CN116300738A - A Complex Shop Scheduling Optimizer Based on Improved Metaheuristic 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

A Complex Shop Scheduling Optimizer Based on Improved Metaheuristic Algorithm

technical field

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

Background technique

The importance of complex process industrial systems to national productivity is self-evident, and production scheduling directly determines the level of manufacturing. As the scale of smart factories continues to increase, the production environment is increasingly complex and dynamically changing. Distributed scheduling in complex process industrial systems rationally allocates various resources in different factory environments and optimizes one or more objectives to maximize enterprise benefits. The complex distributed scheduling optimization problem has obviously become the key to realizing intelligent manufacturing, and it has great practical significance and application prospects in process industry production. In actual production and sales, there is often a delivery time limit agreed between the orderer and the manufacturer. It is disadvantageous for the manufacturer to be earlier or later than this production deadline. Finishing ahead of time and storing in the warehouse will result in waste of cost, and finishing late will result in liquidated damages. Therefore, the delivery window is a key factor that must be considered in production scheduling.

The swarm intelligence optimization algorithm is to simulate the creatures or phenomena in nature, and based on the corresponding criteria, it can adaptively adapt to the environment and solve the problem, and has found the optimal solution. The meta-heuristic method is a typical swarm intelligence optimization algorithm. Through continuous learning and feedback, each parameter value in the population is adaptive to find a satisfactory solution. The improved meta-heuristic algorithm designed in this paper realizes the search behavior through the cooperative cooperation of the population. The algorithm has few parameters and is easy to implement; individuals in the population learn from excellent individuals to quickly guide the evolution process.

The learning mechanism can realize the adaptive adjustment of the corresponding parameters in the improved algorithm according to the specific problem model, and adjust the search direction by referring to better search experience and adding feedback. Integrating learning mechanism and meta-heuristic algorithm to optimize complex shop-shop scheduling problems in the field of manufacturing production scheduling has important research value.

Contents of the invention

The purpose of the present invention is to aim at the problems existing in the prior art, with the support of the postgraduate "Innovation Star" project (No. 2023CXZX-476) funded by the Gansu Provincial Department of Education, to carry out relevant research and propose technical solutions. The invention provides an improved meta-heuristic algorithm, which is applied to a complex workshop scheduling system to improve overall operating efficiency. The technical solutions adopted are:

The present invention is a complex workshop scheduling optimization solver based on an improved meta-heuristic algorithm guided by knowledge, comprising the following steps:

Step 1: Initialize the artifact sequence using heuristic rules guided by problem knowledge;

Step 2: In the global search stage, cooperate with the distribution estimation algorithm (EDA) mechanism to embed the probability model, and realize the selection of the optimal workpiece sequence through the feedback of learning experience and guided by knowledge;

Step 3: In the local search stage, three variable neighborhood descent strategies with different neighborhood structures are used to balance the coarse search and fine search capabilities.

Preferably, in step 1, a high-quality initialization artifact sequence can be obtained by using a knowledge-guided heuristic rule. Abstract the workpiece distance in complex workshop scheduling as knowledge, insert the workpiece with the shortest distance from the previous workpiece or the smallest completion time difference first, and reduce the impact on subsequent workpieces; apply knowledge throughout the entire search stage and the global search stage; through knowledge The bootstrap searches in the better feasible region.

Preferably, in step 2, the EDA algorithm is embedded into the probability model to implement a global search, and the knowledge guides the population to evolve towards a potential direction, increasing the diversity and improving the search efficiency of the algorithm.

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

The probability model matrix is shown in Equation 1:

Among them, q _ij (g) represents the probability that the j-th workpiece of the g-th generation is arranged at the i-th position. Initially, the probability of all workpieces being arranged is equal, q _ij (0)=1/m.

The probability model update formula in the first generation is shown in formula 2:

Among them, D(i,j) represents the distance between the workpiece j at the i-th position and the workpiece at position i-1, W represents the weight, δ(i,j) is the enhancement factor when the workpiece is processed on time, and its definition As shown in formula 3:

Among them, μ>1 represents the probability of enhanced workpiece processing.

