CN101859100A - Improved particle swarm optimization method based on streamline production scheduling of fuzzy due date - Google Patents

Abstract

The invention relates to an improved particle swarm optimization method based on flow production scheduling of a fuzzy due date. The optimal solution of the existing algorithm can not be found easily. The method comprises the following steps: using the penalty function for neighborhood block design of key lines based on the needs of the flow shop scheduling of the fuzzy due date, establishing a taboo table, and adopting the neighborhood search strategy, thereby enhancing the effect of optimal solution of the improved particle swarm algorithm. Since the stagnation can easily occur to the particle swarm optimization, the concepts of exchange operators and exchange sequences are introduced to reconstruct the particle location formula and the speed optimization formula of the particle swarm optimization, and the introduction of the taboo search algorithm helps the particle swarm optimization to search the best solution in the local area. Simulation experiments on the flow production scheduling of the fuzzy due date demonstrate that the improved particle swarm optimization method facilitates the overall solution.

Description

A kind of improvement particle swarm optimization method based on streamline production scheduling of fuzzy due date

Technical field

The invention belongs to information and control technology field, relate to a kind of improved particle swarm optimization algorithm.

Background technology

Along with being growing more intense of market competition, production, the operation and management efficient of production operation management mode preferably with raising enterprise is all being sought by each enterprise, thereby improves Enterprises'Competitiveness.And whole advanced production manufacturing system realizes that the core of administrative skill, optimisation technique, robotization and technical development of computer is the production scheduling problem.The production scheduling problem is the processing sequence of research workpiece on machine, the problem that production lot is divided, therefore, it be with the asymmetric situation in city under the suitable quasi-representative NP difficult problem of traveling salesman problem (TSP) difficulty, the scope of its research specifically comprises Job Shop Scheduling problem, Flow Shop scheduling problem and flexible solve job shop scheduling problems etc.These problems all have the characteristics that complex uncertainty, hierarchical structure, multiple goal, multiple constraint, many resources are coordinated mutually.Therefore, the production scheduling problem has been subjected to the extensive concern of academia and industry member, its research is not only had huge realistic meaning, and have the important in theory meaning.

Particle swarm optimization (Particle Swarm Optimization, PSO) a kind of novel Swarm Intelligent Algorithm that is proposed jointly in nineteen ninety-five by psychologist James Kennedy of American society and electrical engineers Russell Eberhart, it has, and overall performance is good, the search efficiency advantages of higher.Particle swarm optimization keeps simultaneously during evolution and utilizes information on the Position And Velocity, has bigger advantage and feasibility than other optimized Algorithm in the problem searching process.Therefore, the appearance of particle swarm optimization provides strong instrument for numerous areas solves complicated optimum problem.But particle swarm optimization also has in the actual optimization process and is absorbed in local extremum, the situation of evolving not to the optimum solution direction, thus make whole computing present precocious phenomenon.

Summary of the invention

The objective of the invention is according to ubiquitous uncertain factor in the actual production scheduling problem, a kind of improvement particle swarm optimization method based on streamline production scheduling of fuzzy due date is provided.

The inventive method is at the needs of Fuzzy Due Dates flowing water type Workshop Production scheduling problem, operation piece on the critical path is carried out the part coupling intersect and mutation operation, effect is found the solution in the optimization that the use penalty is set up the taboo table and adopted tabu search strategy to improve particle swarm optimization.A difficult problem that occurs stagnation behavior at the particulate algorithm easily, the notion of introducing recon and switching sequence is reconstructed the particle position and the speed-optimization formula of particle swarm optimization, and the introducing of tabu search algorithm then helps particle swarm optimization in the local area search optimum solution.By emulation experiment, proved that improving particle swarm optimization helps obtaining of overall importance separating to flowing water production scheduling problem with Fuzzy Due Dates.

The inventive method comprises the steps:

Step 1. is encoded particle.

Separate for one in the expression solve job shop scheduling problems,

Wherein n represents the dimension that particle has in the population,

The positional value in represent i particle in evolution k generation, if

Be illustrated in k and on j platform machine, do not process for particle i (workpiece), if

Being illustrated in k processes on j platform machine for particle i (workpiece); Represent i particle evolve to k for the time speed, k is an iterations; The desired positions of the individual experience of particulate is designated as P _Best, the desired positions of whole colony particulate experience is designated as G _Best

The definite workpiece of step 2. is finished the objective function of phase.

