111582428A (en) * | 2020-04-01 | 2020-08-25 | 长江大学 | Multi-modal multi-objective optimization method based on grey prediction evolution algorithm |
| CN112380760A (en) * | 2020-10-13 | 2021-02-19 | 重庆大学 | Multi-algorithm fusion based multi-target process parameter intelligent optimization method |
| CN112488283A (en) * | 2020-12-11 | 2021-03-12 | 湖北工业大学 | Improved multi-target grey wolf optimization algorithm |
| CN113011612A (en) * | 2021-03-23 | 2021-06-22 | 合肥工业大学 | Production and maintenance scheduling method and system based on improved wolf algorithm |
| CN113537440A (en) * | 2021-07-05 | 2021-10-22 | 沈阳化工大学 | CSTR period operating parameter optimization method based on Grey wolf algorithm |
| CN113705761A (en) * | 2021-09-08 | 2021-11-26 | 吉林大学 | Gray wolf optimization method based on dimension learning strategy and Levy flight |
| CN113965569A (en) * | 2021-10-22 | 2022-01-21 | 大连理工大学 | High-energy-efficiency low-delay edge node calculation migration framework and configuration system |
| CN115951717A (en) * | 2023-03-09 | 2023-04-11 | 北京卓翼智能科技有限公司 | Unmanned aerial vehicle cluster target distribution method, device and system and storage medium |
| CN117452828A (en) * | 2023-12-22 | 2024-01-26 | 中电行唐生物质能热电有限公司 | Method and system for controlling emission of harmful gas in boiler based on neural network |
| CN117556718A (en) * | 2024-01-12 | 2024-02-13 | 西北工业大学 | Thermal power distribution method based on neural network and multi-strategy combined gray wolf optimization algorithm |
-
2017
- 2017-06-13 CN CN201710443537.9A patent/CN107067121A/en active Pending
Cited By (37)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106896716A (en) * | 2017-04-17 | 2017-06-27 | 华北电力大学（保定） | Micro-capacitance sensor alternating current-direct current section transverter pid parameter optimization method based on grey wolf algorithm |
| CN106896716B (en) * | 2017-04-17 | 2019-12-27 | 华北电力大学（保定） | Micro-grid AC/DC section converter PID parameter optimization method based on gray wolf algorithm |
| CN107832830A (en) * | 2017-11-17 | 2018-03-23 | 湖北工业大学 | Intruding detection system feature selection approach based on modified grey wolf optimized algorithm |
| CN108429633A (en) * | 2018-01-18 | 2018-08-21 | 西南交通大学 | Virtual network function dispositions method based on grey wolf algorithm |
| CN108429633B (en) * | 2018-01-18 | 2020-04-03 | 西南交通大学 | Virtual network function deployment method based on wolf algorithm |
| CN108646560A (en) * | 2018-05-11 | 2018-10-12 | 河北工业大学 | Power of fan model parameter optimization method based on grey wolf algorithm improvement |
| CN108829036A (en) * | 2018-06-12 | 2018-11-16 | 昆明理工大学 | A kind of Optimization Scheduling of metal slab shaping by stock removal process |
| CN108829036B (en) * | 2018-06-12 | 2021-05-14 | 昆明理工大学 | Optimized scheduling method for metal casting blank cutting forming machining process |
| CN109408905A (en) * | 2018-09-30 | 2019-03-01 | 湘潭大学 | A kind of Alpha guiding grey wolf algorithm and its application in two-stage calculation amplifier design |
| CN109670639A (en) * | 2018-12-17 | 2019-04-23 | 邓茂云 | Regional complex energy resource system real-time optimization method based on multiple target grey wolf algorithm |
| CN109858739A (en) * | 2018-12-20 | 2019-06-07 | 电子科技大学中山学院 | logistics transportation scheduling method, computer storage medium and electronic equipment |
| CN109669423B (en) * | 2019-01-07 | 2021-08-31 | 福州大学 | Method for obtaining optimal scheduling scheme of part machining based on improved multi-target wolf algorithm |
| CN109669423A (en) * | 2019-01-07 | 2019-04-23 | 福州大学 | The method that part processes optimal scheduling scheme is obtained based on multiple target grey wolf algorithm is improved |
| CN109657885A (en) * | 2019-02-25 | 2019-04-19 | 华南理工大学 | A kind of electric-thermal net coordinated operation optimization method based on more searcher algorithms |
| CN109993270A (en) * | 2019-03-27 | 2019-07-09 | 东北大学 | Lithium ion battery residual life prediction technique based on grey wolf pack optimization LSTM network |
| CN110145432A (en) * | 2019-03-29 | 2019-08-20 | 广东工业大学 | A kind of wave-power device Poewr control method based on fourier analysis and improvement grey wolf algorithm |
| CN110322692A (en) * | 2019-07-09 | 2019-10-11 | 广东工业大学 | A kind of detection method, device and equipment repeating traffic flow data |
| CN111539508A (en) * | 2020-04-01 | 2020-08-14 | 国家电网公司华东分部 | Generator excitation system parameter identification algorithm based on improved wolf algorithm |
| CN111582428A (en) * | 2020-04-01 | 2020-08-25 | 长江大学 | Multi-modal multi-objective optimization method based on grey prediction evolution algorithm |
| CN111582428B (en) * | 2020-04-01 | 2024-01-05 | 长江大学 | Multi-mode and multi-target optimization method based on gray prediction evolution algorithm |
| CN111539508B (en) * | 2020-04-01 | 2023-09-01 | 国家电网公司华东分部 | Generator excitation system parameter identification algorithm based on improved gray wolf algorithm |
| CN112380760B (en) * | 2020-10-13 | 2023-01-31 | 重庆大学 | Multi-algorithm fusion based multi-target process parameter intelligent optimization method |
| CN112380760A (en) * | 2020-10-13 | 2021-02-19 | 重庆大学 | Multi-algorithm fusion based multi-target process parameter intelligent optimization method |
| CN112488283A (en) * | 2020-12-11 | 2021-03-12 | 湖北工业大学 | Improved multi-target grey wolf optimization algorithm |
