CN104281917A - Fuzzy job-shop scheduling method based on self-adaption inheritance and clonal selection algorithm - Google Patents

Abstract

The invention relates to a fuzzy job-shop scheduling method based on self-adaption inheritance and the clonal selection algorithm. The method includes the steps of determining the coding scheme of the fuzzy job-shop scheduling problem, generating the initial population N at random, defining a solution space, defining and calculating the adaptability function of an individual, conducting clone proliferation operation on the individual according to the size of the adaptability value near each generation of optimal solution, independently conducting self-adaption cross and mutation operation on individuals obtained through reproduction, conducting clonal selection operation on the individuals obtained through cross and mutation to generate the new population N*, ending the circulation if the ending condition is met, and returning to continue the next step if the ending condition is not met. By means of the method, resources can be more reasonably distributed, the completion time of job-shop scheduling fuzziness is shortened, the efficiency of job-shop fuzzy scheduling is improved, and the requirement of actual production scheduling is better met.

Description

Based on the fuzzy job shop scheduling method of Adaptive Genetic and clonal selection algorithm

Technical field

The present invention relates to the concocting method of processing work and machine in industrial plant job scheduling.

Background technology

Due to Production Planning and Controlling problem most typicalness in all scheduling problems of Workshop, so the research dominate in scheduling theory always to solve job shop scheduling problems.And the uncertain factor faced in production run, such as: the ambiguity etc. at mechanical disorder, machining delay, the uncertainty of work pieces process time, each workpiece delivery date, all can affect the arrangement of whole scheduling and the assessment to scheduling result.And for the research of fuzzy solve job shop scheduling problems, more realistic production, the fuzzy solve job shop scheduling problems so increasing scholar begins one's study.

Up to the present, the people such as Han S have studied the single machine scheduling with Fuzzy Due Dates; The people such as SAKAWA adopted genetic algorithm for solving with the fuzzy solve job shop scheduling problems of PROBLEMS WITH FUZZY PROCESSING TIMES and Fuzzy Due Dates in 1999, made minimum customer satisfaction maximum.The people such as Ishibuchi H are studied fuzzy job shop scheduling, and are described PROBLEMS WITH FUZZY PROCESSING TIMES.The people such as Murata T are studied the Multi-Objective Scheduling with Fuzzy Due Dates.Adamopulos G I neighborhood search method is studied the single machine scheduling with variable process time and Fuzzy Due Dates.

The method of Recent study fuzzy job shop scheduling has genetic algorithm, simulated annealing, heuritic approach etc.Algorithm ultimate principle is all based on an initial solution, finds optimum solution by certain method search volume.There are some defects in these researchs:

(1) method comparison is single, finds process relatively blindly.

(2) find optimum solution and be easily absorbed in local optimum, the easy Premature Convergence of algorithm.

(3) Population Regeneration is more random.

Summary of the invention

The technical problem to be solved in the present invention is can rational allocation Job-Shop Production Planning and Controlling problem.

In order to solve the problems of the technologies described above, technical scheme of the present invention there is provided a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm, it is characterized in that, comprises the following steps:

The first step, determine that the encoding scheme of fuzzy Job-Shop is the coded system based on operation, each gene represents a procedure, identical symbol is specified to all process steps of same workpiece, for n × m fuzzy job shop scheduling of n workpiece m platform machine, comprise n × m gene in each chromosome, the symbol of each workpiece will occur m time in chromosome;

Second step, random generation initial population N, definition solution space;

3rd step, definition calculate individual fitness function;

4th step, when first time iteration, the initial fitness value of each individuality is exactly the optimum solution of this individuality, corresponding schedule sequences thinks that initial optimal sequence makes fuzzy completion date minimum, near every generation optimum solution, the size according to fitness value carries out clonal expansion operation, and fitness is higher, the number of individuals cloned is more, otherwise fitness is lower, then the individuality cloned is fewer;

5th step, by breeding after individuality independently carry out self-adaptation intersection and TSP question operation;

6th step, Immune Clone Selection operation is carried out to the individuality after crossover and mutation, generate new population N*;

If the 7th step meets maximum iteration time, then terminate; If do not meet, then turn back to the 3rd step and continue to perform downwards.

Preferably, described second step is specially:

Initialization chromosome population, parameter at least comprises: population scale, clone coefficient, adaptive crossover mutation and mutation probability, generation gap, maximum iteration time.

