Flexible job shop scheduling method and system based on multi-strategy improvement

Abstract

The invention provides a flexible job shop scheduling method and system based on multi-strategy improvement, and the method comprises the steps: obtaining workshop production information, carrying out the coding of the production information, obtaining a process code and a machine code, generating a plurality of initial workshop scheduling strategies through random combination, and enabling the initial workshop scheduling strategies to be an initial population; initializing the population through Circle chaotic mapping to generate a final initial population; and carrying out iterative optimization on the final initial population by utilizing the Harlisia eagle algorithm, dynamically adjusting escape energy in the Harlisia eagle algorithm according to an iteration period, and dynamically adjusting jump intensity in the Harlisia eagle algorithm according to an adjustment result of the escape energy, so as to obtain an optimal scheduling strategy of the flexible job shop. According to the method, the Circle chaotic mapping of the quantum calculation theory is combined, so that the initial population is more diversified, the quality of the initial population is improved, and the possibility of falling into a local optimal solution in the process of solving the flexible job shop scheduling problem is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of flexible job shop scheduling, and in particular to a flexible job shop scheduling method and system based on multi-strategy improvement. Background Art

[0002] In the production process of modern manufacturing industry, Flexible Job-Shop Problem (FJSP) is a core and key problem. Traditional Job-Shop Problem (JSP) usually only considers the processing order of workpieces on fixed machines, but with the development of manufacturing industry, production systems have become more complex and flexible. In the flexible job-shop scheduling problem, each workpiece process can be processed on multiple different machines. It is necessary to determine the processing order of the workpiece and reasonably select the machine for each process. Compared with the traditional job-shop scheduling problem, the flexible job-shop scheduling problem reduces machine constraints and increases machine uncertainty. It has a broader solution space and more complex scheduling methods, which is more in line with the actual production situation. It is a type of scheduling problem that urgently needs to be solved.

[0003] Reasonable solutions to the flexible job shop scheduling problem are of great significance for improving the production efficiency of enterprises, reducing production costs, shortening production cycles and improving product quality. Intelligent optimization algorithms can help enterprises quickly find scheduling solutions that meet production needs. Therefore, the application of intelligent algorithms in solving flexible job shop scheduling problems has received more and more attention.

[0004] Harris Hawks Optimization (HHO) is a new meta-inspiration algorithm proposed by Ali Asghar and Seyedali Mirjalili in 2019. The algorithm mainly simulates the cooperative hunting behavior of Harris Hawks. By simulating the group hunting of Harris Hawks, the raid and capture strategy realizes the global optimization of the optimization algorithm. Because of its simple principle, few parameters, and easy implementation, it is used to solve optimization problems in many fields. However, there are currently two problems in using the Harris Hawk Optimization Algorithm in the field of workshop scheduling: (1) Insufficient diversity of the initial population. The Harris Eagle optimization algorithm usually uses random initialization to generate the initial population. This random initialization method has great limitations. The individuals in the generated population are often distributed more concentratedly and lack sufficient diversity. However, when solving the flexible job shop scheduling problem, the search space is usually very complex and large. If the initial population diversity is insufficient, the algorithm can easily fall into a local optimal solution during the iteration process.

[0005] (2) The global search capability is weak and it is easy to fall into the local optimum. The Harris Eagle optimization algorithm uses linear decrease as the adaptive attenuation mechanism of escape energy. In the early stage of algorithm iteration, the escape energy E decreases quickly. In the early stage of the algorithm, a larger escape energy is required to support the Harris Eagle to conduct a large-scale global search to fully explore the solution space. Therefore, during the iteration process of the algorithm, the global search capability is weak in the early stage and it is easy to have problems such as premature maturity and falling into the local optimum. The jump intensity can change the global search capability of the algorithm, but the optimization effect of the completely random strategy is very random. The greater the jump intensity, the greater the possibility that the algorithm will jump out of the local optimum, but too large a jump intensity will reduce the search accuracy. Summary of the invention

[0006] In view of the above situation, the main purpose of the present invention is to propose a flexible job shop scheduling method and system based on multi-strategy improvement to solve the above technical problems.

