CN108681818A - A kind of Optimization Scheduling of gear mechanism process - Google Patents
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Abstract
The present invention relates to a kind of Optimization Scheduling of gear mechanism process, method is：By scheduling model and optimization aim of the determination molding a collection of gear blank to be processed in mechanical processing process, it is used in combination and target is optimized based on the Optimization Scheduling for mixing discrete harmonic search algorithm；Wherein, scheduling model according to gear in mechanical processing process, establish by process time of each gear on each processing machine, while optimization aim is to minimize longest finishing time.The present invention proposes the scheduling model and optimization aim of gear mechanism process, the excellent solution of the scheduling problem of gear mechanism process can be obtained in a short time, to ensure that gear there can be higher qualification rate in manufacture, while the expression of Gearmaking Technology process is more clear accurately.
Description
Technical field
The present invention relates to a kind of Optimization Schedulings of gear mechanism process, belong to workshop intelligent optimization scheduling
Field.
Background technology
Gear refers to having gear continuously to engage the mechanical organ for transmitting movement and power on wheel rim.Gear answering in transmission
With very early there have been.Late nineteenth century transforms into the principle of cutting method and special purpose machine tool and cutter using this principle cutting
Occur in succession.Gear is widely used in mechanical industry, and especially in automobile and heavy-duty machinery field, the continuous engagement of gear can transmit
Movement and power.Gear Industry as Mechanical Fundamentals industry important component either in scale or in processing technology
On can all have boundless foreground.In view of under the conditions of business equipment and limited other resource production capacities, by reasonably adjusting
Degree can generate strong influence to utilization rate of equipment and installations, delivery date, inventories etc..
The technological process of general Gear Processing has the following steps：Blank manufactures, gear blank heat treatment, gear blank processing, tooth
Face processes, gear teeth heat treatment, flank of tooth finishing and gear teeth finishing.Different process operations needs respectively on different machines
It completes, in the mechanical processing process of entire gear, gear to be processed needs are operated on different machines successively, side
It can complete the molding of gear.Specifically, n gear is processed, then the gear blank needs to pass through in the same order
Different m platform machines, can complete the processing of gear.Therefore, the characteristics of Gear Processing process, is, each gear blank exists
Each time according to M1, M in process2,…,MmMachine sequence be processed, and each piece of gear blank on every machine
Processing sequence is identical, and it is displacement assembly line (Permutation Flow-shop, PFS) that academia, which defines this kind of assembly line, also
The PFS scheduling problems for being proved to two machines or more belong to NP-hard problems, i.e., it is accurate that it can not be acquired in polynomial time
Solution.Clearly for the fluvial incision of the Gear Processing process of research, processing machine is significantly greater than two, also belongs to
The scope of NP-hard problems.The problem is reasonably dispatched, the production efficiency of Gear Production process can be significantly improved.
By the description of said gear process it is found that the fluvial incision of Gear Processing process is NP-hard categories
Property, traditional mathematic programming methods can only solve small-scale problem, and the optimization of Heuristic construction method is second-rate, therefore,
For the present invention from intelligent algorithm angle, design is a kind of based on discrete harmonic search algorithm (the Hybrid Discrete of mixing
Harmony Search Algorithm, HDHSA) Optimization Scheduling, Gear Processing process can be acquired within a short period of time
The excellent solution of scheduling problem.
Invention content
The present invention provides a kind of Optimization Schedulings of gear mechanism process, for obtaining within a short period of time
The excellent solution of Optimal Scheduling of the gear in being machined manufacturing process.
The technical scheme is that：A kind of Optimization Scheduling of gear mechanism process, it is to be processed by determination
Scheduling model and optimization aim of the molding a batch gear blank in mechanical processing process, are used in combination based on the discrete and sonar surveillance system of mixing
The Optimization Scheduling of rope algorithm optimizes target；Wherein, scheduling model foundation gear is each in mechanical processing process
Process time of the gear on each processing machine establishes, while optimization aim is to minimize longest finishing time Cmax(π)：
Cmax(π)=C (πn,m)
In formula,The scale of n × m problem of representation, n indicate that gear sum to be processed, m indicate gear
Number of machines used in process,Indicate the set of positive integer；π=[π1,π2,…,πi] indicate gear to be processed
Process, πkIndicate the gear of k-th of position in π,Indicate πiProcess time of a gear on jth platform machine, C (πi,
J) it is πiCompletion date of a gear on jth platform machine；The optimization aim of the model is in all gears that need to be processed
An optimal sequencing π is found in ordered set Π*So that longest finishing time Cmax(π) is minimum.
