CN115249112A

CN115249112A - Distributed mixed flow shop scheduling optimization method taking glass manufacturing as background

Info

Publication number: CN115249112A
Application number: CN202111521353.2A
Authority: CN
Inventors: 耿雅典; 李俊青; 牛奔; 韩玉艳; 李荣昊; 曾清清
Original assignee: Liaocheng University
Current assignee: Liaocheng University
Priority date: 2021-12-13
Filing date: 2021-12-13
Publication date: 2022-10-28

Abstract

The invention belongs to the field of production scheduling, and particularly relates to a distributed hybrid flow shop scheduling optimization method taking glass manufacturing as a background, wherein two targets, namely maximum completion time and total energy consumption, are considered simultaneously. First, each solution is encoded by a three-dimensional vector, namely factory allocation, scheduling and machine allocation. The two heuristics are then embedded into an efficient initialization strategy to increase population diversity. Then, in order to improve the global search capability, a pareto-based crossover operator is designed to better utilize the non-dominant solution. In addition, a local search heuristic algorithm based on three-part coding is embedded to improve the search performance. In order to improve the local search capability, the cooperation of a search operator is designed to obtain a better non-dominant solution. The summary flow chart is shown in fig. 11. Finally, experimental results show that the algorithm has higher efficiency than the other three latest algorithms.

Description

Distributed mixed flow shop scheduling optimization method taking glass manufacturing as background

Technical Field

The invention belongs to the field of production scheduling, and particularly relates to a scheduling optimization method for a distributed mixed flow shop with glass manufacturing as a background.

Technical Field

The distributed hybrid flow shop scheduling problem (DHFSP) has been studied and applied in many practical industrial applications, such as glass manufacturing systems and steelmaking systems. In the classical HFS process, there are several jobs, machines and stages. There are a certain number of parallel machines per stage, and each arriving job should select one available machine. Each operation follows the same processing route, and the machine is flexible to select. Thus, in HFS, selecting an extra task for each operation to fit the machine, as compared to the classical pipelining problem, has proven to be an NP-hard problem.

As the industry develops, more and more research is focused on distributed scheduling problems, including Distributed Flow Shop Scheduling Problems (DFSSP), and distributed hybrid flow shop scheduling problems (DHFS). However, there is less literature on DHFS than solving flowshop or distributed flowshop. Ying and Lin developed a hybrid algorithm that includes three versions of an iterative greedy algorithm to minimize the maximum completion time of DHFS. Hao et al consider a DHFS with Brain Storm Optimization (BSO) algorithm, where the maximum completion time is minimized. Cai et al propose a new shuffled frog-leaping algorithm with modulo factor (MQSFLA) for minimizing both total pull-off and maximum completion time. Shao et al propose a multi-neighborhood iterative greedy algorithm to solve this problem. Jiang et al studied energy-aware DHFs with multiprocessor tasks (total energy consumption and maximum completion time). Qin et al utilized a realistic DHFS with a new integrated production and distribution scheduling problem being the focus.

In real-world industrial systems, including glass manufacturing systems, scheduling efficiency is becoming increasingly important. Na et al studied the glass optimization problem and solved it using a heuristic approach. Lozano and Medaglia propose a two-stage heuristic method combining an accurate method and a search heuristic. Wang et al propose two heuristic approaches based on decomposition ideas to minimize the total power cost and the maximum completion time. Wang et al formulated a Mixed Integer Program (MIP) for this problem. Typically, there is a high energy consumption stage (i.e., mechanical depreciation) in the glass manufacturing process, which represents a significant portion of the production cost. Therefore, it is feasible and necessary to consider energy consumption in a glass manufacturing system.

Recently, multi-objective optimization algorithms have been applied and considered in many fields. Shahvari and Lognendran consider a TS-based algorithm to minimize two different objectives. Rosenberg uses an evolution-based search to consider multi-objective optimization problems. Hu et al propose a new multi-objective immune algorithm based on a multi-affinity model inspired by the immune system. Zhang et al propose a new multi-objective multi-factor immune algorithm with a new information transfer method for handling the multi-objective multi-task optimization problem. Wang et al improve the overall efficiency of optimizing multiple tasks simultaneously by reusing learned knowledge. Zhou et al propose a two-stage evolution multi-target particle swarm optimization algorithm to solve the problem of multi-target weapon target allocation. Li et al solve the problem of pipelining scheduling with a new decomposition-based multi-objective local search framework. However, few documents have studied the problem of multi-objective optimization of glass manufacturing systems.

