CN112731888B

CN112731888B - Improved migrant bird optimization method for scheduling problem of batch flow mixed flow shop

Info

Publication number: CN112731888B
Application number: CN202110021878.3A
Authority: CN
Inventors: 汤洪涛; 王丹南; 陈贵芳; 任森丽; 郑之恒; 周嘉豪
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2021-01-07
Filing date: 2021-01-07
Publication date: 2022-07-01
Anticipated expiration: 2041-01-07
Also published as: CN112731888A

Abstract

The invention discloses an improved migrant bird optimization method for scheduling problems of a batch flow mixed flow shop, which comprises the following steps: s1: initializing a population: six control parameters of an AMBO algorithm are initialized; s2: leading to solution improvement; s3: improving a follow-up solution; s4: replacing the leader solution; s5: updating the operator weight of the leader solution; s6: and (5) performing sequential partial disturbance on the leader bird through a disturbance mechanism, recalculating the optimal solution, and outputting a calculation result when a termination condition is met. The invention provides a migratory bird migration Algorithm (AMBO) based on an adaptive neighborhood search algorithm, aiming at the characteristic that improvement probabilities of operators of the MBO algorithm are different in different stages of operation of the algorithm, and the technical problem that an existing optimization method for the unequal batch flow mixed flow shop scheduling problem is easy to fall into local optimization is solved through steps of initializing population, improving leading solution, improving following solution, replacing leading solution and updating the operator weight of the leading solution and a disturbance mechanism.

Description

Improved migrant bird optimization method for scheduling problem of batch flow mixed flow shop

Technical Field

The invention relates to the technical field of computer integrated manufacturing, in particular to an improved migrant bird optimization method for scheduling problems of a batch flow mixed flow shop.

Background

The bulk flow Hybrid flow Scheduling Problem (LS-HFSP) is a combination of the bulk flow Problem (LS) and the Hybrid Flow Scheduling Problem (HFSP). In recent years, LS-HFSP has gained widespread attention, and extensive research has shown that bulk streaming can significantly improve scheduling efficiency [2 ]. Depending on whether the given split molecule batches are the same size, the bulk flow problem can be divided into Equal bulk flow problems (ELS) and unequal bulk flow problems (ILS). Equal batch flow mixed flow shop scheduling problem (ELS-HFSP) is currently the most studied LS-HFSP problem, equal batch splitting is the simplest and most straightforward method to solve the batch flow problem, and once the number of sub-batches is determined, the size of each sub-batch can be determined. But equal batch splitting can only optimize the number of sub-batches, and cannot optimize the size of each sub-batch. In reality, the unequal bulk flow Problem is more suitable for actual production life, and because the unequal bulk flow mixed flow shop Scheduling Problem (ILS-HFSP) optimizes the processing sequence and the number of sub-batches and the size of the sub-batches, the computational complexity is greatly increased.

In recent years, scholars at home and abroad have made a lot of research in the ILS-HFSP neighborhood, but the work has certain limitations, and the existing research is mainly based on single-target optimization. Mei Zhang et al studied the variable-size batch splitting scheduling problem of the unequal batch splitting scheduling problem (BS-FJSP) in the flexible job shop, and improved the migratory bird migration algorithm by using a competitive cooperation mechanism to improve the algorithm to solve the RPI value. Nederii and Yazdani aim at minimizing the delay time, study the problem of the non-miscible ILS _ HFSP in the k-phase and the situation of the sublots, and propose an empire competition algorithm to solve the problem. Lalitha et al studied the problem of ILS _ HFSP with k-phase unmixable flow with multiple parallel machines only in the last phase, in terms of minimizing the maximum production time. Zhang et al studied a two-stage ILS _ HFSP problem for a special immiscible plug-in sublot with the goal of minimizing the average completion time, the first stage containing multiple parallel machines and the second stage containing only one machine, to solve the dispatching order of the processed lot, the number of divided lots of the lot, and the size of the lot, respectively. The literature is a few researches on the scheduling problem of the multi-target unequal batch flow mixed flow shop, but related researches aiming at the minimum number of products in process are blank. Zhang et al propose a multi-objective migratory bird migration algorithm (MMBO) for the scheduling problem (ELS-HFSP) of equal batch flow mixed flow shop with random disturbance, and solve the dual-objective optimization problem of minimizing the deviation between the total processing time and the start time of a sub-batch. Li et al have studied the problem of scheduling variable batch-to-batch mixed flow shop with the goal of reducing average dead time, energy consumption, and losses due to advances and delays. Garey and johnson have demonstrated that HFSP is an NP-hard problem, so the unequal batch flow hybrid line shop scheduling problem (ILS-HFSP) studied herein is also an NP-hard problem, it is time-consuming and difficult to obtain an accurate solution using deterministic algorithms, so learners often adopt heuristic algorithms to solve. Migratory bird migration algorithm (MBO) is a new heuristic algorithm, first proposed in 2012 by Duman et al. The algorithm simulates bird migration behavior in V-formation flight, each representing a feasible solution. In the algorithm, the number of birds, the number of neighborhood solutions, the number of neighborhoods shared by following birds and the number of neighborhood searching times are four parameters influencing the performance of the algorithm, and the algorithm has strong local searching capability and a simple structure, and is successfully applied to different research fields such as secondary distribution, flow shop scheduling, credit card fraud and the like.

