CN113011767A - Hybrid genetic method for scheduling multi-target flexible job shop - Google Patents

Abstract

The invention discloses a hybrid genetic method for scheduling a multi-target flexible job workshop, which relates to the technical field of production scheduling.

Description

Hybrid genetic method for scheduling multi-target flexible job shop

Technical Field

The invention relates to the technical field of production scheduling, in particular to a hybrid genetic method for scheduling a multi-target flexible job shop.

Background

The workshop production scheduling is the work of the organization executing the production schedule plan. The workshop production scheduling is based on the production progress plan, and the workshop production progress plan is realized through the production scheduling. The necessity of shop floor production scheduling is determined by the nature of the industrial enterprise shop floor production activities. Modern industrial enterprises have many production links, complex collaboration relations, strong production continuity, fast condition change, partial fault of a certain part or non-scheduled realization of a certain measure, and often spread the operation of the whole production system. Therefore, the workshop production scheduling work is strengthened, and the method is very important for timely knowing and mastering the production progress, researching and analyzing various factors influencing the production, and taking corresponding countermeasures according to different conditions to reduce the gap or recover the gap.

In the Job-shop Scheduling Problem (JSP), a group of machines needs to process a group of workpieces, each workpiece is formed by a series of processes with precedence constraints, each process only needs one machine, the machines are always available, and one operation can be processed at a time without interruption. The decision content includes how to order the processes on the machine to optimize a given performance index. A typical performance indicator for JSP is the completion time (makespan), the time required to complete all work. JSP is a well-known NP problem. The Flexible Job shop Scheduling Problem FJSP (FJSP) is an extension of classical JSP in which each process is allowed to be processed on any one of a set of available machines. FJSP is more difficult than traditional JSP because it introduces another decision context, namely the job path, in addition to ordering. Determining the job path means deciding which machine to use for processing it for each process.

In the prior art, when a complex problem in workshop production scheduling is solved, a theoretical model in an ideal state cannot completely cope with a complex actual workshop scheduling process. The problems in theoretical research and actual production system scheduling cannot be completely connected. When the scale of the generated problem is small, a plurality of research methods can solve the problem at different levels, however, for the large-scale FJSP problem, the state of the solution in the existing method is changed, and the solving efficiency of the existing method is reduced. In the generated multi-target problem, the number of solved target solutions is more than one, and the prior art cannot select a compromise solution suitable for an enterprise from a plurality of target solutions, so that the key problem to be solved urgently by the manufacturing industry type enterprise at present is formed. At present, in the prior art, evaluation criteria for solving the FJSP algorithm are not uniform, so that the selection of data with uniform scale for testing aiming at different FJSP problems is a necessary condition for evaluating the performance of different algorithms.

Aiming at the problems in the prior art, the application provides a hybrid genetic method for scheduling a multi-target flexible job workshop, which is used for establishing a data model for solving the scheduling problem of the multi-target flexible job workshop and solving the problem of the actual workshop, the Kacem problem and the BRdata problem in the international standard example.

Disclosure of Invention

The invention aims to provide a hybrid genetic method for scheduling a multi-target flexible job workshop, which is used for establishing a data model for solving a scheduling problem of the multi-target flexible job workshop and solving the problem of a practical workshop and the Kacem problem and the BRdata problem in an international standard example.

The invention provides a hybrid genetic method for scheduling a multi-target flexible job shop, which comprises the following steps of:

step S1: initializing a coding population, and determining the size P of the population, the iteration times T and the neighborhood searching VT times;

step S2: respectively encoding the workpieces by adopting an OS random encoding method and an MA global sequence encoding method, then decoding according to the sequence of the OS random encoding, processing each procedure on an optional processing machine on the procedure according to the minimum time line until all the procedures are processed according to the minimum time line and matched with the corresponding MA sequence, randomly selecting an OS sequence in the OS random encoding, and selecting to obtain the MA sequence by adopting a method combining GSE selection and random selection;

step S3: calculating the fitness value of each chromosome in the sequence, calculating the Pareto optimal solution set of the current population by using a rapid non-dominated sorting method, and storing the top 20% of the sorted chromosomes in the population into a Pareto archive PA according to the Pareto sorting and crowding distance of each chromosome;

