阅读说明：本技术 一种基于机器速度缩放的作业车间调度风险优化方法 (Job shop scheduling risk optimization method based on machine speed scaling ) 是由 吴自高 慈铁军 于 2021-07-26 设计创作，主要内容包括：本发明公开了一种基于机器速度缩放的作业车间调度风险优化方法,步骤如下：步骤1,设置调度问题信息；步骤2,种群初始化；步骤3,当chr1＜N-(p)时,重复执行以下步骤生成临时新种群P-(tmp)；步骤4,合并种群P-(com)＝P-(cur)∪P-(tmp),并进行适应度评价；步骤5,种群更新；步骤6：结束条件判断。本发明方法采用了双矢量染色体编码和基于速度缩放的受影响工序修复步骤,可以获得在调度性能或调度风险目标上更优的调度方案,从而更好地满足作业车间调度对调度性能和风险的要求。(The invention discloses a job shop scheduling risk optimization method based on machine speed scaling, which comprises the following steps: step 1, setting scheduling problem information; step 2, initializing a population; step 3, when chr1 is less than N p Repeatedly executing the following steps to generate a temporary new population P tmp (ii) a Step 4, merging the population P com ＝P cur ∪P tmp And carrying out fitness evaluation; step 5, updating the population; step 6: and judging the end condition. The method adopts double-vector chromosome coding and speed scaling-based affected procedure repairing steps, and can obtain a better scheduling scheme on scheduling performance or scheduling risk targets, thereby better meeting the requirements of operationThe requirements of plant scheduling on scheduling performance and risk.)

1. A job shop scheduling risk optimization method based on machine speed scaling is characterized in that: the method comprises the following steps:

step 1, setting scheduling problem information:

step 1.1, setting the number of machines to be m and the number of workpieces to be n, wherein each workpiece comprises o working proceduresWhereinIs the ith process of the jth workpiece, in an apparatusThe basic processing time is

Step 1.2, setting the failure rate of the equipment to be lambda₀With an expected downtime of beta₀The selectable speed mode of the device is s_mThe relative difference in velocity between adjacent modes is Δ_s；

Step 1.3, randomly generating N_sPersonal machine fault scenarioWherein each failure scenario B_kFrom a fault distribution matrix L_kAnd a downtime distribution matrix D_kConsists of the following components:

B_k＝{L_k,D_k},k＝1,2,...,N_s (1)

step 1.3.1, a fault distribution matrix L is adopted_kWhether the process has suffered a machine malfunction is marked, wherein,the ith process representing workpiece j can experience a machine fault,i-th tool representing workpiece jThe sequence does not encounter machine failure:

Li_jthe device failure probability calculated by equation (3)Randomly determining according to probability:

step 1.3.2, adopt the distribution matrix D of down time_kThe downtime experienced by the process is recorded,represents the downtime experienced by the ith process for workpiece j:

is determined probabilistically by the exponential distribution defined by equation (5):

step 2, population initialization:

step 2.1, setting parameters: population size N_pThe cross probability is P_cThe mutation probability is P_mMaximum evolution algebra N_max(ii) a And make the current population asThe current number of individuals is chr ═ 0;

step 2.2, setting a coding mode: using double vector encoding, each chromosome p_k＝＜s_k,q_kPriority by workpiece order vectorAnd machine speed pattern allocation vectorIs composed of (a) whereinThe priority list is adopted to code the priority processing sequence of the workpieces on the device i,encoding the assigned speed mode of the workpiece on the device i;

step 2.3, when chr is less than N_pAnd repeatedly executing the following steps:

step 2.3.1, randomly generating a priority list of the workpieces on the equipment to form a workpiece priority processing sequence vector s_chr；

Step 2.3.2, if chr is less than 0.2N_pAssigning the machine speed pattern to a vector q_chrIs set as the minimum value min s of the speed pattern_m}; if chr>0.8N_pAssigning the machine speed pattern to a vector q_chrIs set as the maximum value of the speed pattern max s_m}; otherwise, the machine speed pattern assigns a vector q_chrFrom the speed pattern set s_mDetermining random selection;

step 2.3.3, present Individual p_chr＝{s_chr,q_chrUpdating to the initial population P_cur＝P_cur∪p_chr(ii) a And let chr be chr + 1;

step 3, when chr1 is less than N_pRepeatedly executing the following steps to generate temporaryNew population P_tmp：