It is described to be specially based on the Optimization Scheduling for mixing discrete harmonic search algorithm：
The design of Step1, coding mode：It is encoded with the Gear Processing sequence during Gear Processing, is ordered as π
=[π1,π2,…,πi], i=1,2 ..., n, wherein i are number of gears to be processed；
Step2, parameter initialization：Size HMS, that is, population scale NP of harmony data base, the probability of harmony data base
HMCR, tone finely tunes probability P AR, and the algorithm time started is arranged；
Step3, initialization of population：Using NEH methods generate an initial population individual, it is remaining NP-1 individual use with
Machine method generates, and records the target function value f of each individual until the quantity of initial solution reaches the requirement of population scale；Harmony
The concrete form of data base is as follows：
Wherein, X1,X2,…,XHMSFor HMS harmony of generation, f (X1),f(X2),…,f(XHMS) it is its corresponding target
Functional value；
Step4, new harmony is generated：New harmony is mainly generated by following three kinds of mechanism：Learn harmony data base, tone
Fine tuning and random selection tone, are described in detail below：
1., from 0 to 1 between randomly generate random number rand, if rand ＜ HMCR, Applied Learning harmony data base mechanism,
A harmony variable is randomly selected from existing harmony data base HM as new harmony Xnew；Otherwise, using random selection tone
Mechanism generates a new harmony variable from solution space as new harmony X at randomnew；
2., by 1. can be obtained a harmony variable XnewIf this harmony variable is generated by learning harmony data base
, then it needs to be finely adjusted this harmony variable：If randomly generating the random number rand1 ＜ PAR between one 0 to 1, need
To new harmony XnewIt carries out the tone fine tuning operation based on forward_insert neighborhoods and realizes that tone fine tuning generates new individual；If
Rand1 >=PAR is then needed to new harmony XnewThe tone fine tuning operation based on swap neighborhoods is carried out, new individual is generated, it is specific public
Formula is as follows：
Step5, update harmony data base：According to Step4, a new harmony data base being made of new harmony can be obtained
HMnew, to being assessed per each individual in new harmony data base, its corresponding target function value f can be obtained, by new and sound memory
The individual individual with the initial harmony data base HM generated in Step3 in library is compared one by one, if HMnewIn
Individual XnewBetter than the individual X in HMold, i.e. f (Xnew) ＜ f (Xold), then by HMnewIn individual XnewInstead of the individual in HM
Xold；Otherwise, it does not make an amendment；
Step6, problem-targeted local search：Regard in new population 1/5th individual as " choosing individual ", to every
One " choosing individual " carries out exploratory stage and disturbance stage successively, if the individual that local search obtains is better than " choosing a
Body " is then replaced, and using contemporary population as population of new generation；
Step7, end condition：End condition is set as Riming time of algorithm T=100 × n, if it is satisfied, then output is " most
Excellent individual "；Otherwise step Step4 is gone to, is iterated, until meeting end condition.
The exploratory stage utilizes " backward_insert " neighborhood operation, explores number and is set as work gear to be added
Total n；Realize that disturbance stage, disturbance number are 3 times using the neighborhood operation based on " interchange ", to after disturbance
Body carries out more careful exploration.
The beneficial effects of the invention are as follows：The present invention proposes the scheduling model and optimization aim of gear mechanism process,
The excellent solution that the scheduling problem of gear mechanism process can be obtained in a short time, to ensure that gear can have in manufacture
There is higher qualification rate, while the expression of Gearmaking Technology process is more clear accurately；Using according to it is described it is discrete and
Sonar surveillance system rope algorithm steps obtain when former generation population the next-generation individual of " high-quality individual " update, can preferably bootstrap algorithm into
Row global search；It is (suitable by adjusting the tone of each harmony (individual) in band (population) repeatedly in the renewal process of population
With value), it is finally reached beautiful harmony state, this can not only make the historical information of advantage individual be fully used, also
It can ensure that the global search of algorithm has certain width；It is disturbed using " interchange " operation in local search
It is dynamic, be conducive to algorithm and jump out local optimum, so that the search field of algorithm is more extensive, in conjunction with " backward_
Insert " neighborhood search mechanism makes the local development ability of algorithm be significantly improved, the quality of solution be improved significantly.
