CN109558700A - A kind of level Four design of gears method based on DSM-ABC algorithm - Google Patents
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Abstract
The level Four design of gears method based on DSM-ABC algorithm that the present invention relates to a kind of, using the improved artificial bee colony algorithm of double search mechanisms and optimizes level Four design of gears problem.The mathematical model that level Four design of gears problem is abstracted into 4 structural parameters and 1 objective function is used for the optimization design of algorithm.From design result as can be seen that algorithm (DSM-ABC) proposed by the invention can preferably design the lesser level Four gear of gear ratio.
Description
Technical field
The present invention relates to level Four design of gears field, especially a kind of level Four design of gears side based on DSM-ABC algorithm
Method.
Background technique
Gear is applied in many mechanical power transmission systems, such as automobile, aerospace, machinery field.Gear is answered
Miscellaneous shape and geometry lead to a large amount of design parameters, it is therefore desirable to which optimization method determines while meeting the design of specified criteria
Variable.CS algorithm, GA algorithm, ALO algorithm and ISA algorithm are applied in level Four design of gears problem by existing researcher.
To compact, efficiently it is continuously increased and designer is forced to use optimal method for designing with the demand of reliable gear.
Currently, because gear using more and more extensive, the demand to reliable gear is continuously increased.Gear is set
Meter problem, is certified as a np hard problem, artificial bee colony algorithm (Artificial Bee Colony algorithm) be by
The process in the honeybee search of food source in living nature is introduced into the search process of algorithm, but basic artificial bee colony algorithm have it is following
Disadvantage: search speed is slow, and the training time is long；Optimizing ability is not ideal enough；Local search ability is poor, is easily trapped into precocity etc..
Summary of the invention
In view of this, the purpose of the present invention is to propose to a kind of level Four design of gears method based on DSM-ABC algorithm, not only
It is uneven with exploration ability to overcome basic artificial bee colony algorithm exploitation, also enhance low optimization accuracy and has faster convergence speed
Degree.
The present invention is realized using following scheme: a kind of level Four design of gears method based on DSM-ABC algorithm specifically includes
Following steps:
Step S1: following formula is converted by the design problem of level Four gear:
Variable are as follows:
Objective function:
Variable-definition domain are as follows: 12≤x1,x2,x3,x4≤60；
In formula, nA、nB、nC、nDRespectively indicate gear x1、x2、x3、x4The number of teeth；
Step S2: the parameter of improved artificial bee colony algorithm, including maximum number of iterations maxCycle, Population Size are set
Upper bound ub and lower bound lb is searched in NP, restrictive condition Limit, nectar source；
Step S3: NP nectar source, food source initialization population: are sharedIt is generated at random by following formula:
In formula,It is the position in the jth dimension in i-th of nectar source,WithFood source is upper respectively under jth dimension
In addition mechanism of chaos s [j] is added in initialization of population in boundary and lower bound；
Step S4: employing bee to set out search of food source, in conjunction with the le ' vy flight mechanism of cuckoo algorithm, using as follows
Search for formula:
In formula,It is tieed up for the jth of current optimal solution,For nectar sourceNeighborhood solution, rand (0,1) between 0-1 with
Machine number；
Step S5: the bee search phase is being followed to take following search formula:
In formula, viFor follow the bee stage i-th of nectar source of search position, s be this search in Discontinuous Factors, be [0,
1] random number between, j are the parameters randomly selected from { 1,2 ..., D }, and D indicates the dimension of population, and r1、r2Be 1,
2 ..., NP } in random number, and r1 ≠ r2；
By being passed through the mutation operation of DE algorithm, so that when algorithm has the ability for the trap for jumping out local optimum, in original
Its variation stage is expressed as in beginning differential evolution algorithm:
U=Xr1+Γ*(Xr2-Xr3)
In formula, r1,r2,r3∈ { 1,2 ..., NP }, and r1 ≠ r2 ≠ r3；Γ is called mutagenic factor, is between (0,1)
Random number；
Step S6: the fitness value of each food source is calculated:
In formula, xmIndicate m-th of food source, fit (xm) indicate nectar source xmFitness value；
Calculate the select probability P in each nectar sourcei:
In formula, fitiIndicate the fitness value in i-th of nectar source；After this step, all optimal gbest are updated；
: when current nectar source, which reaches, limits number, then there is Role composition in step S7, and circulation has one to employ bee every time
It is converted into investigation bee；
Step S8: when algorithm reaches termination condition, the optimal solution of searching is exported, terminates algorithm.