step S4: judging whether the convergence standard is met or not, and if any convergence standard is met, ending outputting the Pareto optimal solution; otherwise, executing step S5;

step S5: performing cross operation of a vector OS and a vector MA in the OS sequence and the MA sequence, calculating a Pareto optimal solution set and updating a PA;

step S6: carrying out mutation operation of a vector OS and a vector MA in a coding sequence, and updating PA;

step S7: performing neighborhood search on an OS sequence and an MA sequence in PA, wherein a neighborhood structure is represented as VNS [ i ], setting iteration times VT, sequentially performing neighborhood search according to the sequence from VNS1 to VNS4, obtaining a better solution x 'each time, ending the loop if x' is better than x, entering the next loop until the iteration times VT is reached, outputting a Pareto optimal solution, and finishing workshop scheduling.

Further, in step S2, the OS randomly encodes a machining order of each step in the order of appearance of the workpiece number, and the encoding length is L₁(ii) a The MA global sequence code is a code value of each workpiece according to the selectable number of processing machines of each workpiece procedure, and the code length is L₂And L is₁＝L₂。

Further, the step S3 calculates a Paroto rank i of each individual solution in the encoding population_rankAnd a congestion distance D_iWherein the crowding distance D_iThe calculation formula of (2) is as follows:

d_i,j＝|F₁(i)-F₁(j)|+|F₂(i)-F₂(j)|+|F₃(i)-F₃(j)| (1)

D_i＝min{d_i,k} (k＝1,…,n；k≠i) (2)

wherein n is the number of workpieces, d_i,jIs the distance of solutions with the same Pareto ranking.

Further, the convergence criterion of step S4 is:

the iteration number T reaches a given upper limit L;

successive iterations do not have a new optimal solution to produce.

Further, the vector OS intersection process in step S5 is as follows:

step S501: taking out n parent chromosomes from the random encoding population of the OS, and marking the chromosomes as P₁，P₂；…P_nWherein n represents the total number of workpieces;

step S502: at P_iThe ith work piece is taken out in sequence and copied to the child generation C_iWherein the gene position remains unchanged, wherein i is 1, …, n;

step S503: will P_iThe other workpieces except the i +1 th workpiece are sequentially copied to the child C according to the sequence of the working procedures_i+1Wherein i is 1, …, n-1; finally P is added_nThe other workpieces except the 1 st workpiece in the sequence are copied to the child C_i；

Step S504: obtaining the offspring chromosome C₁，C₂；…C_n。

Further, the mutation operation of the vector MA in step S6 is performed as follows:

step S601: randomly generating r random numbers, wherein r belongs to [1, M ], and M is the total number of the working procedures;

step S602: randomly selecting r positions from the parent chromosomes of the MA sequence;

step S603: and for each process, selecting the machine with the shortest processing time from the available machine set for replacement, and if the original MA parent chromosome gene is processed by the machine with the shortest processing time, selecting the machine with the second shortest processing time for replacement.

Further, i in the neighborhood structure VNSi in the step S7 is more than or equal to 1 and less than or equal to 4;

when i takes a value of 1, the VNS1 performs neighborhood search for the MA sequence, and randomly selects a machine from the MA sequence for replacement;

when i takes a value of 2, the VNS2 performs neighborhood search for the OS sequence, and two workpieces J are randomly selected₁And J₂And make J₁The number of steps is less than J₂The number of steps of (1), respectively, recording J₁And J₂From left to right, sequentially arranging J₁Each process is laid in J₂Then J is placed on₂Each process is placed at the rest positions;

when i takes a value of 3, VNS3 carries out neighborhood search aiming at the OS sequence, randomly selects gene segments t, the length of t is smaller than the total process number, and after the gene segments t are in reverse order, the gene segments are inserted into the original position again;

when i takes a value of 4, the VNS4 performs neighborhood search for the OS sequence, randomly selects the gene segments t, makes the length of t smaller than the total operand, randomly changes the sequence of the gene segments t, and then reinserts the gene segments t into the original position.