Preferably, described 3rd step is specially:

Select a function more adequately can reflect the quality of solution by the size of functional value, this function is fitness function; Fitness function is determined according to the objective function of optimization problem, and this fitness function adopts the inverse of the objective function in optimization problem and a constant c sum to represent.

Preferably, described 6th step comprises the following steps:

Step 6.1, after carrying out genetic manipulation, calculate the fitness value of each individuality, each father's individuality is cloned in the sub-individuality obtained, the individual Y that fitness is the highest _ieasily be preferred;

Step 6.2, utilization climbing update rule, by the antibody Y of certain probability P selected clone _ireplace father's antibody X _iif, clone body set Y _ithe fitness of middle optimum individual is than his father's antibody X _ifitness little, upgrade with probability 1, if the fitness of optimum filial generation is greater than its parent, upgrade with exponential type probability, to keep population diversity.

Preferably, in described step 6.2, in order to preserve the information of initial population, exponential function is not used in X ₁in generation, just can not be replaced for the optimum antibody in individuality.

The present invention is different from other single method, but a kind of new hybrid algorithm that self-adapted genetic algorithm is combined with clonal selection algorithm, there is the advantage of two kinds of algorithms.The present invention can reasonable distribution resource, shortens the fuzzy completion date of Job-Shop, improves the efficiency of job shop fuzzy scheduling, more realistic production scheduling.

Accompanying drawing explanation

Fig. 1 is algorithm flow chart of the present invention;

Fig. 2 is the objective function converges curve of 6 × 6 fuzzy scheduling problems;

Fig. 3 is the objective function converges curve of 10 × 10 fuzzy scheduling problems.

Embodiment

For making the present invention become apparent, hereby with preferred embodiment, and accompanying drawing is coordinated to be described in detail below.Should be understood that these embodiments are only not used in for illustration of the present invention to limit the scope of the invention.In addition should be understood that those skilled in the art can make various changes or modifications the present invention, and these equivalent form of values fall within the application's appended claims limited range equally after the content of having read the present invention's instruction.

The invention provides a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm, the steps include:

Step 1, determine to be specially the encoding scheme of fuzzy solve job shop scheduling problems:

Determine that the encoding scheme of fuzzy Job-Shop is the coded system based on operation, each gene represents a procedure, specifies identical decimal symbol to all process steps of same workpiece.For n × m fuzzy job shop scheduling of n workpiece m platform machine, comprise n × m gene in each chromosome, the symbol of each workpiece will occur m time in chromosome.

Step 2, random generation initial population N, definition solution space, is specially:

Initialization chromosome population, parameter comprises: the parameter such as population scale, clone coefficient, adaptive crossover mutation and mutation probability, generation gap, maximum iteration time.

Step 3, define and calculate individual fitness function, being specially:

Select a function can reflect the quality of solution comparatively accurately by the size of functional value; Fitness function is determined according to the objective function of optimization problem, and fitness value function adopts the inverse of the objective function in optimization problem and a constant c sum to represent herein.

Step 4, near every generation optimum solution, the size according to fitness value carries out clonal expansion operation to individuality, is specially:

When first time iteration, the initial fitness value of each individuality is exactly the optimum solution of this individuality, and corresponding schedule sequences thinks that initial optimal sequence makes fuzzy completion date minimum.Near every generation optimum solution, the size according to fitness value carries out clonal expansion operation, and fitness is higher, and the number of individuals cloned is more; Otherwise fitness is lower, then the individuality cloned is fewer.

Step 5, by breeding after individuality independently carry out adaptive crossover and mutation operation, be specially:

Individualities all after clonal expansion are carried out adaptive crossover and mutation operation independently.

Step 6, Immune Clone Selection operation is carried out to the individuality after crossover and mutation, generate new population N ^*, be specially:

After carrying out genetic manipulation, calculate the fitness value of each individuality, each father's individuality is cloned in the sub-individuality obtained, the individual Y that fitness is the highest _ieasily be preferred.Then, climbing update rule is utilized, by the antibody Y of certain probability P selected clone _ireplace father's antibody X _i.If clone body set Y _ithe fitness of middle optimum individual is than his father's antibody X _ifitness little, upgrade with probability 1.Consequently, the elite in offspring is saved, and enters into the next generation.In contrast, if the fitness of optimum filial generation is greater than its parent, upgrade with exponential type probability, to keep population diversity.In addition, in order to preserve the information of initial population, exponential function is not used in X ₁in generation, just can not be replaced for the optimum antibody in individuality.Carry out the Optimum Operation of next round.