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

是优势种群中的第k个精英个体，其定义如公式5所示：where θ ∈ (0,1) is the learning rate, q _ij (g) is the probability of the j-th artifact in the g-th generation at position i, Ne is the number of elite individuals,

is the kth elite individual in the dominant population, and its definition is shown in formula 5:

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

Preferably, in step 3, use the variable neighborhood descent strategy based on three neighborhood structure selections based on factory interior, factory exterior, and workpiece offset insertion to guide the elite individuals to the suboptimal individuals to conduct local searches in potential areas , to help the candidate solution jump out of the local optimum, and further improve the local search ability.

According to the unit advance or delay weight as the exchange principle, the three neighborhood structures are realized through the three operations of factory internal exchange, factory external exchange and offset insertion to guide the population to search for potential areas; first, individuals start from the internal exchange structure, If the objective function value is optimized, the local search process stops, and the next individual continues to search locally from the internal exchange structure; if the objective function value is not optimized, the search neighborhood is turned to the external exchange structure, if the objective function value is If it is not optimized, the search neighborhood will be shifted to the offset insertion operation, and enter the next generation of iterative process, which balances the coarse search and fine search capabilities of the system.

The beneficial effects of the present invention are as follows:

(1) The present invention adopts a knowledge-guided heuristic rule to establish a high-quality initial workpiece sequence, guides the population to search in a potential search direction, and improves the quality of the initial solution.

(2) The present invention builds a knowledge-guided collaborative search mechanism, runs the abstracted knowledge through the three stages of the optimizer to solve the problem based on the characteristics of the problem, better balances the exploration and development capabilities of the optimizer, and improves production efficiency.

(3) The framework of the present invention is simple, easy to implement and easy to expand the problem, and can extend the optimizer to other more complex production scheduling problems in the field of intelligent manufacturing.

Description of drawings

Fig. 1 is the structure of the complex shop scheduling optimizer based on the improved meta-heuristic algorithm of the present invention.

Fig. 2 is an example diagram of the initialization method of the complex shop-shop scheduling problem model.

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

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

Fig. 5 is a schematic diagram of the local search based on the learning mechanism of the present invention.

Fig. 6 is an interval diagram of the optimization system of the present invention and the advanced IG _ITE system.

Fig. 7 is a trend diagram of the optimization system of the present invention and the advanced IG _ITE system on 120 calculation examples.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific examples described here are only used to explain the present invention, not to limit the present invention.

The structural diagram of a complex shop scheduling optimizer based on the improved meta-heuristic algorithm designed by the present invention is shown in Fig. 1, and the specific process is shown in steps 1-4.

Combined with the accompanying drawings and technical solutions, the complex shop scheduling optimizer based on the improved meta-heuristic algorithm will be further described below, which specifically includes the following steps:

Step 1: Initialize all parameters, set the population size, problem dimension, population location area, maximum evolutionary generation, etc.

Step 2: Initialization of the population, using knowledge-based heuristic rules to generate a better sequence of artifacts. The distance between jobs is abstracted as knowledge, and the job with the shortest distance from the previous job or the smallest completion time difference is inserted first, reducing the impact on subsequent jobs, and then obtaining a high-quality initial solution.

Select the workpiece with the earliest due date as the first processed workpiece in each factory, and then insert the workpiece with the closest distance to the last processed workpiece into the current factory, the distance of the entire workpiece and the delivery window. An example of specific application rules of knowledge-based heuristic rules in the process of workpiece insertion is shown in Figure 2. The abscissa represents time, the ordinate in the first axis system represents the two machines in machine factory 2, and the second axis The ordinate in the system represents the two machines in factory 1, and the squares with different numbers represent different workpieces. Figure 2 shows the insertion process of 6 different workpieces according to the insertion rules of this step, and the optimal process is obtained through this mechanism. The pseudocode of the knowledge-based heuristic rule KNEH is shown in Algorithm 1.

Step 3: Embed the EDA mechanism into the probability model to guide the search process in the global search phase through learning to form feedback. The population center is the key to balance the capabilities of coarse search and fine search in the search process. At this stage, EDA is embedded in the probability model, and some elite individuals are selected as the population center to guide the population to evolve in a better direction.

In the complex shop-shop scheduling problem with the delivery time limit as the objective function, the factors affecting the size of the objective function are: the weight of unit advance or delay and the distance between workpieces, that is, the difference in completion time.