Therefore, to solve the DHFSP problem in glass manufacturing systems, we propose an improved hyperplane assisted evolution algorithm (IhpaEA). The main contributions of this study are as follows: (1) Each solution is represented by a three-dimensional vector, and comprises factory allocation, machine allocation and operation scheduling; (2) The cross operator is designed, so that the searching capability of the population is improved; (4) A collaborative search method is designed, and the local search capability of the algorithm is further improved.

Disclosure of Invention

The invention aims to solve the problems in the prior art, and provides an improved hyperplane assisted evolution algorithm, so that the dispatching efficiency of the distributed hybrid flow shop is improved, the completion time is shortened, and the energy consumption is reduced.

The invention is realized by the following technical scheme:

a method for improved schedule optimization for a glass manufacturing-based distributed hybrid flow shop, comprising:

s1: according to the characteristics of factory distribution diversity in a distributed factory, 30 examples are generated according to actual product data, and the tasks of the examples are read;

s2: determining an optimized target and constraint conditions;

s3: optimizing a scheduling solution by adopting an improved hyperplane assisted evolution algorithm;

s4: two improved effective initialization strategies are provided to improve the diversity of the population;

s5: two new crossover operators are provided to improve the overall performance of the algorithm;

s6: a variation strategy is provided to improve the diversity of the population;

s7: providing a local search strategy to enhance the convergence capability of the algorithm;

s8: the proposed algorithm is effective for solving the problem of distributed hybrid flow shop scheduling.

In the scheduling problem of the S1 distributed mixed flow shop, n independent works are distributed to f factories, and each factory is formed by a series of pi _i Each production stage (or machining center) is composed of k parallel machines, each work can be completed in the same sequence in any factory, each operation can be performed on any selected machine for machining in the corresponding stage, and the constraint conditions of the problem are as follows: each job should be released at time zero and operated from the first stage to the next; all machines are available at time zero and continue to be available throughout the production cycle; one job can be processed on one machine at a time, and one machine can only process one job at a time; at each stage, a job can select a suitable machine from the parallel machines; there is no buffer restriction between different processing stages; all machines belonging to the same phase have similar processing capabilities.

The optimization objective in S2 is as follows:

minC _max (1)

C _max a continuous variable representing the maximum time-out of the workpiece

minTEC (2)

TEC represents Total energy consumption

The S3 is realized by the following steps:

a global search heuristic algorithm based on GA is embedded in the improved hyperplane auxiliary multi-target algorithm, and the search capability of the algorithm is improved. Considering that the dominant solution will be selected first and be in front of the population of the environmental selection, more evolutionary results are assigned to the dominant solution at the time of mating selection, and the offspring are evaluated for convergence to select better solutions. And randomly selecting the mating pool in the population. And calculating the iteration times of the offspring population, and selecting the environment.

The S4 is realized by the following steps:

in order to increase the diversity of the population, the present research embeds two heuristic algorithms into an effective initialization strategy.

The first heuristic first calculates the processing time of all workpieces in each stage. Next, the processing time of each workpiece on the machine at each stage is added to calculate the total processing time. Finally, individuals are generated by arranging the total processing time in a non-increasing order.

The first two steps of the second heuristic are the same as the first heuristic, however, the total processing time is arranged in a non-decreasing order in the third step to generate new individuals.

The S5 is realized by the following steps:

the first method randomly selects two individuals to cross. The method comprises the following specific steps: (1): two different elements are randomly selected from the first parent. (2) The workpiece block between two points of the first parent individual is copied. The tile is then moved to the far right or far left of the child. (3) The other workpiece pieces remaining from the second parent individual are placed.

The second method is to cross two offspring individuals. The method comprises the following specific steps: the building blocks of the parent are directly copied to the children. In addition, a point is randomly selected and the elements preceding the cut point are copied directly to children. To preserve the feasibility of the job sequence, the ISJOXI crossover operator copies the missing elements of each child in the same relative order as the other parents. Finally, by performing a single point crossover operation on parent 1 and parent 2, obtaining the other elements of unassigned positional child 1, parent 1 and parent 2 randomly select a crossover point.

The S6 is realized by the following steps:

step 1: two different elements, named point1 and point2, are randomly selected from the parent element.

Step 2: the elements of these two points are exchanged.