For example, chinese patent CN108287531A, published 2018, 7 and 17, an improved migrant bird optimization method for mixed flow shop scheduling problems, the method comprising: in the previous evolution algebra, decoding the flying bird following individuals and the flying bird leading individuals by adopting a permutation decoding mode to realize the evolution of the flying bird following individuals and the flying bird leading individuals; after the evolution algebra critical value is exceeded, decoding the flying bird following individuals and the flying bird leading individuals by adopting a fine-tuning arrangement decoding mode according to the probability to realize the evolution of the flying bird following individuals and the flying bird leading individuals; and obtaining the optimal scheduling scheme of the hybrid flow shop by judging whether the evolution algebra meets the requirements. In the improved migrant bird optimization method provided by the invention, the fine adjustment arrangement decoding is not strictly in accordance with the first-come first-processed principle in the arrangement decoding method, so that the possibility of searching a better solution is increased; the permutation decoding step and the fine adjustment permutation decoding step are combined, and the convergence speed of the improved migrant optimization algorithm adopting the fine adjustment permutation decoding is accelerated. However, the combination of the bulk flow problem and the hybrid flow shop scheduling problem is not considered, and a new solution is needed to solve the bulk flow hybrid flow shop scheduling problem.

Disclosure of Invention

Aiming at the defects or improvement requirements of the prior art, the invention provides an improved migratory bird migration optimization algorithm for the scheduling problem of unequal mixed flow workshops, and aims to solve the technical problem that the existing optimization method for the scheduling problem of unequal batch flow mixed flow workshops is easy to fall into local optimization.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows: an improved migrant bird optimization method for scheduling problems of a batch flow mixed flow shop comprises the following steps:

s1: initializing a population: initializing six control parameters of an AMBO algorithm;

s2: leading to solution improvement;

s3: improving a follow-up solution;

s4: replacing the leader solution;

s5: updating the operator weight of the leader solution;

s6: and (5) performing sequential partial disturbance on the leader bird through a disturbance mechanism, recalculating the optimal solution, and outputting a calculation result when a termination condition is met. A method for optimizing the migrant bird for the scheduling problem of mixed flow shop features that the migrant bird migration Algorithm (AMBO) based on adaptive neighborhood search algorithm is proposed to solve the problem of MBO algorithm, and the time window operator adaptive to the problem is proposed to increase the convergence speed of algorithm, which is implemented by 5 steps and a disturbance mechanism for preventing the algorithm from falling into local optimum problem.

Preferably, the control parameters in step S1 include the number α of individuals in the population, the number β of neighbors to be considered, the number χ of neighbors to be shared, the number ω of iterations of the population in one evolution round, the adaptive adjustment period m of the operator weight, and the perturbation mechanism trigger period g. Six control parameters of the AMBO algorithm are initialized and used in subsequent calculations.

Preferably, the step S2 includes the following steps:

s21: according to the initial weight probability of each operator, a roulette method is adopted to generate beta neighborhood solutions around a leading solution;

s22: evaluating the fitness value of the neighborhood solution according to a decoding strategy for the obtained neighborhood solution;

s23: judging whether the fitness value of the optimal solution in the neighborhood solutions is smaller than the fitness value of the leader solution, if so, replacing the leader solution with the optimal solution in the neighborhood solutions, and if not, keeping the leader solution unchanged;

s24: selecting optimal 2% solutions for the unused neighborhoods according to the target values of the unused neighborhoods;

s25: an initial set of χ left shared neighbors and a set of χ right shared neighbors are formed. The method comprises the steps that beta is the number of neighbors to be considered, the optimal solution in the neighborhood solutions, namely the neighborhood solution with the minimum fitness value in the neighborhood solutions, is the optimal solution, namely the minimum fitness value, the number of the solutions is 2 times of the number of shared neighbors, namely 2 x, the 2 x solutions are utilized to form initial x left and right shared neighborhood sets, leadership solution is improved, and according to the initial weight probability of operators, a roulette method is adopted to surround the leadership solution to generate the beta neighborhood solutions. Evaluating the obtained neighborhood solution according to a decoding strategy that the fitness value of the neighborhood solution is small, and if the optimal solution in the neighborhood solution is superior to the leader solution, replacing the leader solution; otherwise, the leader solution remains unchanged. And then, selecting optimal 2% solutions for the unused neighborhoods according to target values of the unused neighborhoods, and respectively forming initial x left and right shared neighborhood sets.

Preferably, the step S3 includes the following steps:

s31: generating beta neighborhood solutions around the following solution in a roulette mode according to the weights of the neighborhood operators;

s32: the generated beta neighborhood solutions and the solutions in the left and right shared neighborhood sets are neighborhood sets following the solution Y, and the obtained neighborhood sets are evaluated according to a decoding strategy;

s33: judging whether the fitness value of the optimal neighborhood is smaller than that of Y, if so, replacing the following solution Y by the optimal neighborhood, and if not, keeping the following solution Y unchanged;

s34: selecting the optimal chi solutions in unused neighborhoods, and reconstructing a left shared neighborhood set and a right shared neighborhood set;

s35: judging whether all the follow solutions are improved, if so, entering the step S36, and if not, returning to the step S31;

s36: ending the improvement of the follow-up solution. Following solution refinement, the refinement process is performed along the tail. Two side follow solutions such as Y for the left and right queues produce β neighborhood solutions in roulette based on the neighborhood operator weights. The generated beta neighborhood solutions and the solutions in the left and right shared neighborhood sets are regarded as a neighborhood set of Y, and the fitness value of the obtained neighborhood set is evaluated according to a decoding strategy. If the best neighborhood is more adaptive than Y, then Y is replaced. Then, the optimal χ solutions are selected in the unused neighborhoods for reconstructing the left and right shared neighborhood sets. The above process is repeated until all the following solutions in the left queue and the right queue are traversed.