The present invention is using double improved artificial bee colony algorithms of search mechanisms and optimizes level Four design of gears problem.By level Four tooth
Wheel design problem is abstracted into optimization design of the mathematical model of 4 structural parameters and 1 objective function for algorithm.
Further, in step S3, the mechanism of chaos s [j] meets:
S [j+1]=k*s [j] * (1-s [j])；
In formula, k value is 4.0.
Further, in step S4, le ' vy (λ) meets le ' vy distribution, and formula is as follows:
L (s)~| s |-1-β；0 < β < 2
In formula, L (s) is the flight path of le ' vyflight；S is arbitrary width, parameter of the β between 0-2, wherein with
Machine step-length s is expressed from the next:
S=μ/| v |1/β
In formula, μ and ν are all satisfied and are just distributed very muchWith
Compared with prior art, the invention has the following beneficial effects: algorithm (DSM-ABC) proposed by the invention can be compared with
Good designs the lesser level Four gear of gear ratio.Local optimum is easily trapped into for artificial bee colony algorithm, convergence precision is low etc.
Disadvantage, the invention proposes a kind of double improved artificial bee colony algorithms of search mechanisms, and incorporate mechanism of chaos and adaptive choosing
The system of selecting a good opportunity.General for the level Four design of gears effect of current algorithm, the invention proposes the calculations of the artificial bee colony of double search mechanisms
Method simultaneously optimizes level Four design of gears problem, efficiently solves problems of the prior art.
Detailed description of the invention
Fig. 1 is the level Four design of gears problem case schematic diagram of the embodiment of the present invention.
Fig. 2 is the trajectory diagram of the simulation cuckoo bird flying of the embodiment of the present invention.
Fig. 3 is the scouting pseudocode schematic diagram stage by stage of the embodiment of the present invention.
Fig. 4 is result comparison schematic diagram of the distinct methods in level Four design of gears problem of the embodiment of the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
It is noted that described further below be all exemplary, it is intended to provide further instruction to the application.Unless another
It indicates, all technical and scientific terms used herein has usual with the application person of an ordinary skill in the technical field
The identical meanings of understanding.
It should be noted that term used herein above is merely to describe specific embodiment, and be not intended to restricted root
According to the illustrative embodiments of the application.As used herein, unless the context clearly indicates otherwise, otherwise singular
Also it is intended to include plural form, additionally, it should be understood that, when in the present specification using term "comprising" and/or " packet
Include " when, indicate existing characteristics, step, operation, device, component and/or their combination.
A kind of level Four design of gears method based on DSM-ABC algorithm is present embodiments provided, specifically includes the following steps:
Step S1: as shown in Figure 1, level Four design of gears problem is one, there are four the discrete cases of parameter.Purpose is to look for
To the best number of teeth of four gears of train, to minimize gear ratio.In order to handle discrete parameter, by utilizing four houses to search solution
Five enter to obtain immediate integer.Following formula is converted by the design problem of level Four gear:
Variable are as follows:
Objective function:
Variable-definition domain are as follows: 12≤x1,x2,x3,x4≤60；
In formula, nA、nB、nC、nDRespectively indicate gear x1、x2、x3、x4The number of teeth；
Step S2: the parameter of improved artificial bee colony algorithm, including maximum number of iterations maxCycle, Population Size are set
Upper bound ub and lower bound lb is searched in NP, restrictive condition Limit, nectar source；
Step S3: NP nectar source, food source initialization population: are sharedIt is generated at random by following formula:
In formula,It isiPosition in the jth dimension in a nectar source,WithThe upper bound of food source respectively under jth dimension
With lower bound, mechanism of chaos s [j] in addition is added in initialization of population；
Step S4: employing bee to set out search of food source, in conjunction with the le ' vy flight mechanism of cuckoo algorithm, using as follows
Search for formula:
In formula,It is tieed up for the jth of current optimal solution,For nectar sourceNeighborhood solution, rand (0,1) between 0-1 with
Machine number；
Step S5: the bee search phase is being followed to take following search formula:
In formula, viFor follow the bee stage i-th of nectar source of search position, s be this search in Discontinuous Factors, be [0,
1] random number between, j are the parameters randomly selected from { 1,2 ..., D }, and D indicates the dimension of population, and r1、r2Be 1,
2 ..., NP } in random number, and r1 ≠ r2；
