Multi-target-interval flexible job shop scheduling method and related device

Abstract

The invention discloses a multi-target-interval flexible job shop scheduling method and a related device, and relates to the technical field of shop scheduling, and the method comprises the steps: constructing a multi-target-interval flexible job shop scheduling problem model, the problem model comprises interval maximum completion time, interval machine total load, interval total energy consumption, constraint conditions and interval number correlation operation rules related to the multi-target interval flexible job shop scheduling problem; and based on the interval number correlation operation rule, solving the multi-target interval flexible job shop scheduling problem model by utilizing an interval chameleon group algorithm to obtain a global optimal scheduling solution, and realizing multi-target interval flexible job shop scheduling. According to the method, the problem that multi-objective optimization is difficult to carry out on interval flexible job shop scheduling in the prior art can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of workshop scheduling, and in particular to a multi-objective interval flexible job shop scheduling method and related devices. Background Art

[0002] Shop scheduling refers to the process of rationally allocating production tasks to available resources. In previous studies of shop scheduling problems, the focus was on the determined shop scheduling problem. However, in the actual operation and production process, there are often various uncertainties, which lead to the failure of the initial scheduling plan to proceed smoothly. The uncertainties in the manufacturing workshop mainly include resource-related and workpiece-related. These uncertainties can directly affect and reflect the fluctuation of the process processing time. For example, machine failure can be approximately converted into the impact on the process processing time through statistical analysis of data such as machine failure rate and maintenance time. Uncertainties such as differences in the technical level of operators, cutting parameter adjustments, workpiece rework and repair, and tool fixture wear all make the process processing time present significant uncertainty. It can be seen that the process processing time is a type of uncertainty factor that is common and difficult to accurately characterize in shop scheduling problems.

[0003] The characterization methods commonly used for uncertain working time can be basically divided into three categories: random numbers, fuzzy numbers, and interval numbers. In actual workshop production, it is difficult to accurately obtain the probability distribution function of random processing time and the membership function of fuzzy processing time. It is necessary to analyze and summarize from a large amount of historical data, while the upper and lower bounds of processing time are relatively easy to obtain. In addition, random numbers and fuzzy numbers can also be converted into interval numbers through confidence levels and cut-off levels, respectively. Therefore, using interval numbers to simulate the uncertainty of process processing time has better applicability. At present, the existing technology mainly performs single-objective optimization on interval flexible job shop scheduling, and lacks research on multi-objective optimization. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-objective interval flexible job shop scheduling method and related devices to solve the problem that the prior art is difficult to perform multi-objective optimization on interval flexible job shop scheduling.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: In a first aspect, a multi-objective interval flexible job shop scheduling method comprises the following steps: Constructing a multi-objective interval flexible job shop scheduling problem model, wherein the problem model includes the interval maximum completion time, interval total machine load, interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; Based on the interval number related operation rules, the interval chameleon group algorithm is used to solve the multi-objective interval flexible job shop scheduling problem model, obtain the global optimal scheduling solution, and realize the multi-objective interval flexible job shop scheduling.

[0006] In some embodiments, the constraints include: The start time of each process is non-negative; Each process can only be processed continuously by one machine at a time; The same machine can only process one process at the same time; The processing sequence constraints between the processes of each workpiece are as follows: (7) (8) in, For process In the machine The interval start time is For process In the machine The interval processing time on Process In the machine The interval completion time on is the decision variable; The interval number related operation rules include an interval number maximum operation rule, an interval number sum operation rule and a comparison rule based on interval possibility.

[0007] In some implementations, the step of solving the multi-objective interval flexible job shop scheduling problem model using the interval chameleon swarm algorithm to obtain a global optimal scheduling solution specifically includes: Initialize the chameleon group using hybrid Logistics chaotic mapping; Calculating the fitness of the initial chameleon group, performing non-dominated sorting by using the comparison rule based on interval possibility, and recording the current optimal individual and position; Update the position of the chameleon in the search space according to the golden sine strategy; The traditional chameleon group algorithm is used to update the position of the chameleon's eyes after rotation, and then the speed and position of the chameleon are updated to obtain the updated chameleon group and its position. Calculate the fitness value of the current chameleon group, and update and record the global optimal scheduling plan based on the fitness value; After Gaussian perturbation of the currently existing optimal chameleon group, determine whether the current number of iterations of the interval chameleon group algorithm reaches the maximum number of iterations. If the maximum number of iterations is reached, output the global optimal scheduling solution. If the maximum number of iterations is not reached, repeat the step of updating the position of the chameleon in the search space according to the golden sine strategy and the subsequent steps until the maximum number of iterations is reached.