The completion date of workpiece and main-process stream time blur in the Fuzzy Due Dates Flow-shop problem.One group of n workpiece processing continuously is called a continuous workpiece collection, P _{I, j}The PROBLEMS WITH FUZZY PROCESSING TIMES of expression workpiece i on machine j, d _iThe delivery date of expression workpiece i, C _{I, j}The fuzzy completion date of expression workpiece collection is be exactly total the completion date that the objective function of streamline production scheduling of fuzzy due date problem makes is the shortest.

$\mathrm{Min}{C}_{i,j}=\left\{\begin{array}{c}{C}_{i,j}=C_{i-1,j}+P_{i,j}\\ C_{i,j}=\max (C_{i,j-1},C_{i-1,j})+P_{i,j}\end{array}\right.---\left(1\right)$

Its delay time and pre-set time are respectively:

$T\left[C_{j,i}\right]=\max \{0,\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{C}_{j,1}-d\}\≥0,E\left[C_{j,i}\right]=\max \{0,d-\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{C}_{j,1}\}\≥0---\left(2\right)$

The E/T index can be described below: Min E/T _Max=Max{ β E[C _{J, i}]+γ T[C _{J, i}] (3)

Wherein beta, gamma is the non-negative weighting penalty coefficient of completion of completing in advance delivery date and delay, to by n continuous workpiece collection B ₁, B ₂..., B _nThe scheduling scheme that constitutes, continuous workpiece collection B _nTotal penalty can be expressed as:

$Z_j\left(x\right)=\underset{j=1}{\overset{\mathrm{Bn}}{\mathrm{\Σ}}}{g}_j\left(c_j\right)=\underset{j\∈B1}{\mathrm{\Σ}}{g}_j\left(c_j\right)+\underset{j\∈B2}{\mathrm{\Σ}}{g}_j\left(c_j\right)+...+\underset{j\∈\mathrm{Bn}}{\mathrm{\Σ}}{g}_j\left(c_j\right)---\left(4\right)$

Function Z _j(x) be a continuous linear segmented convex function, the slope of each section is by continuous workpiece collection B _nThe phase penalty coefficient that shift to an earlier date/drags of middle workpiece determines.

Step 3. reconstruct particle swarm optimization position and speed calculation formula.

Recon FO (α _i, α _J) represent exchange to separate machine α among the S _iAnd α _JPut in order.One or more recon FO ₁, FO ₂..., FO _nOrderly formation be exactly switching sequence, note is made FS=(FO ₁, FO ₂..., FO _n).Switching sequence acts on scheduling and separates and mean that all recons act on this successively in the switching sequence and separate, i.e. F '=F+FS=F+ (FO ₁, FO ₂..., FO _n)=[(F+FO ₁)+FO ₂]+...+FO _nSeveral switching sequences can be merged into a switching sequence set.In the switching sequence set, the switching sequence that has minimum recon is called basic switching sequence, with operational character " ⊕ " expression.

The position and the speed calculation formula of PSO algorithm are re-constructed:

V _id(t+1)＝ωV _id(t)⊕(1-α)(P _id(t)-X _id(t))⊕(1-β)(P _gd(t)-X _id(t)) (5)

X _id(t+1)＝X _id(t)+V _id(t+1) (6)

Local exchange sequence S to individual particles and population particulate discovery in formula (5) and (6) _Jk, calculate penalty Z according to formula (2) respectively _j(x) slope is determined parameter alpha, the value of β.If (1-α) value is big, then (P _Id-X _Id) in the operation piece that keeps just many, P _IdJust big to the speed influence; If (1-β) value is big, (P _Gd-X _Id) in the operation that keeps many, P then _GdBigger to the speed influence.

Operation path on the step 4. pair critical path is carried out the part coupling and is intersected and mutation operation.