Compared with the prior art, the invention has the following remarkable advantages:

the hybrid genetic method for scheduling the multi-target flexible job workshop, provided by the invention, is characterized in that a data model is established for the scheduling problem of the multi-target flexible job workshop with the total completion time, the total machine load and the key machine load by adopting the HGA algorithm, and the actual workshop case, the Kacem problem of the international standard algorithm and the BRdata problem are simulated through the data model, so that the Pareto optimal solution can be obtained.

Drawings

FIG. 1 is a general flow chart provided by an embodiment of the present invention;

FIG. 2 is a diagram of the interleaving steps of a vector OS provided by an embodiment of the present invention;

FIG. 3 is a diagram illustrating a variation process of a vector OS according to an embodiment of the present invention;

FIG. 4 is a diagram illustrating a variation process of the vector MA according to an embodiment of the present invention;

fig. 5 is a gantt chart of Pareto optimal solution b1 ═ 10419 of the 6 × 6P-FJSP problem provided by the embodiment of the present invention.

Detailed Description

The technical solutions of the embodiments of the present invention are clearly and completely described below with reference to the drawings in the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.

Referring to fig. 1-5, the invention provides a hybrid genetic method for scheduling a multi-target flexible job shop, which comprises the following steps:

step S1: initializing a coding population, and determining the size P of the population, the iteration times T and the neighborhood searching VT times;

step S2: respectively encoding the workpieces by adopting an OS random encoding method and an MA global sequence encoding method, then decoding according to the sequence of the OS random encoding, processing each procedure on an optional processing machine on the procedure according to the minimum time line (namely as early as possible) until all the procedures are processed according to the minimum time line and are matched with the corresponding MA sequence, randomly selecting an OS sequence in the OS random encoding, and selecting to obtain the MA sequence by adopting a method combining GSE selection and random selection;

step S3: calculating the fitness value of each chromosome in the sequence, calculating the Pareto optimal solution set of the current population by using a rapid non-dominated sorting method, and storing the top 20% of the sorted chromosomes in the population into a Pareto archive PA according to the Pareto sorting and crowding distance of each chromosome;

step S4: judging whether a convergence standard is met, wherein the convergence standard is as follows:

the iteration number T reaches a given upper limit L;

successive iterations do not have a new optimal solution to produce.

If any convergence standard is met, ending outputting the Pareto optimal solution; otherwise, executing step S5;

step S5: performing cross operation of a vector OS and a vector MA in the OS sequence and the MA sequence, calculating a Pareto optimal solution set and updating a PA;

step S6: carrying out mutation operation of a vector OS and a vector MA in a coding sequence, and updating PA;

step S7: performing neighborhood search on an OS sequence and an MA sequence in PA, wherein a neighborhood structure is represented as VNS [ i ], setting iteration times VT, sequentially performing neighborhood search according to the sequence from VNS1 to VNS4, obtaining a better solution x 'each time, ending the loop if x' is better than x, entering the next loop until the iteration times VT is reached, outputting a Pareto optimal solution, and finishing workshop scheduling.

Wherein a large crossover probability p is required for the success of the genetic algorithm_c(0.5＜p_c< 1.0) and a smaller mutation probability p_m(0.001＜p_m< 0.05), crossover probability p_cIs favorable for gene complete recombination and mutation probability p_mIt is beneficial to increase the diversity performance of the population and prevent the population from falling into local optima. In order to ensure sufficient recombination of chromosomal genes, the present application adopts the method of adaptive crossover probability of formula (3) in step S6. To ensure that all are equal to or greater than f_minCan participate in the crossover operation, and set k₁Has a value of 1. In the optimizing process, the adaptability value tends to f_minThe crossover probability decreases. When adapting toValue of f_minThe crossover probability is 0.

The formula for solving the self-adaptive cross probability Pc and the variation probability Pm is as follows:

wherein f' is the smaller of the fitness values of the two chromosomes involved in the crossover operation, and f_minAnd f represents the minimum and average values of the fitness values of the chromosomes in the population, respectively, k₁Value 1, p_mThe value is between 0.001 and 0.005.

Example 1

Each individual in the population is a solution of FJSP, each gene is directly encoded by a workpiece number, the sequence of occurrence of the workpiece numbers represents the processing sequence of each process, the workpiece number that occurs the jth time represents the jth process of the workpiece i, and the number of occurrences of the workpiece number is equal to the total number of processes of the workpiece, so that the generated solutions are all feasible scheduling. Since each process can be performed on multiple machines, balancing the workload of each machine is also a goal of the coding scheme.

