Ship group assembling operation space scheduling method

Abstract

The invention provides a ship group assembly operation space scheduling method. The method comprises the following steps: establishing a group assembly space scheduling problem mathematical model; searching a feasible position in the site based on the discrete grid; and performing spatial position optimization based on multi-rule selection on the basis of the credible position and the mathematical model. According to the invention, spatial scheduling optimization in the ship group assembling process can be realized; the problems that in the prior art, distribution of discrete worker resources and site space resources is difficult to collaboratively optimize, the calculated amount and space waste are difficult to balance, an optimal solution is easy to miss, and poor space layout is generated are solved.

Description

Technical Field

[0001] The present invention relates to the field of shipbuilding, and in particular to a method for scheduling a space for a small ship assembly operation. Background Art

[0002] Ships are typical single-piece customized products, which are produced by order-driven, with highly customized designs, diverse types, complex structures, and low repeatability. As the smallest combination unit of shipbuilding, the small-unit structure is diverse, numerous, and the manufacturing process varies greatly. The assembly task of the small-unit includes multiple processes such as positioning assembly, welding, finishing and polishing. Each process is associated with different worker teams and assembly equipment, involving the coordination of multiple process elements such as workers, equipment, and parts. In addition, the assembly of the small-unit needs to be carried out on the assembly platform, which has a limited area. The assembly task not only takes a certain amount of time, but also occupies the space resources of the site: before the assembly begins, the small-unit should be placed on the assembly platform. After the assembly is completed, the area it occupies will be released to other unprocessed small-units. The above characteristics determine that the assembly problem of the small-unit has the characteristics of time-space coupling. Time and space affect each other and jointly affect the efficiency of the assembly operation. The spatial layout of the small-unit will affect the scheduling arrangement in time, and vice versa, the temporal sorting will also affect the occupation and release of space resources, further affecting the efficiency of space utilization. Therefore, when conducting scheduling and control of small-group assembly operations, it is necessary to consider the coupling effects of time and space, and coordinately optimize the time scheduling sequence and spatial layout.

[0003] The spatial layout of the site in the group assembly scheduling problem usually includes two steps: finding feasible placement positions from the site and selecting the optimal position from the feasible placement positions. The currently commonly used methods for finding feasible positions include methods based on extreme corner point search and methods based on spatial configuration theory.

[0004] The method based on extreme corner search reduces the position search space to the corners or extremes of the configured segments, traverses the above candidate point sets in turn, and adds the point sets that meet the spatial constraints to the feasible point set. The method based on extreme corner search is mostly used for spatial layout configuration of rectangular shapes, but small groups have different shapes, and simplifying them all into rectangles will result in a large waste of space.

[0005] The method based on spatial configuration theory uses an enveloping convex polygon instead of an enveloping rectangle to replace the object shape, and obtains the feasible space by successively calculating the difference between the configuration space in the field and the obstacle space of the existing object. In the assembly scheduling problem of small units, there are a large number of small units. The method based on spatial configuration theory needs to determine the obstacle space of each existing small unit in turn, which requires a large amount of calculation. In addition, it is difficult to achieve accurate positioning in the ship small unit manufacturing workshop, so the method based on spatial configuration theory is not very suitable.

[0006] After determining the feasible placement positions, it is necessary to find the optimal position from the feasible positions. Currently, researchers generally use pre-defined spatial scheduling rules to select the optimal position, and all use a single spatial scheduling rule to select the optimal position. When arranging irregular shapes, using a single spatial layout rule is likely to lead to poor spatial layout, affecting the final scheduling effect. Summary of the invention

[0007] In view of the defects in the prior art, the object of the present invention is to provide a method for scheduling the space of assembly operations of a small ship group.

[0008] According to one aspect of the present invention, a method for scheduling a space for assembly work of a small ship group is provided, comprising:

[0009] Establish a mathematical model for the spatial scheduling problem of small group assembly;

[0010] Based on the mathematical model, searching for feasible positions in the site based on discrete grids;

[0011] Based on the feasible positions and the mathematical model, spatial scheduling optimization based on multi-rule selection is performed.