Preferably, the step S4 includes the following steps:

s41: circularly executing the steps S2 and S3 omega times;

s42: judging whether the fitness value of the optimal solution in the follow-up solutions is smaller than the fitness value of the lead solution, if so, performing step S43, otherwise, performing step S44;

s43: replacing the leader solution with an optimal solution of the follow-up solutions;

s44: the leader solution remains unchanged. And replacing the optimal solution in the follow solutions, namely the follow solution with the minimum fitness value in the plurality of follow solutions is the optimal solution, performing step S2 and step S3 omega times, wherein omega is the number of times of iteration of a population in one evolution tour, and exchanging the optimal follow solution with the current optimal solution to update the lead solution if the optimal solution in the follow solutions is better than the adaptive value of the lead solution, otherwise, keeping the solution unchanged.

Preferably, the step S5 includes the following steps:

s51: updating the operator weight of the leading solution according to the improvement condition of different operators on the leading solution;

s52: judging whether a neighborhood search operator weight updating period is reached, if so, performing step S53, and if not, not updating the probability of the operator being selected in the neighborhood search;

s53: and respectively updating the probability of each operator being selected during neighborhood searching according to a neighborhood operator weight self-adaptive adjustment formula. And updating the operator weight according to the improvement condition of different operators on the solution, judging whether a neighborhood search operator weight updating period is reached, and if the neighborhood search operator weight updating period is reached, respectively updating the probability of each operator being selected in the neighborhood search according to a neighborhood operator weight self-adaptive adjustment formula.

Preferably, the step S6 includes the following steps:

s61: judging whether the termination condition is met, if so, performing step S63, and if not, performing step S62;

s62: performing sequential partial disturbance on the leader bird which is not updated after the g iterations by adopting a Glover operation, taking two new solutions to respectively replace a left following bird and a right following bird behind the leader bird, and returning to the step S1;

s63: and outputting a calculation result. And (4) performing sequential partial disturbance on the leader bird which is not updated after the g iterations by adopting a Glover operation, and taking two new solutions to respectively replace the left following bird and the right following bird behind the leader bird. If the optimal solution of the algorithm is still unchanged after the algorithm is iterated for a plurality of times or the maximum iteration times is reached, the algorithm is terminated; otherwise, repeating the steps S1-S5 until the algorithm termination condition is met, g is a disturbance mechanism trigger period, and the calculation result comprises two iteration times and an optimal solution.

Preferably, the search mode of the neighborhood search is as follows: obtaining an optimal batch Q meeting the maximum production rate according to a bottleneck theory, and defining a push time window, wherein the formula of the time window is as follows:

wherein d is_i ^esIndicating the start time of the task at the internal applicator, d_i ^lfRepresenting the finish time of the task at the inner spraying machine, setting a broadening coefficient gamma to respectively expand the lower bound and the upper bound of the time window for improving the matching degree of the time window, d_i ^es、d_i ^lfThe relation formula with the work order is as follows:

randomly searching two work orders which are not matched with the time window and have different stretcher numbers from the current solution, and matching the time windows to form a new neighborhood solution, wherein the work order relational expression is as follows:

wherein,

and

each represents the number of matched work orders that meet the time window requirements.

The best batch Q meeting the maximum production rate can be obtained by a bottleneck theory; as the number of work order products is different, a push time window is defined by using the basic principle of discrete event simulation for reference

It represents the start time and end time of the task at the internal applicator, and is a time window in the prediction time domain containing a certain number of work orders, and the average width of which is taken to be 2 Qt₃. Since the probability that the order can just form the time windows with the number of just 2Q is very small, in order to improve the matching degree of the time windows, a broadening coefficient gamma is set to respectively expand the lower bound and the upper bound of the time windows, d_i ^es、d_i ^lfThe relation formula with the work order is as follows:

the goal of each search is to randomly find the stretcher number from the current solutionAnd matching the same two work orders which are not matched with the time windows by the time windows to form a new neighborhood solution. The matched work orders meeting the requirements of the time window are respectively counted as

It satisfies the following order relation:

preferably, the step of calculating the time window comprises the steps of:

s91: inputting a work order in a current bird into a search set;

s92: judging whether the search set is empty, if so, adopting exchange operation to form a neighborhood solution and finishing neighborhood search, and if not, entering step S93;

s93: searching a work order with the largest number of products in the search set, and marking the work order as a first work order;

s94: judging whether the first work order and the work order next to the first work order can meet the time window constraint, if so, forming a solution by the first work order and the work order next to the first work order, and if not, entering the step S95;

s95: searching for a work order which can meet time window constraint with the first work order in an individual;

s96: judging whether a work order meeting the time window constraint with the first work order is found, if so, performing step S98, and if not, performing step S97;

s97: removing the first work order from the search set, and entering step S91;

s98: and exchanging the found work order with the position of the work order behind the first work order to form a new solution. The solution can be a domain solution, a following solution or a leading solution, two work orders meeting the time window constraint are distributed together through a time window to form a solution, if the first work order cannot find other work orders meeting the time window constraint, the first work order is removed from the search set, the work order with the largest product quantity is picked out from the rest search set, and time window search is carried out again until the loop exits.