In the step S2, the OS randomly encodes the machining order of each process in the order of appearance of the workpiece number, and the encoding length is L₁(ii) a The MA global sequence code is a code value of each workpiece according to the selectable number of processing machines of each workpiece procedure, and the code length is L₂And L is₁＝L₂。

Wherein, the MA is generated by a Global Sequential Encoding (GSE) method. For randomly generated OS sequences, for example: "1133122" each represents a step O_1,1，O_1,2，O_3,1O_3,2，O_1,3，O_2,1And O_2,2. Wherein the first "1" represents the process O_1,1Selecting the machine M with the shortest processing time in the selectable processing machine set₁The processing time is "2", and "2" is compared with M₁The machining time of the other steps in the row is added in the same wayMethod, sequentially taking the rest of the working procedures O_1,2，O_3,1O_3,2，O_1,3，O_2,1And O_2,2The machine with the shortest processing time is selected each time, and the processing time is as follows: m₄、M₃、M₄、M₂、M₂And M₁The resulting MA sequence is "1434221". The OS random coding and MA global sequence coding method together form a new chromosome, and the coding contrast is shown as follows:

in the step S2, the GSE selects 80% of the samples, randomly selects 20% of the samples, and the OS sequence adopts a random selection method to ensure the diversity of the population. The MA adopts GSE selection, and can search for a machine with the shortest processing time each time, and thus can avoid selecting a machine with a long processing time. The processing time of the machine is adjusted after each machine selection, thereby ensuring the load balance of the machine.

Example 2

The step S3 calculates the pareto ranking i of each individual solution in the encoding population_rankAnd a congestion distance D_iWherein the crowding distance D_iThe calculation formula of (2) is as follows:

d_i,j＝|F₁(i)-F₁(j)|+|F₂(i)-F₂(j)|+|F₃(i)-F₃(j)| (1)

D_i＝min{d_i,k} (k＝1,…,n；k≠i) (2)

wherein n is the number of workpieces, d_i,jIs the distance of solutions with the same Pareto ranking.

The pareto rank i mentioned in the step S3_rankThe fast non-dominated front edge where each solution i is located is obtained by the following specific implementation process of the calculation method:

1) domination number n_pI.e. the number of solutions that dominate solution p;

2)s_pthe solution is a set of solutions governed by p.

First, the dominating number of all solutions of the first non-dominant solution layer is set to zero. I.e. n for each solution p_pA value of 0 (n)_p0), access its set s_pAnd reduces its dominance by 1. If the dominance becomes zero for any member Q, we place it in a separate list Q. These members belong to the second uncontrolled leading edge. The above process is now repeated for each member of Q and a third leading edge is determined. This process continues until all leading edges are determined.

For each solution p at a second or higher level non-dominant solution level, the dominant solution number n_pAt most N-1. Thus, each solution p is accessed a maximum of N-1 times before its dominance becomes zero. At this point, the solution is assigned as a non-dominant solution layer and will no longer be accessed.

Since there are a maximum of N-1 such solutions, the overall complexity is O (N)²). Thus, the overall complexity of the process is O (MN)²). Another way to calculate this complexity is to realize the body of the first inner loop (for each p ∈ F)_i) Exactly N times because each solution can be a member of at most one leading edge, and the second inner loop' S body (for each q ∈ S)_p) Then a maximum of (N-1) comparisons may be performed per individual [ a maximum of (N-1) individuals per individual, each dominance check requiring a maximum of M comparisons]Thus in the global O (MN)²) And obtaining a result in the calculation. Although the time complexity has been reduced to O (MN)²) But the storage requirements have increased to O (N)²)。