[0012] Preferably, the step of establishing a mathematical model for the small group assembly space scheduling problem includes:

[0013] Define the model data parameters, specifically:

[0014] M: Group standing

[0015] m: a specific group, m∈M

[0016] N m :The process set of group m

[0017] P mn : A specific process of the group m, P mn ∈N m

[0018] P mN :Process set N m The last step

[0019] pred mn :Process P mn The set of all preceding processes

[0020] succ mn :Process P mn The set of all subsequent steps

[0021] D mn :Process P mnRated working hours

[0022] L m : The length of the enveloping rectangle of the group m

[0023] W m : The width of the envelope rectangle of the group m

[0024] SH m :The shape of the group is m, which is a size (L m ,W m )

[0025] SH mij :0-1 variable, if the position [i,j] of the envelope rectangle of the group m is empty, it takes 0, otherwise it takes 1

[0026] a m :Assembly site of small group

[0027] WK: All types of work in the workshop

[0028] k: a specific type of work, k∈WK

[0029] C k : The number of workers of type k in the workshop

[0030] c mnk :Process P mn The desired number of workers of type k

[0031] A: All assembly areas in the workshop

[0032] a: a specific assembly site, a∈A

[0033] L a : Length of assembly site a

[0034] W a : Width of assembly site a

[0035] T: Upper bound of the completion time of the assembly task

[0036] t: a specific time, t∈T

[0037] S mn :Process P mn Start time

[0038] F mn :Process P mn End time

[0039] S am :Group m starts to occupy site a m Time

[0040] Fam :The group stands m and ends the occupation of the venue a m Time

[0041] Y mnt : 0-1 variable, if t∈[S mn ,F mn ) takes 0, otherwise takes 1

[0042] (x am ,y am ): The lower left corner of the group stand m is at site a m Occupied positions in

[0043] Region am :Venue a m The state after being occupied by group m is a size of (L a ,W a )

[0044] X amt : 0-1 variable, if Region am If it is occupied at time t, it takes 1, otherwise it takes 0

[0045] Region amij : 0-1 variable, if the group position is a m If the position [i,j] is occupied by group m, it takes 1, otherwise it takes 0;

[0046] Establish a mathematical model based on various defined data parameters:

[0047]

[0048] Constrained by:

[0049]

[0050]

[0051] Formula (1) represents the objective function, which is to minimize the maximum completion time;

[0052] Equations (2)-(10) serve as constraints for the problem, consisting of time constraints (2-4) and space constraints (5-10);

[0053] Formula (2) ensures the non-preemptive nature of the process, that is, once a process is started, it cannot be interrupted;

[0054] Formula (3) ensures that the number of workers engaged in assembly tasks does not exceed the limit;

[0055] Formula (4) ensures that all processes are executed after their predecessor processes are completed;

[0056] Formula (5) indicates that at the earliest start time of the group standing process, the space resource is occupied by a group standing;

[0057] Formulas (6)-(7) determine the release time of spatial resources for different types of groups;

[0058] Formulas (8)-(9) force each group to stay within the boundaries of the site;

[0059] Formula (10) introduces a spatial overlap constraint, that is, all positions in the assembly site cannot be occupied by more than one small group at the same time.

[0060] Preferably, the searching for feasible positions in the site based on discrete grids based on the mathematical model includes:

[0061] First, discretize the sites and groups:

[0062] For the site, it is discretized into multiple grids. If a grid already has a small group of people, the attribute value of the grid is set to 1, otherwise it is set to 0.

[0063] For the small group stand, its envelope rectangle is discretized into grids with the same grid size as the site. If a grid in the envelope rectangle is partially occupied by the small group stand, the attribute of the grid is set to 1, otherwise it is set to 0;

[0064] Next, in the discretized field, the discretized configuration space of the group positions is calculated;

[0065] Finally, within the configuration space within the group positions, the feasible positions of the group positions are calculated:

[0066] Use the convolution formula to multiply the corresponding elements of the discrete matrices of the group and the site in turn and add them together. If the result is not equal to zero, it means that the position is not a feasible configuration point.

[0067]

[0068] H represents the matrix obtained after convolution, F is the sub-group discrete matrix, G is the site discrete matrix, i and j represent the matrix coordinates obtained after the convolution operation is completed, and m and n are the coordinates of the sub-group discrete matrix and the site discrete matrix.

[0069] Preferably, the performing of spatial scheduling optimization based on multi-rule selection based on the feasible position and the mathematical model includes:

[0070] By adopting a multi-chromosome mixed coding method, two chromosomes are designed for each feasible solution individual of the mathematical model in the feasible position, so as to realize the coordinated optimization of the scheduling sequence and the spatial layout;

[0071] On the basis of the collaborative optimization of the scheduling sequence and the spatial layout, a meta-heuristic method is adopted to achieve the final spatial optimization scheduling of the small group assembly.

[0072] Preferably, each feasible solution individual designs two chromosomes, wherein: the first chromosome is a scheduling sequence of all sub-group independent processes, and the length of the first chromosome is equal to the number of all sub-group independent processes; each gene of the first chromosome corresponds to a sub-group independent process number, and each of the sub-group independent process numbers includes a sub-group independent number and a corresponding sub-group independent process number; the first chromosome forms a sub-group independent process number list;

[0073] The second segment of the chromosome is the spatial layout rule called by all subgroups, and the length of the second segment of the chromosome is equal to the number of subgroups; each gene in the second segment of the chromosome is the spatial layout rule corresponding to a single subgroup.