Description of the drawings
Fig. 1 is the process flow diagram of middle gear mechanical processing process of the present invention；
Fig. 2 is the total algorithm flow chart of the present invention；
Fig. 3 is the expression schematic diagram of solution in the present invention；
Fig. 4 is that the tone based on " forward direction insertion " (forward_insert) neighborhood of the present invention finely tunes operation change signal
Figure；
Fig. 5 is that the tone based on " exchange " (swap) neighborhood of the present invention finely tunes operation change schematic diagram；
Fig. 6 is the change schematic diagram based on the operation of " interchange " neck of the present invention；
Fig. 7 is the change schematic diagram based on " backward_insert " neighborhood operation of the present invention.
Specific implementation mode
Embodiment 1：As shown in figs. 1-7, a kind of Optimization Scheduling of gear mechanism process, it is to be processed by determination
Scheduling model and optimization aim of the molding a batch gear blank in mechanical processing process, are used in combination based on the discrete and sonar surveillance system of mixing
The Optimization Scheduling of rope algorithm optimizes target；Wherein, scheduling model foundation gear is each in mechanical processing process
Process time of the gear on each processing machine establishes, while optimization aim is to minimize longest finishing time Cmax(π)：
Cmax(π)=C (πn,m)
In formula,The scale of n × m problem of representation, n indicate that gear sum to be processed, m indicate tooth
Number of machines used in process is taken turns,Indicate the set of positive integer；π=[π1,π2,…,πi] indicate gear to be processed
Process, πkIndicate the gear of k-th of position in π,Indicate πiProcess time of a gear on jth platform machine, C (πi,
J) it is πiCompletion date of a gear on jth platform machine；The optimization aim of the model is in all gears that need to be processed
An optimal sequencing π is found in ordered set Π*So that longest finishing time Cmax(π) is minimum.
It is specially it is possible to further which the Optimization Scheduling based on the discrete harmonic search algorithm of mixing is arranged：
The design of Step1, coding mode：It is encoded with the Gear Processing sequence during Gear Processing, is ordered as π
=[π1,π2,…,πi], i=1,2 ..., n, wherein i are number of gears to be processed；
Such as：Be ranked up coding with gear blank to be processed, for example have 5 processing gears, 3 processing machines, at random
It generates a Gear Processing after coding to be ordered as [5,3,1,2,4], the processing sequence on each machine is the sequence.It is arranging
In sequence [5,3,1,2,4], the 5 of No.1 position indicates that first processing gear is No. 5 gears, and the 3 of No. two positions indicates second
Work gear to be added is No. 3 gears, and the 1 expression third work gear to be added that third place is set is No. 1 gear, and so on.
Step2, parameter initialization：Harmony data base size HMS, that is, population scale NP (population scale NP, i.e., initially
The quantity of solution NP), the probability HMCR of harmony data base, tone finely tunes probability P AR, and the algorithm time started is arranged；
Step3, initialization of population：Using NEH methods generate an initial population individual, it is remaining NP-1 individual use with
Machine method generates, and records the target function value f of each individual until the quantity of initial solution reaches the requirement of population scale；Harmony
The concrete form of data base is as follows：
Wherein, X1,X2,…,XHMSFor HMS harmony of generation, f (X1),f(X2),…,f(XHMS) it is its corresponding target
Functional value；It indicates the 1,2nd in the HMS population ..., n gears to be processed；
Step4, new harmony (individual) is generated：New harmony is mainly generated by following three kinds of mechanism：Study and sound memory
Library, tone fine tuning and random selection tone, are described in detail below：
1., from 0 to 1 between randomly generate random number rand, if rand ＜ HMCR, Applied Learning harmony data base mechanism,
A harmony variable is randomly selected from existing harmony data base HM as new harmony (individual) Xnew；Otherwise, using random choosing
Tone mechanism is selected, generates a new harmony variable at random from solution space as new harmony (individual) Xnew；
2., by 1. can be obtained a harmony variable XnewIf this harmony variable is generated by learning harmony data base
(randomly selecting to obtain from the HM of harmony library) then needs to be finely adjusted this harmony variable, and the present invention devises two kinds of sounds
Fine tuning operation is adjusted, that is, be based on the tone fine tuning operation of " forward direction insertion " (forward_insert) neighborhood and is based on " exchange "
(swap) the tone fine tuning operation of neighborhood.It finely tunes the selections operated for two kinds to be determined by tone fine tuning frequency PAR, concrete mode
For：
From the above equation, we can see that randomly generate the random number rand1 between one 0 to 1 first, if rand1 ＜ PAR, need pair
New harmony XnewIt carries out the neighborhood operation based on " forward direction insertion " (forward_insert) neighborhood and realizes that tone fine tuning generates new
Body, specific implementation are as shown in Figure 4；If rand1 >=PAR, need to new harmony XnewIt carries out and is based on " exchange " (swap) neighborhood
Tone fine tuning operation, generate new individual, specific implementation is as shown in Figure 5.