[0007] The present invention proposes a flexible job shop scheduling method based on multi-strategy improvement, the method comprising the following steps: Step 1: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; Step 2: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; Step 3: Take several initial workshop scheduling strategies as the initial population, each individual in the initial population corresponds to an initial workshop scheduling strategy, and the individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. Use Circle chaotic mapping to adjust the position of each individual in the initial population to obtain the adjusted initial population. Step 4: Using quantum theory to transform the adjusted initial population into a quantum superposition state population, and using a dynamic quantum rotating gate to mutate the quantum bit superposition state population to generate a mutant population; Step 5: Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; Step 6. Taking minimizing the maximum completion time as the optimization goal, use the Harris Hawk algorithm to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual, and take the optimal individual as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

[0008] The present invention also proposes a flexible job shop scheduling system based on multi-strategy improvement, the system applies the above-mentioned flexible job shop scheduling method based on multi-strategy improvement, and the system includes: Encoding module for: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; Decoding module for: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; Several initial workshop scheduling strategies are used as the initial population. Each individual in the initial population corresponds to an initial workshop scheduling strategy. The individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. The Circle chaotic map is used to adjust the position of each individual in the initial population to obtain the adjusted initial population. The adjusted initial population is transformed into a quantum superposition state population using quantum theory, and the quantum bit superposition state population is mutated using a dynamic quantum rotating gate to generate a mutant population; Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; Taking minimizing the maximum completion time as the optimization goal, the Harris Hawk algorithm is used to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual. The optimal individual is taken as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

[0009] Compared with the prior art, the present invention has the following beneficial effects: (1) The Circle chaos map combined with quantum computing theory is proposed to initialize the population: the characteristics of the chaotic map that generates highly random and unpredictable sequences are used to make the initial value of the population evenly distributed in the solution space. The concepts of quantum bits and quantum gates in quantum computing are introduced, and the initial population is constructed through the superposition state of quantum bits. Then, the quality of the initial population is improved and the population diversity is increased through steps such as restoring the superposition state, mutating and updating the population, and selecting the optimal individual. This can effectively reduce the possibility of the algorithm falling into the local optimal solution during the iteration process when solving the flexible job shop scheduling problem, because the search space is usually very complex and large, and the initial population diversity is insufficient, so as to speed up the algorithm to find the optimal solution.

[0010] (2) Propose a strategy combining escape energy and jump intensity based on the golden sine strategy: Aiming at the defects of the Harris Hawk optimization algorithm in that its global search capability is weak and it is easy to fall into the local optimum, the present invention proposes an adaptive attenuation curve based on the golden sine strategy to optimize the escape energy. By utilizing the periodicity and volatility of the golden sine function, the escape energy is varied within a larger range in the early stage of the algorithm iteration, thereby enhancing the global search capability and avoiding premature convergence. In the later stage of the iteration, the fluctuating escape energy is conducive to the algorithm jumping out of the local optimal area. At the same time, the jump intensity is combined with the optimized escape energy, and the jump intensity is dynamically adjusted according to the escape energy. In the early stage of the iteration, the jump range of the prey is increased to enhance the global search capability. As the energy is consumed, the jump intensity is reduced in the later stage to enhance the local search capability.

[0011] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description or learned through embodiments of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flow chart of the flexible job shop scheduling method based on multi-strategy improvement proposed by the present invention; Figure 2 The flowchart of Harris Eagle algorithm proposed by the present invention; Figure 3 This is a schematic diagram of the structure of the flexible job shop scheduling system based on multi-strategy improvement proposed by the present invention. Figure 4 This is a graph showing the calculation results of the present invention and other existing algorithms on the La11 dataset.

[0013] Figure 5 This is a graph showing the calculation results of the present invention and other existing algorithms on the La12 dataset.

[0014] Figure 6 This is a graph showing the calculation results of the present invention and other existing algorithms on the La13 dataset.

[0015] Figure 7 This is a graph showing the calculation results of the present invention and other existing algorithms on the La14 dataset.

[0016] Figure 8 This is a graph showing the calculation results of the present invention and other existing algorithms on the La15 dataset.

[0017] Fig. 9 This is a graph showing the calculation results of the present invention and other existing algorithms on the La16 dataset.

[0018] Fig.10 This is a graph showing the calculation results of the present invention and other existing algorithms on the La17 dataset. DETAILED DESCRIPTION

[0019] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0020] These and other aspects of the embodiments of the present invention will be apparent with reference to the following description and accompanying drawings. In these descriptions and accompanying drawings, some specific implementations of the embodiments of the present invention are specifically disclosed to represent some ways of implementing the principles of the embodiments of the present invention, but it should be understood that the scope of the embodiments of the present invention is not limited thereto.

[0021] See also Figure 1 This embodiment provides a flexible job shop scheduling method based on multi-strategy improvement, the method comprising the following steps: Step 1: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; As a further preferred embodiment of the present invention, obtaining workshop production information, encoding the workshop production information, and obtaining the process code and the machine code specifically includes the following steps: Obtain workshop production information, which includes several workpieces and several machines. Each workpiece includes several processes. Obtain the processing time of each process on each machine. Generate an array according to the number of processes of each workpiece, and then shuffle the array to generate a new process code. For workpieces with a process where the number of optional machines is greater than or equal to 2, define the machine selection probability pi, and determine the machine selection method by generating a random number between 0 and 1 and comparing it with pi; If the random number is greater than pi, a machine is randomly selected. If the random number is less than pi, the machine with the shortest time is selected, and multiple process codes, multiple machine codes and multiple processing time codes are obtained.