For Fuzzy Due Dates Flow Shop scheduling problem, adopt part coupling intersection PMX operation the carrying out ordering of the processing sequence of part on machine.A matching section is determined in two point of crossing of picked at random, and it is individual that the mapping relations that provide according to the interlude between two point of crossing in two father's individualities generate two sons.As to the individual P of following two fathers ₁And P ₂, select two point of crossing " | " randomly.

P ₁：{1?2?3?|?4?5?6?7?|?8?9} P ₂：{4?5?2?|?1?8?7?6?|?9?3}

To the exchange of the interlude between two point of crossing, obtain sub individual O ₁And O ₂:

O ₁：{x?x?x?|?1?8?7?6?|?x?x} O ₂：{x?x?x?|?4?5?6?7?|?x?x}

Wherein x represents temporary undefined OP code, obtains the mapping relations of interlude: 1 ← → 45 ← → 86 ← → 7, according to the mapping relations of interlude, carry out conversion at last to remaining individuality.

O ₁：{4?2?3?|?1?8?7?6?|?5?9} O ₂：{1?8?2?|?4?5?6?7?|?9?3}

Add variation mechanism on the basis of original PSO algorithm, adopt the variation of single-point and multiple spot position alternate form, replace a certain position or some locational gene with another kind of gene, formula is as follows:

mut(x _id)＝x _id×(1+uniform(μ)) (7)

Mut (x wherein _Id) being the position of variation back particulate, uniform (μ) is a uniformly distributed function, and the component of all positions of population is carried out the variation that average length is n * m * μ.The location components of variation is randomly drawed.If population x _Id={ among 123454 3}, the location components d of selected variation is 2 and 3, gets x _I2=3, x _I3=4, back x then makes a variation _Id={ 124354 3}.

It is very effective finding the neighborhood set in the operation path on the critical path by this method.

Step 5. is set up the taboo table and is strengthened the optimization Algorithm effect.

The topmost characteristics of tabu search are to have introduced memory function, and the taboo table is the memory storage that is used for depositing T search procedure resume.

Make T={T ₁, T ₂..., T _LtbBe that a length is L _TbThe taboo table, T wherein _iBe the forbidden 1≤i≤L that moves _TbInitial taboo table is empty table, i.e. a T _i=0, and 0}, (x y) joins among the taboo table T in the following manner: be moved to the left a step the element among the table T is whole, thereby the element that is in primary importance among the table T is extruded, and has been disengaged the taboo state, make L for mobile v= _TbThe position is empty, then mobile v with

Form put into the table T L _TbThe position.

Be called mobile v=(x, inverse move y).In case mobile v=(x, y) be performed after, it just is added in the taboo table, becomes the taboo state.This procedural representation is T=T ⊕ v.Taboo table T is recycled by rolling in algorithm, and each new mobile v is added to the rearmost position of taboo table T.

Step 6. tabu search strategy.

If S is a critical path, V (s) is a mobile set, and H (s) is a neighborhood, and C is the best desired value of up to the present finding, is this process sequence and completes at last last one manufacturing procedure process finishing time of workpiece.Suppose and move set V (s), then can be divided three classes: do not forbid moving (U) moving among the V (s) not for empty; Be under an embargo, but useful (F _P); Be under an embargo, but unhelpful (F _n).Be expressed as with mathematical expression: do not forbid that mobile U is defined as V (s)/T, and mobile V (s) the ∩ T that is defined as of taboo.F _PBe defined as D={v ∈ V (s) ∩ T:C _Max＜C}.F _nBe defined as (V (s) ∩ T)/F _p

Obviously, from U and F _PIt is very natural that middle choosing is moved.There not being the U mobile set, do not have under the situation of FP mobile set yet, if V (s) only comprises single moving, select so and should move.If V (s) comprises a plurality of moving, the step process of Xuan Zeing is so:

Revise the taboo table and repeat T=T ⊕ T _Ltb, up to V (s)/T ≠ θ.T wherein _LtbRepresent to be in L in the former taboo table _TbThe element of position, V (s)/T represents the U mobile set.

If V` is selected moving, the critical path of s` for upgrading, the taboo table of T` for upgrading, (s v) is initial sequencing schemes to Q, and (s` v`) is the sequencing schemes after moving to Q.

The dynamic setting of step 7. inertia weight.