Step 3.1, from the current population P_curRandom selection of two individuals p_k＝＜s_k,q_k> and p_l＝＜s_l,q_lAs parent individuals;

step 3.2, when the cross probability P is satisfied_cThen, a two-vector chromosome crossing operation is performed:

step 3.2.1, randomly selecting two machine numbers from the interval [0, m) as cross points cr1 and cr 2;

step 3.2.2 by exchanging the workpiece priority machining order vectors in the two parent individualsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.2.3, exchange machine speed pattern allocation vectors in two parentsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.3 Generation of two New individuals p_c1＝＜s_c1,q_c1> and p_c2＝＜s_c2,q_c2>. and performing a double vector chromosomal mutation operation thereon:

step 3.3.1, for new individuals p_c1When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut1 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut1Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut1

Step 3.3.2, for new individuals p_c2When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut2 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut2Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut2

Step 3.4, adding two new individuals into the population P_tmp＝P_tmp∪{p_c1,p_c2}，chr1＝chr1+2；

Step 4, merging the population P_com＝P_cur∪P_tmpAnd the fitness evaluation is carried out on the combined population by adopting the following steps:

step 4.1, when chr2 is less than 2N_pAnd repeatedly executing the following steps:

step 4.1.1, chromosome decoding: according to the individual p_chr2Coded workpiece priority machining sequence s_chr2And machine speed distribution pattern q_chr2Arranging the starting and finishing time of the working procedure by adopting an active scheduling method on the premise of meeting the process constraint and the resource constraint to obtain a scheduling scheme pi_chr2Wherein the processAt a given speed modeWorking time ofCalculated from equation (6):

step 4.1.2: evaluating a scheduling scheme pi_chr2Performance target value of (2): calculation of scheduling scheme pi using equation (7)_chr2Maximum time of completionWhereinIs a process stepIn a scheduling scheme pi_chr2Time of completion in (1):

step 4.1.3, evaluate scheduling scheme π_chr2Risk target value of (a):

at step 4.1.3.1, the estimated number of fault scenarios cur < N_sRepeatedly executing the following steps:

(a) for scheduling scheme pi_chr2All the procedures in (1)According to fault scenario B_curJudging whether the equipment is in failure or not;

(b) if the process is carried outFault procedure, according to fault scenario B_curDetermining the downtime it has experiencedOtherwise, turning to the step (e);

(c) adopting the formula (8) update procedureTime of completion

(d) Performing a speed scaling based affected process repair step:

(d.1) if it is not the last process, determining the current processIn the subsequent process of the machineAnd the subsequent process of the process

(d.2) post-processing for machineDetermining its current speed modesm_current(ii) a Then, the subsequent process of the machine is calculated by the formula (9)Delay amount of start-up time Δ_t：

If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need：

sm_need＝sm_current+Δ_t/Δ_s (10)

Further, the updating steps are performed by the respective equations (11), (12) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(d.3) Process post-ProcessDetermining its current speed pattern sm_current(ii) a Then, the subsequent process is calculated by the formula (14)Delay amount of start-up time Δ_t(ii) a If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need；

Further, the updating steps are performed by the respective equations (15), (16) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(e) if the scheduling scheme pi is traversed_chr2All the procedures in (1) calculating the scheduling scheme in the fault situation B_curPractice of

Step 4.1.3.2, calculating the scheduling scheme pi using equation (17)_chr2Risk target value of (a):

and 5, population updating: merging population P by adopting rapid non-dominant sorting method_comRank the individuals in (1), and rank the individuals from the combined population P in order of rank_comSelecting superior individuals to enter a new population P_cur＝cur+1；

Step 6: judging the ending condition: if the maximum evolution algebra N is reached_maxThe algorithm terminates and returns the final non-dominated solution set; otherwise, let chr1 be chr1+1 and return to step 3.

Technical Field

The invention belongs to the technical field of uncertain job shop scheduling control, and particularly relates to a job shop scheduling risk optimization method based on machine speed scaling.