[0022] Step 2: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; As a further preferred embodiment of the present invention, in step 2, the constraints of the flexible job shop scheduling problem specifically include: The same machine can only process one workpiece at a time; The same process of the same workpiece can only be processed by one machine at the same time; After the process of each workpiece begins, the processing cannot be interrupted; Different artifacts have the same priority; There are sequential constraints between the processes of the same workpiece, but there are no sequential constraints between the processes of different workpieces; All workpieces can be processed at time zero.

[0023] Step 3: Take several initial workshop scheduling strategies as the initial population, each individual in the initial population corresponds to an initial workshop scheduling strategy, and the individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. Use Circle chaotic mapping to adjust the position of each individual in the initial population to obtain the adjusted initial population. As a further preferred embodiment of the present invention, in step 3, the position of each individual in the initial population is adjusted by using Circle chaotic mapping, and obtaining the adjusted initial population specifically includes the following steps: According to the total number of processes in the initial population, the Circle chaotic map is used to iteratively generate the corresponding chaotic value sequence for each process code. The corresponding process has the following relationship: ; in, represents the chaotic value generated by the chaotic map, represents the next chaotic value generated by the chaotic map, represents pi, Represents modulo operation; The chaotic value sequence is linearly mapped to the solution space to select machines for each process according to the chaotic value to obtain the adjusted initial population. The corresponding process has the following relationship: ; in, Indicates decision variable dimensions, j=1,2,…,D; D represents the total number of decision variable dimensions, , n represents the number of workpieces, m represents the number of workpiece processes; i=1,2,…,N, N represents the total number of individuals in the initial population, Represents the individuals in the adjusted initial population In the decision variable dimension The position on They represent the upper and lower bounds of the search space respectively. The search space consists of all possible scheduling strategies.

[0024] Step 4: Using quantum theory to transform the adjusted initial population into a quantum superposition state population, and using a dynamic quantum rotating gate to mutate the quantum bit superposition state population to generate a mutant population; In quantum space, a quantum bit is the smallest unit of information. The two basic states of a quantum bit are and It means that the quantum bit can be a superposition of two states, described by equation (1) and satisfying equation (2). When the quantum state is in a superposition state, based on the probability amplitude, the quantum bit can be represented by sine and cosine matrices as shown in equation (3), that is, the probability amplitude is used to represent the position of the individual in the population.

[0025] ; (1) ; (2) ; (3) in, represents the quantum state of superposition, and are the probability amplitudes of being in one of the two states respectively.

[0026] Therefore, the above quantum characteristics can be applied to the population initialization process, and then it can be concluded that the quantum space position of the individual and the state matrix have a corresponding relationship as shown in formula (4): ; (4) in, Indicates The cosine position of each individual in the solution space, Indicates The sinusoidal position of each individual in the solution space, Indicates The cosine value of the rotation angle of an individual in the Dth decision variable dimension, Indicates The sine of the rotation angle of an individual in the Dth decision variable dimension.

[0027] As a further preferred embodiment of the present invention, in step 4, the adjusted initial population is transformed into a quantum bit superposition state population using quantum theory, which specifically includes the following steps: The mapping relationship between quantum space and solution space is established through linear transformation to obtain the cosine position and sine position of individuals in the initial population in the solution space. The corresponding process has the following relationship: ; ; in, represents the cosine position of the individual in the solution space; represents the sinusoidal position of the individual in the solution space, which consists of all possible scheduling strategies that follow the constraints; represents the rotation angle of the quantum bit; The sine position and cosine position of the current individual are inversely transformed to obtain the inverse transformation rotation angle of the sine position and cosine position of the current individual. The corresponding process has the following relationship: ; ; in, Indicates the inverse transformation rotation angle; According to the inverse transformation angle of the current individual sine position or cosine position, the sine position or cosine position corresponding to the current individual is inferred. The current individual sine position and the inferred individual cosine position or the current individual cosine position and the inferred individual sine position constitute the two state bits of the initial quantum bit, and a quantum bit superposition state population is obtained.