Inertia weight (W) is the important parameter that is related to particle swarm optimization speed of convergence and search capability, therefore considers variable W is dynamically changed the weights size according to the situation of searching for.Adjust strategy and be by with individual particles adaptive value f (x _i) and the current optimal target value f (GB of colony ^k) relatively, if f is (x _i)＞f (GB ^k) then to adjust W be a less value, algorithm enters the Local Search state.If f is (x _i)＜f (GB ^k), then adjusting W is a bigger value, increases the search capability of algorithm.By calculating particulate group's adaptive value,

Represent that i particle evolves to k for the desired positions that is experienced, GB ^kRepresent that whole population evolves to the desired positions that k generation experienced.

GB ^kCan calculate by formula (8), (9), when k=0

${\mathrm{PB}}_i^k=\left\{\begin{array}{cc}{\mathrm{PB}}_i^{k-1}& \mathrm{if\; f}\left(x_i^k\right)>f\left({\mathrm{PB}}_i^{k-1}\right)\\ p_i^k& \mathrm{Otherwise}\end{array}\right.---\left(8\right)$

${\mathrm{GB}}^k=\max \left({\mathrm{PB}}_i^k\right),k=\mathrm{1,2}\·\·\·,n---\left(9\right)$

The inertia weight value is progressively adjusted its value from big to small in 0＜W≤1 scope, thus make the algorithm search space by the overall situation to the part steadily excessively.

The present invention is directed to and occur " precocity " phenomenon in the swarm optimization algorithm process easily, the notion of proposition use recon and switching sequence is reconstructed the particle position and the speed-optimization formula of particle swarm optimization, methods such as tabu search improve the ability that particle swarm optimization is jumped out locally optimal solution, have strengthened the search capability of algorithm acquisition globally optimal solution.

Embodiment

A kind of improvement particle swarm optimization method based on production scheduling comprises the steps:

Step 1. is encoded particle.

Separate for one in the expression solve job shop scheduling problems, Wherein n represents the dimension that particle has in the population,

The positional value in represent i particle in evolution k generation, if

Be illustrated in k and on j platform machine, do not process for particle i (workpiece), if

Being illustrated in k processes on j platform machine for particle i (workpiece);

Represent i particle evolve to k for the time speed, k is an iterations; The desired positions of the individual experience of particulate is designated as P _Best, the desired positions of whole colony particulate experience is designated as G _Best

The definite workpiece of step 2. is finished the objective function of phase.

The completion date of workpiece and main-process stream time blur in the Fuzzy Due Dates Flow-shop problem.One group of n workpiece processing continuously is called a continuous workpiece collection, p _{I, j}The PROBLEMS WITH FUZZY PROCESSING TIMES of expression workpiece i on machine j, d _iThe delivery date of expression workpiece i, C _{I, j}The fuzzy completion date of expression workpiece collection is be exactly total the completion date that the objective function of streamline production scheduling of fuzzy due date problem makes is the shortest.

$\mathrm{Min}{C}_{i,j}=\left\{\begin{array}{c}{C}_{i,j}=C_{i-1,j}+P_{i,j}\\ C_{i,j}=\max (C_{i,j-1},C_{i-1,j})+P_{i,j}\end{array}\right.---\left(1\right)$

Its delay time and pre-set time are respectively:

$T\left[C_{j,i}\right]=\max \{0,\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{C}_{j,1}-d\}\≥0,E\left[C_{j,i}\right]=\max \{0,d-\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{C}_{j,1}\}\≥0---\left(2\right)$

The E/T index can be described below: Min E/T _Max=Max{ β E[C _{J, i}]+γ T[C _{J, i}] (3)

Wherein beta, gamma is the non-negative weighting penalty coefficient of completion of completing in advance delivery date and delay, to by n continuous workpiece collection B ₁, B ₂..., B _nThe scheduling scheme that constitutes, continuous workpiece collection B _nTotal penalty can be expressed as:

$Z_j\left(x\right)=\underset{j=1}{\overset{\mathrm{Bn}}{\mathrm{\Σ}}}{g}_j\left(c_j\right)=\underset{j\∈B1}{\mathrm{\Σ}}{g}_j\left(c_j\right)+\underset{j\∈B2}{\mathrm{\Σ}}{g}_j\left(c_j\right)+...+\underset{j\∈\mathrm{Bn}}{\mathrm{\Σ}}{g}_j\left(c_j\right)---\left(4\right)$

Function Z _j(x) be a continuous linear segmented convex function, the slope of each section is by continuous workpiece collection B _nThe phase penalty coefficient that shift to an earlier date/drags of middle workpiece determines.