By being passed through the mutation operation of DE algorithm, so that when algorithm has the ability for the trap for jumping out local optimum, in original
Its variation stage is expressed as in beginning differential evolution algorithm:
U=Xr1+Γ*(Xr2-Xr3)
In formula, r1,r2,r3∈ { 1,2 ..., NP }, and r1 ≠ r2 ≠ r3；Γ is called mutagenic factor, is between (0,1)
Random number；
Step S6: the fitness value of each food source is calculated:
In formula, xmIndicate m-th of food source, fit (xm) indicate nectar source xmFitness value；
Calculate the select probability P in each nectar sourcei:
In formula, fitiIndicate the fitness value in i-th of nectar source；After this step, all optimal gbest are updated；
: when current nectar source, which reaches, limits number, then there is Role composition in step S7, and circulation has one to employ bee every time
It is converted into investigation bee；For its pseudocode as shown in figure 3, in figure, pro is the pre-set adaptively selected factor, in the present embodiment
It is set as 0.25.Parameter r is randomly generated between 0-1, if r < pro, is then generated newly by mode identical with the initial stage
Food source, if r > pro, then be different from the initial stage by way of generate food source.By incorporating adaptively selected machine
System, increases the Population Size of algorithm, to improve the search precision of algorithm.
Step S8: when algorithm reaches termination condition, the optimal solution of searching is exported, terminates algorithm.
The present embodiment is using double improved artificial bee colony algorithms of search mechanisms and optimizes level Four design of gears problem.By level Four
Design of gears problem is abstracted into optimization design of the mathematical model of 4 structural parameters and 1 objective function for algorithm.
In the present embodiment, in step S3, the mechanism of chaos s [j] meets:
S [j+1]=k*s [j] * (1-s [j])；
In formula, k value is 4.0.
In the present embodiment, in step S4, le ' vy (λ) meets le ' vy distribution, and formula is as follows:
L (s)~| s |-1-β；0 < β < 2
In formula, L (s) is the flight path of le ' vyflight；S is arbitrary width, parameter of the β between 0-2, wherein with
Machine step-length s is expressed from the next:
S=μ/| v |1/β
In formula, μ and ν are all satisfied and are just distributed very muchWithLe ' vy flight it mainly walks
It is long to be characterized in that random high frequency short distance search is combined with low frequency search over long distances, as shown in Fig. 2, Fig. 2 is that simulation cuckoo flies
Capable trajectory diagram.Search space can be increased in the search mechanisms for employing the bee stage to combine cuckoo algorithm, thus improve algorithm
Ability of searching optimum, to finally improve the precision of algorithm.
Particularly, improved DSM-ABC algorithm is solved the problems, such as level Four design of gears by the present embodiment, and excellent with ant lion search
Change algorithm (ALO), cuckoo searching algorithm (CS), mine explosion algorithm (MBA), inner search algorithm (ISA) and traditional people
Work ant colony algorithm (ABC) is designed the comparison of result, data result such as Fig. 4.Purpose is to minimize gear ratio.Program is set as
Population 40, maximum number of iterations 650, program repetition running 20 times, output result is as shown in Figure 4.
From fig. 4, it can be seen that DSM-ABC optimizes 4 structural parameters, i.e., it is that dimension is set as 4 in algorithm parameter setting；
From final optimum results it is recognised that DSM-ABC algorithm design effect is substantially better than other 5 kinds of algorithms, DSM-ABC is calculated
To the smallest target function value, followed by ALO, CS, as the result of MBA with ISA algorithm, initial ABC arithmetic result is worst.This
Mean that DSM-ABC algorithm shows well in level Four design of gears problem, and relatively other smaller teeth of method can be designed
Take turns the level Four gear of ratio.
It should be understood by those skilled in the art that, embodiments herein can provide as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, it wherein includes the computer of computer usable program code that the application, which can be used in one or more,
The computer program implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.) produces
The form of product.
The application is referring to method, the process of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that every one stream in flowchart and/or the block diagram can be realized by computer program instructions
The combination of process and/or box in journey and/or box and flowchart and/or the block diagram.It can provide these computer programs
Instruct the processor of general purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine, so that being generated by the instruction that computer or the processor of other programmable data processing devices execute for real
The device for the function of being specified in present one or more flows of the flowchart and/or one or more blocks of the block diagram.