Plant F with maximum completion time _c And plant F with maximum TEC _c ；

(1) Exchange plant section

FA _cs : randomly selecting two jobs J ₁ And J ₂ Wherein J ₁ From F _c ，J ₂ From any other different plant, then swap their two locations;

FA _es : from F _e J of (A) ₁ And J of different plants ₂ In two random choices of job J ₁ And J ₂ Then two of them are exchanged;

FA _ci : will be from F _c Randomly inserting the deleted job into a certain position in the randomly selected factory;

FA _ei : will be from F _e A factory removed job is randomly inserted into a randomly selected location in the factory;

(2) Swapping scheduling vector portions

JS _cs : from F _c Randomly selecting two different operations, and then exchanging;

JS _es : from F _e Randomly selecting two different operations, and then exchanging;

JS _ci : insert randomly selected jobs into F _c A random position in (a);

JS _ei : insert randomly selected jobs into F _e Random position in (2);

(4) Exchanging machine vector parts

The operation steps of the mutation operator are as follows: first, a position r is randomly selected in the machine vector ₁ Then is r ₂ Select different machines.

The S7 is realized by the following steps:

first, in each generation, the maximum completion time and the maximum energy consumption of each solution are calculated, and the maximum completion time of each solution a is expressed as

The energy consumption of each solution is expressed as

Wherein the content of the first and second substances,

and

the minimum TEC, the maximum TEC of the solution in the current population, the minimum completion time and the maximum completion time are shown.

Second, use value

Each solution is calculated and then the population is divided into two groups P according to γ in ascending order _c And P _e ；P _c Size and P of _e Same because P _c The maximum completion time of the solution in (small γ) is large, so F is used _c (plant F with maximum completion time _c ) Associated search operator, again because of P _e TEC comparison of populations in (large gamma)Large, so use with F _e (plant F with maximum TEC _e ) Related search operator because P _e TEC for medium (large gamma) solutions is large, so F is used _e The associated search operator.

The S8 is realized by the following steps:

first we compare the improved algorithm with the previous algorithm. We use the same example, each running 30 times in the same time, and in an infinite number of iterations we choose the best solution, the worst solution, and the average of the solutions to compare. To verify the effectiveness of the improved algorithm. And secondly, verifying the effectiveness of the local search strategy through experiments. Finally to verify the good performance of IhpaEA, we compared it with three popular algorithms NSGAII, GFMMOEA and BiGE. We encode the three algorithms and run under the same environment. For each comparison algorithm, run 30 iterations thousands of times under the same conditions using the same example, resulting in the minimum, maximum, and average values for each algorithm. All comparison algorithms adopt the same stopping criterion, and have strong practicability in an actual production system. The data generated by different algorithms are tested, the superiority of the algorithms is illustrated through a Gantt chart, and the good performance of the algorithms can be seen through a box chart.

Drawings

FIG. 1 actual DHFSP problem in glass manufacturing systems

FIG. 2 shows a general process of a raw glass manufacturing system

FIG. 3 (a) encoding scheme

FIG. 3 (b) decoded Gantt diagram

PTL interleaving operation

FIG. 5 (a) copy operation

FIG. 5 (b) random tangent Point operation

FIG. 5 (c) copy missing element operation

FIG. 6.SJOXI schematic

FIG. 7 (a), ihpaEA-NC and IhpaEA comparison chart

FIG. 7 (b) comparative chart of IhpaEA-NI and IhpaEA

FIG. 7 (c) comparative chart of IhpaEA-NS and IhpaEA

FIG. 7 (d), ihpaEA-NL and IhpaEA comparison

FIG. 8 (a) pareto front of example 1

FIG. 8 (b) pareto front of example 5

FIG. 8 (c) pareto front of example 20

FIG. 9 schematic representation of the mean and 95% LSD intervals of the four comparison algorithms

FIG. 10 Gantt chart of example 7

FIG. 11 is a summary flowchart

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings:

for a distributed mixed flow scheduling optimization method with glass manufacturing as a background, a hyperplane assisted multi-objective algorithm is adopted for solving, wherein a problem to be considered is firstly modeled as a distributed mixed flow scheduling (DHFSP) problem. We propose an improved hyperplane assisted multiobjective algorithm, called ihpaea, with the objective of minimizing the maximum completion time and energy consumption of all workpieces. In the proposed algorithm, each solution is represented by three vectors. Each solution is encoded by a three-dimensional vector, namely factory allocation, scheduling and machine allocation. The two heuristics are then embedded into an efficient initialization strategy to increase population diversity. Then, in order to improve the global search capability, a pareto-based crossover operator is designed to better utilize the non-dominant solution. In addition, a local search heuristic algorithm based on three-part coding is embedded to improve the search performance. In order to improve the local search capability, the cooperation of a search operator is designed to obtain a better non-dominant solution. The experimental result verifies the effectiveness of the improved hyperplane auxiliary multi-target algorithm.