[0028] As a further preferred embodiment of the present invention, in step 4, a dynamic quantum rotating gate is used to mutate the quantum bit superposition state population, and generating a mutant population specifically includes the following steps: The dynamic quantum rotating gate performs a logical transformation on the two state bits of the initial quantum bit to obtain the two state bits of the transformed quantum bit. The corresponding process has the following relationship: ; in, Represent the two state bits of the transformed quantum bit; It indicates the updated value of the angle in the probability amplitude of the quantum bit after the dynamic quantum rotating gate is used, which is used to reflect the change of the quantum bit state after the rotating gate operation; Represents the rotation angle of a given dynamic quantum rotating gate, ranging from ; represents a dynamic quantum bit rotating gate. The calculation process of the dynamic quantum bit rotating gate has the following relationship: ; According to the two state bits of the quantum bit, the position of the individual in the transformed population is calculated to obtain the mutant population. The corresponding process has the following relationship: ; ; in, represents the cosine position of the transformed population individuals in the solution space, Represents the sinusoidal position of the transformed population individuals in the solution space.

[0029] Step 5: Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; The comparison process is to compare the minimized maximum completion time of two individuals and select the individual with the smallest maximum completion time.

[0030] Step 6. Taking minimizing the maximum completion time as the optimization goal, use the Harris Hawk algorithm to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual, and take the optimal individual as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

[0031] like Figure 2 As shown in the figure, the Harris Hawk optimization algorithm is a bionic intelligent optimization algorithm, which is mainly divided into two stages, namely the exploration stage and the development stage, and the transition between the two stages is achieved by changing the size of the prey's escape ability. The position vector of each Harris Hawk in the Harris Hawk population is regarded as a candidate solution to minimize the maximum completion time of the problem to be solved, that is, the corresponding workshop scheduling strategy, and the position vector of the Harris Hawk with the best fitness value is also the position vector of the prey, which is regarded as the current optimal solution to the problem, that is, the current optimal workshop scheduling strategy. Taking minimizing the maximum completion time as the optimization objective function, exploration or development is carried out through continuous iteration to obtain the global optimal solution, and finally the optimal scheduling strategy for the flexible job shop is obtained. The objective function for minimizing the maximum completion time is as follows: ; (5) in, is the maximum completion time, i.e. the completion time of the last process, is the number of workpieces.

[0032] The Harris Hawk optimization algorithm controls the Harris Hawk to enter the exploration phase or the development phase according to the size of the prey's escape energy, and selects different development strategies for development after entering the development phase. In addition, the prey's escape energy will decrease with the increase of the number of algorithm iterations. The current prey's escape energy is determined by formula (6): ; (6) in, It is the escape energy of the prey. is the escape energy of the initial state, is the current iteration number, is the maximum number of iterations. is a random number uniformly distributed in the interval (-1,1). When the prey's physical strength is continuously consumed from 0 to -1, From 0 to 1, the prey's physical strength is constantly restored. Harris's hawk enters the exploration phase, exploring different areas to locate prey; when the escape energy When the hawk enters the exploitation phase, it attacks prey discovered during the exploration phase.

[0033] During the exploration phase, the Harris Hawk population uses two strategies with equal probability to search for prey in the search space. One strategy is that the Harris Hawk randomly updates its position in the search space based on the positions of all members of the population and the current position of the prey; the other strategy is that the Harris Hawk randomly updates its position in the search space based on the position of another randomly selected member of the population. Generate a random number q to represent the two situations of finding prey and not finding prey, including determining the adjustment strategy for the individual position in the final initial population based on the random number q, that is, adjusting the combination of process code and machine code in the workshop scheduling strategy. If the random number q is greater than or equal to 0.5, other workshop scheduling strategies are adjusted according to the current optimal scheduling strategy. If the random number q is less than 0.5, a workshop scheduling strategy is randomly selected, and other workshop scheduling strategies are adjusted according to this randomly selected workshop scheduling strategy. The formula for updating the individual position of the population is as follows: ; (7) in, Indicates the current location of an individual Harris Hawk; Indicates the position of a random individual in the current representative population; Indicates the current location of the prey; Represents different random numbers between (0,1); It represents the average position of individuals in a population. The calculation process of the average position of individuals in a population is as follows: ; (8) in, Indicates the population the location of each individual; During the development phase, the Harris Hawk Optimization Algorithm proposed four strategies to simulate the process of hawks attacking prey. The probability of the prey escaping the encirclement before the hawks launch a surprise attack is represented by a random number p uniformly distributed in the interval (0,1).

[0034] 1. Soft Siege when When , the prey still has enough energy to escape, and tries to avoid the pursuit of the eagles by randomly misleading jumps. The eagles will deceive the prey, consume their energy, and update their position as formula (9): ; (9) ; (10) in, Indicates the relative position of the prey to the current position of the Harris Hawk. t The position vector difference during the iteration is It represents the random jump intensity of the prey during the escape process and is used to describe the motion properties of the prey during the entire iteration process. , here is a random number in [0,1].

