CN110533151A - A kind of firefly optimization algorithm based on the law of universal gravitation - Google Patents
A kind of firefly optimization algorithm based on the law of universal gravitation Download PDFInfo
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Abstract
The firefly optimization algorithm based on the law of universal gravitation that the invention discloses a kind of.Glowworm swarm algorithm (FA) is a kind of novel colony intelligence optimization method.For the problem that glowworm swarm algorithm is when solving globally optimal solution, it is too low and be easily trapped into local convergence that there are solving precisions.The algorithm refers to the law of universal gravitation, using gravitation as the attraction between firefly particle, generate a kind of novel evolutionary computation mode, and when population falls into local optimum region, the diversity of firefly individual is improved using Gaussian mutation, and optimization algorithm convergence with probability 1 is in global optimum.
Description
Technical field
The present invention relates to a kind of firefly optimization algorithms.Especially a kind of firefly based on the law of universal gravitation, which optimizes, to be calculated
Method.
Background technique
In order to solve complicated optimization problem, people after the inspiration of various natural phenomenas or process, mention in by nature
A series of colony intelligence optimization algorithm is gone out, there are commonly ant group algorithm, particle swarm algorithm and glowworm swarm algorithms.Use for reference firefly
The biological nature of information is transmitted using shining, glowworm swarm algorithm is as a kind of new colony intelligence optimization algorithm, in the algorithm,
The firefly individual of initial position random distribution can all fly to the stronger firefly individual of neighbouring fluorescent brightness, by multiple group
After body movement, whole fireflies be may build up near most bright firefly, complete final optimizing.Due to this algorithm structure letter
Parameter that is single, needing to adjust is less, while having preferable optimizing search capability, asks so being widely used in multi-modal optimization
Topic, automatic control, price expectation, compression of images etc..But since development time is still short, there is solving precision it is too low and hold
The problem of easily falling into local convergence.
Summary of the invention
For glowworm swarm algorithm when solving globally optimal solution, it is too low and be easily trapped into local convergence that there are solving precisions
Problem, the present invention disclose a kind of firefly optimization algorithm based on the law of universal gravitation, the law of universal gravitation are introduced into the light of firefly
In worm algorithm, in the hope of globally optimal solution.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The present invention provides a kind of firefly optimization algorithm based on the law of universal gravitation, the specific steps are as follows:
Step 1: dimension n, light intensity absorption coefficient gamma, gravitation primary constant G is arranged in initialization firefly number m0,
Step factor α, step-length attenuation coefficient Δ α etc. parameters set maximum number of iterations, and generate each light of firefly at random in solution room
The initial position of worm；
Step 2: calculating the target fitness value f (x of each fireflyi) and any two firefly before space away from
From rijAnd gravitational constant G；
Step 3: calculating the gravitation of object；
Step 4: the target fitness value of any two firefly individual being compared, by the light of firefly that fitness value is poor
The update of worm progress spatial position；
Step 5: recalculating the fitness value of each firefly, if obtaining the more excellent fitness value of population, update optimal suitable
Response；If population adaptive optimal control degree 5 times all do not update, worst firefly state is replaced using optimal firefly state,
Intermediate population is generated, and Gaussian mutation operation is carried out to intermediate population；
Step 6: region constraint is carried out to all firefly individuals；
Step 7: judging whether to reach maximum number of iterations, if so, going to step 8；Otherwise 2 are gone to step；
Step 8: terminating iteration, export result；
The invention adopts the above technical scheme compared with prior art, has following technical effect that the present invention is based on universal
The firefly optimization algorithm of law of gravitation improves it in terms of two, so that optimization algorithm had both been able to maintain original algorithm
Evolutionary edge, and can effectively improve the precision and convergence capabilities of algorithm, especially when search range and initial value obtain it is larger
When, algorithm still has higher precision and convergence capabilities.
Detailed description of the invention
Fig. 1 is glowworm swarm algorithm schematic diagram of the present invention.
Fig. 2 is the algorithm flow chart of embodiment of the present invention.
Specific embodiment
Combined with specific embodiments below, the present invention is furture elucidated.