[0074] Preferably, a multi-chromosome mixed encoding method is adopted to design two chromosomes for each feasible solution individual in the feasible position of the mathematical model to achieve the coordinated optimization of the scheduling sequence and the spatial layout, including:

[0075] S31, initialize the list of scheduled group process numbers to be empty, initialize the scheduling time t=0, initialize the site occupancy status, and initialize the current number of remaining workers;

[0076] S32, converting the subgroup independent process number list in the first chromosome into a subgroup independent process list;

[0077] S33, traverse the group process list in sequence, if the process corresponding to the group process list is not included in the scheduled group process number list, go to S34, if all processes have been traversed, go to S39;

[0078] S34: Determine whether all the preceding processes have been completed. If yes, go to S35; otherwise, go to S33;

[0079] S35: Determine whether the number of remaining workers at the current moment can meet the requirements of the considered process. If yes, go to S36, otherwise go to S33;

[0080] S36: Determine whether the process is the first process of the group. If yes, go to S37; otherwise, go to S38;

[0081] S37: If there is a feasible spatial position, go to S38, otherwise go to S33;

[0082] S38: Schedule the process according to the rule corresponding to the process in the second chromosome, and update the site occupancy status and the current number of remaining workers;

[0083] S39: Determine whether all processes have been scheduled. If yes, go to S311. If not, go to S10.

[0084] S310: Select the minimum time greater than the current time from the completion time of the scheduled processes as the next scheduling time, update the site occupancy status, update the number of remaining workers, and go to S33;

[0085] S311: Output the scheduling operation plan and site space layout.

[0086] Preferably, based on the coordinated optimization of the scheduling sequence and the spatial layout, a meta-heuristic method is used to achieve the final spatial optimization scheduling of the small group assembly, including:

[0087] After obtaining the scheduling sequence and spatial layout, that is, obtaining the feasible solution individuals of the mathematical model, the fitness function of each individual is calculated;

[0088] Based on the fitness function of each individual, the probability of each individual in the roulette method is obtained, and the first n1 pairs of parents whose probabilities are sorted from large to small are selected from the population N composed of multiple individuals;

[0089] The selected n1 pairs of parents are crossovered using an improved two-point crossover method to generate offspring;

[0090] Select 1 / 5 individuals with the largest fitness function for mutation. For the first chromosome segment of these individuals, use the exchange mutation operator; for the second chromosome segment, use the Breeder Genetic Algorithm mutation operator for mutation.

[0091] The offspring generated by the crossover operation, the offspring generated by the mutation operation, and the original population N are mixed, and the next generation population is generated using a population update operator based on an elite retention strategy.

[0092] Preferably, the scheduling objective based on the mathematical model is to minimize the maximum completion time, and the fitness function value adopts the maximum completion time of the group.

[0093] Preferably, the improved two-point intersection method includes:

[0094] Randomly generate crossover positions n1, n2, where n1 <n2;

[0095] Fill the genes between the parent chromosomes n1 and n2 in each pair of parents to the corresponding positions of offspring 1;

[0096] Traverse the maternal chromosomes in each pair of parents. If a process number of the maternal chromosome in offspring 1 has not reached the upper limit, fill the process number to a gene position in offspring 1. The gene position is the first blank gene position in the order from front to back. If the upper limit is reached, traverse the next process number.

[0097] Fill the genes between maternal chromosomes n1 and n2 in each pair of parents to the corresponding positions of offspring 2;

[0098] Traverse the parent chromosomes in each pair of parents. If a process number of the parent chromosome in offspring 2 has not reached the upper limit, fill the process number into a gene position of offspring 2. The gene position is the first blank gene position in the order from front to back. If the upper limit is reached, traverse the next process number.

[0099] Preferably, the metaheuristic method includes a genetic method and a particle swarm method.

[0100] Compared with the prior art, the embodiments of the present invention have at least one of the following beneficial effects:

[0101] A method for spatial scheduling of a small-group assembly operation of a ship according to an embodiment of the present invention adopts a mathematical modeling method based on small-group assembly processes, which can realize the coordinated consideration of site space resources and discrete worker resources, and solve the problem that only site space resources can be considered in traditional spatial scheduling methods.

