A multi-objective interval flexible job shop scheduling method and related device

Abstract

The application discloses a kind of multi-objective interval flexible job shop scheduling method and related device, it is related to workshop scheduling technical field, the method includes constructing multi-objective interval flexible job shop scheduling problem model, the problem model includes multi-objective interval flexible job shop scheduling problem related interval maximum completion time, interval machine total load, interval total energy consumption, constraint condition and interval number related operation rule;Based on the interval number related operation rule, interval chameleon colony algorithm is used to solve the multi-objective interval flexible job shop scheduling problem model, and the global optimal scheduling solution is obtained, to realize multi-objective interval flexible job shop scheduling.The present application can solve the problem that existing technology is difficult to carry out multi-objective optimization for interval flexible job shop scheduling.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of job shop scheduling, in particular to a multi-objective interval flexible job shop scheduling method and related device. BACKGROUND

[0002] Job shop scheduling refers to the process of reasonably allocating production tasks to available resources. In the past, the focus of job shop scheduling problem research was on deterministic job shop scheduling problems. However, in actual operation and production processes, various uncertain factors often exist, which leads to the failure of the initial scheduling scheme. Uncertain factors in manufacturing workshops mainly include resource-related and workpiece-related factors. These uncertain factors can directly affect and reflect the fluctuation of process processing time. For example, machine failure can be approximately converted into the impact on process processing time through statistical analysis of machine failure rate, repair time, etc. Uncertain factors such as differences in operator skill levels, cutting parameter adjustment, workpiece rework and repair, and tool and fixture wear make the process processing time significantly uncertain. Therefore, process processing time is a type of uncertain factor that is commonly encountered in job shop scheduling problems and is difficult to accurately characterize.

[0003] The representation methods commonly used for uncertain working hours can be 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, and it is necessary to analyze and induce from a large amount of historical data. However, the upper and lower bounds of processing time are relatively easy to obtain. Moreover, random numbers and fuzzy numbers can be converted into interval numbers through confidence levels and cut levels, respectively. Therefore, interval numbers are more suitable for simulating the uncertainty of process processing time. Currently, existing technologies mainly focus on single-objective optimization of interval flexible job shop scheduling, and lack of research on multi-objective optimization. SUMMARY

[0004] The present application aims to provide a multi-objective interval flexible job shop scheduling method and related device to solve the problem that existing technologies cannot perform multi-objective optimization on interval flexible job shop scheduling.

[0005] To achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0006] In a first aspect, a multi-objective interval flexible job shop scheduling method is provided, comprising the following steps:

[0007] A multi-objective interval flexible job shop scheduling problem model is constructed, which includes 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;

[0008] Based on the interval number related operation rules, the interval chameleon group algorithm is used to solve the multi-objective interval flexible workshop scheduling problem model to obtain the globally optimal scheduling solution and realize the multi-objective interval flexible workshop scheduling.

[0009] In some implementations, the constraints include:

[0010] The start time of each process is non-negative;

[0011] Each process can only be processed by one machine continuously at any given time;

[0012] The same machine can only process one operation at a time.

[0013] The processing sequence constraints between operations for each workpiece are given by the following formulas (7) and (8):

[0014] (7)

[0015] (8)

[0016] in, For process In the machine The start time of the above-mentioned intervals For process In the machine The processing time in the interval above, Process In the machine The completion time of the above interval For decision variables;

[0017] The interval number related operation rules include the interval number maximum operation rule, the interval number summation operation rule, and the comparison rule based on the interval probability.

[0018] In some implementations, the step of using the interval chameleon swarm algorithm to solve the multi-objective interval flexible job shop scheduling problem model to obtain the globally optimal scheduling solution specifically includes:

[0019] Initialize the chameleon swarm using a hybrid Logistic chaotic mapping;

[0020] Calculate the fitness of the initial chameleon population, perform non-dominated sorting using the comparison rule based on interval probability, and record the current best individual and its position;

[0021] Update the chameleon's position in the search space according to the golden sine strategy;

[0022] The traditional chameleon swarm algorithm first updates the position of the chameleons after their eyes have rotated, and then updates the speed and position of the chameleons to obtain the updated chameleon swarm and its position.

[0023] Calculate the fitness value of the current chameleon swarm, and update the record of the globally optimal scheduling scheme based on the fitness value;

[0024] After applying Gaussian perturbation to the existing optimal chameleon swarm, determine whether the current iteration count of the interval chameleon swarm algorithm has reached the maximum iteration count. If the maximum iteration count has been reached, output the globally optimal scheduling solution. If the maximum iteration count has not been reached, repeat the steps of updating the chameleon's position in the search space according to the golden sine strategy and the subsequent steps until the maximum iteration count is reached.

