CN116300738A - Complex workshop scheduling optimizer based on improved meta heuristic algorithm - Google Patents

Abstract

The invention provides a complex workshop scheduling optimizer based on an improved meta-heuristic algorithm. The optimizer guides knowledge through three stages of initialization, local search and global search on the basis of a meta heuristic algorithm, and designs a guiding mechanism and a strategy to minimize the total advance or delay weight of the complex workshop scheduling problem. The main content comprises: the system initialization adopts a novel heuristic method taking knowledge as guidance to generate a workpiece sequence; in the local search stage, a probability model is established by adopting a knowledge-driven distribution estimation algorithm mechanism, the search capacity of the optimization system is improved through knowledge accumulation and feedback, and finally, a variable neighborhood descent strategy based on three neighborhood structures is used to ensure that candidate solutions are prevented from falling into local optimum. The system is verified to be efficient in solving the complex shop scheduling problem by examples of different factories, machines and workpieces, and the problem of lead or delay of delivery date can be reduced.

Description

Complex workshop scheduling optimizer based on improved meta heuristic algorithm

Technical Field

The invention belongs to the field of distributed production scheduling in manufacturing industry, and designs a complex workshop scheduling optimizer based on an improved meta-heuristic algorithm.

Background

The importance of complex flow industrial systems to national productivity is self-evident, where production scheduling directly determines manufacturing levels. As intelligent plants continue to grow in size, the production environment becomes increasingly complex and in dynamic change. And in the complex flow industrial system, various resources in different factory environments are reasonably allocated and optimized by distributed scheduling to one or more targets, so that the enterprise benefit is maximized. The problem of complex distributed scheduling optimization obviously becomes a key place for realizing intelligent manufacturing, and has great practical significance and application prospect in flow industrial production. In real-world production and sales, a delivery time period is often contracted between the ordering party and the manufacturer. The manufacturer is unfavourable earlier or later than this production period. Early completion of storage in the warehouse results in cost waste, and late completion necessitates reimbursement of the default. Thus, the lead window is a critical factor that must be considered in the scheduling of production.

The group intelligent optimization algorithm simulates living things or phenomena in the nature, and based on corresponding criteria, the self-adaptive environment adaptation is realized so as to solve the problem, and an optimal solution is found. The meta-heuristic method is a typical intelligent optimization algorithm for groups, and the satisfaction solution is found by continuously learning and feeding back to adapt each parameter value in the group. The improved meta-heuristic designed herein implements search behavior through collaborative cooperation of populations. The algorithm has few parameters and is easy to realize; individuals in the population learn to excellent individuals, and rapidly guide the evolution process.

The learning mechanism can realize the self-adaptive adjustment of corresponding parameters in the improved algorithm according to the specific problem model, and the searching direction is adjusted by adding feedback by referring to better searching experience. The complex workshop scheduling problem in the production scheduling field of the manufacturing industry is fused and optimized by a learning mechanism and a meta heuristic algorithm, so that the method has important research value.

Disclosure of Invention

The invention aims at solving the problems existing in the prior art, expanding related research and providing a technical solution by means of the support of the Innovative star project (No. 2023 CXZX-476) of the Ministry of education and the Ministry of Gansu. The invention provides an improved meta heuristic algorithm which is applied to a complex workshop scheduling system to improve the overall operation efficiency. The adopted technical scheme is as follows:

the invention relates to a complex workshop scheduling optimization solver based on an improved meta-heuristic algorithm of knowledge guidance, which comprises the following steps:

step 1: initializing a workpiece sequence by adopting heuristic rules based on problem knowledge guidance;

step 2: in the global searching stage, a probability model is embedded in cooperation with a distributed estimation algorithm (EDA) mechanism, knowledge is used as a guide through feedback of learning experience, and selection of an optimal workpiece sequence is achieved;

step 3: in the local search stage, three different neighborhood structure variable neighborhood descent strategies are adopted to balance the rough search and the fine search capabilities.

Preferably, in step 1, a high quality initialization sequence of workpieces can be obtained using knowledge-based guided heuristics. Abstracting the workpiece distance in complex workshop scheduling into knowledge, and preferentially inserting the workpiece with the shortest distance to the last workpiece or the smallest finishing time difference, so that the influence on the subsequent workpieces is reduced; knowledge is penetrated through the whole searching stage and the global searching stage; searching in a better feasible domain is conducted through knowledge.

Preferably, in step 2, the EDA algorithm is embedded into the probability model to implement global search, so that knowledge is used for guiding the population to evolve towards the direction with potential, the diversity is increased, and the searching efficiency of the algorithm is improved.