Preferably, the adaptive neighborhood operator weight adjustment formula is as follows:

wherein, pi_oThe score accumulation condition of the operator O after m iterations is shown, and the initial value is 0; theta_oThe number of times the operator O uses the weight adjustment period; r is a reaction factor used to control the speed at which the weight adjustment algorithm reacts to the efficiency change of the heuristic method. Each operator is assigned a weight w_jIn the range of [0, 1]Using roulette in selection operators, the probability of each operator being selected

Updating the weight after each m times of a weight adjustment period, pi_oThe score accumulation condition of the operator O after m iterations is that the initial value is 0, if the performance is better than the optimal solution, the value of pi is taken_o＝π_o+1, taking original values of the rest operators; theta_oThe number of times the operator O uses the weight adjustment period; r is a reaction factor that controls the speed at which the weight adjustment algorithm reacts to the efficiency change of the heuristic method. If r is zero, we will not use the score at all, but keep the initial weight. Let us decide the weight in the score we obtained in the last generation if r is set to 1.

The substantial effects of the invention are as follows: the invention provides a migratory bird migration Algorithm (AMBO) based on an adaptive neighborhood search algorithm, aiming at the characteristic that improvement probabilities of operators of the MBO algorithm are different in different stages of operation of the algorithm, and the technical problem that an existing optimization method for the scheduling problem of unequal batch flow mixed flow workshops is prone to fall into local optimization is solved through the steps of initializing population, improving leading solution, improving following solution, replacing leading solution and updating the operator weight of the leading solution, and a disturbance mechanism can prevent the algorithm from falling into the local optimization.

Drawings

Fig. 1 is a schematic flow chart of the main steps of the present embodiment.

Fig. 2 is a flowchart illustrating specific steps of the embodiment.

Fig. 3 is a flowchart illustrating an implementation of the time window operator according to this embodiment.

Fig. 4 is a schematic diagram illustrating the adjustment of the work order in this embodiment.

Fig. 5 is a diagram of an example production line for the algorithm test of the present embodiment.

FIG. 6 is a diagram illustrating a scheduling of solving a production line by the algorithm of the present embodiment.

Detailed Description

The following provides a more detailed description of the present invention, with reference to the accompanying drawings.

An improved migratory bird optimization method for scheduling problems of a batch flow hybrid flow shop, as shown in fig. 1, includes the following steps: s1: initializing a population: initializing six control parameters of an AMBO algorithm; the control parameters in step S1 include the number α of individuals in the population, the number β of neighbors to be considered, the number χ of neighbors to be shared, the number ω of population iterations in one evolution round, the adaptive adjustment period m of operator weights, and the perturbation mechanism trigger period g. Six control parameters of the AMBO algorithm are initialized and used in subsequent calculations.

S2: leading to solution improvement; as shown in fig. 2, step S2 includes the following steps:

s21: according to the initial weight probability of each operator, adopting a roulette method to generate beta neighborhood solutions around the leader solution;

S3: improving a follow-up solution; step S3 includes the steps of:

s36: ending the improvement of the follow-up solution. Following solution refinement, the refinement process is performed along the tail. Two side pairs of following solutions, e.g., Y, for the left and right queues produce β neighborhood solutions in roulette based on the respective neighborhood operator weights. The generated beta neighborhood solutions and the solutions in the left and right shared neighborhood sets are regarded as a neighborhood set of Y, and the fitness value of the obtained neighborhood set is evaluated according to a decoding strategy. If the best neighborhood is more adaptive than Y, then Y is replaced. Then, the optimal χ solutions are selected in the unused neighborhoods for reconstructing the left and right shared neighborhood sets. The above process is repeated until all the following solutions in the left queue and the right queue are traversed.

S41: circularly executing the steps S2 and S3 omega times;

S5: updating the operator weight of the leader solution; step S5 includes the steps of:

s53: and respectively updating the probability of each operator being selected during neighborhood searching according to a neighborhood operator weight self-adaptive adjustment formula. And updating the operator weight according to the improvement condition of different operators on the solution, judging whether a neighborhood search operator weight updating period is reached, and if the neighborhood search operator weight updating period is reached, respectively updating the probability of each operator being selected in the neighborhood search according to a neighborhood operator weight self-adaptive adjustment formula. The self-adaptive adjusting formula of the neighborhood operator weight is as follows:

wherein, pi_oThe score accumulation condition of the operator O after m iterations is shown, and the initial value is 0; theta_oThe number of times the operator O uses the weight adjustment period; r is a reaction factor for controlling the speed at which the weight adjustment algorithm reacts to the efficiency change of the heuristic method. Each operator is assigned a weight w_jIn the range of [0, 1]Using roulette in selection operators, the probability of each operator being selected

Updating the weight, pi, after each m times of a weight adjustment period_oThe score accumulation condition of the operator O after m iterations is that the initial value is 0, if the performance is better than the optimal solution, the value of pi is taken_o＝π_o+1, taking original values of the rest operators; theta_oThe number of times the operator O uses the weight adjustment period; r is a reaction factor that controls the speed at which the weight adjustment algorithm reacts to the efficiency change of the heuristic method. If r is zero, we will not use the score at all, but keep the initial weight. Let us decide the weight in the score we obtained in the last generation if r is set to 1. The search mode of the neighborhood search is as follows: obtaining an optimal batch Q meeting the maximum production rate according to a bottleneck theory, and defining a propulsion time window, wherein the formula of the time window is as follows:

wherein d is_i ^esIndicates the start time of the completed job at the internal applicator, d_i ^lfRepresenting the finish time of the task at the inner spraying machine, setting a broadening coefficient gamma to respectively expand the lower bound and the upper bound of the time window for improving the matching degree of the time window, d_i ^es、d_i ^lfThe relation formula with the work order is as follows:

wherein,

and

each represents the number of matched work orders that meet the time window requirements. The best batch Q meeting the maximum production rate can be obtained by a bottleneck theory; as the number of work order products is different, a push time window is defined by using the basic principle of discrete event simulation for reference