[0025] In some implementations, the step of using the chameleon swarm algorithm to solve the multi-objective interval flexible workshop scheduling problem model includes chromosome encoding and chromosome decoding. The chromosome encoding is a two-segment encoding with an equal number of genes. The first half of the encoding is the processing machine selected for the corresponding process, and the second half of the encoding is the process order.

[0026] The chromosome decoding is arranged in the order of the steps from left to right, taking into account machine idle time, and the processing of the steps is advanced while meeting the constraints.

[0027] In some implementations, the step of initializing the chameleon swarm using a hybrid Logistic chaotic mapping specifically includes:

[0028] The preferred approach is to initialize the machine code portion using a hybrid Logistic chaotic mapping, where 50% of the machine code portion is generated by random search and 50% is generated by the hybrid Logistic chaotic mapping.

[0029] Based on the machine coding part, multiple 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.

[0030] In some implementations, the step of updating the chameleon's position in the search space according to the golden sine strategy is specifically achieved by the following formula:

[0031]

[0032]

[0033] in, Indicates the first In the nth iteration, the 1st The chameleon in the first the new position of the chameleon; denotes the current position of the chameleon individual; denotes the current position of the chameleon individual; the current optimal position of the chameleon individual in the next iteration; and is a random number uniformly distributed in the range [0, 1]; is the probability that the chameleon individual perceives the prey; influences the direction of the chameleon's exploration and takes the value 1 or -1; and are the lower and upper bounds of the search domain in the d-th dimension, respectively; is a random number uniformly distributed in the range [0, 1]; is a random number uniformly distributed in the range [0, 1]; is a random number uniformly distributed in the range [0, 1]; is a random number uniformly distributed in the range [0, 1]; is a random number uniformly distributed in the range [0, 1]; and are coefficients obtained according to the golden section number.

[0034] In a second aspect, a multi-objective interval flexible job shop scheduling system comprises:

[0035] a problem model construction module, configured to construct a multi-objective interval flexible job shop scheduling problem model, the problem model comprising 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;

[0036] a chameleon global optimization module, configured to solve the multi-objective interval flexible job shop scheduling problem model by using an interval chameleon swarm algorithm to obtain a globally optimal scheduling solution, and realize multi-objective interval flexible job shop scheduling.

[0037] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable in the processor, and the processor implements the steps of the multi-objective interval flexible job shop scheduling method when executing the computer program.

[0038] In a fourth aspect, a computer readable storage medium stores a computer program, and the computer program implements the steps of the multi-objective interval flexible job shop scheduling method when executed by a processor.

[0039] In a fifth aspect, a computer program product comprises a computer program, and the computer program implements the steps of the multi-objective interval flexible job shop scheduling method when executed by a processor.

[0040] Compared with the prior art, the present application has the following beneficial effects:

[0041] This invention provides a multi-objective interval flexible job shop scheduling method. By taking the maximum completion time of the interval, the total machine load of the interval, and the total energy consumption of the interval as optimization objectives, a multi-objective interval flexible job shop scheduling problem model is established. The interval chameleon swarm algorithm (ICSA) proposed in this invention is used to solve the multi-objective interval flexible job shop scheduling problem model, which can solve the problem that existing technologies are difficult to optimize for multiple objectives in interval flexible job shop scheduling.

[0042] Furthermore, in the process of solving the interval chameleon swarm algorithm, this invention uses a hybrid Logistic chaotic mapping to initialize the chameleon swarm, which can improve the quality of the scheduling solution during population initialization, increase the diversity of the population, and avoid the problem of the algorithm getting trapped in local optima in the early stages.

[0043] Furthermore, this 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.

[0044] Furthermore, this invention applies Gaussian perturbation to the existing optimal chameleon swarm in the interval chameleon swarm algorithm, which can improve the diversity of the later positions of individual chameleons. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of chromosome coding in Example 1;

[0046] Figure 2 This is a flowchart illustrating how the interval chameleon swarm algorithm proposed in Example 1 solves the multi-objective interval flexible job shop scheduling problem model.

[0047] Figure 3 Box plots of HV values ​​and C measures for the three algorithms during simulation verification of Example 1, where (a) is a box plot of HV values ​​for the three algorithms and (b) is a box plot of C measures for the three algorithms.