[0008] In some embodiments, the step of solving the multi-objective interval flexible job shop scheduling problem model using the chameleon swarm algorithm includes chromosome encoding and chromosome decoding, wherein the chromosome encoding is a two-segment encoding with equal gene numbers, the first half of which is encoded as a processing machine selected for a corresponding process, and the second half of which is encoded as a process sequence; The chromosome decoding arranges the processing of the operations from left to right in accordance with the process sequence, and while taking into account the idle time of the machine, the processing of the operations is inserted forward while satisfying the constraint conditions.

[0009] In some implementations, the step of initializing the chameleon group using a hybrid Logistics chaotic map specifically includes: Preferably, a hybrid Logistics chaotic mapping is used to initialize the machine coding part, 50% of the machine coding part is generated by random search, and 50% of the machine coding part is generated by the hybrid Logistics chaotic mapping; According to the machine coding part, a plurality of process coding schemes are randomly generated, and the process coding schemes and the machine coding part are combined to complete the initialization of the chameleon group.

[0010] In some embodiments, the step of updating the position of the chameleon in the search space according to the golden sine strategy is specifically implemented by the following formula:

[0011]

[0012] in, Indicates In the iteration, The chameleon in The new location of the dimension; Indicates the current position of the individual chameleon; Indicates that the chameleon individual The current optimal position of the iteration; and is a random number uniformly distributed in the range [0,1]; is the probability of an individual chameleon sensing prey; Affects the direction of chameleon exploration, the value is 1 or -1; and Respectively The lower and upper bounds of the dimensional search domain; yes Random numbers within yes Random numbers within and It is the coefficient obtained based on the golden section number.

[0013] In a second aspect, a multi-objective interval flexible job shop scheduling system includes: A problem model building module is used to build a multi-objective interval flexible job shop scheduling problem model, wherein the problem model includes the interval maximum completion time, interval machine total load, interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; The chameleon global optimization module is used to solve the multi-objective interval flexible job shop scheduling problem model using the interval chameleon group algorithm to obtain the global optimal scheduling solution and realize the multi-objective interval flexible job shop scheduling.

[0014] In a third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein the processor implements the steps of the multi-objective interval flexible job shop scheduling method when executing the computer program.

[0015] In a fourth aspect, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the multi-objective interval flexible job shop scheduling method are implemented.

[0016] In a fifth aspect, a computer program product is provided, the computer product comprising a computer program, characterized in that when the computer program is executed by a processor, the steps of the multi-objective interval flexible job shop scheduling method are implemented.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a multi-objective interval flexible job shop scheduling method. By taking the interval maximum completion time, the interval machine total load and the interval total energy consumption as optimization targets, a multi-objective interval flexible job shop scheduling problem model is established, and the interval chameleon swarm algorithm (ICSA) proposed by the present invention is used to solve the multi-objective interval flexible job shop scheduling problem model, which can solve the problem that the prior art is difficult to perform multi-objective optimization on interval flexible job shop scheduling.

[0018] Furthermore, in the process of solving the interval chameleon swarm algorithm, the present invention uses a hybrid Logistics chaotic mapping to initialize the chameleon swarm, which can improve the quality of the scheduling solution when the population is initialized, increase the diversity of the population, and avoid the problem of the algorithm falling into a local optimum in the early stage.

[0019] Furthermore, the present invention updates the position of the chameleon in the search space according to the golden sine strategy in the interval chameleon swarm algorithm, thereby increasing the convergence speed and convergence accuracy of the interval chameleon swarm algorithm.