Example 3

Referring to fig. 2, the vector OS interleaving process in step S5 is as follows:

step S501: taking out n parent chromosomes from the random encoding population of the OS, and marking the chromosomes as P₁，P₂；…P_nWherein n represents the total number of workpieces;

step S502: at P_iThe ith work piece is taken out in sequence and copied to the child generation C_iWherein the gene position remains unchanged, wherein i is 1, …, n;

step S503: will P_iThe other workpieces except the i +1 th workpiece are sequentially copied to the child C according to the sequence of the working procedures_i+1Wherein i is 1, …, n-1; finally P is added_nThe other workpieces except the 1 st workpiece in the sequence are copied to the child C_iThe sequence of the working procedures in the copying process is kept unchanged so as to ensure that chromosomes obtained after crossing are all feasible to be scheduled;

step S504: obtaining the offspring chromosome C₁，C₂；…C_n。

Example 4

Referring to FIG. 3, a certain gene g 'in one chromosome is randomly selected, and since the process is constrained by the processing order, the precursor process g' of the gene g 'is determined first'_fAnd subsequent process step g'_sThen randomly choose one location between two locations to insert the procedure g' to ensure that the generated schedule is feasible.

Referring to fig. 4, the mutation operation of the vector MA in step S6 is performed as follows:

step S601: randomly generating r random numbers, wherein r belongs to [1, M ], and M is the total number of the working procedures;

step S602: randomly selecting r positions from the parent chromosomes of the MA sequence;

step S603: and for each process, selecting the machine with the shortest processing time from the available machine set for replacement, and if the original MA parent chromosome gene is processed by the machine with the shortest processing time, selecting the machine with the second shortest processing time for replacement.

Example 5

In order to avoid the genetic method from falling into local optimum and obtaining a high-quality solution, i is more than or equal to 1 and less than or equal to 4 in the VNSi of the neighborhood structure in the step S7;

when i takes a value of 1, the VNS1 performs neighborhood search for the MA sequence, and randomly selects a machine from the MA sequence for replacement;

when i takes a value of 2, the VNS2 performs neighborhood search for the OS sequence, and two workpieces J are randomly selected₁And J₂And make J₁The number of steps is less than J₂Number of steps (2)Separately record J₁And J₂From left to right, sequentially arranging J₁Each process is laid in J₂Then J is placed on₂Each process step of (a) is put in the rest of the positions, for example: for chromosomal OS sequences: 3212311;

randomly selecting two workpieces J₁And J₂For example: 1 and 3. Since the number of steps for the workpiece 3 is smaller than that for the workpiece 1, J is provided₁3 and J ₂1. Exchange J₁And J₂The new OS sequence is then obtained as: 1232131.

when i takes a value of 3, the VNS3 performs neighborhood search on the OS sequence, randomly selects the gene segment t, the length of t is smaller than the total process number, inserts the gene segment t into the original position again after the gene segment t is reversely sequenced, and for the OS of the chromosome: 3212311, randomly selecting gene fragment: 21231, after operation in VNS3 neighborhood, the new OS sequence is 3132121;

when i takes a value of 4, the VNS4 performs neighborhood search for the OS sequence, randomly selects the gene segments t, makes the length of t smaller than the total operand, randomly changes the sequence of the gene segments t, and then reinserts the gene segments t into the original position.

For chromosomal OS sequences: 3212311.

randomly selecting two workpieces J₁And J₂For example: 1 and 3. Since the number of steps for the workpiece 3 is smaller than that for the workpiece 1, J is provided₁3 and J ₂1. Exchange J₁And J₂The new OS sequence is then obtained as: 1232131.

the above disclosure is only for a few specific embodiments of the present invention, however, the present invention is not limited to the above embodiments, and any variations that can be made by those skilled in the art are intended to fall within the scope of the present invention.

Claims (7)

1. A hybrid genetic method for scheduling a multi-target flexible job shop is characterized by comprising the following steps:

step S1: initializing a coding population, and determining the size P of the population, the iteration times T and the neighborhood searching VT times;

step S2: respectively encoding the workpieces by adopting an OS random encoding method and an MA global sequence encoding method, then decoding according to the sequence of the OS random encoding, processing each procedure on an optional processing machine on the procedure according to the minimum time line until all the procedures are processed according to the minimum time line and matched with the corresponding MA sequence, randomly selecting an OS sequence in the OS random encoding, and selecting to obtain the MA sequence by adopting a method combining GSE selection and random selection;

step S3: calculating the fitness value of each chromosome in the sequence, calculating the Pareto optimal solution set of the current population by using a rapid non-dominated sorting method, and storing the top 20% of the sorted chromosomes in the population into a Pareto archive PA according to the Pareto sorting and crowding distance of each chromosome;