If step 7 meets end condition, then circulate end; If do not meet, then turn back to step 3) continue to perform downwards, be specially: after meeting maximum iteration time, the optimal objective value that output function obtains, and corresponding optimal scheduling sequence and fuzzy scheduling completion date.

Composition graphs 1 to Fig. 3 and table 1, to table 6, for a certain job shop fuzzy scheduling model, applies said method.

1, parameter and variable-definition

(1) the individual workpiece set N to be processed of pa-rameter symbols definition: n _i(i=1,2 ..., n); M collection of machines: M _k(k=1,2 ..., m); P _ijrepresent workpiece N _ijth (j=1,2 ..., m) procedure; O _ijkrepresent P _ijat machine M _kupper processing, Triangular Fuzzy Number T _ijk=(t ¹ _ijk, t ² _ijk, t ³ _ijk) represent operation P _ijmachine M _kthe PROBLEMS WITH FUZZY PROCESSING TIMES of upper processing.Triangular Fuzzy Number T _ic=(t ¹ _ic, t ² _ic, t ³ _ic) represent workpiece N _ifuzzy completion date.

(2) objective function:

$T_c=(t_c^1,t_c^2{,t}_c^3)---\left(1\right)$

$f\left(\underset{\mathrm{\σ}\∈\mathrm{\Π}}{\mathrm{\σ}}\right)=\min \left({(a_1{t}_c^1+a_2{t}_c^2+a_3{t}_c^3)}_{\max }\right)---\left(2\right)$

Wherein (t in formula (1) ¹ _c, t ² _c, t ³ _c) be the fuzzy completion date of last procedure dispatched; α in formula (2) ₁, α ₂, a ₃a decimal between (0,1), be the fuzzy completion date of last procedure is done regular after numerical value; Formula (2) is objective function, and ∏ represents the feasible schedule set of workpiece, for a feasible scheduling σ ∈ ∏, makes f (σ) represent corresponding target function value.Target finds optimal sequencing σ ^*, make fuzzy completion date T _ccorresponding regular after numerical value T _maxminimum.

(3) constraint condition

S _ij≥S _i(j-i)+T _i(j-1)，i＝1，2，3，...n，j＝1，2，3，...m； (3)

M _ik≥M _(i-1)k+T _(i-1)k,i＝1，2，3，...n；k＝1，2，...m； (4)

S _ij≥0i＝1，2，3，...n；j＝1，2，...，m； (5)

Constraint (3) is constraint to work pieces process order, before representing the processing of any one workpiece face one procedure upon start, must first complete last procedure; Constraint (4) is constraint to machine, after representing on same machine that a processing tasks completes, could start another processing tasks; Constraint (5) is time-constrain, represents that the on-stream time of every procedure of each workpiece is necessarily more than or equal to zero.

(4) formula definition

$\tilde{A}+\tilde{B}=((a_1+b_1),(a_2+b_2),(a_3+b_3))---\left(6\right)$

$q_i=\mathrm{ceil}(a*\frac{f\left(i\right)}{{\mathrm{\Σ}}_{i=1}^{N}f\left(i\right)})---\left(8\right)$

$P_c=\left\{\begin{array}{cc}{P}_{c1}+\frac{k_1\&times;(f_{\max }-f_1)}{f_{\max }-f_{\mathrm{avg}}}& f_1\&GreaterEqual;f_{\mathrm{avg}}\\ k_2& f_1<f_{\mathrm{avg}}\end{array}\right.---\left(9\right)$

$P_m=\left\{\begin{array}{cc}{P}_{m1}+\frac{k_3\&times;(f_{\max }-f_2)}{f_{\max }-f_{\mathrm{avg}}}& f_2\&GreaterEqual;f_{\mathrm{avg}}\\ k_4& f_2<f_{\mathrm{avg}}\end{array}\right.---\left(10\right)$

$P_i=\left\{\begin{array}{cc}1& f\left(Y_i\right)<f\left(X_i\right)\\ \exp \left(\frac{f\left(X_i\right)-f\left(Y_i\right)}{k}\right)& f\left(Y_i\right)\&GreaterEqual;f\left(X_i\right)\\ 0& f\left(Y_1\right)\&le;f\left(X_1\right)\end{array}\right.---\left(11\right)$