The present invention provides a kind of firefly optimization algorithm based on the law of universal gravitation, the specific steps are as follows:
Step 1: dimension n, light intensity absorption coefficient gamma, gravitation primary constant G is arranged in initialization firefly number m0,
Step factor α, step-length attenuation coefficient Δ α etc. parameters set maximum number of iterations, and generate each light of firefly at random in solution room
The initial position of worm；
Step 2: calculating the target fitness value f (x of each fireflyi) and any two firefly before space away from
From rijAnd gravitational constant G；
Step 3: calculating the gravitation of object；
Step 4: the target fitness value of any two firefly individual being compared, by the light of firefly that fitness value is poor
The update of worm progress spatial position；
Step 5: recalculating the fitness value of each firefly, if obtaining the more excellent fitness value of population, update optimal suitable
Response；If population adaptive optimal control degree 5 times all do not update, worst firefly state is replaced using optimal firefly state,
Intermediate population is generated, and Gaussian mutation operation is carried out to intermediate population；
Step 6: region constraint is carried out to all firefly individuals；
Step 7: judging whether to reach maximum number of iterations, if so, going to step 8；Otherwise 2 are gone to step；
Step 8: terminating iteration, export result；
As further technical solution of the present invention, initial firefly population number is m in step 1 and step 2, and search is empty
Between for n tie up, the position of i-th firefly in space isWhereinI-th firefly is represented n-th
Position in dimension space.The maximum fluorescence brightness for defining i-th firefly is
I0i=f (xi) (1)
Wherein, f (xi) it is the corresponding target fitness value in i-th firefly position.Define the phase of i-th firefly
It is to fluorescent brightness
Wherein, γ is the light intensity absorption factor, indicates that the fluorescent brightness of firefly is influenced by propagation medium and gradually changed
Characteristic, value with solve the section in domain it is related, be generally set to constant .rij=| | xi-xj| | indicate i-th firefly and jth
Space length between firefly.Define firefly Attraction Degree be
Wherein: β0For the maximum Attraction Degree factor, the Attraction Degree size of position at maximum fluorescence brightness is indicated.Formula (3) description
The fluorescence that firefly issues attractions of other individuals will be increased with distance and the absorption of propagation medium and be gradually reduced
Characteristic.
The position of i-th firefly is evolved and can be indicated by formula (4) in searching process:
xi(t+1)=xi(t)+β(xj(t)-xi(t))+α(rand-1/2) (4)
Wherein: α is step factor, and value is the constant in [0,1]；Rand is that obedience is equally distributed random in [0,1]
The factor；Disturbance term α (rand-1/2) can effectively expande the search range of firefly, prevent firefly from falling into local optimum too early.
As further technical solution of the present invention, step 3 defines object j and is to the gravitation of object i
Wherein,Indicate the universal gravitational constant in moment t, G0For gravitation primary constant, rijFor
Euclidean distance between object and i object j, miIndicate the quality of object i.Define object i quality be
Wherein, f (xi) indicate the corresponding target fitness value in i-th firefly position, it is asked if solving minimum
Topic, thenIf solving maximum problem,
As further technical solution of the present invention, step 4 defines the update of position
Wherein, rand is the random number of [0,1], and α is step factor, and in [0,1] interior value, Δ α is step-length attenuation coefficient,
The interior value in [0.95,1].
As further technical solution of the present invention, if step 5 firefly population does not all send out in continuous 5 iteration
It is raw to evolve, then judge that it has fallen into local optimum region.It is disturbed at this time using Gaussian mutation factor pair firefly population,
It is set to restore evolvability.It operates as follows:
First by all fireflies according to fitness size sort, then using optimal firefly by worst firefly group into
The replacement of row state updates, and obtains intermediate population, finally carries out Gaussian mutation processing to intermediate population according to formula (8).
xi=xi+xi*N(0,1) (8)
Wherein, N (0,1) is to obey the random vector for being desired for the Gaussian Profile that 0, variance is 1.
As further technical solution of the present invention, step 6 is being searched for always for the individual guaranteed in firefly population
It is effectively searched in space, region constraint processing has been carried out to all firefly individuals, a physical efficiency is made to be detached from specified model
When other than enclosing, individual is effectively withdrawn into designated space, to complete global optimizing task.Region constraint processing is such as formula (9) institute
Show:
Wherein, xminFor search space lower limit, xmaxFor the search space upper limit.
As further technical solution of the present invention, step 7 exports optimal solution:
Judge whether to reach maximum number of iterations, if then terminating iteration output optimal solution, otherwise, and return step 2 is suitable
Sequence executes.