Step 3. reconstruct particle swarm optimization position and speed calculation formula.

Recon FO (α _i, α _J) represent exchange to separate machine α among the S _iAnd α _JPut in order.One or more recon FO ₁, FO ₂..., FO _nOrderly formation be exactly switching sequence, note is made FS=(FO ₁, FO ₂..., FO _n).Switching sequence acts on scheduling and separates and mean that all recons act on this successively in the switching sequence and separate, i.e. F '=F+FS=F+ (FO ₁, FO ₂..., FO _n)=[(F+FO ₁)+FO ₂]+...+FO _nSeveral switching sequences can be merged into a switching sequence set.In the switching sequence set, the switching sequence that has minimum recon is called basic switching sequence, with operational character " ⊕ " expression.

The position and the speed calculation formula of PSO algorithm are re-constructed:

V _id(t+1)＝ωV _id(t)⊕(1-α)(P _id(t)-X _id(t))⊕(1-β)(P _gd(t)-X _id(t)) (5)

X _id(t+1)＝X _id(t)+V _id(t+1) (6)

Local exchange sequence S to individual particles and population particulate discovery in formula (5) and (6) _Jk, calculate penalty Z according to formula (2) respectively _j(x) slope is determined parameter alpha, the value of β.If (1-α) value is big, then (P _Id-X _Id) in the operation piece that keeps just many, P _IdJust big to the speed influence; If (1-β) value is big, (P _Gd-X _Id) in the operation that keeps many, P then _GdBigger to the speed influence.

Operation path on the step 4. pair critical path is carried out the part coupling and is intersected and mutation operation.

For Fuzzy Due Dates Flow Shop scheduling problem, adopt part coupling intersection PMX operation the carrying out ordering of the processing sequence of part on machine.A matching section is determined in two point of crossing of picked at random, and it is individual that the mapping relations that provide according to the interlude between two point of crossing in two father's individualities generate two sons.As to the individual P of following two fathers ₁And P ₂, select two point of crossing " | " randomly.

P ₁：{1?2?3?|?4?5?6?7?|?8?9} P ₂：{4?5?2?|?1?8?7?6?|?9?3}

To the exchange of the interlude between two point of crossing, obtain sub individual O ₁And O ₂:

O ₁：{x?x?x?|?1?8?7?6?|?x?x} O ₂：{x?x?x?|?4?5?6?7?|?x?x}

Wherein x represents temporary undefined OP code, obtains the mapping relations of interlude: 1 ← → 45 ← → 86 ← → 7, according to the mapping relations of interlude, carry out conversion at last to remaining individuality.

O ₁：{4?2?3?|?1?8?7?6?|?5?9} O ₂：{1?8?2?|?4?5?6?7?|?9?3}

Add variation mechanism on the basis of original PSO algorithm, adopt the variation of single-point and multiple spot position alternate form, replace a certain position or some locational gene with another kind of gene, formula is as follows:

mut(x _id)＝x _id×(1+uniform(μ)) (7)

Mut (x wherein _Id) being the position of variation back particulate, uniform (μ) is a uniformly distributed function, and the component of all positions of population is carried out the variation that average length is n * m * μ.The location components of variation is randomly drawed.If population x _Id={ among 123454 3}, the location components d of selected variation is 2 and 3, gets x _I2=3, x _I3=4, back x then makes a variation _Id={ 124354 3}.

It is very effective finding the neighborhood set in the operation path on the critical path by this method.

Step 5. is set up the taboo table and is strengthened the optimization Algorithm effect.

The topmost characteristics of tabu search are to have introduced memory function, and the taboo table is the memory storage that is used for depositing T search procedure resume.