Background

The document "Risk measure of job shop scheduling with random machine breakdowns, Computers & Operations Research,2018, Vol99, p 1-12" discloses a job shop scheduling Risk optimization control method under random equipment failure, aiming at the job shop scheduling problem under random equipment failure, taking the maximum completion time of a scheduling scheme as a scheduling performance index, taking the expected delay of the maximum completion time as a scheduling Risk target, and further adopting a genetic evolution algorithm based on proxy Risk index evaluation to optimize the scheduling scheme with low Risk in a solution space. The method improves the stability of job shop scheduling in actual execution to a certain extent, and reduces the risk level of job shop scheduling. However, the method described in the document only considers the case where the machining speed of the machine is constant, ignoring the fact that the machine has multiple speed modes. However, the speed mode of the machine is adjusted timely, so that the performance index of job shop scheduling can be improved, the influence of equipment faults on scheduling performance can be absorbed, and the risk level of a scheduling scheme is obviously reduced. Since the method described in the literature does not take this point into account, the generated scheduling scheme still has poor performance indexes and high risk level, and it is difficult to meet the actual requirements of job shop scheduling.

Through searching, no patent publication related to the present patent application has been found.

Disclosure of Invention

The invention aims to overcome the defects of the existing scheduling risk optimization method in improving scheduling performance and risk, and provides a job shop scheduling risk optimization method based on machine speed scaling.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a job shop scheduling risk optimization method based on machine speed scaling comprises the following steps:

step 1, setting scheduling problem information:

step 1.1, setting the number of machines to be m and the number of workpieces to be n, wherein each workpiece comprises o working proceduresWhereinIs the ith workpieceA process of using the apparatusThe basic processing time is

Step 1.2, setting the failure rate of the equipment to be lambda₀With an expected downtime of beta₀The selectable speed mode of the device is s_mThe relative difference in velocity between adjacent modes is Δ_s；

Step 1.3, randomly generating N_sPersonal machine fault scenarioWherein each failure scenario B_kFrom a fault distribution matrix L_kAnd a downtime distribution matrix D_kConsists of the following components:

B_k＝{L_k,D_k},k＝1,2,...,N_s (1)

step 1.3.1, a fault distribution matrix L is adopted_kWhether the process has suffered a machine malfunction is marked, wherein,the ith process representing workpiece j can experience a machine fault,the ith process, representing workpiece j, does not encounter machine failure:

the device failure probability calculated by equation (3)Randomly determining according to probability:

step 1.3.2, adopt the distribution matrix D of down time_kThe downtime experienced by the process is recorded,represents the downtime experienced by the ith process for workpiece j:

is determined probabilistically by the exponential distribution defined by equation (5):

step 2, population initialization:

step 2.1, setting parameters: population size N_pThe cross probability is P_cThe mutation probability is P_mMaximum evolution algebra N_max(ii) a And make the current population asThe current number of individuals is chr ═ 0;

step 2.2, setting a coding mode: using double vector encoding, each chromosome p_k＝＜s_k,q_kPriority by workpiece order vectorAnd machine speed pattern allocation vectorIs composed of (a) whereinThe priority list is adopted to code the priority processing sequence of the workpieces on the device i,encoding the assigned speed mode of the workpiece on the device i;

step 2.3, when chr is less than N_pAnd repeatedly executing the following steps:

step 2.3.1, randomly generating a priority list of the workpieces on the equipment to form a workpiece priority processing sequence vector s_chr；

Step 2.3.2, if chr is less than 0.2N_pAssigning the machine speed pattern to a vector q_chrIs set as the minimum value min s of the speed pattern_m}; if chr>0.8N_pAssigning the machine speed pattern to a vector q_chrIs set as the maximum value of the speed pattern max s_m}; otherwise, the machine speed pattern assigns a vector q_chrFrom the speed pattern set s_mDetermining random selection;

step 2.3.3, present Individual p_chr＝{s_chr,q_chrUpdating to the initial population P_cur＝P_cur∪p_chr(ii) a And let chr be chr + 1;

step 3, when chr1 is less than N_pRepeatedly executing the following steps to generate a temporary new population P_tmp：

Step 3.1, from the current population P_curRandom selection of two individuals p_k＝＜s_k,q_k> and p_l＝＜s_l,q_lAs parent individuals;

step 3.2, when the cross probability P is satisfied_cThen, a two-vector chromosome crossing operation is performed:

step 3.2.1, randomly selecting two machine numbers from the interval [0, m) as cross points cr1 and cr 2;

step 3.2.2 by exchanging the workpiece excels in the two parent individualsSequence of first order vectorAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.2.3, exchange machine speed pattern allocation vectors in two parentsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.3 Generation of two New individuals p_c1＝＜s_c1,q_c1> and p_c2＝＜s_c2,q_c2>. and performing a double vector chromosomal mutation operation thereon:

step 3.3.1, for new individuals p_c1When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut1 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut1Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut1