[0035] 2. Hard Siege when When , the prey has insufficient energy to escape and fails to escape the encirclement. The eagle flock launches a surprise attack on the prey, and the position is updated as formula (11): ; (11) 3. Soft siege with gradual rapid dive when When the prey has sufficient escape ability and escapes the encirclement, the eagle group uses a gentle siege method to induce the prey, control its direction and consume its physical strength. The eagle group will decide the next action according to the result of formula (12): ; (12) in, It indicates the current position of individual Harris Hawks before the strong attack; If the fitness value does not improve after the induction is successful, a strong raid is performed. The formula of the strong raid strategy is as follows: ; (13) Among them, S represents a dimension A one-dimensional array of Indicates the updated position of the current Harris Hawk individual after a strong attack. is the Levy flight function. Combining equation (12) and equation (13), the position update is equation (14): ; (14) in, represents the fitness function, which is used to calculate the individual's minimized maximum completion time; 4. Hard siege with gradual rapid dive when When , the prey escapes the encirclement, but the escape energy is insufficient. The eagle group will try to reduce the average distance with all prey, as shown in formula (15): ; (15) If the fitness value does not improve, the eagle group will make a strong raid, as shown in formula (16): ; (16) Combining equations (15) and (16), the position update is equation (17): ; (17) From the above, it can be seen that the ordinary Harris optimization algorithm is a random operation when executing the shop scheduling problem, so there is a possibility of duplication, and the development stage only conducts local search around the current optimal solution, and the search direction is single, which makes it difficult to cope with the coupling constraints of multiple processes and multiple machines in FJSP (flexible shop scheduling problem). And due to the lack of perturbation mechanism, it is easy to fall into local optimality in FJSP due to strong constraints on process sequence or machine allocation. For this reason, a short-term taboo table is set to record the process pairs that have been exchanged as a short-term restriction to prevent the same operation from being repeated.

[0036] Therefore, after the Harris hard optimization algorithm is improved, the four strategies in the development phase can be implemented as follows: In the soft siege strategy, the prey still has high energy at this time, but the probability of success is higher, tending to be a more stable search method. Soft siege balances exploration and development by introducing neighborhood operations of jump intensity and dynamic weights, and searches for potential solution areas in the global stage. The formula of neighborhood perturbation soft siege can be expressed as: ; in, represents the first adaptive coefficient, , when the energy is lower, the proportion of local search is larger; Indicates FJSP neighborhood operation, Indicates that the FJSP neighborhood operation is performed on the current Harris Hawk individual position. represents the total number of neighborhood operation types, ; It means randomly exchanging the processing order of two processes on the machine. Indicates that the process on the current longest path is selected for forward or backward operation. Represents the operation of reallocating machines to reduce the time of the optional parallel machine processes. represents the domain weight, , Indicates k The historical success rate of the neighborhood operation, Indicates i The historical success rate of the neighborhood operation, ,in, Indicates the number of neighborhood operations.

[0037] Therefore, the success rate The lower the neighborhood operation, the higher the domain weight. The larger the value, the more it forces the algorithm to explore inefficient but possibly unexplored areas. This can prevent the algorithm from over-relying on efficient neighborhood operations (local development), prevent premature convergence, and encourage exploration of inefficient but possibly unexplored areas (global exploration).

[0038] In the hard siege strategy, the prey has low energy and a high probability of success, and enters local development, which requires more direct convergence. Hard siege omits jump intensity and directly searches around the current optimal solution. Combined with dynamic weights, it quickly converges to the local optimum. The formula for neighborhood perturbation hard siege can be expressed as: ; in, represents the second adaptive coefficient, , when the energy is high, the global exploration is enhanced to escape from the local optimum, and when the energy is low, the local development is strengthened for fine optimization and to reduce random disturbances; In the soft siege and hard siege stages, the variable neighborhood search mechanism is used to dynamically adjust different neighborhood structures to enhance local search capabilities while avoiding falling into local optimality. This improves the quality of the scheduling solution, shortens the maximum completion time, and accelerates convergence.

[0039] In the soft siege of progressive fast dive, the prey has high energy and low success probability, which may lead to local optimality and require stronger perturbation. At this time, Levy step size and weighted neighborhood are introduced to enhance diversity and help jump out of local optimality.

[0040] Therefore, firstly, use formula (12) to calculate the position of the current Harris Hawk individual before the strong attack. If the fitness value does not improve, a strong raid is performed; then combine formula (14) to update the position.