To do this, construct a probabilistic model:

Among them, q _ij (g) represents the probability that the j-th workpiece of the g-th generation is arranged at the i-th position. Initially, the probability of all workpieces being arranged is equal, q _ij (0)=1/m. The greater the value of q _i,j (g) in the probability model, the greater the processing priority of the workpiece j. The smaller the probability value, the lower the priority. In the update process of each generation, the priority of the artifact sequence is determined according to the probability matrix. The shorter the distance between the previous workpiece j-1 and the current workpiece j, the less impact it will have on subsequent processing when it is preferentially inserted; the greater the unit advance or delay weight, the greater the priority of the workpiece being inserted. If the workpiece can be completed on time within the delivery period, it should be rewarded. In generation 1, the probability that a workpiece J _j is inserted at position i is defined as:

Among them, D(i, j) represents the distance between the workpiece j at the i-th position and the workpiece at position i-1, W represents the weight, δ(i, j) is the enhancement factor when the workpiece is processed on time, and its definition As shown in formula 3:

Among them, μ>1 represents the probability of enhanced workpiece processing.

After the second generation, the probability update is performed according to formula 4:

是优势种群中的第k个精英个体，其定义如公式5所示：where θ ∈ (0,1) is the learning rate, q _ij (g) is the probability of the j-th artifact in the g-th generation at position i, Ne is the number of elite individuals,

is the kth elite individual in the dominant population, and its definition is shown in formula 5:

An example diagram of the global search stage based on the learning mechanism is shown in Figure 3. The abscissa represents time, the ordinate table represents two machines in the factory, and the squares with different numbers represent different workpieces. The described method inserts 3 different workpiece processes on two machines. Pseudocode is shown below.

Step 4: Variable Neighborhood Descent Strategy Based on Three Neighborhood Structures. According to the size of unit advance or delay weight, three kinds of neighborhood structures are selected. As shown in Figure 4, the corresponding operations are: factory internal exchange, factory external exchange, and workpiece offset insertion, and the quality of the solution is improved through local search. . Specifically, in the internal exchange structure, the unit advances or delays the workpiece with a large weight and the workpiece with a small weight to perform exchange operations until the total weight value inside the factory is optimized; in the external exchange structure, two different Factories perform swap operations according to the unit advance or delay weight value until the total advance or delay weight is optimized; in the offset insertion operation structure, the workpiece in a certain factory is randomly inserted into other factories until the factory's The total early or late weight is greater than the other plant's total early or late weight.

In the local search stage, the elite individuals in the center of the population guide the suboptimal individuals to learn and evolve. The local search process is shown in Figure 5, and the elite guides the accelerated search. Among them, the five-pointed star represents the elite individual, and the circle represents other individuals. First, the individual starts with the internal exchange structure and stops the local search if the objective function is optimized. The next individual continues to start from the internal exchange structure, but if the objective function value has not been optimized, the neighborhood structure will be converted to an external exchange structure; if it is still not optimized, then it will be converted to an offset insertion operation.

The pseudocode based on the three neighborhood structures is:

In order to verify the performance advantages of the optimizer designed in the present invention, it will be compared with the optimizer based on the IG _ITE algorithm of Jing et al. (Jing, XL, Pan, QK, Gao, L., & Wang, YL (2020). An effective Iterated Greedy algorithm for the distributed permutation flowshop scheduling with duewindows. AppliedSoft Computing, 96, 106629.)

The number of factories tested are 2, 3, 4, 5, 6, and 7 respectively. Different factories contain 120 test cases. Among them, there are 12 different combinations of the number of workpieces and machines: {20×5, 20×10, 20×20, 50×5, 50×10, 50×20, 100×5, 100×10, 100×20, 200×10, 200× 20,500×20}. Calculate the value of the average relative deviation index (ARDI) to evaluate the system performance. ARDI is defined as:

是个体i的目标函数值，/>

当距离相同时优化系统的最优值。ARDI越小，则当前解越好。独立运行5次，停止准则设为：工件数*机器数*30ms。对比结果如表1所示。Among them, R represents the running time,

is the objective function value of individual i, />

The optimal value of the optimized system when the distances are the same. The smaller the ARDI, the better the current solution. Run 5 times independently, and the stop criterion is set to: number of workpieces * number of machines * 30ms. The comparison results are shown in Table 1.