Claims (7)
1. a kind of firefly optimization algorithm based on the law of universal gravitation, it is characterized in that the law of universal gravitation is referred to, it will be universal
Gravitation generates a kind of novel evolutionary computation mode as the attraction between firefly particle, and falls into part in population
When optimal region, the diversity of firefly individual is improved using Gaussian mutation, and optimization algorithm convergence with probability 1 is in the overall situation
It is optimal, and carry out as follows:
Step 1: dimension n, light intensity absorption coefficient gamma, gravitation primary constant G is arranged in initialization firefly number m0, step-length because
Sub- α, step-length attenuation coefficient Δ α etc. parameters set maximum number of iterations, and generate the first of each firefly at random in solution room
Beginning position；
Step 2: calculating the target fitness value f (x of each fireflyi) and any two firefly before space length rij
And gravitational constant G；
Step 3: calculating the gravitation of object；
Step 4: the target fitness value of any two firefly individual is compared, by the poor firefly of fitness value into
The update of row spatial position；
Step 5: recalculating the fitness value of each firefly, if obtaining the more excellent fitness value of population, update adaptive optimal control degree；
If population adaptive optimal control degree 5 times all do not update, worst firefly state is replaced using optimal firefly state, in generation
Between population, and to intermediate population carry out Gaussian mutation operation；
Step 6: region constraint is carried out to all firefly individuals；
Step 7: judging whether to reach maximum number of iterations, if so, going to step 8；Otherwise 2 are gone to step；
Step 8: terminating iteration, export result.
2. firefly according to claim 1 introduces the law of universal gravitation, solves group and be easily trapped into asking for local convergence
Topic, optimization algorithm seek optimal solution.
3. the firefly optimization algorithm according to claim 1 based on the law of universal gravitation, which is characterized in that step 3 is fixed
Adopted object j solves maximum value minimum problem to the gravitation of object i, the quality of definition object i.
4. the firefly optimization algorithm according to claim 1 based on the law of universal gravitation, which is characterized in that step 4 is fixed
The update that adopted position is set.
5. the firefly optimization algorithm according to claim 1 based on the law of universal gravitation, which is characterized in that step 5 is such as
Fruit firefly population all there is no evolving, then judges that it has fallen into local optimum region in continuous 5 iteration.It adopts at this time
It is disturbed with Gaussian mutation factor pair firefly population, it is made to restore evolvability.
6. the firefly optimization algorithm according to claim 1 based on the law of universal gravitation, which is characterized in that step 6 is
Guarantee that the individual in firefly population is effectively searched in search space always, all firefly individuals are carried out
Region constraint processing makes a physical efficiency when being detached from other than specified range, individual is effectively withdrawn into designated space, to complete
Global optimizing task.
7. the firefly optimization algorithm according to claim 1 based on the law of universal gravitation, which is characterized in that step 7 is defeated
Optimal solution out judges whether to reach maximum number of iterations, if then terminating iteration output optimal solution, otherwise, and return step 2 is suitable
Sequence executes.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112395059A (en) * | 2020-11-16 | 2021-02-23 | 哈尔滨工程大学 | CMP task scheduling method for improving firefly algorithm |
| CN113971329A (en) * | 2021-09-22 | 2022-01-25 | 广州杰赛科技股份有限公司 | Layout method of modeled camera |
| CN116633830A (en) * | 2023-05-25 | 2023-08-22 | 哈尔滨工业大学 | Seed mutation operation scheduling method based on firefly algorithm |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112395059A (en) * | 2020-11-16 | 2021-02-23 | 哈尔滨工程大学 | CMP task scheduling method for improving firefly algorithm |
| CN112395059B (en) * | 2020-11-16 | 2024-07-02 | 哈尔滨工程大学 | CMP task scheduling method for improving firefly algorithm |
| CN113971329A (en) * | 2021-09-22 | 2022-01-25 | 广州杰赛科技股份有限公司 | Layout method of modeled camera |
| CN116633830A (en) * | 2023-05-25 | 2023-08-22 | 哈尔滨工业大学 | Seed mutation operation scheduling method based on firefly algorithm |
| CN116633830B (en) * | 2023-05-25 | 2024-01-23 | 哈尔滨工业大学 | Seed mutation operation scheduling method based on firefly algorithm |
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Application publication date: 20191203 |