[0048] Figure 4 The following are line graphs showing the midpoints of the objective functions of the three algorithms in each test case during simulation verification of Example 1: (a) is a line graph showing the midpoints of the maximum completion time of the three algorithms in each test case; (b) is a line graph showing the midpoints of the total machine load of the three algorithms in each test case; and (c) is a line graph showing the midpoints of the total energy consumption of the three algorithms in each test case.

[0049] Figure 5The following are the Pareto front hyperbody midpoint distribution diagrams for the three algorithms in the simulation verification of Example 1: (a) shows the Pareto front hyperbody midpoint distribution diagram for the three algorithms in Example IMK01, (b) shows the Pareto front hyperbody midpoint distribution diagram for the three algorithms in Example IMK03, (c) shows the Pareto front hyperbody midpoint distribution diagram for the three algorithms in Example IMK07, and (d) shows the Pareto front hyperbody midpoint distribution diagram for the three algorithms in Example IMK10. Detailed Implementation

[0050] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. The content described herein is for explanation rather than limitation of the present invention.

[0051] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification and claims of this invention are intended to cover a non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, systems, products, or devices.

[0052] Example 1

[0053] In actual manufacturing processes, the multi-objectives interval flexible job shop scheduling problem (MOIFJSP) can be described as follows: One workpiece exist Taiwanese machine Processing is carried out on each workpiece. Includes one or more processes , Indicates workpiece The total number of processes included. Indicates workpiece The Each process involves several steps. Processing can be performed on some or all of the machines, and on different machines The processing time and energy consumption vary for each step, and all processes are carried out according to the established process route. (Process) In the machine The processing time is an interval number. ,in, , respectively. Therefore, the scheduling problem can be described as: selecting a machine for each process and sequencing all processes assigned to each machine to achieve the optimal set of optimization objectives. In order to more clearly describe the interval flexible job shop scheduling problem considering interval processing time, an IFJSP (interval flexible job shop scheduling problem) example of 3 workpieces processed on 3 devices is shown in Table 1. The numerical interval represents the processing time of the process on the machine on the machine is not the candidate machine of the process

[0054] Table 1 IFJSP processing schedule

[0055]

[0056] In order to simplify the above problem model, the following assumptions are made in this embodiment:

[0057] All machines are independent of each other and all machines are available at time zero;

[0058] The same machine can only process one workpiece at the same time, and the workpiece cannot be interrupted once it starts processing;

[0059] The same workpiece can only proceed to the next process after the previous process is completed;

[0060] The same process can only be processed by one machine at the same time;

[0061] Different workpieces have the same priority, and there are sequence constraints between processes of the same workpiece.

[0062] In order to better describe the multi-objective interval flexible job shop scheduling problem and construct the mathematical model, the following related symbols are introduced to define the variables, as shown in Table 2:

[0063] Table 2 Symbol definitions

[0064]

[0065] The multi-objective interval flexible job shop scheduling method provided in this embodiment includes the following steps:

[0066] S1, an interval maximum completion time, an interval machine total load, and an interval total energy consumption are used as optimization objectives to construct a multi-objective interval flexible job shop scheduling problem model, and the calculation formula of the objective function is as follows:

[0067] ​​ (1)

[0068] (2)

[0069] (3)

[0070] The constraint conditions of the multi-objective interval flexible job shop scheduling problem model are as follows:

[0071] (4)

[0072] (5)

[0073] (6)

[0074] (7)

[0075] (8)

[0076] Formula (4) ensures that the start time of each process is non-negative; formula (5) indicates that each process can only be continuously processed by one machine at the same time; formula (6) indicates that the same machine can only process one process at the same time; formula (7) and formula (8) indicate the processing order constraint between each workpiece process.

[0077] In the above multi-objective interval flexible job shop scheduling problem model, since interval numbers are used to represent optimization objectives, for two interval numbers and , and are the interval widths of , then the interval number related operation rules are as follows:

[0078] Interval number taking large operation rule:

[0079] Interval number summation operation rule:

[0080] The comparison rule based on the possibility of interval numbers is as follows:

[0081] First, define the possibility of interval number as:

[0082] (9)

[0083] Similarly, the possibility of interval number is , and the possibility of comparing interval numbers has the following properties: (1) ; (2) if , then interval number (3) If Then the interval number .

[0084] S2, based on the interval number related operation rules in S1, uses the interval chameleon group algorithm to solve the multi-objective interval flexible workshop scheduling problem model and obtain the global optimal scheduling solution.