It represents the start time and end time of the task at the internal applicator, and is a time window in the prediction time domain containing a certain number of work orders, and the average width of which is taken to be 2 Qt₃. Because the probability that the order can just form the time windows with the number of just 2Q is very small, a widening factor gamma is added, and in order to improve the matching degree of the time windows, the widening factor gamma is set to respectively expand the lower bound and the upper bound of the time windows, d_i ^es、d_i ^lfThe relation formula with the work order is as follows:

as shown in fig. 3, the step of calculating the time window comprises the steps of:

s91: inputting a work order in a current bird into a search set;

s96: judging whether a work order meeting the time window constraint with the first work order is found, if so, performing step S98, otherwise, performing step S97;

s97: removing the first work order from the search set, and entering step S91;

The target of each search is to randomly search two work orders which are not matched with the time window and have different stretcher numbers from the current solution, and perform time window matching on the work orders to form a new neighborhood solution. The matched work orders meeting the time window requirement are recorded as

It satisfies the following order relation:

s6: and (5) performing sequential partial disturbance on the leader bird through a disturbance mechanism, recalculating the optimal solution, and outputting a calculation result when a termination condition is met. Step S6 includes the following steps:

s61: judging whether the termination condition is met, if so, performing step S63, otherwise, performing step S62;

s62: performing sequential partial disturbance on the leader bird which is not updated after g iterations by adopting a Glover operation, taking two new solutions to replace a left following bird and a right following bird behind the leader bird respectively, and returning to the step S1;

The embodiment provides a migratory bird migration Algorithm (AMBO) based on an adaptive neighborhood search algorithm aiming at the characteristic that improvement probabilities of operators of the MBO algorithm are different in different stages of the operation of the algorithm, provides a time window operator adaptive to a problem aiming at problem characteristics so as to accelerate the convergence speed of the algorithm, and is mainly realized by adding a disturbance mechanism in 5 steps, wherein the disturbance mechanism is added to prevent the algorithm from falling into the local optimum problem.

To further illustrate the present invention, the following example is solved, a mixing line is shown in fig. 5, two stretchers and an internal sprayer can produce only one product at the same time, and the two stretchers and the internal sprayer can not produce mixed flow, and each order is provided with only one set of mold. The productivity of the two stretching machines is 450 per hour, the productivity of the inner spraying section is 900 per hour, and the productivity of the packaging section is 800 per hour. The inner spraying only can produce one product at a time, and before different products produced by the stretcher 1 and the stretcher 2 enter the inner spraying, one product needs to enter the inner spraying machine after the other product is sprayed in the buffer area B1.

The requirements to satisfy the following constraints include: the raw materials are supposed to be supplied continuously on line, so that the situation of material shortage does not exist; the processing time of each machine is a fixed value; the machine does not have faults; each sub-batch is assumed to be non-miscible; the die changing time exists in each wire changing of the drawing machine and the inner spraying machine, and the time is a fixed value; the setup time for the packaging line is very short, assuming no retooling time.

Assume that the products of any two orders do not share a set of molds. By analyzing the production rate of the production line, the production bottleneck of the production line is the packaging section, the maximum production rate thereof is 800 pieces/hour in total, and the capacity of other machines of the production line is remained. In addition, the product quantity of the order is greatly different, and the production speed of a production line can not reach the speed of a packaging line due to the production of small-batch orders and the mold changing time, so that the capacity loss is caused; this may also lead to work-in-process build problems if large batches of orders are produced at all times.

Some symbols are defined according to the above examples as shown in the following table:

TABLE 1 symbols and their meanings

From the table above, constraints can be derived:

an objective function:

represents rounding down

In the above formula, formula (1) represents that the processing starting time of the same work order on the inner spraying machine is more than or equal to the time of the work order completing half of the product quantity of the work order at the stretching

machines

1 and 2; the formula (2) indicates that the machining start time of each work order must be 0 or more; the formula (3) is a work order S on the machine k_ijAt the start of machining ofThe relationship between time and completion time; formulas (4), (5), (6) and (7) respectively represent the constraint of the starting time of the next work order and the finishing time of the previous work order on the stretcher 1, the stretcher 2, the inner spraying machine and the packaging line; formula (8) indicates that different batches of work orders are not interflowable; formula (9) represents the minimum number of products per work order after splitting; equation (10) represents the minimum completion time to complete production of all orders; equation (11) indicates that the average in-process quantity is minimized.

The embodiment applies an improved migratory bird migration algorithm, and aims at the specific definition of the ILS-HFSP problem, namely the scheduling problem of the batch flow mixed flow shop, including,

(1) batch splitting rules

For the bulk flow problem, a splitting rule of the order needs to be clarified. A common order splitting mode is that a random number is given, the order to be split is split into the number of sub-orders [3,4], and the selection range of the random number needs to be specifically analyzed according to the size of the order and the specific problem of the problem characteristic. The sizes of the batches of the research are not completely the same, and the upper limit and the lower limit of the split batches are adjusted according to the size of each order.

Orders with large product quantity are the cause of accumulation of work-in-process, since the order has a minimum batch Q_minStipulate only the product quantity of the order

Can be split, so that large orders at least need to be split into

Representing rounding down) of work orders, which can be split into at most

And (6) processing each work order.