A learning type global search optimization method for establishing a probability selection model on elite individuals by using a probability updating mechanism for updating the model based on a distribution estimation algorithm;

the probability model matrix is shown in equation 1:

wherein q _ij (g) Representing the probability that the jth workpiece of the g generation is arranged at the ith position, the probability that all workpieces are arranged is equal initially, q _ij (0)＝1/m。

The probability model update formula at generation 1 is shown in formula 2:

where D (i, j) represents the distance of the workpiece j at the i-th position from the workpiece at position i-1, W represents the weight, and δ (i, j) is the enhancement factor when the workpiece is processed on time, which is defined as shown in equation 3:

where μ >1 represents the probability of enhancing the work piece processing.

In the iterative process of each subsequent generation, the probability model is updated according to the formula 4:

wherein θ ε (0, 1) is learning rate, q _ij (g) Is the probability that the jth workpiece of the g-th generation is at position i, ne is the number of elite individuals,

is the kth elite individual in the dominant population, whose definition is shown in equation 5:

if a workpiece is selected for insertion into the sequence, the probability of the corresponding position in the probability matrix is set to 0, the other probability values for the row are set to 1, until all values in the probability matrix are 0, and all workpieces are inserted into the sequence.

Preferably, in step 3, using a variable neighborhood descent strategy selected based on offset insertion of the factory interior, factory exterior, and workpiece into three neighborhood structures, elite individuals are guided to perform local search in a potential area, helping candidate solution jump out of local optimum, and further improving local search capability.

According to the unit advance or delay weight as an exchange principle, three operations of factory internal exchange, factory external exchange and offset insertion are performed to realize that three neighborhood structure guide populations search a potential area; firstly, an individual starts from an internal exchange structure, if the objective function value is optimized, the local searching process is stopped, and the next individual continues to perform local searching from the internal exchange structure; if the objective function value is not optimized, the search neighborhood is turned to an external switching structure, if the objective function value is not optimized at the moment, the search neighborhood is turned to offset insertion operation, the next generation iteration process is entered, and the rough search and the fine search capability of the system are balanced.

The beneficial effects of the invention are as follows:

(1) The invention establishes the initial workpiece sequence with high quality by adopting a heuristic rule based on knowledge guidance, guides the population to search towards a potential searching direction, and improves the quality of initial solutions.

(2) According to the invention, a knowledge-guided collaborative search mechanism is constructed, the abstracted knowledge penetrates through three stages of solving the problem by the optimizer based on the problem characteristics, so that the exploration and development capabilities of the optimizer are well balanced, and the production efficiency is improved.

(3) The invention has simple framework, easy implementation and convenient expansion of problems, and can expand the optimizer to other more complex production scheduling problems in the intelligent manufacturing field.

Drawings

FIG. 1 is a diagram of the architecture of a complex shop scheduling optimizer based on an improved meta-heuristic of the present invention.

FIG. 2 is an exemplary diagram of a method for initializing a complex shop scheduling problem model.

Fig. 3 is a diagram of a feedback learning type global search process of the present invention.

FIG. 4 is a diagram of a local search process for three neighborhood structures of the present invention.

FIG. 5 is a schematic diagram of a learning-based local search of the present invention.

FIG. 6 is an optimized system and advanced IG of the present invention _ITE Interval diagram of the system.

FIG. 7 is an illustration of the optimization system and advanced IG of the present invention _ITE Trend graph of the system over 120 examples.

Detailed Description

The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific examples described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

The structural schematic diagram of the complex workshop scheduling optimizer based on the improved meta-heuristic algorithm is shown in fig. 1, and the specific process is shown in steps 1-4.

In combination with the drawings and the technical scheme, the complex workshop scheduling optimizer based on the improved meta-heuristic algorithm is further described below, and specifically comprises the following steps:

step 1: initializing all parameters, and setting the size of a population, the dimension of a problem, the position area of the population, the maximum algebra of evolution and the like.

Step 2: the initialization of the population uses knowledge-based heuristic rules to produce a better sequence of workpieces. The distance between work pieces is abstracted into knowledge, and the work piece with the shortest distance to the last work piece or the smallest finishing time difference is inserted preferentially, so that the influence on the subsequent work pieces is reduced, and further, the high-quality initial solution is obtained.