[0102] A method for spatial scheduling of assembly operations of a ship group according to an embodiment of the present invention adopts a feasible position calculation method based on discrete grid search, which can avoid the space waste caused by traditional rectangular simplification while effectively reducing the amount of calculation, and solves the problem that traditional extreme point search and spatial configuration theory methods are difficult to balance the amount of calculation and space waste;

[0103] A method for spatial scheduling of assembly operations of a ship group in an embodiment of the present invention adopts a spatial layout optimization method based on multi-rule selection, which can realize adaptive selection and optimization of spatial layout positions, and solve the problem that traditional layout optimization methods based on a single rule are prone to miss the optimal solution.

[0104] In summary, a method for spatial scheduling of ship group assembly operations in an embodiment of the present invention can realize spatial scheduling optimization of the ship group assembly process, overcoming the problems existing in the prior art of difficulty in collaboratively optimizing the allocation of discrete worker resources and site space resources, difficulty in balancing computational complexity and space waste, and easy missing of the optimal solution and generating a poor spatial layout. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0106] Figure 1 It is a flow chart of a method for scheduling a space for a ship assembly operation in an embodiment of the present invention;

[0107] Figure 2 A small group discretization diagram in a preferred embodiment of the present invention;

[0108] Figure 3 is a site discretization map in a preferred embodiment of the present invention;

[0109] Figure 4 A feasible configuration space diagram in a preferred embodiment of the present invention;

[0110] Figure 5 A schematic diagram of a feasible configuration point set in a preferred embodiment of the present invention;

[0111] Figure 6 A schematic diagram of feasible position calculation based on convolution in a preferred embodiment of the present invention;

[0112] Figure 7 A schematic diagram of a two-stage encoding method in a preferred embodiment of the present invention;

[0113] Figure 8a A schematic diagram of an improved crossover operation in a preferred embodiment of the present invention;

[0114] Figure 8b It is a schematic diagram of conventional crossover operation;

[0115] Fig. 9 A comparison chart of the average winning rate of a specific embodiment of the method of the present invention and other methods;

[0116] Fig.10 The figure is a comparison chart of the optimal value winning rate of a specific embodiment of the method of the present invention and other methods. DETAILED DESCRIPTION

[0117] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0118] like Figure 1 FIG. 1 is a flow chart of a method for scheduling a space for a ship assembly operation in an embodiment of the present invention. In this embodiment, the method for scheduling a space for a ship assembly operation includes the following steps:

[0119] Step 1, establish a mathematical model for the small group assembly space scheduling problem;

[0120] Step 2, based on the mathematical model, searching for feasible locations in the site based on discrete grids;

[0121] Step 3: Based on the feasible locations and mathematical models, perform spatial scheduling optimization based on multi-rule selection.

[0122] The above-mentioned embodiments can realize the coordinated consideration of site space resources and discrete worker resources, and solve the problem that only site space resources can be considered in the traditional space scheduling method.

[0123] In step 1 of the above embodiment, a mathematical model of the small-group assembly space scheduling problem is established, wherein the mathematical model takes the small-group assembly process rather than the entire small-group as the scheduling object, and in addition to the site space resources, the allocation of discrete resources such as workers is also considered. Specifically, in some embodiments of the present invention, in order to obtain the mathematical model of the small-group assembly space scheduling problem, the following steps can be followed:

[0124] Step 1.1: Data parameter definition

[0125] Define the various data parameters that need to be used, as follows:

[0126] M: Group standing

[0127] m: a specific group, m∈M

[0128] N m :The process set of group m

[0129] P mn : A specific process of the group m, P mn ∈N m

[0130] P mN :Process set N m The last step

[0131] pred mn :Process P mn The set of all preceding processes

[0132] succ mn :Process P mn The set of all subsequent steps

[0133] D mn :Process P mn Rated working hours

[0134] L m: The length of the enveloping rectangle of the group m

[0135] W m : The width of the envelope rectangle of the group m

[0136] SH m :The shape of the group is m, which is a size (L m ,W m )

[0137] SH mij :0-1 variable, if the position [i,j] of the envelope rectangle of the group m is empty, it takes 0, otherwise it takes 1

[0138] a m :Assembly site of small group

[0139] WK: All types of work in the workshop

[0140] k: a specific type of work, k∈WK

[0141] C k : The number of workers of type k in the workshop

[0142] c mnk :Process P mn The desired number of workers of type k

[0143] A: All assembly areas in the workshop

[0144] a: a specific assembly site, a∈A

[0145] L a : Length of assembly site a

[0146] W a : Width of assembly site a

[0147] T: Upper bound of the completion time of the assembly task

[0148] t: a specific time, t∈T

[0149] S mn :Process P mn Start time

[0150] F mn :Process P mn End time

[0151] S am :Group m starts to occupy site a m Time

[0152] F am :The group stands m and ends the occupation of the venue a m Time

[0153] Y mnt : 0-1 variable, if t∈[S mn ,F mn ) takes 0, otherwise takes 1

[0154] (x am ,y am ): The lower left corner of the group stand m is at site a m Occupied positions in