[0020] Furthermore, the present invention performs Gaussian perturbation on the currently existing optimal chameleon group in the interval chameleon group algorithm, which can improve the diversity of the later positions of chameleon individuals. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a schematic diagram of chromosome coding in Example 1; Figure 2 A flowchart of solving the multi-objective interval flexible job shop scheduling problem model using the interval chameleon group algorithm proposed in Example 1; Figure 3 The box plots of HV values ​​and C measures of the three algorithms during the simulation verification of Example 1, wherein (a) is the box plot of HV values ​​of the three algorithms, and (b) is the box plot of C measures of the three algorithms; Figure 4 The midpoint line graphs of the objective functions of the three algorithms in each test example in the simulation verification of the first embodiment, wherein (a) is the midpoint line graph of the maximum completion time of the three algorithms in each test example; (b) is the midpoint line graph of the total machine load of the three algorithms in each test example; (c) is the midpoint line graph of the total energy consumption of the three algorithms in each test example; Figure 5 The figures are the midpoint distribution diagrams of the Pareto frontier superbody of the three algorithms in the examples used for the simulation verification of Example 1, wherein (a) is the midpoint distribution diagram of the Pareto frontier superbody of the three algorithms in the example IMK01, (b) is the midpoint distribution diagram of the Pareto frontier superbody of the three algorithms in the example IMK03, (c) is the midpoint distribution diagram of the Pareto frontier superbody of the three algorithms in the example IMK07, and (d) is the midpoint distribution diagram of the Pareto frontier superbody of the three algorithms in the example IMK10. DETAILED DESCRIPTION

[0022] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings, and the described content is intended to explain the present invention rather than to limit it.

[0023] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or are inherent to these processes, methods, systems, products or apparatus.

[0024] Embodiment 1 In the actual manufacturing process, the multi-objectives interval flexible job shop scheduling problem (MOIFJSP) can be described as follows: Workpieces exist Machine Each workpiece is processed Contains one or more processes , Representation of workpiece The total number of processes included, Representation of workpiece No. Each process Can be processed on some or all machines, and on different machines The processing time and energy consumption are different for each process, and all processes are processed according to the established process route. In the machine The processing time on the ,in, , are the upper and lower bounds of the interval processing time, respectively. Therefore, the scheduling problem can be expressed as: select a machine for each process to process, and sort all the processes assigned to each machine so that the set multiple optimization objectives are optimal. In order to more clearly describe the flexible workpiece shop scheduling problem considering interval working time, an example of IFJSP (interval flexible job shop scheduling problem) in which three workpieces are processed on three devices is shown in Table 1. The numerical intervals represent the process In the machine The processing time on the machine. The symbol '—' indicates the processing time on the machine. Not a process Candidate machines.

[0025] Table 1 IFJSP processing schedule

[0026] In order to simplify the above problem model, this embodiment makes the following assumptions: All machines are independent of each other and all machines are available at time zero; Only one workpiece can be processed on the same machine at the same time, and once the workpiece is processed, it cannot be interrupted; The same workpiece can only proceed to the next process after the previous process is completed; The same process can only be processed by one machine at the same time; Different workpieces have the same priority, and there are sequence constraints between the processes of the same workpiece.

[0027] In order to better describe the multi-objective interval flexible job shop scheduling problem and build a mathematical model, the following related symbols are introduced to define the variables, as shown in Table 2: Table 2 Symbol definitions

[0028] This embodiment provides a multi-objective interval flexible job shop scheduling method, including the following steps: S1, taking the interval maximum completion time, interval machine total load and interval total energy consumption as optimization targets, a multi-objective interval flexible job shop scheduling problem model is constructed. The calculation formula of the objective function is as follows: (1) (2) (3) The constraints of the multi-objective interval flexible job shop scheduling problem model are as follows: (4) (5) (6) (7) (8) Formula (4) ensures that the start time of each process is non-negative; Formula (5) indicates that each process can only be processed continuously by one machine at the same time; Formula (6) indicates that the same machine can only process one process at the same time; Formulas (7) and (8) represent the processing order constraints between each workpiece process.

[0029] In the above multi-objective interval flexible job shop scheduling problem model, since the interval number is used to represent the optimization objective, for two interval numbers and , and They are The interval width is , then the interval number related operation rules are as follows: The operation rules for taking the largest number in the interval are:

[0030] Interval number summation operation rules:

[0031] The comparison rules based on interval possibility are as follows: First define the number of intervals The possibility is: (9) The same interval number The probability is , the possibility of comparing the size of interval numbers has the following properties: (1) ; (2) If , then the number of intervals ; (3) If , then the number of intervals .

[0032] S2, based on the interval number related operation rules in S1, the interval chameleon group algorithm is used to solve the multi-objective interval flexible job shop scheduling problem model to obtain the global optimal scheduling solution.