The splitting rule for the order is therefore:

number of orders

The order form is not split, and the number of the orders is

Number of orders

From

Randomly selecting an integer as the number of work orders

(2) ILS-HFSP problem based encoding

The ILS-HFSP problem should optimize both the order splitting problem and the job scheduling problem, so the encoding should consider both aspects simultaneously, and a two-stage encoding scheme is employed herein. The natural number sequence is used to represent all possible work order arrangements, and the code is divided into two sections: the first stage represents the process sequence; the second segment represents the work order codes to be distributed, and each work order code corresponds to a processing sequence number. Each work order code consists of a work order number and the number of the work orders corresponding to the work order number, the number of the work order numbers is an integer of 4 bits, and the number of the work orders is an integer of 5 bits. For example, the work order number is 101, and the work order code for 3000 work orders is 010103000. An example of the encoding is shown in fig. 3:

(3) ILS-HFSP based decoding

Each code represents the scheduling result of the order split work order on the internal spraying machine, and in order to further obtain the processing time sequence of each work order on each machine, the fitness value of each solution is calculated, and the code needs to be decoded. Because the stretcher 1 and the stretcher 2 work in parallel, each work order can be processed on only one machine, and two problems need to be considered during decoding: firstly, the final time of finishing the processing time of all work orders; second is the system average work-in-process quantity. The specific process is as follows:

if n work orders are provided, the processing steps on the inner spraying machine are listed as

I.e. to sequentially order the work orders

From

The following steps are taken out and executed:

step 1: selecting the stretcher with the first idle time, and dividing the batch

Distributing the raw material to the machine, and determining the starting time and the finishing time of the raw material on the stretching machine;

and 2, step: repeating the step 1 until the distribution of the stretching machines of all work orders is completed;

and step 3: sequentially calculating the starting processing time and the finishing time of each work order on the inner spraying machine according to the processing sequence and the finishing time of each work order on the stretching machine;

and 4, step 4: calculating the starting processing time and the finishing time of each work order on a packaging line according to the finishing time of each work order on an inner spraying machine to obtain the final finishing time of finishing processing all the work orders;

and 5: and calculating the average number of products in process from the beginning to the end of the process in the flow shop according to the beginning and the end of the process time of each work order on the corresponding processing machine obtained by decoding.

(4) Fitness function value

After the processing time of the solution on each machine is obtained, the fitness value of the solution needs to be evaluated to complete leader solution selection and follow solution sorting selection. The research adopts a weight sum method to process a double-target optimization problem, and because two targets of the research have different dimensions, target normalization processing needs to be carried out firstly, and the specific process is as follows:

wherein

Is a target of f_yNormalized value, max (f)_y) And min (f)_y) Respectively represent the object f_iUpper and lower bounds. In this way, each target can be normalized to the interval [0, 1%]A value in between. The upper and lower bounds of the target are updated in real time as the algorithm runs, i.e., the upper and lower bounds are updated with their target values each time a new solution is generated. The normalized fitness function is:

minimizing the total time and minimizing the average work-in-process quantity are two objectives of the present study, the primary objective of line optimization is to maximize the production rate and maximize the business benefits, and the objective of minimizing the average work-in-process quantity is to reduce the cost, which is a secondary objective with a weight λ₁＝0.6，λ₂＝0.4。

Self-adaptive variable neighborhood search strategy:

the MBO algorithm is a meta-heuristic algorithm based on neighborhood search, and therefore it is necessary to determine an efficient neighborhood search operator for it. An ILS-HSFP-based coding mechanism introduces four common neighborhood operators, namely an insertion operator, a greedy insertion operator, an exchange operator and a greedy exchange operator. Based on the best batch theory provided by the research, operators capable of effectively reducing the time window of the average number of products being processed are provided, the operators are all scheduling sub-problems, and batch adjustment operators are provided for batch splitting sub-problems according to problem characteristics.

Because the crossover operator has randomness, the solution obtained through the crossover operator can reduce the local searching capability of the solution; the greedy operator can improve the result of the local search, but the calculation amount of the algorithm is greatly increased. To balance the computational burden with the local search results, a time window operator is proposed that yields a better solution in a shorter time. The mechanism is as follows: the other machines except the packing section need to be set for die change when changing lines, the production rate of the packing section is 800/hour, and the production rate of the other machines is 900/hour under the condition of die change. To match the capacity of the two, there is a minimum batch Q at which each product is processed such that the stretcher, internal spray section processing time plus the die change time is exactly the same as the package section processing time.

It can be known from the bottleneck theory that the minimum lot Q can reach the maximum production rate only if the minimum lot Q is equal to the minimum lot of the bottleneck process, and because the die change time of each machine is different, the minimum lot of each machine is as follows:

minimum batch of inner spray:

stretcher 1 is the same machine as stretcher 2, so their cycle times are the same, the lowest run of stretcher 1/2

Max (maximum quality) (Q) in lowest processing batch of whole production line₃，Q_1/2}。

As the number of work order products is different, a push time window is defined by using the basic principle of discrete event simulation for reference

It represents the start time and end time of the task at the internal applicator, and is a time window in the prediction time domain containing a certain number of work orders, and the average width of which is taken to be 2 Qt₃. Since the order can just constitute a time window of just 2Q in number, the probability is very small, so that a widening factor gamma, d is increased_i ^es、d_i ^lfThe relation formula with the work order is as follows:

the target of each search is to randomly search two work orders which are not matched with the time window and have different stretcher numbers from the current solution, and perform time window matching on the work orders to form a new neighborhood solution. The matched work orders meeting the requirements of the time window are respectively counted as