[0155] Region am :Venue a m The state after being occupied by group m is a size of (L a ,W a )

[0156] X amt : 0-1 variable, if Region am If it is occupied at time t, it takes 1, otherwise it takes 0

[0157] Region amij : 0-1 variable, if the group position is a m If the position [i,j] is occupied by group m, it takes 1, otherwise it takes 0

[0158] Step 1.2: Mathematical model establishment

[0159] A mathematical model is established based on the various data parameters defined above. The feasible solution of the mathematical model is a scheduling plan, including the start time and end time of all group standing processes and the placement positions of the group standing in the site.

[0160] Specifically, the mathematical model is as follows:

[0161]

[0162] Constrained by:

[0163]

[0164]

[0165] Formula (1) represents the objective function, which is to minimize the maximum completion time. Formulas (2)-(10) serve as constraints for the problem, consisting of time constraints (2-4) and space constraints (5-10). Formula (2) ensures the non-preemptive nature of the process, that is, once a process is started, it cannot be interrupted. Formula (3) ensures that the number of workers engaged in assembly tasks does not exceed the limit. Formula (4) ensures that all processes are executed after their predecessors are completed. It can be seen from formula (5) that at the earliest start time of the group process, the space resources are occupied by a group. Formulas (6)-(7) determine the release time of space resources for different types of groups. Formulas (8)-(9) force each group to remain within the site boundary. Formula (10) introduces the spatial overlap constraint, that is, all positions in the assembly site cannot be occupied by more than one group at the same time.

[0166] In the above embodiment, a mathematical model is established for the characteristics of the ship group assembly operation, which is used for the spatiotemporal coupling optimization of the subsequent ship group assembly process. The model is modeled based on the group assembly process, which can realize the coordinated consideration of site space resources and discrete worker resources, and solve the problem that only site space resources can be considered in the traditional space scheduling method.

[0167] After the required mathematical model is established, step 2 further determines the feasible position in the site based on the mathematical model. Due to the large differences in the shapes of the ship groups and the large number of them, the calculation of the feasible configuration space will become complicated and time-consuming. At the same time, considering the large size of the ship segments, the spatial layout accuracy requirements are lower than the general parts and leather layout problems. Therefore, a discretization method can be used to describe the geometric information of the site space and the segmented projection. Specifically, in some embodiments of the present invention, searching for feasible positions in the site based on discrete grids may include the following steps:

[0168] Step 2.1, discretize the site and the small group. The results of the small group and site discretization are shown in the attached figure. Figure 2 , Attachment Figure 3 As shown. For the small group, it is discretized into irregular shapes in the envelope rectangle. If a grid in the envelope rectangle is partially occupied by a small group, the attribute of the grid is set to 1, otherwise it is set to 0. For the site, it is discretized into multiple grids. If a grid already has a small group, the attribute value of the grid is set to 1, otherwise it is set to 0.

[0169] Step 2.2, calculate the configuration space within the group stand. In order to avoid exceeding the scope of the venue, calculate the configuration space within the venue based on the envelope rectangle of the group stand, as shown in the attached figure. Figure 4As shown, the reference point is a point in the group stand, which is used to define the origin of the group stand. It can be set arbitrarily. In this embodiment, it is set to the point in the lower left corner. When the reference point falls within the configuration space in the field, the group stand will not exceed the scope of the field, that is, the configuration space in the field is a point set, which satisfies that when the reference origin of the group stand is placed on a point in the configuration space in the field, the group stand will not exceed the scope of the field.

[0170] Step 2.3, the group calculates feasible positions. After determining the configuration space in the field, determine whether each point in the configuration space satisfies the overlap constraint. That is, place the reference origin at the discrete points in the configuration space in the field in turn, and add up the values ​​at each position. If the sum of the values ​​of each point is less than or equal to 1, it means that the discrete point is a feasible configuration point. Figure 5 As shown. By traversing all points in the field configuration space in turn, a feasible configuration point set can be obtained.

[0171] In the above-mentioned embodiment of the present invention, a discretization method is used to describe the geometric information of the site space and the segmented projection. Such a processing method can not only reduce the difficulty of processing irregular shape geometric information, but also effectively reduce the amount of calculation of space-related constraints in scheduling, while avoiding the waste of space caused by simplification into rectangles. It is suitable for the spatial scheduling of large structures such as ship panels.