[0033] Before introducing the interval chameleon swarm algorithm, we first introduce the traditional chameleon swarm algorithm. The traditional chameleon swarm algorithm (CSA) has three main stages of obtaining food: finding prey, turning eyes to find prey, and capturing prey; CSA first randomly generates a set of initial solutions, which are evenly distributed in the search space. Their number and dimensions are based on the specific requirements of the problem, as shown in the following equation (10): (10) in For the The initial vector of the chameleon, and Respectively The lower and upper bounds of the dimensional search domain, is a random value in the range [0,1].

[0034] (1) Searching for prey In the chameleon swarm algorithm, chameleons adjust their positions in the search space according to the changes in the prey's position, tracking and approaching the prey. The movement behavior during foraging can be mathematically modeled using the position update strategy, as shown in the following formula: (11) In formula (11), when When , the chameleon can change its position by observing the prey in the search space; if , chameleons randomly explore the search space from different directions and areas when looking for prey, which makes it very likely that they can perceive nearby target prey. The specific meanings of the variables are: Indicates In the iteration, The chameleon in The new location of the dimension; Indicates the current position of the individual chameleon; Indicates that the chameleon individual The current optimal position of the iteration; Indicates that the chameleon individual The global optimal position of the iteration; and are two positive numbers that control the exploration ability, with values ​​of 0.25 and 1.50 respectively; , , , is a random number uniformly distributed in the range [0,1]; is the probability of an individual chameleon sensing prey, with a value of 0.1; Affects the direction of the chameleon's exploration, with a value of 1 or -1. The parameter for controlling the search capability is defined as shown in formula (12): (12) in , Represent the current number of iterations and the maximum number of iterations respectively. To control the constant value of exploration and development capabilities, the value is 3.5.

[0035] (2) Eye movement to detect prey The significant advantage of chameleons is that they can use the rotation characteristics of their eyes to identify the position of prey and can rotate 360° to find prey. There are four main stages for chameleons to rotate their eyes to find prey: 1) the chameleon translates from its original position to the center of gravity; 2) determines the rotation matrix of the prey position; 3) updates the chameleon's position based on the rotation matrix at the center of gravity; 4) the chameleon returns to its original position. This position update process can be mathematically modeled as: (13) (14) (15) Where: Indicates the new position of the chameleon after rotation; Indicates the current location; Indicates that the chameleon is The center position of the iteration; for and The transformed rotation matrix represents the rotation of the chameleon's eyes; yes Two orthogonal vectors in the dimensional search space, express Vectors that are orthogonal to each other.

[0036] In formula (15): Indicates the random rotation angle of the chameleon's eyes, r is a random number in the range of [0,1], achieving a rotation angle from 0 to 180 degrees; Controls the direction of the chameleon's rotation, with a value of +1 or -1.

[0037] (3) Capturing prey The chameleon's tongue can reach up to twice its own length, so the chameleon can search a larger area and capture prey more efficiently. When prey gets too close to the chameleon, the chameleon will quickly attack the prey with its tongue to end the hunt. During this process, the chameleon will slightly adjust its position, allowing it to capture the prey more accurately. The mathematical model of the chameleon's tongue speed when attacking prey is: (16) Where: Indicates that an individual has The speed after the iteration update; Indicates the current speed of the individual; and Yes Control and Two positive constants affecting the speed of a chameleon's tongue; and is a random number in the range [0,1]; is the inertia weight of the velocity, which decreases linearly with the number of iterations, as shown in formula (17): (17) The position adjustment of the chameleon when attacking prey with its tongue is shown in formula (18): (18) in: represents the speed of the previous iteration, is the acceleration, which gradually increases until it reaches a maximum value of 2590 m / s 2The definition of acceleration is shown in formula (19): (19) This embodiment improves the above-mentioned traditional chameleon swarm algorithm and uses the interval chameleon swarm algorithm to solve the multi-objective interval flexible job shop scheduling problem model. The solution process involves chromosome encoding and decoding. The encoding adopts a two-segment encoding with equal gene numbers, and the encoding length is ( The first half is the machine selection (MS), and the number indicates the processing machine selected for the corresponding process; the second half is the process order (OS), and the number appears in the code The number represents the number of processes of the workpiece. Figure 1 This is a chromosome coding diagram, which means that there are 3 workpieces processed on 3 machines. Each workpiece has 3 processes. The processing order of the processes is:

[0038] In this embodiment, the interval number operation is combined with the active decoding method, and a left shift strategy is designed to decode the chromosome. The operations are arranged from left to right in the order of the process sequence, and the machine idle time is considered. The operation is inserted forward when the machine and workpiece processing constraints are met to ensure that the machine can start processing at the earliest allowed time.