[0085] Before introducing the interval chameleon swarm algorithm, we will first introduce the traditional chameleon swarm algorithm. The traditional chameleon swarm algorithm (CSA) has three main stages for obtaining food: finding prey, moving eyes to find prey, and capturing prey.

[0086] CSA will first randomly generate a set of initial solutions, which are uniformly distributed in the search space. Their number and dimensionality are based on the specific requirements of the problem, as shown in equation (10) below:

[0087] (10)

[0088] in For the first The initial vector of a chameleon. and The first The lower and upper bounds of the dimensional search domain. It is a random value in the range [0,1].

[0089] (1) Searching for prey

[0090] In the chameleon swarm algorithm, chameleons adjust their position in the search space based on changes in the prey's location, tracking and approaching the prey. The movement behavior during foraging can be mathematically modeled using a position update strategy, as shown in the following equation:

[0091] (11)

[0092] In equation (11), when At times, chameleons can change their position by observing their prey within their search space; if Chameleons randomly explore their search space from different directions and areas when looking for prey, which makes it highly likely that they will detect nearby target prey. The specific meanings of the variables are as follows:

[0093] Indicates the first In the nth iteration, the 1st The chameleon in the first Wei's new position; Indicates the current location of the individual chameleon; represents the individual chameleon's position in the current iteration; represents the individual chameleon's position in the current iteration; represents the individual chameleon's position in the current iteration; represents the individual chameleon's position in the current iteration; represents the individual chameleon's position in the current iteration; 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 the chameleon perceiving the prey, with a value of 0.1; influences the direction of the chameleon's exploration, taking values of 1 or -1. is a parameter that controls the search ability, defined as shown in equation (12):

[0094] (12)

[0095] where , represent the current iteration number and the maximum iteration number, respectively, is a constant that controls the exploration development ability, with a value of 3.5.

[0096] (2) Eye rotation to find prey

[0097] The significant advantage of the chameleon is its ability to identify prey positions using the rotation characteristics of the eyes, which can rotate 360° to find prey. The process of the chameleon's eye rotation to find prey has four main stages: 1) the chameleon moves from the original position to the center of gravity position; 2) the rotation matrix of the prey position is determined; 3) the chameleon's position is updated according to the rotation matrix at the center of gravity; 4) the chameleon returns to the original position. This position updating process can be mathematically modeled as:

[0098] (13)

[0099] (14)

[0100] (15)

[0101] where: represents the new position of the chameleon after rotation; represents the current position; represents the center position of the chameleon in the iteration; is the rotation matrix of the and transformations, representing the rotation of the chameleon's eyes; is two orthogonal vectors in the search space, denote the vectors after being orthogonal to each other.

[0102] In formula (15), denotes the random rotation angle of the chameleon's eye, r is a random number in the range of [0, 1], and the rotation angle is realized from 0 to 180 degrees; control the direction of the chameleon rotation, and take the value of +1 or -1. (3) Capture prey

[0103] The chameleon's tongue can reach twice its own length, so the chameleon can search a larger area and capture prey more effectively. When the prey is too close to the chameleon, the chameleon will quickly attack the prey with the tongue to end the hunt. In this process, the chameleon will slightly adjust its position so that it can capture the prey more accurately. The mathematical model of the speed of the chameleon's tongue when attacking prey is as follows:

[0104]

[0105] (16) In the formula, denotes the speed of the individual after the

[0106] iteration update; denotes the current speed of the individual; and are two normal numbers that control the influence of and on the speed of the chameleon's tongue; and are random numbers in the range of [0, 1]; is the inertia weight of the speed, which decreases linearly with the number of iterations, as shown in formula (17): (17)

[0107] The adjustment of the chameleon's position during the process of attacking prey with the tongue is as follows:

[0108] (18)

[0109] wherein: denotes the speed of the last iteration,

[0110] is the acceleration, which gradually increases until it reaches a maximum value of 2590 m / s 2 . The definition of acceleration is as follows: (19)

[0111]

[0112] ​​The embodiment improves the traditional chameleon swarm algorithm, and solves a multi-objective interval flexible job shop scheduling problem model by using an interval chameleon swarm algorithm. Chromosome coding and decoding are involved in the solving process. Two-section coding is adopted for the coding, the coding length is ( N is the total number of processes). The first half is machine selection (MS), and the numbers represent the corresponding process selection of the processing machine; the second half is process sequencing (OS), and the number of times the number appears in the code represents the first process of the workpiece. Figure 1 A chromosome coding diagram is shown in the figure, which shows that there are 3 workpieces processed on 3 machines, each workpiece has 3 processes, and the process processing order is:

[0113]

[0114] The embodiment combines the interval number operation and the active decoding method, and designs a left shift strategy to decode the chromosome. According to the process sequencing order from left to right, the processing of the operation is arranged, the machine idle time is considered, and the operation is inserted in advance under the condition of meeting the machine and workpiece processing constraints, so that the machine can start processing at the earliest allowed time.