[0172] It should be noted that the method of determining whether it is feasible in step 2.3 may require multiple addition calculations, which is not conducive to computational efficiency. In order to solve this problem, in a preferred embodiment of the present invention, it is considered that a single site discrete value has only two states, namely 0 or 1, and inside the envelope rectangle of the discretized small group, there are also only two values ​​0 or 1. Only when the site discrete value and the small group discrete value at a certain position are both 1, it means that the position does not meet the overlapping constraint. Therefore, the convolution operation can be used instead of the sequential addition operation, and the vectorization operation can be used to improve the computational efficiency. The convolution formula is shown below. The corresponding elements in the two matrices are multiplied and added in sequence. If the result is not equal to 0, it means that the position does not belong to a feasible configuration point, as shown in the attached figure. Figure 6 As shown. The convolution calculation formula is:

[0173]

[0174] The above embodiment adopts a feasible position calculation method based on discrete grid search, which can avoid the space waste caused by traditional rectangular simplification while effectively reducing the amount of calculation, and solves the problem that traditional pole search and space configuration theory methods are difficult to balance the amount of calculation and space waste.

[0175] After steps 1 and 2 have completed the search for feasible placement positions in the venue, it is necessary to further perform step 3 to select the optimal position from the feasible placement positions. In order to obtain the optimal position more accurately, in some embodiments of the present invention, the spatial position optimization based on multi-rule selection in step 3 can specifically adopt the following steps:

[0176] Step 3.1, hybrid coding based on multi-rule selection.

[0177] The scheduling of group vertical welding operations involves the formulation of plans in terms of time (task sequence) and space (welding site). The solution to the problem has a certain coupling relationship between time and space. In view of the above characteristics, this embodiment adopts a multi-chromosome mixed encoding method and designs two chromosomes for each individual to achieve the coordinated optimization of the scheduling sequence and spatial layout. Figure 6 shown.

[0178] The length of the first chromosome segment is equal to the number of all sub-group independent processes; each gene of the first chromosome segment corresponds to a sub-group independent process number, and each sub-group independent process number includes a sub-group independent number and a corresponding sub-group independent process number; the first chromosome segment forms a sub-group independent process number list;

[0179] The second segment of the chromosome is the spatial layout rule called by all subgroups, and the length of the second segment of the chromosome is equal to the number of subgroups; each gene in the second segment of the chromosome is the spatial layout rule corresponding to a single subgroup.

[0180] Step 3.2, optimization of small group assembly spatial scheduling based on metaheuristic method. After the encoding is generated based on the above encoding method, the encoding is optimized through metaheuristic optimization methods such as genetic method and particle swarm method, and finally the spatial optimization scheduling of small group assembly is realized.

[0181] The above-mentioned embodiment adopts a spatial layout optimization method based on multi-rule selection, which can realize adaptive selection and optimization of spatial layout positions and solve the problem that the traditional layout optimization method based on a single rule is prone to miss the optimal solution.

[0182] In order to verify the feasibility and effect of the spatial scheduling method for the vertical assembly operation of a ship group in the above-mentioned embodiment, the present invention provides an experiment in a specific application as an example. This example is an example of using a genetic method as an optimization algorithm. At the same time, four commonly used spatial scheduling rules are used as a set of spatial optimization candidate rules, namely, the bottom left rule (BLF), the top right rule (TRF), the maximum remaining rectangle rule (MREC), and the maximum contact area rule (MCA).

[0183] Specifically, in this example, the method for scheduling the space of the ship assembly operation group is performed according to the following steps S100-S800:

[0184] S100, obtaining modeling data. A set of cases of different sizes including 30-120 small units collected from a small unit assembly workshop of a large shipbuilding company are simulated to test the effectiveness of the method of the above embodiment. The small unit assembly workshop has 15 assemblers, 20 welders, and 10 polishers. The assembly site is divided into two adjacent areas, namely the rib welding area and the small unit component welding area. The site areas are 25m*15m and 40m*15m respectively.

[0185] S200, site discretization. The site is discretized into square grids with a length and width of 0.5m, and a unique number is determined for each grid, which is converted into a 0-1 matrix.

[0186] S300, discretization of small groups. The envelope rectangle of the small group is also discretized into a square grid with a length and width of 0.5m based on the same size, and converted into a 0-1 matrix.

[0187] S400, population encoding and initialization. The population is initialized using the hybrid encoding method proposed in step 3.1 above, and each individual represents a feasible solution. The first chromosome is the scheduling sequence of each process, and the chromosome length is equal to the number of all small-scale processes. The second chromosome is the spatial layout rule corresponding to each small-scale process, and the chromosome length is equal to the number of all small-scale processes.