step S4: judging whether the convergence standard is met or not, and if any convergence standard is met, ending outputting the Pareto optimal solution; otherwise, executing step S5;

step S5: performing cross operation of a vector OS and a vector MA in the OS sequence and the MA sequence, calculating a Pareto optimal solution set and updating a PA;

step S6: carrying out mutation operation of a vector OS and a vector MA in a coding sequence, and updating PA;

step S7: performing neighborhood search on an OS sequence and an MA sequence in PA, wherein a neighborhood structure is represented as VNS [ i ], setting iteration times VT, sequentially performing neighborhood search according to the sequence from VNS1 to VNS4, obtaining a better solution x 'each time, ending the loop if x' is better than x, entering the next loop until the iteration times VT is reached, outputting a Pareto optimal solution, and finishing workshop scheduling.

2. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein the OS randomly encodes the processing order of the processes in the order of occurrence of the workpiece numbers in step S2, the encoding length being L₁(ii) a The MA global sequence coding is the coding value and the coding length of each workpiece according to the selectable processing machine number of each workpiece procedureIs L₂And L is₁＝L₂。

3. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein the step S3 is implemented by calculating a pareto rank i of each individual solution in the encoding population_rankAnd a congestion distance D_iWherein the crowding distance D_iThe calculation formula of (2) is as follows:

d_i,j＝|F₁(i)-F₁(j)|+|F₂(i)-F₂(j)|+|F₃(i)-F₃(j)| (1)

D_i＝min{d_i,k} (k＝1,…,n；k≠i) (2)

wherein n is the number of workpieces, d_i,jIs the distance of solutions with the same Pareto ranking.

4. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein the convergence criterion of step S4 is:

the iteration number T reaches a given upper limit L;

successive iterations do not have a new optimal solution to produce.

5. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein the vector OS intersection process in step S5 is as follows:

step S501: taking out n parent chromosomes from the random encoding population of the OS, and marking the chromosomes as P₁，P₂，…P_nWherein n represents the total number of workpieces;

step S502: at P_iThe ith work piece is taken out in sequence and copied to the child generation C_iWherein the gene position remains unchanged, wherein i is 1, …, n;

step S503: will P_iThe other workpieces except the i +1 th workpiece are sequentially copied to the child C according to the sequence of the working procedures_i+1Wherein i is 1, …, n-1; finally P is added_nExcept for the 1 st workpieceCopying other workpieces to descendant C according to the sequence of other workpieces_i；

Step S504: obtaining the offspring chromosome C₁，C₂，…C_n。

6. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein the mutation operation of the vector MA in the step S6 is performed as follows:

step S601: randomly generating r random numbers, wherein r belongs to [1, M ], and M is the total number of the working procedures;

step S602: randomly selecting r positions from the parent chromosomes of the MA sequence;

step S603: and for each process, selecting the machine with the shortest processing time from the available machine set for replacement, and if the original MA parent chromosome gene is processed by the machine with the shortest processing time, selecting the machine with the second shortest processing time for replacement.

7. The hybrid genetic method for multi-target flexible job shop scheduling according to claim 1, wherein 1 ≦ i ≦ 4 in the neighborhood structure VNSi in the step S7;

when i takes a value of 1, the VNS1 performs neighborhood search for the MA sequence, and randomly selects a machine from the MA sequence for replacement;

when i takes a value of 2, the VNS2 performs neighborhood search for the OS sequence, and two workpieces J are randomly selected₁And J₂And make J₁The number of steps is less than J₂The number of steps of (1), respectively, recording J₁And J₂From left to right, sequentially arranging J₁Each process is laid in J₂Then J is placed on₂Each process is placed at the rest positions;

when i takes a value of 3, VNS3 carries out neighborhood search aiming at the OS sequence, randomly selects gene segments t, the length of t is smaller than the total process number, and after the gene segments t are in reverse order, the gene segments are inserted into the original position again;

when i takes a value of 4, the VNS4 performs neighborhood search for the OS sequence, randomly selects the gene segments t, makes the length of t smaller than the total operand, randomly changes the sequence of the gene segments t, and then reinserts the gene segments t into the original position.

Images