1 distributed hybrid flow shop scheduling optimization problem description in glass manufacturing context

The distributed hybrid flow shop scheduling (DHFS) studied herein can be described as follows. There are n independent jobs assigned to the f plants. Each plant consisting of a series of pi _i Group of production stages (or machining centers)In this way, there are k parallel machines per stage. Further, each job may be completed in the same order at any plant. Each operation may be performed on any selected machine at the corresponding stage. To solve this problem, minimum completion time and total energy consumption are targeted. And proposes the following assumptions:

each job should be released at time zero and operated from the first phase to the next.

All machines are available at time zero and continue to be available throughout the production cycle.

One job can only be processed on one machine at a time, and one machine can only process one job at a time.

At each stage, a job can select an appropriate machine from the parallel machines.

There is no buffer restriction between different processing stages.

1.1 modeling of scheduling optimization problem of distributed hybrid flow shop

The indices are as follows:

i machine index

j workpiece index

f factory index

Index of k stages

The parameters are as follows:

n number of workpieces

m number of machines

Number of stages w

h number of plants

m _k The number of machines in the k-th stage k =1,2

J _j Workpiece j, i =1,2

M _i Machine i, i =1,2

O _ij Ith operation of workpiece j

n _i At machine M _i Number of workpieces operated on i =1,2

J _ir r in machine M _i The upper work piece i =1,2,.. Multidot.m, r =1,2,. Multidot.m

The decision variables are as follows:

x _jf binary decision variables, when work J _j Assigned to plant f, the decision variable is equal to 1, otherwise equal to 0.

z _ij Binary decision variables, as workpiece J _j Is distributed to plant M _i The decision variable is equal to 1, otherwise it is equal to 0.

SJ _jk Workpiece J _j At the start time of the operation of phase k, k =1,2.., w, j =1,2.., n

CJ _jk Workpiece J _j Operation completion time at stage k, k =1,2.. W, j =1,2.. N

S(O _ij ) Operation O _ij I =1,2,.., m, j =1,2,.., n

C(O _ij ) Operation O _ij Is i =1,2.., m, j =1,2.., n

C _max Maximum completion time.

PM _fki K machines M in stage f of the plant _i K =1,2,.., w, i =1,2,.., m, f =1,2,.., h

TM _fki K machines M in stage f of the plant _i K =1,2,.. W, i =1,2,... M, f =1,2,... H

TEC Total energy consumption

The objective function is as follows:

based on the above symbols and variables, maximum completion time and energy consumption are considered as two goals. The first objective is to minimize the maximum completion time, where C _max ≤max(CJ _jk ). The second objective is to minimize energy consumption, wherein

2 proposing an optimization algorithm

We propose an improved hyperplane assisted multi-objective algorithm, called ihpaea. In the proposed algorithm, each solution is represented by three vectors. Each solution is encoded by a three-dimensional vector, namely factory allocation, scheduling and machine allocation. The two heuristics are then embedded into an efficient initialization strategy to increase population diversity. Then, in order to improve the global search capability, a pareto-based crossover operator is designed to better utilize the non-dominant solution. In addition, a local search heuristic algorithm based on three-part coding is embedded to improve the search performance. In order to improve the local search capability, the cooperation of a search operator is designed to obtain a better non-dominant solution.

2.1 coding scheme

In this algorithm, each solution is represented by a three-dimensional vector.

The first dimension vector is called a scheduling vector, the length of the scheduling vector is equal to the total number of operations pi = { pi = { (pi) } ₁ ,π ₂ ,...,π _n }. Each job number represents a scheduling vector pi _i The order of arrangement of one element of (a) is the order of processing.

The name of the second dimension vector is called machine allocation vector Z = { δ = } ₁ ,δ ₂ ,...,δ _k Element of the vector δ _i Indicated by machine numbers, assigned to the machines of the respective jobs.

The third dimension vector is named as the factory allocation vector, and the length of the factory allocation vector is equal to the total number of operations

Factory allocation vector

Is represented by a plant number, which represents the plant assigned to the corresponding job.

FIG. 3 (a) shows a solution representation example, where there are five jobs. The total number of phases per job is 2. The factory assignment vector tells the factory number for each job and the routing vector reports the machine number. The scheduling vector then represents the scheduling sequence for each job.

2.2 decoding scheme

Fig. 3 (b) shows a gantt chart. The detailed decoding steps are as follows.