Step 3.3.2, for new individuals p_c2When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut2 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut2Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut2

Step 3.4, adding two new individuals into the population P_tmp＝P_tmp∪{p_c1,p_c2}，chr1＝chr1+2；

Step 4, merging the population P_com＝P_cur∪P_tmpAnd the fitness evaluation is carried out on the combined population by adopting the following steps:

step 4.1, when chr2 is less than 2N_pAnd repeatedly executing the following steps:

step 4.1.1, chromosome decoding: according to the individual p_chr2Coded workpiece priority machining sequence s_chr2And machine speed distribution pattern q_chr2Arranging the starting and finishing time of the working procedure by adopting an active scheduling method on the premise of meeting the process constraint and the resource constraint to obtain a scheduling scheme pi_chr2Wherein the processAt a given speed modeWorking time ofCalculated from equation (6):

step 4.1.2: evaluating a scheduling scheme pi_chr2Performance target value of (2): calculation of scheduling scheme pi using equation (7)_chr2Maximum time of completionWhereinIs a process stepIn a scheduling scheme pi_chr2Time of completion in (1):

step 4.1.3, evaluate scheduling scheme π_chr2Risk target value of (a):

at step 4.1.3.1, the estimated number of fault scenarios cur < N_sRepeatedly executing the following steps:

(a) for scheduling scheme pi_chr2All the procedures in (1)According to fault scenario B_curJudging whether the equipment is in failure or not;

(b) if the process is carried outFault procedure, according to fault scenario B_curDetermining the downtime it has experiencedOtherwise, turning to the step (e);

(c) adopting the formula (8) update procedureTime of completion

(d) Performing a speed scaling based affected process repair step:

(d.1) if it is not the last process, determining the current processIn the subsequent process of the machineAnd the subsequent process of the process

(d.2) post-processing for machineDetermining its current speed pattern sm_current(ii) a Then, the subsequent process of the machine is calculated by the formula (9)Delay amount of start-up time Δ_t：

If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need：

sm_need＝sm_current+Δ_t/Δ_s (10)

Further, the updating steps are performed by the respective equations (11), (12) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(d.3) Process post-ProcessDetermining its current speed pattern sm_current(ii) a Then, the subsequent process is calculated by the formula (14)Delay amount of start-up time Δ_t(ii) a If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need；

Further, divide intoRespectively adopting the updating procedures of the formulas (15), (16) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(e) if the scheduling scheme pi is traversed_chr2All the procedures in (1) calculating the scheduling scheme in the fault situation B_curPractice of

Step 4.1.3.2, calculating the scheduling scheme pi using equation (17)_chr2Risk target value of (a):

and 5, population updating: merging population P by adopting rapid non-dominant sorting method_comRank the individuals inAnd from the merged population P in rank order_comSelecting superior individuals to enter a new population P_cur＝cur+1；

Step 6: judging the ending condition: if the maximum evolution algebra N is reached_maxThe algorithm terminates and returns the final non-dominated solution set; otherwise, let chr1 be chr1+1 and return to step 3.

The invention has the advantages and positive effects that:

1. according to the method, the combination of the double-vector chromosome coding workpiece processing sequence and the machine speed mode is adopted, so that the comprehensive influence of workpiece sequencing and machine processing speed on scheduling risks can be considered in the optimization process, and the possibility of obtaining a scheduling scheme with lower scheduling risks is increased; by adopting the affected procedure repairing step based on speed scaling, the machine speed mode of the affected procedure can be timely adjusted when a machine fault occurs, the delay of the completion time of the subsequent procedure is reduced, the local adaptive control on the influence of the machine fault is realized, and the scheduling scheme is ensured to have lower scheduling risk under the condition that the processing sequence of workpieces is the same; by adopting non-dominated dual-target optimization, a non-dominated scheduling scheme set which is widely distributed on scheduling performance and risk targets can be generated, so that scheduling decision makers with different risk preferences are better satisfied.

