CN110458478A - Job-shop scheduling method based on discrete invasive weed algorithm - Google Patents
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Abstract
Based on the dispatching method of discrete invasive weed algorithm, algorithm steps include: the initial solution that a random number is given to all weeds, and carry out encoding and decoding to initial random sequence by the coding mode of process;In iterative process each time, each weeds calculate its seed number to be generated;In the space dispersion operation of algorithm, seed generates the standard deviation of control diffusion length, seed STOCHASTIC DIFFUSION in a manner of normal distribution around parent according to this standard deviation according to the fitness value of parent plant;The optimizing that part is carried out for newly-generated seed changes the sequence of workpiece, the local search ability of boosting algorithm using the thought of VNS;When the total number of weeds reaches the maximum value of setting, algorithm removes poor individual, only retains the weeds of maximum value number.The invention proposes a kind of dispatching method based on advanced novel evolution algorithm, and the job-shop scheduling problem in the solution manufacturing industry for keeping it more intelligent.
Description
Technical field
The present invention relates to production line scheduling fields in manufacturing industry, specifically to job-shop scheduling problem in production scheduling environment
The method optimized.
Background technique
Job-shop scheduling problem (Job Shop Scheduling Problem, abbreviation JSP) is manufacturing industry production scheduling
An extremely important problem in problem.Field applied by job-shop scheduling problem is also very extensive simultaneously, in addition to being related to
Except manufacturing production scheduling, aircraft carrier scheduling, airport aircraft scheduling, the scheduling of port and pier freighter, automobile processing have been further related to
The practical property problem such as pipeline schedule.Therefore research Job-Shop has very important significance, and traditional mathematical method
It can no longer meet the demand of production scheduling.Scholar mostly solves problems using approximate algorithm at present, wherein very big by one
Class branch is meta-heuristic algorithm.Representative algorithm in meta-heuristic algorithm includes: GA, DE, PSO, HS etc..For Operation Van
Between dispatch this NP-hard problem, this patent proposes a kind of novel invasive weed algorithm mainly to solve problems.Invasion
Weeds algorithm is a kind of New Type of Numerical Stochastic Optimization Algorithms based on weeds, and basic thought is theoretical from the invasion of weeds.
The powerful accommodative ability of environment of weeds is utilized in the algorithm, and imitated 4 stages of weed invasion: initialization of population, growth are numerous
It grows, space is spread and competition exclution.Algorithm mainly controls each weeds institute by the fitness value of each weeds in reproductive stage
The seed number of generation.In the standard deviation σ that space diffusion phase, algorithm pass through control normal distributioncurControl seed dis persal away from
From, allow seed in algorithm iteration early period the long range diffusion around parent weeds, in algorithm iteration later period seed in father
It is spread for small range around weeds.One weed population of algorithm initial setting up sets the variation model of weed seed and standard deviation
It encloses.Later in the iterative process of algorithm, by execute repeatedly growth and breeding, space diffusion and competition exclution these three operation pair
Population optimizes.And it is applied in job-shop scheduling problem.The it is proposed of the algorithm is for solving the existing fortune of current algorithm
The shortcomings that row unstable result, the calculating time is long, low precision, convergence gear shaper without theoretical instructs.
Summary of the invention
The object of the present invention is to provide a kind of job-shop scheduling methods based on discrete invasive weed algorithm.