Formula (6), (7) are the operations of fuzzy number, wherein: α (a ₁, a ₂, a ₃), b (b ₁, b ₂, b ₃) represent the triangle PROBLEMS WITH FUZZY PROCESSING TIMES of workpiece two procedures.In the research of problem, utilize the fuzzy of formula (7) to get large operation, determine the start time that workpiece operation is processed; Utilize the fuzzy add operation of formula (6) to determine the completion date of operation.Owing to being process time Triangular Fuzzy Number, so after suing for peace or getting large operation, the start time of its operation and completion date are also all fuzzy numbers.Formula (8) is individual clone's number when carrying out clone operations; Wherein: α is clone's coefficient, and f (i) is the fitness of chromosome i, and ceil () represents the number that rounds up.Maximum clone number q is set in literary composition _ifor: q _i< N/2, N are population size.Formula (9), (10) are the Adaptive Genetic crossover and mutation probability after improving; Wherein: k ₁, k ₂, k ₃, k ₄it is the constant between (0,1); f ₁for the larger fitness value in two individualities that will intersect, f ₂the individual fitness value that will make a variation, f _avgfor the average fitness often for colony, f _maxfor the maximum adaptation angle value in colony.P _c1for initial crossover probability, P _m1for initial mutation probability.Formula (11) utilizes climbing update rule, by certain probability P _ithe antibody Y of selected clone _ireplace father's antibody X _i.Wherein each father's individuality is cloned in the sub-individuality obtained, the individual Y that fitness is the highest _ieasily be preferred, that is: $Y_i=X_{i,j}={\min }_j\{f\left(X_{i,1}\right),...,f\left(X_{i,j}\right),...,f\left(X_{i,m_i}\right)\},$ K is the positive number relevant with diversity, k ∈ (10,100).

2, concrete solution procedure

(1) stochastic generation antibody population scale is N=100, population maximum iteration time is Nc=200; α in formula (2) ₁=0.25, α ₂=0.75, a ₃=0.25; In formula (8), clone's factor alpha is 50; Adaptive crossover mutation P in formula (9), (10) _c1initial value is 0.5, initial mutation probability P _m1be 0.1, constant k ₁=k ₂=0.5, k ₃=k ₄=0.2; K=80 in formula (11);

(2) fitness function is defined, i.e. the inverse of objective function (2) and a constant c sum in model, that is: 1/ (f (σ)+c), c=1.

(3) problem is encoded, generate initial population.Under the situation meeting constraint condition (3), (4), (5), problem is studied, when first time iteration, the initial fitness value of each individuality is exactly the optimum solution of this individuality, and corresponding schedule sequences thinks that initial optimal sequence makes fuzzy completion date minimum.

(4) near every generation optimum solution, the size according to fitness value carries out clonal expansion operation, and clone's rule of each individuality meets formula (8).Fitness is higher, and the number of individuals cloned is more; Otherwise fitness is lower, then the individuality cloned is fewer.Thus expand hunting zone, achieve the diversity of colony, contribute to preventing the precocity of evolution and search to be limited to local minimum.

(5) by individualities all after clonal expansion, according to formula (9), (10) of adaptive crossover mutation and mutation probability, independently adaptive crossover and mutation operation is carried out to individuality.Utilize this adaptive probability formula, when ideal adaptation angle value equals maximum adaptation angle value, also can carry out crossover and mutation operation by certain probability, thus improve the optimizing ability of algorithm, more easily jump out local optimum.

(6) after carrying out genetic manipulation, calculate the fitness value of each individuality, utilize climbing update rule (11), by certain probability P _ithe antibody Y of selected clone _ireplace father's antibody X _i.If clone body set Y _ithe fitness of middle optimum individual is than his father's antibody X _ifitness little, upgrade with probability 1.Consequently, the elite in offspring is saved, and enters into the next generation.In contrast, if the fitness of optimum filial generation is greater than its parent, upgrade with exponential type probability, to keep population diversity.In addition, in order to preserve the information of initial population, exponential function is not used in X ₁in generation, just can not be replaced for the optimum antibody in individuality.Immune Clone Selection operation can avoid the loss of effective gene, selects the chromosome that vitality is strong from current group, makes it have an opportunity to retain in order to raise up seed, thus convergence speedup speed and counting yield.