2. The method adopts double-vector chromosomes to simultaneously encode the processing sequence of the workpiece and the speed mode of a machine, and firstly, an initial population with different double-vector chromosomes is randomly generated; then, double-vector chromosome crossing and mutation operations are carried out on the current population to generate a new population with the same scale; further, scheduling and decoding the individuals in the merging population according to the encoded workpiece processing sequence and the machine speed mode, and evaluating a performance target value and a risk target value of a generated scheduling scheme by adopting a speed scaling-based affected procedure repairing step; and finally, performing non-dominated sorting on the merged population according to the scheduling performance target and the scheduling risk target, and updating the next generation population. The method of the invention obtains a group of non-dominated solution sets which are widely distributed on a scheduling performance target and a risk target by repeating the steps till the maximum evolution algebra. Because the method adopts double-vector chromosome coding and speed scaling-based affected procedure repairing steps, a better scheduling scheme on scheduling performance or scheduling risk targets can be obtained, and the requirements of job shop scheduling on scheduling performance and risk are better met.

Drawings

FIG. 1 is an overall flow diagram of the process of the present invention;

FIG. 2 is a flow chart of a risk assessment of the method of the present invention;

FIG. 3 is a graph showing the comparative results of the method of the present invention.

Detailed Description

The following detailed description of the embodiments of the present invention is provided for the purpose of illustration and not limitation, and should not be construed as limiting the scope of the invention.

The raw materials used in the invention are conventional commercial products unless otherwise specified; the methods used in the present invention are conventional in the art unless otherwise specified.

A job shop scheduling risk optimization method based on machine speed scaling comprises the following steps:

step 1, setting scheduling problem information:

step 1.1, setting the number of machines to be m and the number of workpieces to be n, wherein each workpiece comprises o working proceduresWhereinIs the ith process of the jth workpiece, in an apparatusThe basic processing time is

Step 1.2, setting the failure rate of the equipment to be lambda₀With an expected downtime of beta₀The selectable speed mode of the device is s_mThe relative difference in velocity between adjacent modes is Δ_s；

Step 1.3, randomly generating N_sPersonal machine fault scenarioWherein each failure scenario B_kFrom a fault distribution matrix L_kAnd a downtime distribution matrix D_kConsists of the following components:

B_k＝{L_k,D_k},k＝1,2,...,N_s (1)

step 1.3.1, a fault distribution matrix L is adopted_kWhether the process has suffered a machine malfunction is marked, wherein,the ith process representing workpiece j can experience a machine fault,the ith process, representing workpiece j, does not encounter machine failure:

the device failure probability calculated by equation (3)Randomly determining according to probability:

step 1.3.2, adopt the distribution matrix D of down time_kThe downtime experienced by the process is recorded,represents the downtime experienced by the ith process for workpiece j:

is determined probabilistically by the exponential distribution defined by equation (5):

step 2, population initialization:

step 2.1, setting parameters: population size N_pThe cross probability is P_cThe mutation probability is P_mMaximum evolution algebra N_max(ii) a And make the current population asThe current number of individuals is chr ═ 0;

step 2.2, setting a coding mode: using double vector encoding, each chromosome p_k＝＜s_k,q_kPriority by workpiece order vectorAnd machine speed pattern allocation vectorIs composed of (a) whereinThe priority list is adopted to code the priority processing sequence of the workpieces on the device i,distribution of coded work on device iThe speed mode of (1);

step 2.3, when chr is less than N_pAnd repeatedly executing the following steps:

step 2.3.1, randomly generating a priority list of the workpieces on the equipment to form a workpiece priority processing sequence vector s_chr；

Step 2.3.2, if chr is less than 0.2N_pAssigning the machine speed pattern to a vector q_chrIs set as the minimum value min s of the speed pattern_m}; if chr>0.8N_pAssigning the machine speed pattern to a vector q_chrIs set as the maximum value of the speed pattern max s_m}; otherwise, the machine speed pattern assigns a vector q_chrFrom the speed pattern set s_mDetermining random selection;

step 2.3.3, present Individual p_chr＝{s_chr,q_chrUpdating to the initial population P_cur＝P_cur∪p_chr(ii) a And let chr be chr + 1;

step 3, when chr1 is less than N_pRepeatedly executing the following steps to generate a temporary new population P_tmp：

Step 3.1, from the current population P_curRandom selection of two individuals p_k＝＜s_k,q_k> and p_l＝＜s_l,q_lAs parent individuals;

step 3.2, when the cross probability P is satisfied_cThen, a two-vector chromosome crossing operation is performed:

step 3.2.1, randomly selecting two machine numbers from the interval [0, m) as cross points cr1 and cr 2;

step 3.2.2 by exchanging the workpiece priority machining order vectors in the two parent individualsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.2.3, exchange machine speed pattern allocation vectors in two parentsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.3 Generation of two New individuals p_c1＝＜s_c1,q_c1> and p_c2＝＜s_c2,q_c2>. and performing a double vector chromosomal mutation operation thereon:

step 3.3.1, for new individuals p_c1When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut1 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut1Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut1