The present invention is the steps include: based on the job-shop scheduling method of discrete invasive weed algorithm
Step 1: initialization population, Population Size N;
Step 2: initiation parameter, including seed and standard deviation constant interval,
Step 3: the population comprising n solution (weeds) is generated according to the coding mode based on process;
Step 4: evaluating the fitness value of each solution;When algorithm meets termination condition, algorithm returns to the current solution found at present,
Algorithm terminates;
Step 5: the seed number that the standard deviation and parent individuality for calculating population generate;
Step 6: weeds being ranked up, the weeds individual of optimal and worst fitness value is found;
Step 7: calculating the seed that each weeds generate, and calculate its fitness value;
Step 8: local searching strategy is executed to the weeds individual in population;
Step 8.1: according to local searching strategy, generating Wnew;
Step 8.2: if randi<PARg, then:
Step 8.2.1: weeds individual choosing value from current best weeds;
Step 8.2.2: otherwise: weeds individual selective value from all weeds that the present age retains;
Step 8.3: if randi< HMCR, then:
Step 8.3.1: weeds individual directly inherits the individual of weeds obtained in step 10.2;
Step 8.3.2: otherwise: algorithm generates new explanation in solution space;
Step 9: VNS operation is executed to the new weeds individual that generates:
Step 9.1: insertion operation being executed to the weeds individual x in population, obtains weeds individual x*;
Step 9.2: to the weeds individual x in population*Crossover operation is executed, weeds individual x ' is obtained;
Step 9.3: if f (x ')≤f (x), is updated to x ' for x;
Step 10: newly generated seed and weeds being put together, sorted according to fitness value;
Step 11: eliminating the lower weeds of grade of fit to reach the maximum allowable group in group;
Step 12: updating the globally optimal solution of entire population, go to step 4.
Usefulness of the present invention is:
(1) in the initial phase of population, population is generated using the coding rule based on process.
(2) local searching strategy and VNS thought is added in space diffusion phase, is calculated by the insertion of VNS and swap operation enhancing
The local search ability and deep search ability of method.
(3) in an iterative process, the local search of algorithm is carried out according to following formula.
(4) in the dispersion operation of space, change the way of search of algorithm by the standard deviation of control algolithm, by the overall situation of early period
Way of search is gradually changed into local search mode.
(5) algorithm eliminates poor of fitness value in population according to the maximum population number set in the competition exclution stage
Body, so that population number is no more than maximum population number.
Detailed description of the invention
Fig. 1 is flow chart of the invention, and Fig. 2 is the P of job-shop scheduling methodsizeParameter variation tendency figure, Fig. 3 are to make
The S of industry Job-Shop methodmaxParameter variation tendency figure, Fig. 4 are the n parameter variation tendency figure of job-shop scheduling method, Fig. 5
For coding mode Gantt chart, Fig. 6 is convergence graph, and Fig. 7 is the box figure of job-shop scheduling method.
Specific embodiment
The application of the job-shop scheduling method based on discrete invasive weed algorithm:
There is M platform machine in job-shop scheduling problem, be expressed as [1,2 ..k, m ..., M], m and k are respectively in scheduling problem
One machine, and m ≠ k.Every machine can only process a procedure, and the process on each machine is different from;No
The deadline of process of the same workpiece on different machines is independent from each other, and guarantees that event will not occur for all machines
Barrier.
There is N number of workpiece to need to process in job-shop scheduling problem, indicate are as follows: [1,2 ..i, n ..., N], i and n difference
For a workpiece in scheduling problem, and n ≠ i.The processing sequence of each workpiece can be different, and deadline phase
It is mutually independent.
Assuming that deadline of the workpiece n on machine m is Cn,m;Process time of the workpiece n on machine m is ln,m;As
When the target of industry Job-Shop is minimizes Maximal Makespan, objective function are as follows:
min max1≤n≤NCnM
The order of the different manufacturing procedures of each workpiece should meet the following conditions simultaneously:
Cnm-lnm+D(1-ankm)≥Cnk
In formula Eq. (1.2), D is a sufficiently large positive number;ankmFor index coefficient, meaning are as follows:
The operation order for meeting each workpiece under constraint condition is indicated in formula Eq. (1.2);Every machine difference work
The processing sequence of part should meet condition below:
Cnm-Cim+D(1-xinm)≥lnm
In formula, xinmFor indicator variable, meaning are as follows:
Formula indicate each workpiece when being processed on machine, the sequencing of each machine.