[0188] For the first chromosome, first, based on the information of the subgroups to be scheduled, get the number of times each subgroup number should appear in the chromosome (the number of times each subgroup appears is equal to the number of its processes), and get a list containing all subgroup process numbers. Randomly shuffle the list of subgroup process numbers to get the initial subgroup process numbers. For example, Figure 7 As shown, the list of process numbers of the group is: 1-1, 3-8, 2-1, 3-4, 3-5, 3-6, 3-7, 1-3, 3-9, 3-3, 2-3, 2-2, 3-1, 3-2, where 3-8 means that the second process is the 8th process of the third group.

[0189] The second chromosome adopts a random initialization method, and randomly selects a specified number of numbers from the candidate rule list to form a layout rule list. Figure 7 As shown, 1, 4, and 2 indicate that the three groups selected rules 1, 4, and 2 respectively.

[0190] S500, population decoding.

[0191] The chromosome sequence is converted into a specific scheduling plan based on the parallel progress generation mechanism PSGS, which mainly includes the following steps:

[0192] Step 501: Initialize the list of scheduled process numbers to be empty, the scheduling time t=0, initialize the site occupancy status, and initialize the current number of remaining workers.

[0193] Step 502: Convert the subgroup number list in the first chromosome into a subgroup process list. For example, the subgroup number list is 1 3 2 1 3 3 3 3 1 3 3 2 2 3 2, and remove the process number with the suffix in the first chromosome, for example, convert 1-1 to 1.

[0194] Step 503: traverse the process list in sequence. If the process is not included in the list of scheduled process numbers, go to step 504. If all processes have been traversed, go to S509.

[0195] Step 504: Determine whether all the preceding processes have been completed. If so, go to step 505; otherwise, go to step 503.

[0196] Step 505: Determine whether the number of remaining workers at the current moment can meet the requirements of the considered process. If so, go to step 506, otherwise go to step 503.

[0197] Step 506: Determine whether the process is the first process established by the group. If so, go to step 507, otherwise go to step 508.

[0198] Step 507: Use the spatial layout algorithm of steps 2.1-2.3 and steps 3.1-3.2 of the above embodiment to select a suitable spatial position. If there is a feasible spatial position, go to step 508; otherwise, go to step 503.

[0199] Step 508: Schedule the process, update the site occupancy status and the current number of remaining workers.

[0200] Step 509: Determine whether all processes have been scheduled. If so, go to step 5011; if not, go to step 510.

[0201] Step 510: Select the minimum time greater than the current time from the completion time of the scheduled processes as the next scheduling time, update the site occupancy status, update the number of remaining workers, and go to step 503.

[0202] Step 5011: End the decoding algorithm and output the scheduling operation plan and site space layout.

[0203] S600, fitness function calculation. After generating a specific scheduling plan, the fitness function of the individual is calculated. Since the scheduling goal designed in the model is to minimize the maximum completion time, the maximum completion time of all small groups is directly used as the fitness function value of the individual.

[0204] S700, Selection operation. Based on the fitness value, calculate the roulette probability, and use the roulette algorithm to select n1 pairs of parents with higher probabilities from the population N.

[0205] S800, Crossover operation. Use the improved two-point crossover method to generate the first segment of the chromosome of the offspring. Use the conventional crossover method to generate the second segment of the chromosome of the offspring.

[0206] As can be seen from the definition of chromosome coding in the foregoing embodiments (refer to step 3.1): the number of each sub-assembly number in the first segment of the chromosome is equal to its process number. The crossover operation needs to ensure that the obtained offspring still meet the above requirements. Each pair of parents includes two chromosomes, one paternal chromosome and one maternal chromosome. Use the improved two-point crossover method to perform the crossover operation on these two chromosomes to generate two chromosomes of the offspring (offspring 1 and offspring 2), as Figure 8a shown. The specific steps of the two-point crossover method for the crossover operation are as follows:

[0207] First, randomly generate crossover positions n1 and n2, where n1 < n2, fill the genes between n1 and n2 of the paternal chromosome into the corresponding positions of offspring 1, and then traverse the maternal chromosome. If the number of this type of number in offspring 1 does not reach the upper limit (the upper limit refers to the number of occurrences of this type of number in the maternal chromosome), then fill it into each gene position of offspring 1 from front to back. Similarly, the first segment of the chromosome of offspring 2 can be generated.

[0208] There is no such restriction for the second segment of the chromosome, and the ordinary two-point crossover method can be used, as shown in the appendix Figure 8b shown.

[0209] S900, Mutation operator. To avoid destroying the structure of the excellent solution, the mutation adopts the last 1 / 5 mutation method. For the first segment of the chromosome, use the swap mutation operator. For the second segment of the chromosome, use the Breeder Genetic Algorithm mutation operator to perform the mutation operation.

[0210] S1000, Population update. To avoid destroying the structure of the excellent solution by the crossover and mutation operations, mix the offspring generated by S900 and S700 - 800 and the original population N, and use the population update operator based on the elitist retention strategy to generate the next generation of population.