Step 3.3.2, for new individuals p_c2When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut2 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut2Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut2

Step 3.4, adding two new individuals into the population P_tmp＝P_tmp∪{p_c1,p_c2}，chr1＝chr1+2；

Step 4, merging the population P_com＝P_cur∪P_tmpAnd the fitness evaluation is carried out on the combined population by adopting the following steps:

step 4.1, when chr2 is less than 2N_pAnd repeatedly executing the following steps:

step 4.1.1, chromosome decoding: according to the individual p_chr2Coded workpiece priority machining sequence s_chr2And machine speed distribution pattern q_chr2Arranging the starting and finishing time of the working procedure by adopting an active scheduling method on the premise of meeting the process constraint and the resource constraint to obtain a scheduling scheme pi_chr2Wherein the processAt a given speed modeWorking time ofCalculated from equation (6):

step 4.1.2: evaluating a scheduling scheme pi_chr2Performance target value of (2): calculation of scheduling scheme pi using equation (7)_chr2Maximum time of completionWhereinIs a process stepIn a scheduling scheme pi_chr2Time of completion in (1):

step 4.1.3, evaluate scheduling scheme π_chr2Risk target value of (a):

at step 4.1.3.1, the estimated number of fault scenarios cur < N_sRepeatedly executing the following steps:

(a) for scheduling scheme pi_chr2All the procedures in (1)According to fault scenario B_curJudging whether the equipment is in failure or not;

(b) if the process is carried outFault procedure, according to fault scenario B_curDetermining the downtime it has experiencedOtherwise, turning to the step (e);

(c) adopting the formula (8) update procedureTime of completion

(d) Performing a speed scaling based affected process repair step:

(d.1) is asIf the last process is not the result, determining the current processIn the subsequent process of the machineAnd the subsequent process of the process

(d.2) post-processing for machineDetermining its current speed pattern sm_current(ii) a Then, the subsequent process of the machine is calculated by the formula (9)Delay amount of start-up time Δ_t：

If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need：

sm_need＝sm_current+Δ_t/Δ_s (10)

Further, the updating steps are performed by the respective equations (11), (12) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(d.3) Process post-ProcessDetermining its current speed pattern sm_current(ii) a Then, the subsequent process is calculated by the formula (14)Delay amount of start-up time Δ_t(ii) a If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need；

Further, the updating steps are performed by the respective equations (15), (16) and (13)Time of operationTime of completionAnd a current speed pattern sm_current：

If the process is carried outIf not the last process, then orderIs the current process O_cAnd step (d.1);

(e) if the scheduling scheme pi is traversed_chr2All the procedures in (1) calculating the scheduling scheme in the fault situation B_curPractice of

Step 4.1.3.2, calculating the scheduling scheme pi using equation (17)_chr2Risk target value of (a):

and 5, population updating: merging population P by adopting rapid non-dominant sorting method_comRank the individuals in (1), and rank the individuals from the combined population P in order of rank_comSelecting superior individuals to enter a new population P_cur＝cur+1；

Step 6: judging the ending condition: if the maximum evolution algebra N is reached_maxThe algorithm terminates and returns the final non-dominated solution set; otherwise, let chr1 be chr1+1 and return to step 3.

An overall flow chart and a risk evaluation flow chart of the method of the invention can be shown in fig. 1 and fig. 2.

Specifically, the preparation and detection are as follows:

a scheduling risk optimization method based on machine speed scaling comprises the following specific steps:

step 1, setting scheduling problem information:

step 1.1, the number of machines is set to m-10, the number of workpieces is set to n-10, and each workpiece includes 10 processes oWhereinFor the ith process of the jth workpiece, in the apparatusThe basic processing time isThe process information of each workpiece is set as follows:

process information of the workpiece 1: <0,29>, <1,78>, <2,9>, <3,36>, <4,49>, <5,11>, <6,62>, <7,56>, <8,44>, <9,21 >;

process information of the workpiece 2: <0,43>, <2,90>, <4,75>, <9,11>, <3,69>, <1,28>, <6,46>, <5,46>, <7,72>, <8,30 >;