[0041] During the strong raid, the jump range of the neighborhood disturbance is controlled by the flight step length, so as to balance the local search and global exploration by taking advantage of the long tail characteristics of the flight. The strong raid strategy formula corresponding to the progressive fast dive soft siege is: ; in, represents the disturbance intensity coefficient, , the lower the energy, the stronger the disturbance.

[0042] In a hard siege with progressive and rapid dives, the prey has low energy and a low probability of success, so a more refined search is required. By guiding the taboo search, we can avoid repeating invalid steps and improve the efficiency of local search.

[0043] Therefore, first use formula (15) to calculate the position of the current Harris hawk individual before the strong attack. If the fitness value does not improve, a strong raid is performed, and then the position is updated in combination with formula (17).

[0044] During the strong raid, the taboo search replaces the random direction vector, and the directional search guided by the taboo table is used to improve the local optimization efficiency. The short-term memory mechanism of the taboo table is combined with the fast dive behavior of HHO to avoid repeated searches. The strong raid strategy formula corresponding to the hard siege of progressive fast dive is: ; in, represents a neighborhood search operation based on the tabu table, returning untabooed and improved solutions; represents the perturbation weight, ; In the strong raid strategy corresponding to the hard siege of progressive fast dive, Levy flight and taboo search are integrated into it. The long step length characteristic of Levy flight can be used to enhance global exploration, while taboo search can be used to guide local development and memory avoidance. This can balance exploration and development and improve the robustness of the algorithm in complex scenarios.

[0045] Finally, according to the neighborhood operations recorded in the short-term taboo table, the updated individual positions are checked to determine whether to update the partial positions and obtain the final accepted individual positions. The corresponding process is as follows: ; in, represents the final accepted individual position, Represents a short-term taboo table, which records the tabooed neighborhood operations.

[0046] From the above, it can be seen that the escape energy in the Harris Eagle optimization algorithm adopts a linear decreasing update strategy, which cannot be dynamically adjusted according to the actual situation during the iteration process. In the early stage of the algorithm, a strong global search capability is required to widely explore the solution space, but the linear decrease makes the escape energy decrease too early, which easily makes the global search capability of the early stage of the algorithm poor; in the later stage of the algorithm, a fine local search is required, and the fixed update strategy cannot provide a suitable search step and direction adjustment, which makes the algorithm easy to fall into the local optimal solution.

[0047] In view of this situation, the sine function and the golden ratio in the golden sine algorithm are used to construct an adaptive factor. The periodicity of the golden sine function can help the algorithm in the early stage of iteration. The sine function value fluctuates greatly, and the escape energy varies in a larger range under its influence, thereby enhancing the global search capability of the algorithm and avoiding premature convergence. The volatility of the sine function causes the escape energy to fluctuate accordingly, which is beneficial for the algorithm to jump out of the local optimal area. Therefore, the present invention proposes an adaptive attenuation curve based on the golden sine algorithm to optimize the escape energy, which can dynamically adjust the escape energy in the Harris Eagle algorithm according to the iteration period, and the corresponding process has the following relationship: ; in, represents the golden ratio factor, .

[0048] From the above, we can see that in the Harris Hawk algorithm, the jump intensity is a random number (0,2) to simulate the jump of the prey. The process of prey jumping helps to enhance the diversity of the population and to a certain extent prevent the algorithm from falling into the local optimum in the later iteration. However, the jump intensity of the prey should not be fixed. In nature, the jumping ability of the prey is related to its own energy. The higher the energy, the higher the jump intensity. During the escape process, the prey's own energy consumption is large, and the jump intensity will also decrease accordingly.

[0049] In view of this situation, the present invention proposes to first use the golden sine algorithm to optimize the adaptive decay curve of the escape energy, and then combine the jump intensity with the escape energy. The upper limit of the prey's jump intensity is set to , which can make the prey jump over a larger range in the early stage of iteration, which helps to strengthen the global search ability in the early stage. As the energy is consumed, the jump intensity decreases, which helps to strengthen the local search ability in the later stage of search. The jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy, and the corresponding process has the following relationship: ; in, Represents a random number between (0,1).