Therefore, solving job shop scheduling problem model are as follows:
Specific steps are as follows:
Initiation parameter: setting Population Size N;Maximum seed number Smax;Minimum seed number Smin;Primary standard difference sigmainit, most
Whole standard deviation σfinal;Maximum population number Pmax, disturb select probability HMCR and PARg。
Step 1: initialization population, Population Size N;
Step 2: initiation parameter, including seed and standard deviation constant interval,
Step 3: the population comprising n solution (weeds) is generated according to the coding mode based on workpiece;
Step 4: evaluating the fitness value of each solution;When algorithm meets termination condition, algorithm returns to the current solution found at present,
Algorithm terminates;
Step 5: the seed number that the standard deviation and parent individuality for calculating population generate;
Step 6: weeds being ranked up, the weeds individual of optimal and worst fitness value is found;
Step 7: calculating the seed that each weeds generate, and calculate its fitness value;
Step 8: newly generated seed and weeds being put together, sorted according to fitness value;
Step 9: eliminating the lower weeds of grade of fit to reach the maximum allowable group in group;
Step 10: local searching strategy is executed to the weeds individual in population:
Step 10.1: according to local searching strategy, generating Wnew;
Step 10.2: if randi<PARg, then:
Step 10.2.1: weeds individual choosing value from current best weeds;
Step 10.2.2: otherwise: weeds individual selective value from all weeds that the present age retains;
Step 10.3: if randi< HMCR, then:
Step 10.3.1: weeds individual directly inherits the individual of weeds obtained in step 10.2;
Step 10.3.2: otherwise: algorithm generates new explanation in solution space;
Step 11: VNS operation is executed to the new weeds individual that generates:
Step 11.1: crossover operation being executed to the weeds individual x in population, obtains weeds individual x*;
Step 11.2: to the weeds individual x in population*Crossover operation is executed, weeds individual x ' is obtained;
Step 11.3: if f (x ')≤f (x), is updated to x ' for x;
Step 12: updating the globally optimal solution of entire population, go to step 4.
Specific method flow diagram is as shown in Figure 1.
(1) in the initial phase of population, population is generated using the coding rule based on process;
(2) local searching strategy and VNS thought is added in space diffusion phase, enhances the local search ability of algorithm;
(3) in an iterative process, the local search of algorithm is carried out according to following formula;
(4) in the dispersion operation of space, change the way of search of algorithm by the standard deviation of control algolithm, by the overall situation of early period
Way of search is gradually changed into local search mode;
(5) algorithm eliminates poor of fitness value in population according to the maximum population number set in the competition exclution stage
Body, so that population number is no more than maximum population number.
In order to more intuitively verify performance of the present invention in practical problem, we have taken out 10 workpiece, 5 machine
Job-shop scheduling problem, this algorithm (DIWO) encoded using the coding mode based on process, and the active of acquisition is encoded
It is as shown in Figure 5 to dispatch Gantt chart.Simultaneously using this algorithm (DIWO) and other some epidemic algorithms IWO (Mehrabian A
R,Lucas C.A novel numerical optimization algorithm inspired from weed
Colonization [J] .Ecological Informatics, 2006,1 (4): 355-366.), PSO and IPSO (Liu Hongming,
Zeng Hongyan, Zhou Wei wait based on optimization [J] journal of Shandong university (engineering for improving particle swarm algorithm job-shop scheduling problem
Version), 2019,49:10-17.) it compares, the convergence graph of algorithm such as Fig. 6.It is obvious that DWWO algorithm is solving scheduling problem
When convergence rate and algorithm performance be better than other algorithms.The box figure of algorithm is as shown in Figure 7, it can be seen that DIWO algorithm is solving
Certainly algorithm stability when scheduling problem is better than other algorithms.
The above is a preferred embodiment of the present invention, it is noted that for those skilled in the art
For, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also considered as
Protection scope of the present invention.