process information of the workpiece 3: <1,91>, <0,85>, <3,39>, <2,74>, <8,90>, <5,10>, <7,12>, <6,89>, <9,45>, <4,33 >;

process information of the workpiece 4: <1,81>, <2,95>, <0,71>, <4,99>, <6,9>, <8,52>, <7,85>, <3,98>, <9,22>, <5,43 >;

process information of the workpiece 5: <2,14>, <0,6>, <1,22>, <5,61>, <3,26>, <4,69>, <8,21>, <7,49>, <9,72>, <6,53 >;

process information of the workpiece 6: <2,84>, <1,2>, <5,52>, <3,95>, <8,48>, <9,72>, <0,47>, <6,65>, <4,6>, <7,25 >;

process information of the workpiece 7: <1,46>, <0,37>, <3,61>, <2,13>, <6,32>, <5,21>, <9,32>, <8,89>, <7,30>, <4,55 >;

process information of the workpiece 8: <2,31>, <0,86>, <1,46>, <5,74>, <4,32>, <6,88>, <8,19>, <9,48>, <7,36>, <3,79 >;

process information of the workpiece 9: <0,76>, <1,69>, <3,76>, <5,51>, <2,85>, <9,11>, <6,40>, <7,89>, <4,26>, <8,74 >;

process information of the workpiece 10: <1,85>, <0,13>, <2,61>, <6,7>, <8,64>, <9,76>, <5,47>, <3,52>, <4,90>, <7,45 >;

step 1.2, setting the failure rate of the equipment to be lambda₀0.005, the desired downtime is β₀20.0, the device selectable speed mode is s_mWith {0,1,2,3,4,5}, the relative difference in velocity between adjacent modes is Δ_s＝0.05。

Step 1.3, randomly generating N_s200 machine failure scenariosWherein each failure scenario B_kFrom a fault distribution matrix L_kAnd a downtime distribution matrix D_kAnd (4) forming.

B_k＝{L_k,D_k},k＝1,2,...,N_s (1)

Step 1.3.1, a fault distribution matrix L is adopted_kWhether a process has suffered a machine fault is flagged, wherein,the ith process representing workpiece j can experience a machine fault,the ith process, representing workpiece j, does not experience a machine failure.

The value of (A) is calculated according to the equation (3)And (4) randomly determining.

Step 1.3.2, adopt the distribution matrix D of down time_kThe down time of the process subject to machine failure is recorded,representing the downtime experienced by the ith pass of workpiece j,

is randomly determined by the exponential distribution defined by equation (5).

Step 2, population initialization:

step 2.1, setting parameters: initializing population size to N_p1024, the crossover probability is P_c0.95, the mutation probability is P_m0.05, maximum evolution generation N_maxLet the current population be 128The current number of individuals is chr ═ 0;

step 2.2, setting a coding mode: using double vector encoding, each chromosome p_k＝＜s_k,q_kPriority by workpiece order vectorAnd machine speed pattern allocation vectorIs composed of (a) whereinThe priority list is adopted to code the priority processing sequence of the workpieces on the device i,coding the speed distribution mode adopted by the workpiece on the device i;

step 2.3, when chr is less than N_pAnd repeatedly executing the following steps:

step 2.3.1, randomly generating a priority list of the workpieces on each device to form a workpiece priority processing sequence vector s_chr；

Step 2.3.2, if chr is less than 0.2N_pAssigning the machine speed pattern to a vector q_chrIs set as the minimum value min s of the speed pattern_m0; if chr>0.8N_pAssigning the machine speed pattern to a vector q_chrIs set as the maximum value of the speed pattern max s_m5; otherwise, the machine speed pattern assigns a vector q_chrFrom speed modeSet s_mDetermining random selection;

step 2.3.3, present Individual p_chr＝{s_chr,q_chrUpdating to the initial population P_cur＝P_cur∪p_chr(ii) a And let chr be chr + 1;

step 3, when chr1 is less than N_pRepeatedly executing the following steps to generate a temporary new population P_tmp：

Step 3.1, from the current population P_curRandom selection of two individuals p_k＝＜s_k,q_k> and p_l＝＜s_l,q_lAs parent individuals;

step 3.2, when the cross probability P is satisfied_cThen, a two-vector chromosome crossing operation is performed:

step 3.2.1, randomly selecting two machine numbers from the interval [0, m) as cross points cr1 and cr 2;

step 3.2.2 by exchanging the workpiece priority machining order vectors in the two parent individualsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.2.3, exchange machine speed pattern allocation vectors in two parentsAndthe part located between the intersection points cr1 and cr2, generatesAnd

step 3.3 Generation of two New individuals p_c1＝＜s_c1,q_c1> and p_c2＝＜s_c2,q_c2>. and performing a double vector chromosomal mutation operation thereon:

step 3.3.1, for new individuals p_c1When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut1 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut1Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut1