The first step is as follows: scheduling the assigned jobs according to the order in the scheduling vector is the first stage of each plant.

The second step is that: after the factory is determined, each job should select the appropriate machine with the earliest time rule available.

The third step: for the other phases, each job is scheduled as soon as possible after the previous operation is completed. The first available suitable machine is also selected.

2.3 initialization of improved hyperplane assisted Multi-target Algorithm

To solve the problem under consideration, one solution is coded into two scheduling rules. One is called the first stage Longest Processing Time (LPTF), and the other is called the first stage Shortest Processing Time (SPTF). The LPTF generates a permutation based on the total processing time that is not increased. Meanwhile, the SPTF generates a permutation by ordering jobs based on a non-decreasing total processing time.

A valuable method is embedded in order to influence the initial population. Assuming that the population size is N, the specific steps are as follows:

the first N-2 individuals were generated in a random manner. For the factory allocation vector, each job is allocated to a randomly selected factory. For scheduling vectors, all jobs are ordered in random order.

One individual is generated from LPTF. First, the processing time of all jobs in each stage is calculated. Second, each job in each stage has a processing time, and the sum of these times is referred to as the total processing time. Third, individuals are generated by arranging the total processing time in a non-increasing order.

The SPTF generates the last individual. The first two steps are identical to the LPTF. However, the third step is to arrange the processing times in a non-decreasing order.

2.4 Cross strategy

Based on the coded representation, a new cross-heuristic algorithm is proposed, which comprises two parts:

(1) PTL crossover

The crossover operator used is called the PLT crossover operator. The PLT crossover is used here because it can produce different offspring from two identical parents. The steps of PLT interleaving can be described as follows:

step 1: two different elements are randomly selected from the first parent element.

Step 2: the job block cut by the two points of the first parent object is copied. The tile is then moved to the far right or far left of the child.

And 3, step 3: the empty elements of the jobs remaining from the second parent are placed.

The process by which the PLT produces offspring is shown in FIG. 4.

Table 1 PTL interleaving example

Table 1 provides an example of how an element may be updated. The mutation and crossover probability was 1.0.

(2) ISJOXI crossing

The proposed crossover operator is an improved similar job order crossover I or ISJOXI, with the specific steps as follows: the building blocks of the parent are directly copied to the children. In addition, a point is randomly selected and the elements preceding the cut point are copied directly to children. To preserve the feasibility of the job sequence, the ISJOXI crossover operator copies the missing elements of each child in the same relative order as the other parents. Finally, by performing a single point crossover operation on parent 1 and parent 2, obtaining the other elements of unassigned positional child 1, parent 1 and parent 2 randomly select a crossover point.

3.6 mutation strategy

The mutation strategy for the DHFS problem is described as follows:

Step 2: the elements of these two points are exchanged.

Plant F with maximum completion time _c And plant F with maximum TEC _c ；

(1) Exchange plant section

FA _es : from F _e J of (A) ₁ And J of different factories ₂ In two random choices of job J ₁ And J ₂ Then two of them are exchanged;

FA _ci : will be derived from F _c Randomly inserting the deleted job into a randomly selected position in the factory;

FA _ei : will be from F _e Randomly inserting a factory removed job into a randomly selected location in a factory;

(2) Swapping scheduling vector portions

JS _ci : insert randomly selected jobs into F _c A random position in (a);

JS _ei : insert randomly selected jobs into F _e At random positions in (a).

(3) Exchanging machine vector parts

The mutation operator operates as follows. First, a position r is randomly selected in the machine vector ₁ . Then is r ₂ Select different machines.

3.7 local search

The energy consumption of each solution is expressed as

Wherein the content of the first and second substances,

and

Second, use value

Each solution is calculated and then the population is divided into two groups P according to γ in ascending order _c And P _e ；P _c Size and P of _e Same because P _c The maximum completion time of the solution in (small γ) is large, so the sum of F is used _c (plant F with maximum completion time _c ) Related search operator, again because of P _e TEC for the population in (large γ) is larger, so F is used _e (plant F with maximum TEC _e ) Related search operator because P _e TEC for medium (large gamma) solution is large, so F is used _e The associated search operator.

Table 2 collaborative search operation example

4 results and analysis of the experiments

This section will discuss computational experiments for testing performance of the IhpaEA algorithm. The improved algorithm is implemented on Intel Core i 7.4-GHz PC on PlatEMO v3.0 with a memory of 16GB. To test the performance of the IhpaEA algorithm, 20 examples of different sizes were generated from the real flow shop.