[0115] As shown in Figure 2 , the steps of solving the multi-objective interval flexible job shop scheduling problem model by using the interval chameleon swarm algorithm, specifically include:

[0116] S2.1, first, set the ICSA parameters;

[0117] S2.2, initialize the chameleon swarm by using the hybrid Logistics chaotic mapping;

[0118] The mathematical expression of the hybrid Logistics chaotic mapping is:

[0119] (20)

[0120] In the formula: Xn represents the current state, Xn+1 represents the next state, is a logistics parameter, when the value is close to 4, and the value is in the interval (0, 1), the hybrid Logistics mapping will exhibit complete chaotic characteristics, and the generated sequence has ergodicity and randomness, which is suitable for generating the initial population of the optimization algorithm.

[0121] Since this embodiment employs a two-stage encoding method, during population initialization, a hybrid logistic chaotic mapping approach is first used to initialize the machine code portion, where 50% is generated by random search and 50% by the hybrid logistic chaotic mapping approach. Based on the machine code portion generated during population initialization, multiple process encoding schemes are randomly generated. The machine code portion and process encoding are then combined to generate a scheduling solution population to complete the initialization of the population. This hybrid method improves the diversity and quality of the initial population.

[0122] S2.3 Calculate the fitness of the initial chameleon population, and perform non-dominated sorting using the comparison rule based on interval probability, and record the current best individual and its position;

[0123] In this embodiment, interval numbers are 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.

[0124] Two bodies Solve the first The interval function values ​​obtained when there are optimization objectives are respectively and ,for If all are possible and at least , making This indicates that the individual Dominant Individual If an individual Non-dominant individuals ,individual It does not control individuals If the two entities do not control each other, then the two entities do not control each other.

[0125] S2.4, convert the scheduling scheme into the chameleon's position in the search space;

[0126] S2.5 Update the chameleon's position in the search space according to the golden sine strategy. The specific implementation is as follows:

[0127] (twenty one)

[0128] in: yes Random numbers within; yes Random numbers within; , The coefficient is derived from the golden ratio, and the specific calculation method is as follows:

[0129] (22)

[0130] Based on the golden sine strategy guide, ICSA can search more fully in the optimal solution field, and enhance the convergence speed and accuracy of the algorithm.

[0131] S2.6, update the position of the chameleon after rotating the eyes according to the above formula (12) ~ formula (14) in the traditional chameleon group algorithm, and then update the speed and position of the chameleon according to formula (15) ~ formula (17), to obtain the updated chameleon group and its position;

[0132] S2.7, convert the updated chameleon group position into a scheduling scheme;

[0133] S2.8, calculate the fitness value of the current chameleon group, and update the record global optimal scheduling scheme according to the fitness value;

[0134] S2.9, Gaussian disturbance is carried out on the optimal chameleon group existing at present, and the following method is adopted:

[0135] (23)

[0136] wherein, is a step size parameter, and the value is 0.0005; is a random number with mean 0 and standard deviation 1 and satisfying Gaussian disturbance, that is, .

[0137] Finally, it is judged whether the current iteration number of the interval chameleon group algorithm reaches the maximum iteration number, if the maximum iteration number is reached, the global optimal scheduling solution is output, if the maximum iteration number is not reached, the step S2.5 and the steps after it are repeated until the maximum iteration number is reached.

[0138] The simulation experiment and analysis of the multi-objective interval flexible job shop scheduling method provided in the embodiment are carried out below, which is programmed by using MATLAB 2017b, and the parameter configuration of the computer used is Windows10 system, Intel(R) Core(TM) i5-8265U CPU @ 1.60GHz 1.80GHz, 8GB RAM.

[0139] 1. Instance and evaluation index

[0140] 1.1 Instance and metrics

[0141] Since there is no standard test case for IFJSP, all test cases in this paper are generated based on Brandimarte benchmark cases (MK01~MK10). The deterministic processing times are converted into interval processing times , where is the processing time in Brandimarte test set, , is a random integer in [0, 10]. The scales of the generated test cases IMK01~IMK10 are shown in Table 3.