Claims (7)
1. the job-shop scheduling method based on discrete invasive weed algorithm, which is characterized in that the steps include:
Step 1: initialization population, Population Size N;
Step 2: initiation parameter, including seed and standard deviation constant interval;
Step 3: the population comprising n solution (weeds) is generated according to the coding mode based on process;
Step 4: evaluating the fitness value of each solution;When algorithm meets termination condition, algorithm returns to the current solution found at present,
Algorithm terminates;
Step 5: the seed number that the standard deviation and parent individuality for calculating population generate;
Step 6: weeds being ranked up, the weeds individual of optimal and worst fitness value is found;
Step 7: calculating the seed that each weeds generate, and calculate its fitness value;
Step 8: local searching strategy is executed to the weeds individual in population:
Step 8.1: according to local searching strategy, generating Wnew;
Step 8.2: if randi<PARg, then:
Step 8.2.1: weeds individual choosing value from current best weeds;
Step 8.2.2: otherwise: weeds individual selective value from all weeds that the present age retains;
Step 8.3: if randi< HMCR, then:
Step 8.3.1: weeds individual directly inherits the individual of weeds obtained in step 10.2;
Step 8.3.2: otherwise: algorithm generates new explanation in solution space;
Step 9: VNS operation is executed to the new weeds individual that generates:
Step 9.1: insertion operation being executed to the weeds individual x in population, obtains weeds individual x*;
Step 9.2: to the weeds individual x in population*Crossover operation is executed, weeds individual x ' is obtained;
Step 9.3: if f (x ')≤f (x), is updated to x ' for x;
Step 10: newly generated seed and weeds being put together, sorted according to fitness value;
Step 11: eliminating the lower weeds of grade of fit to reach the maximum allowable group in group;
Step 12: updating the globally optimal solution of entire population, go to step 4.
2. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
Population Size N is arranged in initial phase;Maximum seed number Smax;Minimum seed number Smin;Primary standard difference sigmainit, final to mark
Quasi- difference sigmafinal;Maximum population number Pmax, disturb select probability HMCR and PARg。
3. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
In step 1, by the present invention in that being encoded with a kind of coding mode based on process, a weeds are expressed as one group 0 to 1
Between random number, it is ranked up later, and obtain can be used for the work of algorithm calculating with the calculation of coding
Sequence can will be applied to the algorithm of continuous problem, for solving job-shop scheduling problem.
4. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
In step 8, local searching strategy is added in the frame of algorithm, local searching strategy can select again obtained solution
It selects and combines, in the hope of being different from the new explanation solved, and the process time solved obtained by calculating, in the hope of more excellent solution;Such as
Fruit can obtain solution more better than current optimal solution, then current optimal with obtained more preferable solution replacement
Solution;Algorithm can also generate when algorithm falls into stagnation and be totally different from the new explanation solved in current population, with this simultaneously
To increase the diversity of population;It avoids algorithm from falling into local optimum, enhances the local search ability of algorithm.
5. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
In step 8, the local search of algorithm is carried out according to following formula:
6. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
In step 9, the thought of VNS is added in algorithm frame, algorithm to the new weeds generated in step 9 using intersecting in VNS and
Insertion operation compares the new weeds obtained after two kinds of operations with the weeds individual in step 10;Retain two weeds
More preferably weeds are individual in individual, the local search ability and deep search ability of boosting algorithm.
7. the job-shop scheduling method according to claim 1 based on discrete invasive weed algorithm, which is characterized in that In
In step 9.1, crossover operation is the order for successively exchanging main exchange workpiece and other workpiece, to obtain new sequence;Each
The process time that the sequence newly obtained is calculated after exchange, the optimal job sequence after obtaining swap operation;Enhance the office of algorithm
Portion's search capability strengthens research of the algorithm to particular sequence, the search capability of further boosting algorithm.
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