The work piece with the earliest expiration date is selected as the first processed work piece in each factory, and then the work piece closest to the last processed work piece is preferentially inserted into the current factory, the distance of the whole work piece and the delivery date window. The specific application rules of the heuristic rules based on knowledge in the process of inserting workpieces are shown in fig. 2, the abscissa represents time, the ordinate in the first coordinate system represents 2 machines of the machine factory 2, the ordinate in the second coordinate system represents 2 machines of the factory 1, the squares with different numbers represent different workpieces, and fig. 2 is the process of inserting 6 different workpieces according to the insertion rules of this step, and the optimal procedure is obtained by this mechanism. The pseudo code of knowledge-based heuristic KNEH is shown in algorithm 1.

Step 3: the EDA mechanism is embedded into a probability model, and feedback is formed through learning to guide the searching process of the global searching stage. Population centers are key to balancing the ability of coarse and fine searches in the search process. At this stage, EDA is embedded into the probability model, and part of elite individuals are selected as population centers to guide the population to evolve towards a better direction.

In the complex shop scheduling problem with delivery date constraints as objective functions, factors influencing the size of the objective function are: the unit advances or retards the distance between the weight and the workpiece, i.e., the finishing time difference.

To this end, a probabilistic model is constructed:

wherein q _ij (g) Representing the probability that the jth workpiece of the g generation is arranged at the ith position, the probability that all workpieces are arranged is equal initially, q _ij (0) =1/m. Q in probability model _i，j (g) The greater the value, the greater the priority with which the workpiece j is processed. The smaller the probability value, the lower the priority. At each generationIn the updating process, the priority of the workpiece sequence is determined according to the probability matrix. The shorter the distance between the previous workpiece j-1 and the current workpiece j is, the smaller the influence on the subsequent treatment is when the previous workpiece j-1 is preferentially inserted; the greater the weight for unit advance or retard, the greater the priority that the workpiece is inserted. If the work piece can be completed on time during the delivery period, then a reward should be given. At generation 1, work J _j The probability of being inserted at position i is defined as:

where D (i, j) represents the distance of the workpiece j at the i-th position from the workpiece at position i-1, W represents the weight, and δ (i, j) is the enhancement factor when the workpiece is processed on time, which is defined as shown in equation 3:

where μ >1 represents the probability of enhancing the work piece processing.

After passage 2, the probability update proceeds according to equation 4:

wherein θ ε (0, 1) is learning rate, q _ij (g) Is the probability that the jth workpiece of the g-th generation is at position i, ne is the number of elite individuals,

is the kth elite individual in the dominant population, whose definition is shown in equation 5:

an example diagram of a global search phase based on learning mechanisms is shown in fig. 3, with the abscissa representing time, the ordinate representing two machines within the plant, the blocks of different numerical numbers representing different workpieces, and fig. 3 showing the insertion of 3 different workpieces on the two machines according to the method described in this step. The pseudocode is shown below.

Step 4: variable neighborhood descent policies based on three neighborhood structures. The selection of three neighborhood structures is performed according to the unit advance or delay weight, and the corresponding operations shown in fig. 4 are respectively: the intra-factory exchange, the external-factory exchange and the offset insertion of the workpiece improve the quality of the solution by local search. Specifically, in the internal exchange structure, exchanging the work piece with large unit advance or delay weight with the work piece with small weight until the total weight value in the factory is optimized; in the external exchange structure, two different factories are exchanged randomly according to the unit advance or delay weight value until the total advance or delay weight is optimized; in the offset insertion operation configuration, workpieces in one factory are inserted into other factories at random until the total advance or retard weight of the factory is greater than the total advance or retard weight of another factory.

In the local search stage, elite individuals in the population center guide suboptimal individual learning evolution, the local search process is shown in fig. 5, elite guide accelerated search is carried out, wherein five-pointed star represents elite individuals, and circle represents other individuals. First, the individual starts from the internal switching fabric and if the objective function is optimized, the local search is stopped. The next individual continues starting from the internal switching fabric, but if the objective function value is not optimized, the neighborhood structure is switched to the external switching fabric; if not, then the offset insert operation is shifted.

Pseudo codes based on three neighborhood structures are:

the optimizer designed for verifying the invention has excellent performancePotential will be based on IG with Jing et al _ITE The optimizer of the algorithm compares. (jin, X.L., pan, Q.K., gao, L.,&Wang,Y.L.(2020).An effective Iterated Greedy algorithm for the distributed permutation flowshop scheduling with due windows.AppliedSoft Computing,96,106629.)

the number of factories tested was 2,3,4,5,6,7, respectively. Different factories contain 120 test cases. Wherein, the combination of 12 different work pieces and machine numbers is divided into: {20×5,20×10,20×20,50×5,50×10,50×20,100×5,100×10,100×20,200×10,200×20,500×20}. The Average Relative Deviation Index (ARDI) was calculated to evaluate system performance, defined as:

wherein R represents the running time,

is the objective function value of individual i,>

optimizing the optimal value of the system when the distances are the same. The smaller the ARDI, the better the current solution. Independently run 5 times, the stopping criterion is set as: workpiece count machine count 30ms. The comparison results are shown in Table 1.