It satisfies the following order relation:

the common amplification factors are 0.05, 0.1, 0.2 and the like, and in order to match more orders as much as possible, the amplification factor of the research is 0.2. The specific implementation process of the time window operator is as follows:

step 1: inputting a work order in a current bird into a search set;

step 2: judging whether the search set is empty or not, if so, adopting random exchange operation to form a neighborhood solution and finishing neighborhood search;

and step 3: searching a work order with the largest quantity of products in the search set;

and 4, step 4: judging whether the work order and the next work order can meet time window constraint, exchanging the found processing serial number of the order 2 with the processing serial number after the order 1 if the time window constraint is met, and jumping to the step 5 if the time window constraint cannot be met;

and 5: and searching for the work order which can meet the time window constraint with the individual, if the work order can not be found, removing the work order from the search set and repeating the steps 1-5, and if the work order is found, exchanging the found work order with the position of the next work order to form a new solution.

Optionally, an order having more than two work orders is selected in the work order code segment, and two adjacent work orders are selected to be reallocated so that the reallocated work orders do not fall below the minimum batch size. For example, a 1300 and 4400 work order combination is randomly adjusted to a 1600 and 4100 combination. A schematic diagram of which is shown in fig. 4.

The neighborhood search operators respectively aim at different subproblems, and if only one of the subproblems is adopted, the global optimal solution is difficult to find. To effectively combine the two sub-problems, the following hybrid structure is proposed:

hybrid structure 1: first, an insert operator is executed, and then a batch adjust operator is executed.

Hybrid structure 2: first, a greedy insertion operator is performed, followed by a batch adjustment operator.

Hybrid structure 3: first, the swap operator is executed, and then the batch adjustment operator is executed.

Hybrid structure 4: first, a greedy exchange operator is performed, followed by a batch adjustment operator.

Hybrid structure 5: first, a time window operator is executed, and then a batch adjustment operator is executed.

Self-adaptive variable neighborhood search strategy:

in order to effectively utilize 11 different neighborhood operators, the neighborhood of each operator can be fully explored by adopting a variable neighborhood search strategy. The traditional variable neighborhood searching method is suitable for the condition that the size containing relationship exists among neighborhood operators, and when a solution which is better than a target value cannot be found in an operator with a smaller neighborhood range, the range of the neighborhood is expanded to continue searching until all neighborhoods are searched. The neighborhood set of the neighborhood operators proposed by the method does not have a complete inclusion relationship, the insertion operator and the greedy insertion operator have a common neighborhood set, the exchange operator and the greedy exchange operator have a common neighborhood set, and the neighborhood sets of the other operators are not completely the same. Therefore, a roulette method is adopted, each operator is given an initial weight, and a neighborhood search operator is randomly selected to obtain a neighborhood solution according to the weight probability of each operator in the total operator weight during each neighborhood search operation.

In the operation of the MBO algorithm, the improvement probability of each operator of the neighborhood search to the solution at different stages is different, for example, the operator with strong global search capability is selected at the initial stage of the algorithm solution to accelerate the search rate of the global optimal solution of the algorithm, but is adjusted at the later stageThe integral stage selects an operator with strong local searching capability to accelerate the searching speed of the local optimal solution. Thus introducing an adaptive adjustment strategy [18 ] herein]And enabling the weight of each neighborhood operator to be automatically adjusted along with the iteration of the algorithm, wherein the specific calculation is as follows: each operator is assigned a weight w_jIn the range of [0, 1]Using roulette with selection operators, the probability of each operator being selected

The weights are updated after every m times of a weight adjustment period:

π_othe score accumulation condition of the operator O after m iterations is that the initial value is 0, if the performance is better than the optimal solution, the value of pi is taken_o＝π_o+1, taking original values of the rest operators; theta_OThe number of times the operator O uses the weight adjustment period; r is a reaction factor that controls the speed at which the weight adjustment algorithm reacts to changes in efficiency of the heuristic method. If r is zero, we will not use the score at all, but keep the initial weight. Let us decide the weight in the score we obtained in the last generation if r is set to 1. The r is taken to be 0.5, so that the change rate is better while the change is ensured. Setting the selection weight of the initial neighborhood search operator of each operator as 1, and setting the initial weight of the operator as 1 again after the algorithm finishes one period of iteration and determines the selected probability of each migration.

The disturbance mechanism is as follows:

the neighborhood search mechanism of the MBO algorithm excessively focuses on the local search capability of the algorithm, and a disturbance mechanism is introduced into the MBO algorithm for balancing the global search capability and the local search capability of the algorithm. If the leader solution is not updated for g consecutive iterations, the perturbation mechanism triggers. In the basic perturbation mechanism, the method to prevent the solution from getting trapped in the local search is to replace it with a new solution that is randomly generated. The completely random method can affect the execution efficiency of the algorithm, and in order to improve the execution efficiency of the algorithm, when the continuous g-th leader solution is not updated, the leader solution is taken as a seed, and Glover operation is introduced to generate two solutions to respectively replace the left and right following solutions of the leader solution.

The Glover operation can be diverged from the seed solution to generate a new solution, and the new solution inherits the sequence information of the solution, so that the execution efficiency of the algorithm is improved, the Glover operation is widely applied to preventing the algorithm from falling into the local optimal solution, and a good effect is achieved.