Step 3.3.2, for new individuals p_c2When the mutation probability P is satisfied_mThen, randomly selecting a machine number mut2 from the interval [0, m) as a variation point; randomly generating a priority list to replace the priority machining order of workpieces on the machine mut2Randomly generating a velocity distribution pattern sub-vector to replace the velocity distribution pattern sub-vector of the workpiece on the machine mut2

Step 3.4, adding two new individuals into the population P_tmp＝P_tmp∪{p_c1,p_c2}，chr1＝chr1+2；

Step 4, merging the population P_com＝P_cur∪P_tmpAnd carrying out fitness evaluation:

step (ii) of4.1, when chr2 < 2N_pAnd repeatedly executing the following steps:

step 4.1.1, chromosome decoding: according to the individual p_chr2Coded workpiece priority machining sequence s_chr2And machine speed distribution pattern q_chr2On the premise of meeting the process constraint and resource constraint, the start-up time of the working procedure is arranged by adopting an active scheduling method to obtain a scheduling scheme pi_chr2Wherein the processAt a given speed modeWorking time ofCalculated from equation (6).

Step 4.1.2: evaluating a scheduling scheme pi_chr2Performance target value of (2): calculation of scheduling scheme pi using equation (7)_chr2Maximum time of completionWhereinIs a process stepIn a scheduling scheme pi_chr2The finishing time in (1).

Step 4.1.3, evaluate scheduling scheme π_chr2Risk target value of (a):

step 4.1.3.1, evaluated soThe number of the scene of the obstacle cur is less than N_sRepeatedly executing the following steps:

(a) for scheduling scheme pi_chr2All the procedures in (1)According to fault scenario B_curJudging whether the equipment is in failure or not;

(b) if the process is carried outFault procedure, according to fault scenario B_curDetermining the downtime it has experiencedOtherwise, turning to the step (e);

(c) adopting the formula (8) update procedureTime of completion

(d) Performing a speed scaling based affected process repair step:

(d.1) if it is not the last process, determining the current processIn the subsequent process of the machineAnd the subsequent process of the process

(d.2) post-processing for machineDetermining its current speed pattern sm_current. Then, the subsequent process of the machine is calculated by the formula (9)Delay amount of start-up time Δ_t。

If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need。

sm_need＝sm_current+Δ_t/Δ_s (10)

Further, the updating steps are performed by the respective equations (11), (12) and (13)Time of operationTime of completionAnd a current speed pattern sm_current。

If the process is carried outIf not the last process, then orderIs the current process O_cAnd (d.1) is turned on.

(d.3) Process post-ProcessDetermining its current speed pattern sm_current. Then, the subsequent process is calculated by the formula (14)Delay amount of start-up time Δ_t. If Δ_tIf the speed is more than 0, the speed mode sm required by the working procedure is calculated by adopting the formula (10)_need。

Further, the updating steps are performed by the respective equations (15), (16) and (13)Time of operationTime of completionAnd a current speed pattern sm_current。

If the process is carried outIf not the last process, then orderIs the current process O_cAnd (d.1) is turned on.

(e) If the scheduling scheme pi is traversed_chr2All the procedures in (1) calculating the scheduling scheme in the fault situation B_curPractice of

Step 4.1.3.2, calculating the scheduling scheme pi using equation (17)_chr2The risk target value of (c).

And 5, population updating: merging population P by adopting rapid non-dominant sorting method_comRank the individuals in (1), and rank the individuals from the combined population P in order of rank_comSelecting superior individuals to enter a new population P_cur＝cur+1。

Step 6: judging the ending condition: if the maximum evolution algebra N is reached_maxThe algorithm terminates and returns the final non-dominated solution set; otherwise, let chr1 be chr1+1 and return to step 3.

According to FIG. 3, the following results are obtained: the risk objective is worse under the condition that the performance objective is the same by the reference method; the performance target is worse with the same risk target; the method provided by the invention is superior to a reference method, and can better solve the problems of scheduling performance and risk optimization of the job shop.

Although the embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments disclosed.