[0142] Table 3 Scales of test cases

[0143]

[0144] Since the optimal results obtained by multi-objective optimization algorithms are a set of Pareto front solutions, the traditional method cannot compare the effectiveness of algorithms, so based on the constructed test cases, two performance indicators, hypervolume measure (HV) and coverage measure (C-measure), are used to evaluate the performance of algorithms.

[0145] The calculation method of HV measure adopts Monte Carlo estimation method, and 100000 sampling points are used to ensure the accuracy of calculation. Since the values of objective functions in interval flexible job shop scheduling problem are all 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 equation (24):

[0146] (24)

[0147] where , are the maximum and minimum values of the non-dominated solution set .

[0148] C Measure is used to compare the relative coverage of the Pareto solution sets obtained by different algorithms, and the calculation expression is:

[0149] (25)

[0150] where and are two sets of Pareto front obtained by different algorithms, is the number of non-dominated solutions in the front , is the ratio of solutions in the front dominated by the front to the entire solution set. When , it indicates that the algorithm The obtained Pareto front is superior to the algorithm Since the Pareto dominance relation in the sense of intervals has been defined in this embodiment, the C measure is still applicable.

[0151] 1.2 Performance Analysis of the Interval Chameleon Group Algorithm

[0152] Since there is a lack of algorithms that can be directly compared with the performance of the Interval Chameleon Swarm Algorithm (ICSA) proposed in this embodiment, this embodiment modifies the Chameleon Swarm Algorithm (CSA) and the Sparrow Search Algorithm (SSA) to compare with the improved algorithm proposed in this embodiment. The interval number-based operations and individual dominance relations under the interval meaning in ICSA are applied to CSA and SSA, enabling them to solve the multi-objective interval flexible job shop scheduling problem (MOIFJSP) with uncertain processing time.

[0153] The parameters for CSA and ICSA follow the settings in the previous example. For the Sparrow Algorithm, the warning value is set to 0.8, the scaling factor is 0.2, and the perturbation deviation factor is 0.1. The population size for all three algorithms is 200, and the number of iterations is 200. To ensure the accuracy of the results, each case is run independently 10 times and the average value is taken. The corresponding simulation results are shown in Tables 4 and 5. The optimal value for each case is indicated in bold black.

[0154] Table 4 shows the mean HV values ​​obtained by the three algorithms for each test problem.

[0155]

[0156] Table 5 Objective function values

[0157]

[0158] Table 4 shows the average HV values ​​obtained by the three algorithms for each test case. As can be seen from Table 4, ICSA achieved the optimal HV value for all test cases. This result indicates that ICSA has better diversity than the other two algorithms, and the distribution of the obtained solution set is wider. The box plots of the average HV values ​​of the three algorithms are as follows: Figure 3 As shown in (a).

[0159] Table 5 shows the optimal objective function values ​​obtained by the three algorithms for each test case. The bold black text 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 achieved the optimal values ​​for most interval completion times, total interval energy consumption, and total interval load. The line graphs of the interval midpoints of the objective functions obtained by the three algorithms in each test case are shown below. Figure 4 As shown, by Figure 4It can be seen that ICSA can obtain better scheduling solution than the other two algorithms, so it is more suitable for real-world job shop scheduling problem under uncertain conditions.

[0160] In order to further test the performance of ICSA and the quality of the solution set, the Pareto front obtained by the three algorithms is analyzed.

[0161] Table 6 shows the number of non-dominated solutions in the Pareto front obtained by the three algorithms. It can be seen that ICSA obtains more non-dominated solutions in most test cases.

[0162] Table 6 Number of Pareto solutions obtained by three algorithms for each test case

[0163]

[0164] The relative coverage of the Pareto front obtained by different algorithms, i.e. C measure, is calculated, and the results are shown in Table 7. Compared with the comparison algorithms, ICSA achieves the maximum C measure. The C measure box plot of the three algorithms is shown in Figure 3 (b), and the C measure value of ICSA is much larger than that of the comparison algorithms, indicating that multiple individuals in the population obtained by the two algorithms are dominated by individuals in the population obtained by ICSA. Therefore, it can be known that ICSA can obtain better scheduling solution when solving IFJSP.