Step5, update harmony data base.According to Step4, we can obtain one and are made of new harmony (new individual)
New harmony data base (new population) HMnew, to being assessed per each individual in new harmony data base, its corresponding target can be obtained
Functional value f.Individual in the initial harmony data base HM generated in individual and Step3 in new harmony data base is carried out one by one
It is compared, if HMnewIn individual XnewBetter than the individual X in HMold, i.e. f (Xnew) ＜ f (Xold), then by HMnewIn individual
XnewInstead of the individual X in HMold；Otherwise, it does not make an amendment.
Step6, problem-targeted local search.Global search for balanced algorithm and local search improve algorithm pair
The exploration efficiency of quality area.The present invention is directed in updated new population 1/5th individual, devises and is based on
The local search of " interchange " and " backward_insert " two kinds of neighborhood operations.The local search is divided into the disturbance stage
And the exploratory stage, the disturbance stage is realized using the neighborhood operation based on " interchange ", disturbance number is 3 times, after disturbance
Individual carry out more careful exploration, the exploratory stage utilizes " backward_insert " neighborhood operation, explores number and is set as
The total n of work gear to be added.Regard in new population 1/5th individual as " choosing individual ", to each " choosing individual " according to
Secondary exploratory stage and disturbance stage are replaced, and will be contemporary if the individual that local search obtains is better than " choosing individual "
Population is as population of new generation；
Step7, end condition：End condition is set as Riming time of algorithm T=100 × n, if it is satisfied, then output is " most
Excellent individual "；Otherwise step Step4 is gone to, is iterated, until meeting end condition.
It, will in order to verify the validity and robustness of the discrete harmonic search algorithm of mixing (HDHSA) that the present invention is put forward
HDHSA is compared with standard harmonic search algorithm (HSA).Specific contrast test is as follows：
The Rec classes problem for commonly using Flow shop test problems concentrations is chosen in the present invention as test problem, in identical item
Under part, the required target letter for the discrete harmonic search algorithm (HDHSA) that standard harmonic search algorithm (HSA) is carried with the present invention
Numerical result compares.The Riming time of algorithm of the problem of for different scales is T=100 × n (units：ms).Each algorithm
And its test program realizes that operating system Win10, CPU frequency 2.2GHz are inside saved as by 2010 editions programmings of Delphi
4GB.The parameter setting of the discrete harmonic search algorithm of mixing (HDHSA) carried is as follows：Population scale popsize=2 × n, and
The probability HMCR=0.9 in sound memory library, tone finely tune probability P AR=0.3.Each algorithm independently reruns 20 times,
Wherein AVG indicates that optimal value mean value, SD indicate standard deviation.Table 1 gives under same test environment, standard harmonic search algorithm
(HSA) the required target function value Comparative result of the discrete harmonic search algorithm (HDHSA) carried with the present invention.As known from Table 1,
The carried algorithm obtained AVG and SD on most test problems of the present invention is superior to standard harmonic search algorithm, this table
The validity of the put forward algorithm of the present invention is illustrated, also demonstrates discrete harmonic search algorithm and is to solve for the optimization of gear mechanism process
A kind of efficient algorithm of scheduling problem.
Obtained target function value in the case of the different problem scales of table 1
The specific implementation mode of the present invention is explained in detail above in conjunction with attached drawing, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
Put that various changes can be made.