[0050] See also Figure 3 This embodiment also proposes a flexible job shop scheduling system based on multi-strategy improvement. The system applies the above-mentioned flexible job shop scheduling method based on multi-strategy improvement. The system includes: Encoding module for: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; Decoding module for: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; Several initial workshop scheduling strategies are used as the initial population. Each individual in the initial population corresponds to an initial workshop scheduling strategy. The individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. The Circle chaotic map is used to adjust the position of each individual in the initial population to obtain the adjusted initial population. The adjusted initial population is transformed into a quantum superposition state population using quantum theory, and the quantum bit superposition state population is mutated using a dynamic quantum rotating gate to generate a mutant population; Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; Taking minimizing the maximum completion time as the optimization goal, the Harris Hawk algorithm is used to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual. The optimal individual is taken as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

[0051] In order to verify the effectiveness of the present invention, the present invention and the existing algorithm are tested under the same conditions, as follows The experimental data comes from the Ladata dataset in the open source website http: / / people.idsia.ch / ~monaldo / fjsp.html, which is used to verify the performance of the proposed algorithm. The present invention adopts a configuration with a population size of 200 and a maximum number of iterations of 100, and independently runs the algorithm 10 times to ensure the reliability of the results. The optimization goal is set to minimize the maximum completion time.

[0052] In order to comprehensively evaluate the performance of the algorithm, this paper conducted a comparative analysis with various existing optimization algorithms, including Artificial Bee Colony (ABC), Fick's Law Algorithm (FLA) and Harris Hawks Optimization (HHO). The specific comparison data are shown in Table 1. Among them, n and m represent the number of workpieces and the number of machines, respectively. Best represents the optimal solution of 10 running results, and avg represents the average value of 10 running results. Taking example La11 as an example, the four comparison algorithms can all find the optimal solution, but the Avg of the present invention is significantly lower than that of other algorithms, which verifies its superiority in solution accuracy. From Figures 4 to 9 It can be seen from the fitness value curve that the present invention is superior to other algorithms in iteration speed and iteration effect in the La11 to La17 datasets. The test results of the present invention and the three existing algorithms in the calculation examples La11 to La17 are shown in the following table.

[0053]

[0054] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0055] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0056] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0057] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A flexible job shop scheduling method based on multi-strategy improvement, characterized in that: The method comprises the following steps: Step 1: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; Step 2: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; Step 3: Take several initial workshop scheduling strategies as the initial population, each individual in the initial population corresponds to an initial workshop scheduling strategy, and the individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. Use Circle chaotic mapping to adjust the position of each individual in the initial population to obtain the adjusted initial population. Step 4: Using quantum theory to transform the adjusted initial population into a quantum superposition state population, and using a dynamic quantum rotating gate to mutate the quantum bit superposition state population to generate a mutant population; Step 5: Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; Step 6. Taking minimizing the maximum completion time as the optimization goal, use the Harris Hawk algorithm to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual, and take the optimal individual as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

2. The flexible job shop scheduling method based on multi-strategy improvement according to claim 1 is characterized in that: In step 1, obtaining workshop production information and encoding the workshop production information to obtain process codes and machine codes specifically includes the following steps: Obtain workshop production information, which includes several workpieces and several machines. Each workpiece includes several processes. Obtain the processing time of each process on each machine. Generate an array according to the number of processes of each workpiece, and then shuffle the array to generate a new process code. For workpieces with a process where the number of optional machines is greater than or equal to 2, define the machine selection probability pi, and determine the machine selection method by generating a random number between 0 and 1 and comparing it with pi; If the random number is greater than pi, a machine is randomly selected; if the random number is less than pi, the machine with the shortest time is selected, and multiple process codes, multiple machine codes and multiple processing time codes are obtained.

3. The flexible job shop scheduling method based on multi-strategy improvement according to claim 2 is characterized in that: In step 2, the constraints of the flexible job shop scheduling problem specifically include: The same machine can only process one workpiece at a time; The same process of the same workpiece can only be processed by one machine at the same time; After the process of each workpiece begins, the processing cannot be interrupted; Different artifacts have the same priority; There are sequential constraints between the processes of the same workpiece, but there are no sequential constraints between the processes of different workpieces; All workpieces can be processed at time zero.

4. The flexible job shop scheduling method based on multi-strategy improvement according to claim 3 is characterized in that: In step 3, the position of each individual in the initial population is adjusted by using the Circle chaotic map, and the adjusted initial population is obtained, which specifically includes the following steps: According to the total number of processes in the initial population, the Circle chaotic map is used to iteratively generate the corresponding chaotic value sequence for each process code. The corresponding process has the following relationship: ； in, represents the chaotic value generated by the chaotic map, represents the next chaotic value generated by the chaotic map, represents pi, Represents modulo operation; The chaotic value sequence is linearly mapped to the solution space to select machines for each process according to the chaotic value to obtain the adjusted initial population. The corresponding process has the following relationship: ； in, Indicates j decision variable dimensions, j=1,2,…,D; D represents the total number of decision variable dimensions, , n represents the number of workpieces, m represents the number of workpiece processes; i=1,2,…,N, N represents the total number of individuals in the initial population, Represents the individuals in the adjusted initial population i In the decision variable dimension j Position on; They represent the upper and lower bounds of the search space respectively. The search space consists of all possible scheduling strategies.