To verify the practical application of the present invention, a specific example of the order quantity 20 distributed by taking table 1 as the order is randomly generated as shown in table 2. The AMBO algorithm is used for carrying out batch flow splitting scheduling on the average number of products in process and the minimum total processing time by taking calculation as targets, and the obtained optimal solution is as follows: the average number of articles in process was 2934.4 and the total processing time was 285640. The final scheduled gantt chart results obtained by AMBO for the proposed algorithm are shown in fig. 6.

TABLE 2 specific examples

Numbering	Number of orders	Order coding	Short for code
				1	1410	10101410	101
2	2620	10202620	102
				3	2680	10302680	103
4	1640	10401640	104
				5	2490	10502490	105
6	2050	10602050	106
				7	1260	10701260	107
8	2630	10802630	108
				9	5240	10905240	109
10	4120	11004120	110
				11	1670	11101670	111
12	2020	11202020	112
				13	1880	11301880	113
14	1190	11401190	114
				15	1970	11501970	115
16	2340	11602340	116
				17	1780	11701780	117
18	2410	11802410	118
				19	5340	11905340	119
20	12470	12012470	120

Aiming at the scheduling problem of unequal batch flow mixed flow workshops, the invention improves the migratory bird optimization algorithm to ensure that the algorithm solving performance is better. According to the characteristic that neighborhood operators have different degrees of algorithm improvement at different stages, an operator weight self-adaptive adjustment strategy is provided, and a time window operator is provided aiming at the problem characteristic that the minimum number of products in process is taken as a target, so that the target neighborhood is searched more effectively. The designed algorithm uses a self-adaptive large neighborhood search algorithm for reference, and the method designs a time window operator aiming at the characteristics of the problem and an iterative self-adaptive adjustment strategy of the selected weight along with the algorithm at a neighborhood operator, so that the global search capability of the algorithm and the algorithm solving speed are improved. The multiple repeated experiment results of multiple groups of random generation examples with different scales show that the established scheduling mathematical model and the improved migratory bird algorithm are feasible and effective, and compared with an MBO algorithm and a GA algorithm, the AMBO algorithm has the advantages of higher solving speed and smaller standard deviation of the optimal solution. The problem of reducing the number of products in process in factories can be solved, the blank of the ILS-HFSP problem about the multi-objective optimization research of the minimum maximum production time and the minimum number of products in process is filled, and the method is more suitable for the actual production of factories.

The above examples only show some embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

Claims

1. An improved migrant bird optimization method for scheduling problems of a batch flow mixed flow shop is characterized by comprising the following steps:

s2: leading to solution improvement;

s3: improving a follow-up solution;

s4: replacing the leader solution;

s5: updating the operator weight of the leader solution;

s6: performing sequential partial disturbance on the leader bird through a disturbance mechanism, recalculating an optimal solution, and outputting a calculation result when a termination condition is met;

the step S5 includes the following steps:

s53: respectively updating the probability of each operator being selected in the neighborhood search according to a neighborhood operator weight self-adaptive adjustment formula;

the search mode of the neighborhood search is as follows: obtaining an optimal batch Q meeting the maximum production rate according to a bottleneck theory, and defining a push time window, wherein the formula of the time window is as follows:

wherein,

and

all represent the number of matched work orders, t, meeting the time window requirement₃Is the time of the beat of the machine 3,

is the retooling time of the machine 3.

2. The method for optimizing migratory birds for scheduling problems in a batch flow hybrid flow shop according to claim 1, wherein the control parameters in step S1 include the number α of individuals in the population, the number β of neighbors to be considered, the number χ of neighbors to be shared, the number ω of population iterations in one evolution round, the adaptive adjustment period m of operator weight, and the triggering period g of perturbation mechanism.

3. The method for improving migratory bird optimization of a batch flow hybrid flow shop scheduling problem in accordance with claim 1 or 2, wherein said step S2 comprises the steps of:

s25: an initial set of χ left shared neighbors and a set of χ right shared neighbors are formed.

4. The method for improving migratory bird optimization of a batch flow hybrid flow shop scheduling problem in accordance with claim 1 or 2, wherein said step S3 comprises the steps of:

s36: ending the improvement of the follow-up solution.

5. The method for improving migratory bird optimization of a batch flow hybrid flow shop scheduling problem of claim 2, wherein said step S4 comprises the steps of:

s41: circularly executing the steps S2 and S3 omega times;

s42: judging whether the fitness value of the optimal solution in the follow solutions is smaller than the fitness value of the leader solution, if so, performing step S43, otherwise, performing step S44;

s44: the leader solution remains unchanged.

6. The method for improving migratory bird optimization of a batch flow hybrid flow shop scheduling problem in accordance with claim 1 or 5, wherein said step S6 comprises the steps of:

s63: and outputting a calculation result.

7. The method of claim 1, wherein the step of calculating the time window comprises the steps of:

s91: inputting a work order in a current bird into a search set;

s97: removing the first work order from the search set, and entering step S91;

s98: and exchanging the found work order with the position of the work order behind the first work order to form a new solution.

8. The improved migrant bird optimization method for the scheduling problem of the batch flow mixed flow shop according to claim 1, wherein the neighborhood operator weight adaptive adjustment formula is as follows:

wherein, pi_OThe score accumulation condition of the operator O after m iterations is shown, and the initial value is 0; theta_OThe number of times the operator O uses the weight adjustment period; r is a reaction factor for controlling the speed at which the weight adjustment algorithm reacts to the efficiency change of the heuristic method.