Make T={T ₁, T ₂..., T _LtbBe that a length is L _TbThe taboo table, T wherein _iBe the forbidden 1≤i≤L that moves _TbInitial taboo table is empty table, i.e. a T _i=0, and 0}, (x y) joins among the taboo table T in the following manner: be moved to the left a step the element among the table T is whole, thereby the element that is in primary importance among the table T is extruded, and has been disengaged the taboo state, make L for mobile v= _TbThe position is empty, then mobile v with

Form put into the table T L _TbThe position.

Be called mobile v=(x, inverse move y).In case mobile v=(x, y) be performed after, it just is added in the taboo table, becomes the taboo state.This procedural representation is T=T ⊕ v.Taboo table T is recycled by rolling in algorithm, and each new mobile v is added to the rearmost position of taboo table T.

Step 6. tabu search strategy.

If S is a critical path, V (s) is a mobile set, and H (s) is a neighborhood, and C is the best desired value of up to the present finding, is this process sequence and completes at last last one manufacturing procedure process finishing time of workpiece.Suppose and move set V (s), then can be divided three classes: do not forbid moving (U) moving among the V (s) not for empty; Be under an embargo, but useful (F _P); Be under an embargo, but unhelpful (F _n).Be expressed as with mathematical expression: do not forbid that mobile U is defined as V (s)/T, and mobile V (s) the ∩ T that is defined as of taboo.F _PBe defined as D={v ∈ V (s) ∩ T:C _Max＜C}.F _nBe defined as (V (s) ∩ T)/F _p

Obviously, from U and F _PIt is very natural that middle choosing is moved.There not being the U mobile set, do not have under the situation of FP mobile set yet, if V (s) only comprises single moving, select so and should move.If V (s) comprises a plurality of moving, the step process of Xuan Zeing is so:

Revise the taboo table and repeat T=T ⊕ T _Ltb, up to V (s)/T ≠ θ.T wherein _LtbRepresent to be in L in the former taboo table _TbThe element of position, V (s)/T represents the U mobile set.

If V` is selected moving, the critical path of s` for upgrading, the taboo table of T` for upgrading, (s v) is initial sequencing schemes to Q, and (s` v`) is the sequencing schemes after moving to Q.

The dynamic setting of step 7. inertia weight.

Inertia weight (W) is the important parameter that is related to particle swarm optimization speed of convergence and search capability, therefore considers variable W is dynamically changed the weights size according to the situation of searching for.Adjust strategy and be by with individual particles adaptive value f (x _i) and the current optimal target value f (GB of colony ^k) relatively, if f is (x _i)＞f (GB ^k) then to adjust W be a less value, algorithm enters the Local Search state.If f is (x _i)＜f (GB ^k), then adjusting W is a bigger value, increases the search capability of algorithm.By calculating particulate group's adaptive value,

Represent that i particle evolves to k for the desired positions that is experienced, GB ^kRepresent that whole population evolves to the desired positions that k generation experienced. GB ^kCan calculate by formula (8), (9), when k=0

${\mathrm{PB}}_i^k=\left\{\begin{array}{cc}{\mathrm{PB}}_i^{k-1}& \mathrm{if\; f}\left(x_i^k\right)>f\left({\mathrm{PB}}_i^{k-1}\right)\\ p_i^k& \mathrm{Otherwise}\end{array}\right.---\left(8\right)$

${\mathrm{GB}}^k=\max \left({\mathrm{PB}}_i^k\right),k=\mathrm{1,2}\·\·\·,n$ (9)

The inertia weight value is progressively adjusted its value from big to small in 0＜W≤1 scope, thus make the algorithm search space by the overall situation to the part steadily excessively.

The present invention proposes the Flow Shop scheduling problem that improved particle swarm optimization is found the solution Fuzzy Due Dates, intersect and mutation operation by the operation piece on the critical path being carried out the part coupling, effect is found the solution in the optimization of using penalty to set up the taboo table and adopting tabu search strategy to improve particle swarm optimization, improve production of machinery scheduling efficient, reduced the production cost of enterprise.