5. The flexible job shop scheduling method based on multi-strategy improvement according to claim 4 is characterized in that: In step 4, the adjusted initial population is transformed into a quantum bit superposition state population using quantum theory, which specifically includes the following steps: The mapping relationship between quantum space and solution space is established through linear transformation to obtain the cosine position and sine position of individuals in the initial population in the solution space. The corresponding process has the following relationship: ； ； in, represents the cosine position of the individual in the solution space, represents the sinusoidal position of the individual in the solution space, which consists of all possible scheduling strategies that follow the constraints. represents the rotation angle of the quantum bit; Perform an inverse transformation on the current individual's sine position or cosine position to obtain the inverse transformation rotation angle of the current individual's sine position or cosine position. The corresponding process has the following relationship: ； ； in, Indicates the inverse transformation rotation angle; According to the inverse transformation rotation angle of the current individual sine position or cosine position, the sine position or cosine position corresponding to the current individual is inferred. The current individual sine position and the inferred individual cosine position or the current individual cosine position and the inferred individual sine position constitute the two state bits of the initial quantum bit, and a quantum bit superposition state population is obtained.

6. The flexible job shop scheduling method based on multi-strategy improvement according to claim 5 is characterized in that: In step 4, a dynamic quantum rotating gate is used to mutate the quantum bit superposition state population, and generating a mutant population specifically includes the following steps: The dynamic quantum rotating gate performs a logical transformation on the two state bits of the initial quantum bit to obtain the two state bits of the transformed quantum bit. The corresponding process has the following relationship: ； in, Represent the two state bits of the transformed quantum bit; It represents the updated value of the angle in the probability amplitude of the quantum bit after passing through the dynamic quantum rotating gate; Represents the rotation angle of a given dynamic quantum rotating gate, ranging from ; represents a dynamic quantum bit rotating gate. The calculation process of the dynamic quantum bit rotating gate has the following relationship: ； According to the two state bits of the quantum bit, the position of the individual in the transformed population is calculated to obtain the mutant population. The corresponding process has the following relationship: ； ； in, represents the cosine position of the transformed population individuals in the solution space, Represents the sinusoidal position of the transformed population individuals in the solution space.

7. The flexible job shop scheduling method based on multi-strategy improvement according to claim 6 is characterized in that: In step 6, the process corresponding to the dynamic adjustment of the escape energy in the Harris Hawk algorithm according to the iteration cycle has the following relationship: ； in, It indicates escape energy; Represents the escape energy of the initial state, which is a random number uniformly distributed in the interval (-1,1); Indicates the current iteration number, represents the maximum number of iterations, represents the golden ratio, .

8. The flexible job shop scheduling method based on multi-strategy improvement according to claim 7 is characterized in that: In step 6, the process of dynamically adjusting the jump strength in the Harris Hawk algorithm according to the adjustment result of the escape energy is represented by the following relationship: ； in, represents the random jump intensity of the prey during its escape, Represents a random number in the range 0-1.

9. A flexible job shop scheduling system based on multi-strategy improvement, characterized in that: The system applies the flexible job shop scheduling method based on multi-strategy improvement as described in any one of claims 1 to 8, and the system includes: Encoding module for: Obtain workshop production information, encode the workshop production information, and obtain process code and machine code; Decoding module for: Set the constraints of the flexible job shop scheduling problem, and randomly combine the process codes and machine codes according to the constraints to generate several initial job shop scheduling strategies; Several initial workshop scheduling strategies are used as the initial population. Each individual in the initial population corresponds to an initial workshop scheduling strategy. The individual position corresponds to the combined order of the process code and the machine code in the initial workshop scheduling strategy. The Circle chaotic map is used to adjust the position of each individual in the initial population to obtain the adjusted initial population. The adjusted initial population is transformed into a quantum superposition state population using quantum theory, and the quantum bit superposition state population is mutated using a dynamic quantum rotating gate to generate a mutant population; Compare the corresponding individuals in the quantum bit superposition state population and the mutant population, and select the best individuals to form the final initial population; Taking minimizing the maximum completion time as the optimization goal, the Harris Hawk algorithm is used to iteratively optimize the final initial population while following the constraints. In each iterative optimization process, the escape energy in the Harris Hawk algorithm is dynamically adjusted according to the iteration cycle, and then the jump intensity in the Harris Hawk algorithm is dynamically adjusted according to the adjustment result of the escape energy to confirm the optimal individual. The optimal individual is taken as the global optimal solution to obtain the optimal scheduling strategy for the flexible job shop.

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