Table 1 Comparison of ARDI values of the two systems

The interval diagram of the two optimizers in different numbers of factories is shown in Figure 6, where the abscissa is each optimizer, and the ordinate is the ARDI value, showing the advantages of this optimizer. It can be seen from the results in Fig. 6 and Table 1 that in most problems, the optimizer designed by the present invention is better than the IG _ITE optimizer. Table 2 shows the Wilcoxon rank sum test results of the two systems on the test set. R ⁺ represents the function rank sum of this optimizer better than IG _ITE optimizer, R ^- represents the function rank sum of IG _ITE better than this optimizer; Yes represents when α=0.05, as can be seen from the results in Table 2, two There are significant differences.

Table 2 Wilcoxon test sequence

The trend graph of the optimizer of the present invention and the advanced IG _ITE optimizer on 120 workpieces and machine combinations is shown in Figure 7, wherein the abscissa is the number of workpieces, and the ordinate is the ARDI value. From the above results, it can be seen that the optimizer designed by the present invention has the best performance, which can shorten the delivery time and improve the production efficiency.

The basic principles, main features and advantages of the present invention have been described above with reference to the accompanying drawings. For those skilled in the art, modifications or variations can be made without departing from the principle of the present invention, and these improvements are also regarded as the protection scope of the present invention.

Claims (4)

1. A complex shop scheduling optimizer based on an improved meta-heuristic algorithm, characterized in that, comprising the following steps: Step 1: Initialize the sequence of artifacts using problem-knowledge-based heuristic rules; Step 2: Guide the global search using a learning-type global search method with a feedback mechanism; Step 3: Use the knowledge-guided variable neighborhood descent strategy based on the three neighborhood structures of factory interior, factory exterior, and workpiece offset insertion to improve local search capabilities. 2. The complex shop scheduling optimizer based on the improved meta-heuristic algorithm according to claim 1, characterized in that, in step 1, this optimization method abstracts the distance between jobs as knowledge, and the shortest distance with the previous job Or the workpiece with the smallest completion time difference is inserted first, reducing the impact on subsequent workpieces, and then obtaining a high-quality initial solution. 3. The complex shop scheduling optimizer based on the improved meta-heuristic algorithm according to claim 1, wherein in step 2, after generating the initialization workpiece sequence, the probability update mechanism based on the distribution estimation algorithm to update the model is used in A learning-based global search optimization method for building a probabilistic selection model on elite individuals; The probability model matrix is shown in Equation 1:

Among them, q _ij (g) represents the probability that the j-th workpiece of the g-th generation is arranged at the i-th position, and the probability that all workpieces are arranged at the beginning is equal, q _ij (0)=1/m; The probability model update formula in the first generation is shown in formula 2:

Among them, D(i,j) represents the distance between the workpiece j at the i-th position and the workpiece at position i-1, W represents the weight, μ(i,j) is the enhancement factor when the workpiece is processed on time, and its definition As shown in formula 3:

Among them, μ>1 represents the probability of enhanced workpiece processing; In the iterative process of subsequent generations, the probability model is updated according to formula 4:

where θ ∈ (0,1) is the learning rate, q _ij (g) is the probability of the j-th artifact in the g-th generation at position i, Ne is the number of elite individuals,

is the kth elite individual in the dominant population, and its definition is shown in formula 5:

If a certain workpiece is selected to be inserted into the sequence, the probability of the corresponding position in the probability matrix is set to 0, and the other probability values of the row are set to 1, until all the values in the probability matrix are 0, all workpieces are inserted into the sequence middle. 4. The complex workshop scheduling optimizer based on the improved meta-heuristic algorithm according to claim 1, characterized in that, in step 3, after the above-mentioned operations, the elite individual guides the suboptimal individual to carry out a local search, using the method based on Variable neighborhood descent strategies for three neighborhood structures; According to the unit advance or delay weight as the exchange principle, the three neighborhood structures are realized through the three operations of factory internal exchange, factory external exchange and offset insertion to guide the population to search for potential areas; first, individuals start from the internal exchange structure, If the objective function value is optimized, the local search process stops, and the next individual continues to search locally from the internal exchange structure; if the objective function value is not optimized, the search neighborhood is turned to the external exchange structure, if the objective function value is If it is not optimized, the search neighborhood will be shifted to the offset insertion operation, and enter the next generation of iterative process, which balances the coarse search and fine search capabilities of the system.

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