Claims (1)

1. the improvement particle swarm optimization method based on streamline production scheduling of fuzzy due date is characterized in that this method comprises the steps:

Step 1. is encoded particle;

Separate for one in the expression solve job shop scheduling problems,

Wherein n represents the dimension that particle has in the population, The positional value in represent i particle in evolution k generation,

Be illustrated in k and on j platform machine, do not process for particle i,

Being illustrated in k processes on j platform machine for particle i;

Represent i particle evolve to k for the time speed, k is an iterations; The desired positions of the individual experience of particulate is designated as P _Best, the desired positions of whole colony particulate experience is designated as G _Best

The definite workpiece of step 2. is finished the objective function of phase;

The completion date of workpiece and main-process stream time blur in the Fuzzy Due Dates Flow-shop problem, and one group of n workpiece processing continuously is called a continuous workpiece collection, p _{I, j}The PROBLEMS WITH FUZZY PROCESSING TIMES of expression workpiece i on machine j, d _iThe delivery date of expression workpiece i, C _{I, j}The fuzzy completion date of expression workpiece collection, be exactly total the completion date that the objective function of streamline production scheduling of fuzzy due date problem makes is the shortest,

$\mathrm{Min}{C}_{i,j}=\left\{\begin{array}{c}{C}_{i,j}=C_{i-1,j}+P_{i,j}\\ C_{i,j}=\max (C_{i,j-1},C_{i-1,j})+P_{i,j}\end{array}\right.---\left(1\right)$

Its delay time and pre-set time are respectively:

$T\left[c_{j,i}\right]=\max \{0,\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{c}_{j,1}-d\}\≥0,E\left[c_{j,i}\right]=\max \{0,d-\underset{l=1}{\overset{i}{\mathrm{\Σ}}}{c}_{j,1}\}\≥0---\left(2\right)$

The E/T index can be described below: Min E/T _Max=Max{ β E[c _{J, i}]+γ T[c _{J, i}] (3)

Wherein beta, gamma is expressed as the non-negative weighting coefficient of punishment of the completion of completing in advance delivery date and delay respectively, to by n continuous workpiece collection B ₁, B ₂..., B _nThe scheduling scheme that constitutes, continuous workpiece collection B _nTotal penalty is expressed as:

$Z_j\left(x\right)=\underset{j=1}{\overset{\mathrm{Bn}}{\mathrm{\Σ}}}{g}_j\left(c_j\right)=\underset{j\∈B1}{\mathrm{\Σ}}{g}_j\left(c_j\right)+\underset{j\∈B2}{\mathrm{\Σ}}{g}_j\left(c_j\right)+...+\underset{j\∈\mathrm{Bn}}{\mathrm{\Σ}}{g}_j\left(c_j\right)---\left(4\right)$

Function Z _i(x) be a continuous linear segmented convex function, the slope of each section is by continuous workpiece collection B _nThe phase penalty coefficient that shift to an earlier date/drags of middle workpiece determines;

Step 3. reconstruct particle swarm optimization evolutionary equation;

Recon FO (α _i, α _J) represent exchange to separate machine α among the S _iAnd α _JPut in order one or more recon FO ₁, FO ₂..., FO _nOrderly formation be exactly switching sequence, note is made FS=(FO ₁, FO ₂..., FO _n), switching sequence acts on scheduling and separates and mean that all recons act on this successively in the switching sequence and separate, i.e. F '=F+FS=F+ (FO ₁, FO ₂..., FO _n)=[(F+FO ₁)+FO ₂]+... + FO _n, several switching sequences can be merged into a switching sequence set, and in the switching sequence set, the switching sequence that has minimum recon is called basic switching sequence, with operational character " ⊕ " expression;

The evolutionary equation of PSO algorithm is re-constructed:

V _id(t+1)＝ωV _id(t)⊕(1-α)(P _id(t)-X _id(t))⊕(1-β)(P _gd(t)-X _id(t)) (5)

X _id(t+1)＝X _id(t)+V _id(t+1) (6)

Local exchange sequence S to individual particles and population particulate discovery in formula (5) and (6) _Jk, calculate penalty Z according to formula (2) respectively _j(x) slope is determined parameter alpha, the value of β; If (1-α) value is big, then (P _Id-X _Id) in the operation piece that keeps just many, P _IdJust big to the speed influence; If (1-β) value is big, (P _Gd-X _Id) in the operation that keeps many, P then _GdBigger to the speed influence;