[0039] like Figure 2 As shown in FIG. 1 , the steps of using the interval chameleon swarm algorithm to solve the multi-objective interval flexible job shop scheduling problem model specifically include: S2.1, first set ICSA parameters; S2.2, using hybrid Logistics chaotic mapping to initialize the chameleon group; The mathematical expression of hybrid Logistics chaos mapping is: (20) Where: Indicates the current state. Indicates the next state, is the logistics parameter, and its value is close to 4, and When the value of is in the interval (0,1), the hybrid logistic mapping will show completely chaotic characteristics, and the generated sequence is ergodic and random, which is suitable for initial population generation of the optimization algorithm.

[0040] Since the encoding method of this embodiment adopts two-stage encoding, when initializing the population, the machine coding part is first initialized by a hybrid logistics chaotic mapping method, of which 50% is generated by random search and 50% is generated by a hybrid logistics chaotic mapping method. According to the machine coding part generated by the initialized population, multiple process coding schemes are randomly generated, and then the machine coding part and the process coding are combined to generate a scheduling solution group to complete the initialization population. This hybrid method can improve the diversity and quality of the initial population.

[0041] S2.3, calculating the fitness of the initial chameleon group, and performing non-dominated sorting by the comparison rule based on interval possibility, and recording the current optimal individual and position; In this embodiment, the number of intervals is used to represent multiple optimization objectives. The traditional Pareto dominance relationship based on determining the objective function value is no longer applicable. Therefore, it is necessary to redefine the dominance relationship between two individuals in the sense of intervals, and introduce the above-mentioned comparison rule based on interval possibility to determine the dominance relationship between individuals and sort them. Two bodies Solve The interval function values ​​obtained when the optimization objectives are and ,for If both are possible , and at least , so that , it means that individual Dominant Individual If the individual No domination of individuals ,individual Nor does it dominate individuals , then the two bodies do not dominate each other.

[0042] S2.4, converting the scheduling scheme into the position of the chameleon in the search space; S2.5, update the position of the chameleon in the search space according to the golden sine strategy, the specific implementation method is as follows: (twenty one) in: yes Random numbers within yes Random numbers within , It is a coefficient obtained based on the golden section number. The specific calculation method is as follows: (twenty two) ICSA guided by the golden sine strategy can search the optimal solution field more fully, enhancing the convergence speed and convergence accuracy of the algorithm.

[0043] S2.6, update the position of the chameleon's eyes after rotation through equations (12) to (14) in the above-mentioned traditional chameleon group algorithm, and then update the chameleon's speed and position according to equations (15) to (17), and obtain the updated chameleon group and its position; S2.7, converting the updated chameleon group positions into a scheduling plan; S2.8, calculate the fitness value of the current chameleon group, and update and record the global optimal scheduling plan according to the fitness value; S2.9, Gaussian perturbation is performed on the currently existing optimal chameleon group, specifically in the following way: (twenty three) in, is the step size parameter, the value is 0.0005; is a random number with mean 0 and standard deviation 1 and satisfies Gaussian perturbation, that is, .

[0044] Finally, determine whether the current number of iterations of the interval chameleon swarm algorithm has reached the maximum number of iterations. If so, output the global optimal scheduling solution. If not, repeat step S2.5 and subsequent steps until the maximum number of iterations is reached.

[0045] The following simulation experiment and analysis are conducted on a multi-objective interval flexible job shop scheduling method provided in this embodiment. MATLAB 2017b is used for programming. The computer parameters used are configured as Windows 10 system, Intel(R) Core(TM) i5-8265U CPU @ 1.60GHz 1.80 GHz, and 8GB RAM.