| CN112488283B (en) * | 2020-12-11 | 2024-03-22 | 湖北工业大学 | Improved multi-objective gray wolf optimization algorithm implementation method |
| CN113011612B (en) * | 2021-03-23 | 2022-09-20 | 合肥工业大学 | Production and maintenance scheduling method and system based on improved wolf algorithm |
| CN113011612A (en) * | 2021-03-23 | 2021-06-22 | 合肥工业大学 | Production and maintenance scheduling method and system based on improved wolf algorithm |
| CN113537440A (en) * | 2021-07-05 | 2021-10-22 | 沈阳化工大学 | CSTR period operating parameter optimization method based on Grey wolf algorithm |
| CN113705761B (en) * | 2021-09-08 | 2024-02-09 | 吉林大学 | Grey wolf optimization method based on dimension learning strategy and Lev flight |
| CN113705761A (en) * | 2021-09-08 | 2021-11-26 | 吉林大学 | Gray wolf optimization method based on dimension learning strategy and Levy flight |
| CN113965569A (en) * | 2021-10-22 | 2022-01-21 | 大连理工大学 | High-energy-efficiency low-delay edge node calculation migration framework and configuration system |
| CN113965569B (en) * | 2021-10-22 | 2022-08-12 | 大连理工大学 | High-energy-efficiency low-delay edge node calculation migration configuration system |
| CN115951717A (en) * | 2023-03-09 | 2023-04-11 | 北京卓翼智能科技有限公司 | Unmanned aerial vehicle cluster target distribution method, device and system and storage medium |
| CN117452828B (en) * | 2023-12-22 | 2024-03-01 | 中电行唐生物质能热电有限公司 | Method and system for controlling emission of harmful gas in boiler based on neural network |
| CN117452828A (en) * | 2023-12-22 | 2024-01-26 | 中电行唐生物质能热电有限公司 | Method and system for controlling emission of harmful gas in boiler based on neural network |
| CN117556718A (en) * | 2024-01-12 | 2024-02-13 | 西北工业大学 | Thermal power distribution method based on neural network and multi-strategy combined gray wolf optimization algorithm |
| CN117556718B (en) * | 2024-01-12 | 2024-03-29 | 西北工业大学 | Thermal power distribution method based on neural network and multi-strategy combined gray wolf optimization algorithm |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107067121A (en) | A kind of improvement grey wolf optimized algorithm based on multiple target | |
| Qiao et al. | Nature-inspired hybrid techniques of IWO, DA, ES, GA, and ICA, validated through a k-fold validation process predicting monthly natural gas consumption | |
| Meng et al. | Crisscross optimization algorithm for solving combined heat and power economic dispatch problem | |
| Xiao et al. | Artificial bee colony algorithm based on adaptive neighborhood search and Gaussian perturbation | |
| Naderi et al. | A comprehensive study of practical economic dispatch problems by a new hybrid evolutionary algorithm | |
| CN106931453B (en) | The forecasting system and method for circulating fluid bed domestic garbage burning emission of NOx of boiler | |
| CN103324862B (en) | A kind of coal-burning boiler optimization method based on improving neural network and genetic algorithm | |
| Wang et al. | Balancing risk and cost in fuzzy economic dispatch including wind power penetration based on particle swarm optimization | |
| CN108038306A (en) | A kind of method of power boiler burning modeling and optimization towards magnanimity high dimensional data | |
| CN107958424A (en) | A kind of Economic Dispatch strategy based on improvement gravitation search algorithm | |
| CN109084415A (en) | Central air-conditioning operating parameter optimization method based on artificial neural network and genetic algorithms | |
| Hassan et al. | A modified Marine predators algorithm for solving single-and multi-objective combined economic emission dispatch problems | |
| CN106372756A (en) | Thermal power plant load optimization distribution method based on breeding particle swarm optimization | |
| CN104037757A (en) | Brainstorming-based thermal power plant economic environment scheduling method | |
| Jiang et al. | Multiobjective optimization by artificial fish swarm algorithm | |
| Hosseini-Hemati et al. | Society-based Grey Wolf Optimizer for large scale Combined Heat and Power Economic Dispatch problem considering power losses | |
| CN106527176A (en) | MFOA (modified fruit fly optimization algorithm)-SVM (support vector machine)-based boiler thermal efficiency and NOX modeling method | |
| CN112906292A (en) | Method, system, equipment and storage medium for plant-level heat and power load online optimal distribution of cogeneration unit | |
| CN105512755A (en) | Decomposition-based multi-objective distribution estimation optimization method | |
| CN108038797B (en) | Two-term coefficient method and multi-target planning hybrid evaluation method for power distribution network scheduling control level | |
| CN107400935A (en) | Adjusting method based on the melt-spinning technology for improving ELM | |
| Shang et al. | Production scheduling optimization method based on hybrid particle swarm optimization algorithm | |
| Liu et al. | Opposition-mutual learning differential evolution with hybrid mutation strategy for large-scale economic load dispatch problems with valve-point effects and multi-fuel options | |
| Zhou et al. | Advances in teaching-learning-based optimization algorithm: A comprehensive survey | |
| Farhat et al. | Multi-objective economic-emission optimal load dispatch using bacterial foraging algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20170818 |
|
| RJ01 | Rejection of invention patent application after publication |