Operation path on the step 4. pair critical path is carried out the part coupling and is intersected and mutation operation;

For Fuzzy Due Dates Flow Shop scheduling problem, adopt part coupling intersection PMX operation the carrying out ordering of the processing sequence of part on machine, a matching section is determined in two point of crossing of picked at random, and it is individual that the mapping relations that provide according to the interlude between two point of crossing in two father's individualities generate two sons;

Step 5. is set up the taboo table and is strengthened the optimization Algorithm effect; The taboo table is the memory storage that is used for depositing T search procedure resume;

Make T={T ₁, T ₂..., T _LtbBe that a length is L _TbThe taboo table, T wherein _iBe the forbidden 1≤i≤L that moves _TbInitial taboo table is empty table, i.e. a T _i=0, and 0}, (x y) joins among the taboo table T in the following manner: be moved to the left a step the element among the table T is whole, thereby the element that is in primary importance among the table T is extruded, and has been disengaged the taboo state, make L for mobile v= _TbThe position is empty, then mobile v with

Form put into the table T L _TbThe position;

Be called mobile v=(x, inverse move y), in case mobile v=(x, y) be performed after, it just is added in the taboo table, becomes the taboo state, this procedural representation is T=T ⊕ v; Taboo table T is recycled by rolling in algorithm, and each new mobile v is added to the rearmost position of taboo table T;

Step 6. neighborhood search strategy;

If S is a critical path, V (s) is a mobile set, and H (s) is a neighborhood, and C is the best desired value of up to the present finding, is this process sequence and completes at last last one manufacturing procedure process finishing time of workpiece; Suppose and move set V (s), then be divided three classes: do not forbid moving (U) moving among the V (s) not for empty; Be under an embargo, but useful (F _P); Be under an embargo, but unhelpful (F _n), be expressed as with mathematical expression: do not forbid that mobile U is defined as V (s)/T, and mobile V (s) the ∩ T that is defined as of taboo, F _PBe defined as D={v ∈ V (s) ∩ T:C _Max＜C}, F _nBe defined as (V (s) ∩ T)/F _p

There not being the U mobile set, do not have under the situation of FP mobile set yet, if V (s) only comprises single moving, select so and should move, if V (s) comprises a plurality of moving, the step process of Xuan Zeing is so:

Revise the taboo table and repeat T=T ⊕ T _Ltb, up to V (s)/T ≠ θ, wherein T _LtbRepresent to be in L in the former taboo table _TbThe element of position, V (s)/T represents the U mobile set;

If V` is selected moving, the critical path of s` for upgrading, the taboo table of T` for upgrading, (s v) is initial sequencing schemes to Q, and (s` v`) is the sequencing schemes after moving to Q;

The dynamic setting of step 7. inertia weight;

Inertia weight W is the important parameter that is related to particle swarm optimization speed of convergence and search capability, therefore considers variable W is dynamically changed the weights size according to the situation of searching for; Adjust strategy and be by with individual particles adaptive value f (x _i) and the current optimal target value f (GB of colony ^k) relatively, if f is (x _i)＞f (GB ^k) then to adjust W be a less value, algorithm enters the Local Search state; If f is (x _i)＜f (GB ^k), then adjusting W is a bigger value, increases the search capability of algorithm; By calculating particulate group's adaptive value,

Represent that i particle evolves to k for the desired positions that is experienced, GB ^kRepresent that whole population evolves to the desired positions that k generation experienced;

GB ^kCan calculate by formula (8), (9), when k=0

${\mathrm{PB}}_i^k=\left\{\begin{array}{cc}{\mathrm{PB}}_i^{k-1}& \mathrm{if\; f}\left(x_i^k\right)>f\left({\mathrm{PB}}_i^{k-1}\right)\\ p_i^k& \mathrm{Otherwise}\end{array}\right.---\left(8\right)$

${\mathrm{GB}}^k=\max \left({\mathrm{PB}}_i^k\right),k=\mathrm{1,2}\·\·\·,n---\left(9\right)$

The inertia weight value is progressively adjusted its value from big to small in 0＜W≤1 scope, thus make the algorithm search space by the overall situation to the part steadily excessively.