[0046] 1. Examples and evaluation indicators 1.1 Instance and metrics Since there are few standard examples for IFJSP, all test examples in this embodiment are constructed based on the Brandimarte benchmark examples (MK01~MK10). Convert to interval processing time ,in is the processing time in the Brandimarte test set, , is a random integer in [0,10]. The scales of the reconstructed examples IMK01~IMK10 are shown in Table 3.

[0047] Table 3 Example scale

[0048] Considering that the optimal result obtained by the multi-objective optimization algorithm is a set of Pareto front solutions, the traditional method cannot compare the effectiveness of the algorithm. Therefore, based on the constructed example, two performance indicators, hypervolume measure (HV) and covering set measure (C measure), are used to evaluate the performance of the algorithm.

[0049] The calculation method of HV measure adopts Monte Carlo estimation method, and 100,000 sampling points are used to ensure the accuracy of calculation. Since the values ​​of each objective function in the interval flexible job shop scheduling problem are interval numbers, in order to facilitate the calculation of HV value, all solutions in the non-dominated solution set obtained by different algorithms in each test problem are normalized, as shown in formula (24): (twenty four) in, , The obtained non-dominated solution sets are The maximum and minimum values ​​of .

[0050] C The measure is used to compare the relative coverage of the Pareto solution sets obtained by different algorithms. The calculation expression is: (25) in, and are two sets of Pareto frontiers obtained by different algorithms, It is cutting-edge The number of non-dominated solutions in For the cutting edge Frontier The ratio of the dominated solution to the entire solution set. When The obtained Pareto frontier is better than the algorithm ,Since this embodiment has defined the Pareto dominance relationship in the interval sense, the C measure is still applicable.

[0051] 1.2 Performance Analysis of Interval Chameleon Swarm Algorithm Due to the lack of algorithms that can directly compare the performance of the interval chameleon swarm algorithm (ICSA) proposed in this embodiment, this embodiment partially modifies the chameleon swarm algorithm (CSA) and the sparrow search algorithm (SSA) to compare with the improved algorithm proposed in this embodiment, and uses the operations based on the number of intervals and the individual dominance relationship in the sense of intervals in ICSA in CSA and SSA, so that they can solve the multi-objective interval flexible job shop scheduling problem (MOIFJSP) with uncertain processing time; The relevant parameters of CSA and ICSA follow the settings in the embodiment. For the sparrow algorithm, the warning value is set to 0.8, the proportional factor is selected to be 0.2, and the disturbance deviation factor is 0.1. The population size of the three algorithms is 200, and the number of iterations is 200. To ensure the accuracy of the results, each example is independently run 10 times to take the average value. The corresponding simulation results are shown in Tables 4 and 5. The optimal value of each example is represented by black bold.

[0052] Table 4 Mean values ​​of HV obtained by the above three algorithms for each test problem

[0053] Table 5 Objective function values

[0054] Table 4 shows the average HV values ​​obtained by the three algorithms for each test case. It can be seen from Table 4 that ICSA has achieved the optimal HV value for all test cases. This result shows that ICSA is more diverse than the other two algorithms and the distribution of the solution set is wider. The box plot of the average HV values ​​of the three algorithms is as follows Figure 3 (a) shown.

[0055] Table 5 shows the optimal objective function values ​​obtained by the three algorithms for solving each test case. The black bold font indicates the optimal values ​​of the three algorithms in each test case obtained based on the interval possibility comparison method. As shown in Table 5, ICSA obtains the optimal values ​​of most interval completion time, interval total energy consumption, and interval total load. The line graph of the midpoint of the interval of the objective function obtained by the three algorithms in each test case is shown in Figure 5. Figure 4 As shown by Figure 4 It can be seen that compared with the other two algorithms, ICSA can obtain higher quality scheduling solutions when solving IFJSP, and is therefore more suitable for actual workshop scheduling problems under uncertain conditions.

[0056] In order to further test the performance of ICSA in solving IFJSP and the quality of the solution set, the Pareto frontiers obtained by the three algorithms are analyzed.

[0057] Table 6 shows the number of non-dominated solutions in the Pareto front obtained by the three algorithms when solving the test cases. It can be seen from Table 6 that ICSA obtains more non-dominated solutions in most test cases.