(7) repeated cloning breeding, genetic manipulation, Immune Clone Selection process, after meeting maximum iteration time, the optimal objective value that output function obtains, and corresponding optimal scheduling sequence.

According to specific embodiment, in fuzzy job shop scheduling process, use the method that the present invention proposes, i.e. the algorithm that combines of self-adapted genetic algorithm and clonal selection algorithm, to record and to filter out fitness value individual preferably.For simple genetic algorithm, although have stronger problem solving ability and stronger robustness, in the process solving fuzzy job shop scheduling, target solution is also easily made to be absorbed in local optimum.But add clonal selection algorithm in the self-adapted genetic algorithm improved, the speed that desired value is approached towards optimal value is accelerated, and towards optimum solution direction Population Regeneration, turn reduces the probability that population is absorbed in local optimum.Immune Clone Selection operates the detection and search dynamics that increase near more excellent solution, improves the operational efficiency of algorithm.In sum, the ability that the present invention jumps out local optimum is strong, and find the probability of optimum solution large, good stability, can effectively solve global optimum's problem.Self-adapted genetic algorithm combines with clone operations by the present invention, has the advantage of two kinds of algorithms.The present invention can reasonable distribution resource, shortens the fuzzy completion date of Job-Shop, improves the efficiency of job shop fuzzy scheduling, more realistic production scheduling.

Above describe ultimate principle of the present invention, feature and advantage.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Table 13 × 3 fuzzy scheduling process data

Table 26 × 6 fuzzy scheduling process data

Table 3 10 × 10 fuzzy scheduling process data

Table 43 × 3 fuzzy scheduling completion data

Table 56 × 6 fuzzy scheduling completion data

Table 6 10 × 10 fuzzy scheduling completion data

Claims (5)

1., based on a fuzzy job shop scheduling method for Adaptive Genetic and clonal selection algorithm, it is characterized in that, comprise the following steps:

The first step, determine that the encoding scheme of fuzzy Job-Shop is the coded system based on operation, each gene represents a procedure, identical symbol is specified to all process steps of same workpiece, for n × m fuzzy job shop scheduling of n workpiece m platform machine, comprise n × m gene in each chromosome, the symbol of each workpiece will occur m time in chromosome;

Second step, random generation initial population N, definition solution space;

3rd step, definition calculate individual fitness function;

4th step, when first time iteration, the initial fitness value of each individuality is exactly the optimum solution of this individuality, corresponding schedule sequences thinks that initial optimal sequence makes fuzzy completion date minimum, near every generation optimum solution, the size according to fitness value carries out clonal expansion operation, and fitness is higher, the number of individuals cloned is more, otherwise fitness is lower, then the individuality cloned is fewer;

5th step, by breeding after individuality independently carry out self-adaptation intersection and TSP question operation;

6th step, Immune Clone Selection operation is carried out to the individuality after crossover and mutation, generate new population N*;

If the 7th step meets maximum iteration time, then terminate; If do not meet, then turn back to the 3rd step and continue to perform downwards.

2. a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm as claimed in claim 1, it is characterized in that, described second step is specially:

Initialization chromosome population, parameter at least comprises: population scale, clone coefficient, adaptive crossover mutation and mutation probability, generation gap, maximum iteration time.

3. a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm as claimed in claim 1, it is characterized in that, described 3rd step is specially:

Select a function more adequately can reflect the quality of solution by the size of functional value, this function is fitness function; Fitness function is determined according to the objective function of optimization problem, and this fitness function adopts the inverse of the objective function in optimization problem and a constant c sum to represent.

4. a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm as claimed in claim 1, it is characterized in that, described 6th step comprises the following steps:

Step 6.1, after carrying out genetic manipulation, calculate the fitness value of each individuality, each father's individuality is cloned in the sub-individuality obtained, the individual Y that fitness is the highest _ieasily be preferred;

Step 6.2, utilization climbing update rule, by the antibody Y of certain probability P selected clone _ireplace father's antibody X _iif, clone body set Y _ithe fitness of middle optimum individual is than his father's antibody X _ifitness little, upgrade with probability 1, if the fitness of optimum filial generation is greater than its parent, upgrade with exponential type probability, to keep population diversity.

5. a kind of fuzzy job shop scheduling method based on Adaptive Genetic and clonal selection algorithm as claimed in claim 4, it is characterized in that, in described step 6.2, in order to preserve the information of initial population, exponential function is not used in X ₁in generation, just can not be replaced for the optimum antibody in individuality.