[0165] Table 7 Mean value of C measure obtained by three algorithms for each test problem

[0166]

[0167] The distribution of the midpoint of the Pareto front hyper-volume obtained by the three algorithms in the four selected examples IMK01, IMK03, IMK07 and IMK10 is shown in Figure 5 It can be seen from the figure that ICSA can obtain better scheduling solution and better distribution of the Pareto solution set.

[0168] The above experiments show that ICSA has better comprehensive performance than the other two comparison algorithms in solving multi-objective interval flexible job shop scheduling problem, so it is more suitable for real-world job shop scheduling problem.

[0169] This embodiment provides a multi-objective interval flexible job shop scheduling method. It solves the multi-objective interval flexible job shop scheduling problem using an improved interval chameleon swarm algorithm. The optimization objectives are maximum interval completion time, total machine load within the interval, and total interval energy consumption. The main advantages are as follows: 1) An initial population is generated using a chaotic mapping mixed random search strategy, improving the quality of the scheduling solution during population initialization, increasing population diversity, and avoiding the problem of the algorithm getting trapped in local optima early on; 2) A method based on the golden sine wave is used to improve the position update method when the chameleon swarm searches for prey, enhancing the algorithm's convergence speed and accuracy; 3) Gaussian perturbation is added to the CSA to perturb the current optimal position of individual chameleons, improving the diversity of individual positions in the later stages.

[0170] Finally, simulation experiments were conducted using 10 test cases to compare CSA, SSA, and the proposed ICSA. The comprehensive performance of the three algorithms was evaluated and analyzed using two performance indicators: hypervolume (HV) and cover set measure (C measure). The experiments showed that ICSA's solution set quality and optimization convergence were significantly better than the other two algorithms, proving the feasibility and effectiveness of the improved algorithm proposed in this embodiment in solving MOIFJSP.

[0171] Example 2

[0172] This embodiment provides a multi-target interval flexible workshop scheduling system, including:

[0173] The problem model construction module is used to construct a multi-objective interval flexible job shop scheduling problem model. The problem model includes the maximum completion time of the interval, the total machine load of the interval, the total energy consumption of the interval, the constraints, and the calculation rules related to the number of intervals.

[0174] The Chameleon Global Optimization Module is used to solve the multi-objective interval flexible workshop scheduling problem model using the interval Chameleon swarm algorithm to obtain the globally optimal scheduling solution and realize the multi-objective interval flexible workshop scheduling.

[0175] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0176] The embodiment also provides a computer device, which comprises a processor and a memory for storing a computer program (the computer program in the embodiment comprises a computing component and an iteration component, and can perform model computing and model updating), the computer program comprises program instructions, and the processor is used for executing the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be 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 and the like, which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions in the computer storage medium to implement a corresponding method flow or a corresponding function; the processor in the embodiment can be used for the operation of the multi-target interval flexible job shop scheduling method.

[0177] The embodiment also provides a storage medium, specifically a computer readable storage medium (Memory), which is a memory device in the computer device, and is used for storing programs and data. It can be understood that the computer readable storage medium herein can include an internal storage medium in the computer device, and of course can also include an extended storage medium supported by the computer device. The computer readable storage medium provides a storage space, and the storage space stores an operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and the instructions can be one or more computer programs (including program codes). It should be noted that the computer readable storage medium herein can be a high-speed RAM memory, or a non-volatile memory such as at least one disk memory. One or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the multi-target interval flexible job shop scheduling method in the above embodiment.

[0178] The embodiment also provides a computer program product, which comprises a computer program, and when the computer program is executed by the processor, the corresponding steps of the multi-target interval flexible job shop scheduling method in the above embodiment are implemented.

[0179] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0180] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processing device or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0181] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0183] Finally, it should be noted that the above-mentioned embodiments are only intended to illustrate the technical solutions of the present application, and are not intended to limit the present application. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that the specific embodiments of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and any modifications or equivalent replacements without departing from the spirit and scope of the present application should be covered within the protection scope of the claims of the present application.