[0058] Table 6 Number of Pareto solutions obtained by three algorithms for each test case

[0059] The relative coverage of the Pareto frontier obtained by different algorithms, namely the C measure, is calculated. The results are shown in Table 7. Compared with the comparison algorithm ICSA, the maximum value of all C measures is obtained. The C measure box plots of the three algorithms are shown in Figure 3 As shown in (b), the C measure value of ICSA is much larger than that of the comparison algorithm, which means that there are multiple individuals in the populations obtained by the two algorithms that are dominated by individuals in the population obtained by ICSA. It can be seen that the ICSA algorithm can obtain a better scheduling solution when solving IFJSP.

[0060] Table 7 Mean C-measure values ​​obtained by three algorithms for each test problem

[0061] The distribution diagrams of the midpoints of the Pareto frontier superbody obtained by the three algorithms in the four selected examples IMK01, IMK03, IMK07 and IMK10 are shown in the figure below. Figure 5 As shown in the figure, it can be seen that ICSA can obtain higher quality scheduling solutions and better distribution of Pareto solution sets.

[0062] The above experiments show that ICSA has significantly better comprehensive performance than the other two comparison algorithms in solving multi-objective interval flexible job shop scheduling problems, and is therefore more suitable for actual job shop scheduling problems.

[0063] A multi-objective interval flexible job shop scheduling method provided in this embodiment solves the multi-objective interval flexible job shop scheduling problem through an improved interval chameleon swarm algorithm, and the optimization objectives are the maximum interval completion time, the total load of the machine interval and the total energy consumption of the interval. It mainly has the following advantages: 1) The strategy of chaotic mapping mixed random search is adopted to generate the initial population, thereby improving the quality of the scheduling solution when the population is initialized, increasing the diversity of the population, and avoiding the problem of the algorithm falling into the local optimal state in the early stage; 2) The golden sine-based method is used to improve the position update method of the chameleon swarm when searching for prey, thereby enhancing the convergence speed and convergence accuracy of the algorithm; 3) Gaussian perturbation is added to the CSA to perturb the current optimal position of the chameleon individual, thereby improving the diversity of the individual's later position.

[0064] Finally, simulation experiments were carried out through 10 groups of test cases, and CSA, SSA and the proposed ICSA were compared. The comprehensive performance of the three algorithms was evaluated and analyzed by two performance indicators: hypervolume (HV) and covering set measure (C measure). The experiments showed that the solution set quality and optimization convergence of ICSA are significantly better than those of the other two algorithms, which proves the feasibility and effectiveness of the improved algorithm proposed in this embodiment in solving MOIFJSP.

[0065] Embodiment 2 This embodiment provides a multi-objective interval flexible job shop scheduling system, including: A problem model building module is used to build a multi-objective interval flexible job shop scheduling problem model, wherein the problem model includes the interval maximum completion time, interval machine total load, interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; The chameleon global optimization module is used to solve the multi-objective interval flexible job shop scheduling problem model using the interval chameleon group algorithm to obtain the global optimal scheduling solution and realize the multi-objective interval flexible job shop scheduling.

[0066] The division of modules in the embodiments of the present invention is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional module in each embodiment of the present invention may be integrated into one processor, or may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated modules may be implemented in the form of hardware or in the form of software functional modules.

[0067] In this embodiment, a computer device is also provided, which includes a processor and a memory, the memory is used to store a computer program (in this embodiment, the computer program includes a computing component and an iterative component, which can perform model calculation and model update), the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions in the computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of a multi-objective interval flexible job shop scheduling method.

[0068] This embodiment also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device for storing programs and data. It is understandable that the computer-readable storage medium here can include both built-in storage media in a computer device and, of course, extended storage media supported by the computer device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of a multi-objective interval flexible job shop scheduling method in the above embodiment.

[0069] This embodiment also provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the corresponding steps of a multi-objective interval flexible job shop scheduling method in the above embodiment are implemented.

[0070] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0071] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0072] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0073] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0074] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A multi-objective interval flexible job shop scheduling method, characterized in that: The following steps are involved: Constructing a multi-objective interval flexible job shop scheduling problem model, wherein the problem model includes the interval maximum completion time, interval total machine load, interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; Based on the interval number related operation rules, the interval chameleon group algorithm is used to solve the multi-objective interval flexible job shop scheduling problem model, obtain the global optimal scheduling solution, and realize the multi-objective interval flexible job shop scheduling.