Table 1 comparison of the ARDI values for two systems

The interval diagrams of two optimizers at different numbers of plants are shown in fig. 6, where the abscissa is the respective optimizer and the ordinate is the ARDI value, showing the advantage of the present optimizer. From the results of FIG. 6 and Table 1, it can be seen that in most of the problems, the design of the present invention has better optimizer effect than IG _ITE And an optimizer.Table 2 gives the Wilcoxon rank sum test results for both systems on the test set. R is R ⁺ Representing the present optimizer being superior to IG _ITE Function rank sum of optimizer, R ^- Represents IG _ITE The function rank sum is superior to that of the optimizer; yes represents a significant difference between the two at α=0.05, as can be seen from the results in Table 2.

TABLE 2 Wilcoxon test sequence

The optimizer and advanced IG of the invention _ITE The trend graph of the optimizer over 120 workpiece and machine combinations is shown in fig. 7, where the abscissa is the workpiece number and the ordinate is the ARDI value. From the above results, it can be seen that the optimizer designed by the invention has optimal performance, and can shorten delivery period and improve production efficiency.

The basic principles and main features of the present invention have been described above with reference to the accompanying drawings. Modifications and variations may be made by those skilled in the art without departing from the principles of the present invention, and such modifications are intended to be included within the scope of the present invention.

Claims (4)

1. A complex shop scheduling optimizer based on an improved meta-heuristic algorithm, comprising the steps of:

step 1: initializing a sequence of parts using heuristic rules based on knowledge of the problem;

step 2: guiding global search by using a learning global search method with a feedback mechanism;

step 3: knowledge-guided variable neighborhood descent strategies based on intra-factory, out-of-factory, and workpiece offset insertion for three neighborhood structures are used to promote local search capability.

2. The sophisticated shop scheduling optimizer based on improved meta-heuristics according to claim 1, wherein in step 1, the optimization method abstracts the work distance to knowledge, inserts the work piece with the shortest distance to the last work piece or the smallest finishing time difference preferentially, reduces the influence on the subsequent work pieces, and thus obtains a high quality initial solution.

3. The improved meta-heuristic based complex shop scheduling optimizer of claim 1, wherein in step 2, after generating an initialization sequence of work pieces, a probabilistic update mechanism based on a distribution estimation algorithm update model is used to build a learning-based global search optimization method of probabilistic selection model on elite individuals;

the probability model matrix is shown in equation 1:

wherein q _ij (g) Representing the probability that the jth workpiece of the g generation is arranged at the ith position, the probability that all workpieces are arranged is equal initially, q _ij (0)＝1/m；

The probability model update formula at generation 1 is shown in formula 2:

where D (i, j) represents the distance of the workpiece j at the i-th position from the workpiece at position i-1, W represents the weight, and μ (i, j) is the enhancement factor of the workpiece when it is being processed on time, and its definition is as shown in equation 3:

wherein μ >1 represents the probability of enhancing workpiece processing;

in the iterative process of each subsequent generation, the probability model is updated according to the formula 4:

wherein θ ε (0, 1) is learning rate, q _ij (g) Is the probability that the jth workpiece of the g-th generation is at position i, ne is the number of elite individuals,

is the kth elite individual in the dominant population, whose definition is shown in equation 5:

if a workpiece is selected for insertion into the sequence, the probability of the corresponding position in the probability matrix is set to 0, the other probability values for the row are set to 1, until all values in the probability matrix are 0, and all workpieces are inserted into the sequence.

4. The complex shop scheduling optimizer based on the improved meta-heuristic algorithm according to claim 1, wherein in step 3, after the above operation, elite individuals are guided to sub-optimal individuals for local search, and a variable neighborhood descent strategy based on three neighborhood structures is adopted;

according to the unit advance or delay weight as an exchange principle, three operations of factory internal exchange, factory external exchange and offset insertion are performed to realize that three neighborhood structure guide populations search a potential area; firstly, an individual starts from an internal exchange structure, if the objective function value is optimized, the local searching process is stopped, and the next individual continues to perform local searching from the internal exchange structure; if the objective function value is not optimized, the search neighborhood is turned to an external switching structure, if the objective function value is not optimized at the moment, the search neighborhood is turned to offset insertion operation, the next generation iteration process is entered, and the rough search and the fine search capability of the system are balanced.

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