Claims

1. A multi-objective interval flexible job shop scheduling method, characterized in that, The method comprises the following steps: a multi-objective interval flexible job shop scheduling problem model is constructed, the problem model comprises an interval maximum completion time, an interval total machine load, an interval total energy consumption, constraint conditions and interval number related operation rules related to the multi-objective interval flexible job shop scheduling problem; the interval number related operation rules are used to solve the multi-objective interval flexible job shop scheduling problem model by using an interval chameleon swarm algorithm, so that a globally optimal scheduling solution is obtained, and the multi-objective interval flexible job shop scheduling is realized; the interval number related operation rules comprise an interval number maximum operation rule, an interval number summation operation rule and a comparison rule based on an interval possibility degree; the step of solving the multi-objective interval flexible job shop scheduling problem model by using the interval chameleon swarm algorithm to obtain the globally optimal scheduling solution specifically comprises the following steps: a hybrid Logistics chaotic mapping is used to initialize the chameleon swarm; the fitness of the initial chameleon swarm is calculated, and the non-dominated sorting is performed through the comparison rule based on the interval possibility degree, and the current optimal individual and position are recorded; the position of the chameleon in the search space is updated according to a golden sine strategy; the position of the chameleon after the eyes are rotated is updated first, and then the speed and position of the chameleon are updated, so that the updated chameleon swarm and position are obtained; the fitness value of the current chameleon swarm is calculated, and the globally optimal scheduling scheme is updated according to the fitness value; after the optimal chameleon swarm currently existing is disturbed by Gauss, it is judged whether the current iteration number of the interval chameleon swarm algorithm reaches a maximum iteration number, if the maximum iteration number is reached, the globally optimal scheduling solution is output, if the maximum iteration number is not reached, the step of updating the position of the chameleon in the search space according to the golden sine strategy and the steps following the step are repeated until the maximum iteration number is reached.

2. The multi-objective interval flexible job shop scheduling method according to claim 1, characterized in that, the constraint conditions comprise: the start time of each process is non-negative; each process can be continuously processed by only one machine at the same time; one machine can process only one process at the same time; the processing sequence constraint between processes of each workpiece is as follows (7) and (8): （7） （8） wherein, is the process on the machine interval start time, is the process on the machine interval processing time, is the process on the machine interval finish time, is the decision variable.

3. The multi-objective interval flexible job shop scheduling method according to claim 2, characterized in that, the step of solving the multi-objective interval flexible job shop scheduling problem model by using the interval chameleon swarm algorithm comprises chromosome coding and chromosome decoding, the chromosome coding is two-section coding with equal gene numbers, the first half section coding is the processing machine selected by the corresponding process, and the second half section coding is the process sorting; the chromosome decoding arranges the processing of operations from left to right according to the process sorting, considers the machine idle time, and performs the processing of the operations in front insertion under the condition of satisfying the constraint conditions.

4. The multi-objective interval flexible job shop scheduling method according to claim 1, characterized in that, the step of initializing the chameleon swarm by using the hybrid Logistics chaotic mapping specifically comprises the following steps: firstly, the machine coding part is initialized by using the hybrid Logistics chaotic mapping, 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 code part, a plurality of process code schemes are randomly generated, the process code schemes and the machine code part are combined, and an initial chameleon group is completed.

5. The multi-objective interval flexible job shop scheduling method according to claim 1, wherein, 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 the first In the nth iteration, the 1st The chameleon in the first Wei's new position; Indicates the current location of the individual chameleon; Indicates the individual chameleon The current optimal position in the next iteration; and It is a random number that is uniformly distributed in the range [0,1]. It is the probability that an individual chameleon senses its prey; Influences the direction the chameleon explores, with a value of 1 or -1; and The first The lower and upper bounds of the dimensional search domain; yes Random numbers within; yes Random numbers within; and The coefficients are derived from the golden ratio; Parameters used to control search capabilities.

6. A multi-objective interval flexible job shop scheduling system, characterized by, The multi-objective interval flexible job shop scheduling method according to any one of claims 1-5 comprises: A problem model construction module is configured to construct a multi-objective interval flexible job shop scheduling problem model, the problem model comprising 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; A chameleon global optimization module is configured to solve the multi-objective interval flexible job shop scheduling problem model by using an interval chameleon group algorithm to obtain a globally optimal scheduling solution, thereby realizing multi-objective interval flexible job shop scheduling.

7. A computer device, comprising: The computer program is stored in the memory and executable in the processor, and the processor implements the steps of the multi-objective interval flexible job shop scheduling method according to any one of claims 1-5 when executing the computer program.

8. A computer-readable storage medium, characterized in that, The computer program is stored in the memory and executable in the processor, and the processor implements the steps of the multi-objective interval flexible job shop scheduling method according to any one of claims 1-5 when executing the computer program.

9. A computer program product comprising a computer program, characterized in that, The computer program is stored in the memory and executable in the processor, and the processor implements the steps of the multi-objective interval flexible job shop scheduling method according to any one of claims 1-5 when executing the computer program.

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