2. A multi-objective interval flexible job shop scheduling method according to claim 1, characterized in that: The constraints include: The start time of each process is non-negative; Each process can only be processed continuously by one machine at a time; The same machine can only process one process at the same time; The processing sequence constraints between the processes of each workpiece are as follows: （7） （8） in, For process In the machine The interval start time is For process In the machine The interval processing time on Process In the machine The interval completion time on is the decision variable; The interval number related operation rules include an interval number maximum operation rule, an interval number sum operation rule and a comparison rule based on interval possibility.

3. A multi-objective interval flexible job shop scheduling method according to claim 2, characterized in that: The steps of solving the multi-objective interval flexible job shop scheduling problem model by using the interval chameleon group algorithm to obtain the global optimal scheduling solution specifically include: Initialize the chameleon group using hybrid Logistics chaotic mapping; Calculating the fitness of the initial chameleon group, performing non-dominated sorting by using the comparison rule based on interval possibility, and recording the current optimal individual and position; Update the position of the chameleon in the search space according to the golden sine strategy; The traditional chameleon group algorithm is used to update the position of the chameleon's eyes after rotation, and then the speed and position of the chameleon are updated to obtain the updated chameleon group and its position. Calculate the fitness value of the current chameleon group, and update and record the global optimal scheduling plan based on the fitness value; After Gaussian perturbation of the currently existing optimal chameleon group, determine whether the current number of iterations of the interval chameleon group algorithm reaches the maximum number of iterations. If the maximum number of iterations is reached, output the global optimal scheduling solution. If the maximum number of iterations is not reached, repeat the step of updating the position of the chameleon in the search space according to the golden sine strategy and the subsequent steps until the maximum number of iterations is reached.

4. The multi-objective interval flexible job shop scheduling method according to claim 2 is characterized in that: The step of solving the multi-objective interval flexible job shop scheduling problem model by using the chameleon swarm algorithm includes chromosome encoding and chromosome decoding, wherein the chromosome encoding is a two-segment encoding with equal gene numbers, the first half of which is the processing machine selected for the corresponding process, and the second half of which is the process sequence; The chromosome decoding arranges the processing of the operations from left to right in accordance with the process sequence, and while taking into account the idle time of the machine, the processing of the operations is inserted forward while satisfying the constraint conditions.

5. The multi-objective interval flexible job shop scheduling method according to claim 3 is characterized in that: The step of initializing the chameleon group by using the hybrid Logistics chaotic map specifically includes: Preferably, a hybrid Logistics chaotic mapping is used to initialize the machine coding part, 50% of the machine coding part is generated by random search, and 50% of the machine coding part is generated by the hybrid Logistics chaotic mapping; According to the machine coding part, a plurality of process coding schemes are randomly generated, and the process coding schemes and the machine coding part are combined to complete the initialization of the chameleon group.

6. A multi-objective interval flexible job shop scheduling method according to claim 3, characterized in that: The step of updating the position of the chameleon in the search space according to the golden sine strategy is specifically implemented by the following formula: in, Indicates In the iteration, The chameleon in The new location of the dimension; Indicates the current position of the individual chameleon; Indicates that the chameleon individual The current optimal position of the iteration; and is a random number uniformly distributed in the range [0,1]; is the probability of an individual chameleon sensing prey; Affects the direction of chameleon exploration, the value is 1 or -1; and Respectively The lower and upper bounds of the dimensional search domain; yes Random numbers within yes Random numbers within and It is the coefficient obtained based on the golden section number.

7. A multi-objective interval flexible job shop scheduling system, characterized in that: include: A problem model building module is used to build a multi-objective interval flexible job shop scheduling problem model, wherein the problem model includes the interval maximum completion time, interval machine total load, interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; The chameleon global optimization module is used to solve the multi-objective interval flexible job shop scheduling problem model using the interval chameleon group algorithm to obtain the global optimal scheduling solution and realize the multi-objective interval flexible job shop scheduling.

8. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable in the processor, wherein the processor implements the steps of a multi-objective interval flexible job shop scheduling method as described in any one of claims 1 to 6 when executing the computer program.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of a multi-objective interval flexible job shop scheduling method as described in any one of claims 1 to 6 are implemented.

10. A computer program product, the computer product comprising a computer program, characterized in that: When the computer program is executed by a processor, the steps of a multi-objective interval flexible job shop scheduling method as described in any one of claims 1 to 6 are implemented.

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