All comparative algorithms are used to solve the problem under consideration, including encoding and decoding methods, and initialization procedures. The parameters are set according to their literature. For each example, the stop condition was set to 3000 iterations.

The performance of the algorithm was tested using 30 independent runs and all the results of the non-dominant solutions found by the comparison algorithm were collected for performance comparison. Analysis of variance comparison using Relative Percent Increase (RPI), the formula is calculated as follows:

wherein C is _b Represents the best solution, C, calculated by all comparison algorithms _c Is the best solution for the test algorithm.

4.1 simulation experiment parameter settings

And randomly generating 20 large-scale test cases of the DHFS problem to solve the DHFS problem, and testing the effectiveness of the hpaEA algorithm based on actual production data. For example, example 1 can represent 20 workpieces, 2 stages and 3 parallel machines of the first stage and 5 parallel machines of the second stage, where the workpiece index is {20,30,50,80100}, the machine parameter is {2,3,4,5}, the stage parameter is {2,3,5,10}, and the plant parameter is {2,3,4,5,6}, and these four algorithms are run 30 times respectively.

4.2 validity of initialization policy

Section 3.4 discusses initialization heuristics. Two types of IhpaEA algorithms are encoded to test the initialization heuristic: the random initialization heuristic, we call IhpaEA-NI, and IhpaEA which contains all the components mentioned in section 3.4. All other values of the two comparison algorithms are the same.

Table 3 reports the results of the comparison between IhpaEA-NI and IhpaEA. Example numbers are given in the first column, and HV results collected from the two comparison algorithms are listed in the following two columns, respectively. In addition, the last two columns illustrate the IGD values derived for IhpaEA-NI and IhpaEA, respectively.

From the comparison results it can be concluded that: (1) Considering the HV value of the IhpaEA-NI algorithm, the IhpaEA algorithm obtains 16 better results, and the results are slightly worse for the other two cases; (2) For IGD values, ihpaEA gave 20 better results in 20 different scale examples given; (3) From the average performance of HV and IGD given in the last row and the analysis of variance results in fig. 7 (a), it can be seen that IhpaEA is significantly better than IhpaEA-NI algorithm, which verifies the efficiency of the proposed initialization heuristic algorithm.

4.3 effectiveness of crossover strategy

Section 3.5 discusses the performance of the cross-heuristic algorithm, encoding two different types of ihpa ea algorithms, namely the ihpa ea NC algorithm with the classical two-point cross and the ihpa ea algorithm with all the components mentioned in section 3.5.

As can be seen from the comparison results given in table 4: (1) Compared with IhpaEA-NC, ihpaEA algorithm obtains 17 better results by comparing HV values; (2) The analysis of variance results in fig. 7 (b) show that IhpaEA achieves significantly better results in view of HV results, where the p-value for IGD values equals 4.30527e-06 (3), ihpaEA achieves 18 better results; the average performance of HV and IGD given from the last row can verify the effectiveness of the proposed cross-heuristic algorithm.

4.4 effectiveness of the mutation strategy

Section 3.6 discusses the effectiveness of the mutation operator, encoding two different types of IhpaEA algorithms, namely the proposed IhpaEA NS algorithm without using a mutation operator and the IhpaEA algorithm that contains all the components mentioned in section 3.6.

Table 5 shows that the proposed heuristic algorithm with population diversity is effective. Therefore, the operator improves the population diversity of the algorithm.

From the comparison results given in table 5, it can be concluded that: (1) Considering the HV value, ihpaEA obtained 18 better results compared to IhpaEA-NS algorithm; (2) The analysis of variance results in fig. 7 (c) show that IhpaEA achieves significantly better results in view of HV results, where the p value is equal to 0.0009; (3) for IGD values IhpaEA gave 18 better results; the average performance of HV and IGD given from the last row can verify the validity of the proposed heuristic algorithm.

4.5 effectiveness of local search strategy

To evaluate the performance of the local search heuristic discussed in section 3.7, two types of IphaEA algorithms were encoded: ihpaEA-NL without local search heuristics and IhpaEA that contains all the components mentioned in section 3.7.

Table 6 shows that the proposed heuristic algorithm with population diversity is effective. It can be concluded from the table that the local search operator can obtain a better non-dominated solution.

From the comparison results given in table 6 it can be seen that: (1) Considering the HV value, ihpaEA achieved 18 better results compared to IhpaEA-NL algorithm; (2) The analysis of variance results in FIG. 7 (d) show that IhpaEA achieves significantly better results in view of HV results, where the p-value of the IGD value is equal to 3.56712e-06 (3) IhpaEA achieves 20 better results; the average performance of HV and IGD given from the last row can verify the validity of the proposed heuristic algorithm.