Claims (3)
1. a kind of Optimization Scheduling of gear mechanism process, it is characterised in that：Pass through determination molding a batch to be processed
Scheduling model and optimization aim of the gear blank in mechanical processing process are used in combination based on the excellent of the discrete harmonic search algorithm of mixing
Change dispatching method to optimize target；Wherein, scheduling model is according to gear in mechanical processing process, and each gear is at each
Process time on processing machine establishes, while optimization aim is to minimize longest finishing time Cmax(π)：
Cmax(π)=C (πn,m)
In formula,The scale of n × m problem of representation, n indicate that gear sum to be processed, m indicate Gear Processing
Used in the process of number of machines,Indicate the set of positive integer；π=[π1,π2,…,πi] indicate gear to be processed process,
πkIndicate the gear of k-th of position in π,Indicate πiProcess time of a gear on jth platform machine, C (πi, j) and it is
πiCompletion date of a gear on jth platform machine；The optimization aim of the model is the sequence collection in all gears that need to be processed
It closes in Π and finds an optimal sequencing π*So that longest finishing time Cmax(π) is minimum.
2. the Optimization Scheduling of gear mechanism process according to claim 1, it is characterised in that：It is described to be based on mixing
The Optimization Scheduling for closing discrete harmonic search algorithm is specially：
The design of Step1, coding mode：With during Gear Processing Gear Processing sequence encoded, be ordered as π=
[π1,π2,…,πi], i=1,2 ..., n, wherein i are number of gears to be processed；
Step2, parameter initialization：Size HMS, that is, population scale NP of harmony data base, the probability of harmony data base
HMCR, tone finely tunes probability P AR, and the algorithm time started is arranged；
Step3, initialization of population：One initial population individual is generated using NEH methods, remaining NP-1 individual uses random side
Method generates, and records the target function value f of each individual until the quantity of initial solution reaches the requirement of population scale；And sound memory
The concrete form in library is as follows：
Wherein, X1,X2,…,XHMSFor HMS harmony of generation, f (X1),f(X2),…,f(XHMS) it is its corresponding object function
Value；
Step4, new harmony is generated：New harmony is mainly generated by following three kinds of mechanism：Learn harmony data base, tone fine tuning
With random selection tone, it is described in detail below：
1., from 0 to 1 between randomly generate random number rand, if rand ＜ HMCR, Applied Learning harmony data base mechanism, from
A harmony variable is randomly selected in some harmony data base HM as new harmony Xnew；Otherwise, using random selection tone machine
Reason, a new harmony variable is generated from solution space as new harmony X at randomnew；
2., by 1. can be obtained a harmony variable XnewIf this harmony variable is generated by learning harmony data base,
It needs to be finely adjusted this harmony variable：If randomly generating the random number rand1 ＜ PAR between one 0 to 1, need to new
Harmony XnewIt carries out the tone fine tuning operation based on forward_insert neighborhoods and realizes that tone fine tuning generates new individual；If rand1
>=PAR is then needed to new harmony XnewThe tone fine tuning operation based on swap neighborhoods is carried out, generates new individual, specific formula is such as
Under：
Step5, update harmony data base：According to Step4, a new harmony data base HM being made of new harmony can be obtainednew,
To being assessed per each individual in new harmony data base, its available corresponding target function value f will be in new harmony data base
Individual is compared one by one with the individual in the initial harmony data base HM generated in Step3, if HMnewIn individual Xnew
Better than the individual X in HMold, i.e. f (Xnew) ＜ f (Xold), then by HMnewIn individual XnewInstead of the individual X in HMold；Otherwise,
It does not make an amendment；
Step6, problem-targeted local search：Regard in new population 1/5th individual as " choosing individual ", to each
" choosing individual " carries out exploratory stage and disturbance stage successively, if the individual that local search obtains is better than " choosing individual ",
It is replaced, and using contemporary population as population of new generation；
Step7, end condition：End condition is set as Riming time of algorithm T=100 × n, if it is satisfied, then output " optimal
Body "；Otherwise step Step4 is gone to, is iterated, until meeting end condition.
3. the Optimization Scheduling of gear mechanism process according to claim 2, it is characterised in that：The exploration rank
Duan Liyong " backward_insert " neighborhood operation explores the total n that number is set as work gear to be added；Using based on
The neighborhood operation of " interchange " realizes that disturbance stage, disturbance number are 3 times, and it is more careful to be carried out to the individual after disturbance
Exploration.
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| CN117669988A (en) * | 2023-12-26 | 2024-03-08 | 中建八局第一数字科技有限公司 | Q-Learning algorithm improvement NEH-based prefabricated part production scheduling method |
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