These computer program instructions, which may also be stored in, is able to guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works, so that it includes referring to that instruction stored in the computer readable memory, which generates,
Enable the manufacture of device, the command device realize in one box of one or more flows of the flowchart and/or block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device, so that counting
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, thus in computer or
The instruction executed on other programmable devices is provided for realizing in one or more flows of the flowchart and/or block diagram one
The step of function of being specified in a box or multiple boxes.
The above described is only a preferred embodiment of the present invention, being not that the invention has other forms of limitations, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
Imitate embodiment.But without departing from the technical solutions of the present invention, according to the technical essence of the invention to above embodiments institute
Any simple modification, equivalent variations and the remodeling made, still fall within the protection scope of technical solution of the present invention.
Claims (3)
1. a kind of level Four design of gears method based on DSM-ABC algorithm, it is characterised in that: the following steps are included:
Step S1: following formula is converted by the design problem of level Four gear:
Variable are as follows:
Objective function:
Variable-definition domain are as follows: 12≤x1,x2,x3,x4≤60；
In formula, nA、nB、nC、nDRespectively indicate gear x1、x2、x3、x4The number of teeth；
Step S2: setting the parameter of improved artificial bee colony algorithm, including maximum number of iterations maxCycle, Population Size NP,
Upper bound ub and lower bound lb is searched in restrictive condition Limit, nectar source；
Step S3: NP nectar source, food source initialization population: are sharedIt is generated at random by following formula:
In formula,It is the position in the jth dimension in i-th of nectar source,WithThe upper bound of food source is under respectively under jth dimension
In addition mechanism of chaos s [j] is added in initialization of population in boundary；
Step S4: employing bee to set out search of food source, in conjunction with the le ' vy flight mechanism of cuckoo algorithm, using following search
Formula:
In formula,It is tieed up for the jth of current optimal solution,For nectar sourceNeighborhood solution, rand (0,1) is random between 0-1
Number；
Step S5: the bee search phase is being followed to take following search formula:
In formula, viFor follow the bee stage i-th of nectar source of search position, s be this search in Discontinuous Factors, be between [0,1]
Random number, j is the parameter randomly selected from { 1,2 ..., D }, and D indicates the dimension of population, and r1、r2Be 1,2 ...,
NP } in random number, and r1 ≠ r2；
By being passed through the mutation operation of DE algorithm, so that when algorithm has the ability for the trap for jumping out local optimum, in original difference
Its variation stage in evolution algorithm is divided to be expressed as:
U=Xr1+Γ*(Xr2-Xr3)
In formula, r1,r2,r3∈ { 1,2 ..., NP }, and r1 ≠ r2 ≠ r3；Γ is called mutagenic factor, be between (0,1) with
Machine number；
Step S6: the fitness value of each food source is calculated:
In formula, xmIndicate m-th of food source, fit (xm) indicate nectar source xmFitness value；
Calculate the select probability P in each nectar sourcei:
In formula, fitiIndicate the fitness value in i-th of nectar source；After this step, all optimal gbest are updated；
: when current nectar source, which reaches, limits number, then there is Role composition in step S7, and circulation has one bee is employed to convert every time
To investigate bee；
Step S8: when algorithm reaches termination condition, the optimal solution of searching is exported, terminates algorithm.
2. a kind of level Four design of gears method based on DSM-ABC algorithm zhogn according to claim 1, feature exist
In: in step S3, the mechanism of chaos s [j] meets:
S [j+1]=k*s [j] * (1-s [j])；
In formula, k value is 4.0.
3. according to a kind of level Four design of gears method based on DSM-ABC algorithm according to claim 1, feature exists
In: in step S4, le ' vy (λ) meets le ' vy distribution, and formula is as follows:
L (s)~| s |-1-β；O < β < 2
In formula, L (s) is the flight path of le ' vy flight；S is arbitrary width, parameter of the β between 0-2；Wherein chance move
Long s is expressed from the next:
S=μ/| v |1/β
In formula, μ and ν are all satisfied and are just distributed very muchWith
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| CN106875050A (en) * | 2017-04-01 | 2017-06-20 | 哈尔滨工业大学 | A kind of Engineering constraint parameter optimization method based on improvement chaos ant colony algorithm |
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