4.6 multiple Algorithm comparison

To test the effectiveness of the IhpaEA algorithm in more detail, three algorithms were chosen, namely NSGAII, GFMOEA, biGE. Table 7 shows HV and IGD results after 30 independent runs.

As can be seen from the comparison results, the proposed IhpaEA algorithm has better performance than other comparison algorithms. The performance analysis was as follows: (1) The hybrid coding and decoding method adopted by the algorithm balances the diversity of performance and solution; (2) The proposed crossover and mutation operators further improve the quality of understanding; (3) The proposed cooperative local search operator can obtain a better non-dominated solution.

The pareto frontier plots are shown in FIGS. 8 (a) - (c) for solving 20 operators, namely "operator 1" to "operator 20". The solution of the IhpaEA algorithm is close to the pareto frontier and is evenly distributed on the basis of the three graphs.

A multi-factor analysis of variance (ANOVA) was also performed to verify differences from the table above, taking into account three comparison algorithms, namely NSGAII, GFMMOEA and BiGE. FIG. 9 shows the average of the best values and the 95% LSD (Fisher least significant Difference) interval for the three comparison algorithms. The results of the three comparison algorithms show that the differences are statistically significant. As can be seen from fig. 9, the IhpaEA algorithm is significantly better than the other three comparison algorithms.

Fig. 8 reports the results of a comparison of HV values given 20 different scale examples. The first column represents the number of instances. Then, the results of NSGAII, GFMMOEA, biGE and IhpaEA collection are illustrated in the following four columns, respectively. Table 8 shows: (1) In the 20 examples given, the 13 better values obtained by the proposed IhpaEA algorithm are clearly superior to the other 3 comparison algorithms; (2) The average of the last row further evaluated the efficiency of IhpaEA.

As can be seen from the comparison of IGD values reported in table 8, the proposed IhpaEA algorithm yielded 19 better values, which further verifies the superiority of the IhpaEA algorithm.

Different non-dominated solutions correspond to different scheduling schemes, so that the obtained optimal scheduling Gantt chart is different. IhpaEA was tested using the test data of example 7. As shown in fig. 10, an optimal scheduling scheme is obtained in which the abscissa represents the completion time and the ordinate represents the machine. From fig. 10, the processing conditions for different processes on different machines can be obtained, where the same job has the same color, and the optimal processing time obtained is 135.

4.7 analysis of the results

From the comparison results discussed above, the effectiveness of the proposed IhpaEA algorithm has been tested. The main advantages of IhpaEA are as follows: (1) The provided heuristic initialization algorithm can improve the diversity and quality of the population; (2) The cross operator based on Pareto enhances the global searching capability; (3) the mutation operator proves the convergence of the optimization process; collaborative searching improves local search capabilities.

A class of DHFS problems with completion time and total energy consumption is studied herein. In order to solve the problem, a multi-objective optimization algorithm is provided. The main contributions are as follows: (1) an efficient encoding and decoding mechanism is embedded; (2) An effective initialization strategy embedded into the two heuristic algorithms is provided; (3) designing a Pareto-based crossover operator; (4) In order to improve the local search capability, a cooperative mechanism of search operators is provided.

TABLE 3 comparison of IhpaEA-NI and IhpaEA test results

TABLE 4 comparison of IhpaEA-NC and IhpaEA experimental results

TABLE 5 comparison of IhpaEA-NS and IhpaEA test results

TABLE 6 comparison of results of IhpaEA-NL and IhpaEA experiments

TABLE 7 HV value comparison of results

TABLE 8 IGD value results comparison

Claims

1. A glass manufacturing distributed mixed flow shop scheduling method and system are characterized in that: the method comprises the following steps:

s1: generating 30 examples according to the characteristics of factory distribution diversity in a distributed factory and actual product data and reading the tasks of the examples;

s2: determining an optimized target and constraint conditions;

2. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 1, characterized in that:

in the scheduling problem of the S1 distributed mixed flow shop, n independent works are distributed to f factories, and each factory is formed by a series of pi _i Each production stage (or machining center) is composed of k parallel machines, each work can be completed in the same sequence in any factory, each operation can be performed on any selected machine for machining in the corresponding stage, and the constraint conditions of the problem are as follows: each job should be released at time zero and operated from the first stage to the next; all machines are available at time zero and continue to be available throughout the production cycle; one job can be processed on one machine at a time, and one machine can be processed on one machine at a timeCarrying out operation; at each stage, a job can select a suitable machine from the parallel machines; there is no buffer restriction between different processing stages; all machines belonging to the same phase have similar processing capabilities.

3. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 2, characterized in that: the objective function in S2 is:

min C _max (1)

C _max a continuous variable representing the maximum time of completion of the workpiece

min TEC (2)

TEC represents Total energy consumption

4. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 3, wherein said S3 is implemented by:

in the improved hyperplane auxiliary multi-target algorithm, a global search heuristic algorithm based on GA is embedded, so that the search capability of the algorithm is improved; considering that the dominant solution is selected firstly and is positioned in the front of the population of the environment selection, more evolutionary results are distributed to the dominant solution during the mating selection, the convergence of the offspring is evaluated, a better solution is selected, the offspring is randomly selected from the population to form a mating pool, the number of iterations of the offspring population is calculated, and the environment selection is carried out.

5. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 4, characterized in that: the S4 is realized by the following steps:

in order to increase the diversity of the population, two heuristic algorithms are embedded into an effective initialization strategy;

the first heuristic algorithm first calculates the processing time of all the workpieces in each stage, secondly calculates the total processing time by adding the processing time of each workpiece on the machine of each stage, and finally generates individuals by arranging the total processing time in a non-increasing order;

6. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 5, characterized in that: the S5 is realized by the following steps:

the first method randomly selects two individuals to be crossed, and specifically comprises the following steps: (1): randomly selecting two different elements from a first parent; (2) Copying the workpiece block between two points of the first parent individual and then moving the block to the far right or far left of the child; (3) Placing the other workpiece blocks remaining from the second parent individual;

the second method is that two filial generation individuals are crossed, and the specific steps are as follows: in order to keep the feasibility of the job sequence, the ISJOXI crossover operator copies the missing elements of each child, which are in the same relative order as the other parents, and finally, the other elements of the unassigned position child 1 are obtained by performing a single-point crossover operation on the parent 1 and the parent 2, and the parent 1 and the parent 2 randomly select the crossover point.

7. The method and system of claim 6, wherein the system comprises: said S6 is thus realized

Step 1: randomly selecting two different elements from the parent elements, and respectively naming the two different elements as point1 and point2;

step 2: exchanging elements of the two points;

plant F with maximum completion time _c And having the maximum TECPlant F _c ；

(1) Exchange plant section

FA _ci : will be from F _c Randomly inserting the deleted job into a randomly selected position in the factory;

(2) Swapping scheduling vector portions

JS _ci : insert randomly selected jobs into F _c A random position in (a);

JS _ei : insert randomly selected jobs into F _e A random position in (a);

(3) Exchanging machine vector parts

The mutation operator operates as follows: first, a position r is randomly selected in the machine vector ₁ Then is r ₂ Select different machines.

8. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 7, characterized in that: the S7 is realized by the following steps:

The energy consumption of each solution is expressed as

Wherein, the TEC ^min 、TEC ^max 、

And

representing the minimum TEC, the maximum TEC, the minimum completion time and the maximum completion time of the solution in the current population;

second, use value

Each solution is calculated and then the population is divided into two groups P according to γ in ascending order _c And P _e ；P _c Size and P of _e Same because P _c The maximum completion time of the solution in (small γ) is large, so the sum of F is used _c (plant F with maximum completion time _c ) Related search operator, again because of P _e TEC for the population in (large γ) is larger, so F is used _e (plant F with maximum TEC _e ) Related search operator because of P _e TEC for medium (large gamma) solution is large, so F is used _e The associated search operator.

9. The glass manufacturing distributed hybrid flow shop scheduling method and system according to claim 8, characterized in that: the S8 is realized by the following steps:

first we compare the improved algorithm with the previous one, we use the same examples, each example runs 30 times in the same time, in the infinite number of iterations we choose the best solution, the worst solution, and the average of the solutions to compare to verify the effectiveness of the improved algorithm; secondly, verifying the effectiveness of a local search strategy through experiments, and finally comparing the IhpaEA with three popular algorithms NSGAII, GFMMOEA and BiGE in order to verify the good performance of the IhpaEA, wherein the three algorithms are encoded and run in the same environment, and for each comparison algorithm, the same example is used to run for 30 iterations and thousands of iterations under the same condition to obtain the minimum value, the maximum value and the average value of each algorithm; all comparison algorithms adopt the same stopping criterion, have strong practicability in an actual production system, test data generated by different algorithms, illustrate the superiority of the algorithms through Gantt charts, and show that the algorithms have good performance through box charts.