[0211] The results obtained by the ship sub-assembly operation space scheduling method proposed in the above example of the present invention were compared with four single-rule-based methods. To reduce random errors, each method was calculated three times for each case, and the average value and the optimal value of the solutions obtained three times were compared.

[0212] The comparison results are specifically as Fig. 9 、10 As shown, Fig. 9 and Fig.10 The average values ​​of the results of various methods and the winning rates of the optimal values ​​under all scale cases are given, where the winning rate represents the number of cases where the method achieves the best result divided by the total number of cases. As can be seen from the figure, the winning rates of other methods based on a single rule in terms of the average value are only 16.7% at most, and the winning rates in terms of the optimal value are only 20.8% at most, while the spatial scheduling method for the vertical assembly operation of the ship group proposed in this embodiment has a winning rate of 58% in terms of the average value and the optimal value, which is much higher than other methods based on a single rule.

[0213] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various modifications or variations within the scope of the claims, which does not affect the essence of the present invention. The above preferred features can be used in any combination without conflicting with each other.

Claims

1. A method for scheduling the space of a ship assembly operation, characterized in that: include: Establish a mathematical model for the spatial scheduling problem of small group assembly; Based on the mathematical model, searching for feasible positions in the site based on discrete grids; Based on the feasible positions and the mathematical model, spatial scheduling optimization based on multi-rule selection is performed.

2. A method for scheduling space for assembly work of a ship group according to claim 1, characterized in that: The mathematical model for the small group assembly space scheduling problem is established, including: Define the model data parameters, specifically: M: Group standing m: a specific group, m∈M N m :The process set of group m P mn : A specific process of the group m, P mn ∈N m P mN :Process set N m The last step pred mn :Process P mn The set of all preceding processes succ mn :Process P mn The set of all subsequent steps D mn :Process P mn Rated working hours L m : The length of the enveloping rectangle of the group m W m : The width of the envelope rectangle of the group m SH m :The shape of the group is m, which is a size (L m ,W m ) SH mij :0-1 variable, if the position [i,j] of the envelope rectangle of the group m is empty, it takes 0, otherwise it takes 1 a m :Assembly site of small group m WK: All types of work in the workshop k: a specific type of work, k∈WK C k : The number of workers of type k in the workshop c mnk :Process P mn The required number of workers of type k A: All assembly areas in the workshop a: a specific assembly site, a∈A L a : The length of the assembly site a W a : Width of assembly site a T: Upper bound of the completion time of the assembly task t: a specific time, t∈T S mn :Process P mn Start time F mn :Process P mn End time S am :Group m starts to occupy site a m Time F am :The group stands m and ends the occupation of the venue a m Time Y mnt : 0-1 variable, if t∈[S mn ,F mn ) takes 0, otherwise takes 1 (x am ,y am ): The lower left corner of the group stand m is at site a m Occupied positions in Region am :Venue a m The state after being occupied by group m is a size of (L a ,W a ) X amt : 0-1 variable, if Region am If it is occupied at time t, it takes 1, otherwise it takes 0 Region amij : 0-1 variable, if the group position is a m If the position [i,j] is occupied by group m, it takes 1, otherwise it takes 0; Establish a mathematical model based on various defined data parameters: Constrained by: Formula (1) represents the objective function, which is to minimize the maximum completion time; Equations (2)-(10) serve as constraints for the problem, consisting of time constraints (2-4) and space constraints (5-10); Formula (2) ensures the non-preemptive nature of the process, that is, once a process is started, it cannot be interrupted; Formula (3) ensures that the number of workers engaged in assembly tasks does not exceed the limit; Formula (4) ensures that all processes are executed after their predecessor processes are completed; Formula (5) indicates that at the earliest start time of the group standing process, the space resource is occupied by a group standing; Formulas (6)-(7) determine the release time of spatial resources for different types of groups; Formulas (8)-(9) force each group to stay within the boundaries of the site; Formula (10) introduces a spatial overlap constraint, that is, all positions in the assembly site cannot be occupied by more than one small group at the same time.

3. A method for scheduling space for assembly work of a ship group according to claim 1, characterized in that: The method of searching for feasible positions in a site based on a discrete grid based on the mathematical model includes: First, discretize the sites and groups: For the site, it is discretized into multiple grids. If a grid already has a small group of people, the attribute value of the grid is set to 1, otherwise it is set to 0. For the small group stand, its envelope rectangle is discretized into grids with the same grid size as the site. If a grid in the envelope rectangle is partially occupied by the small group stand, the attribute of the grid is set to 1, otherwise it is set to 0; Next, in the discretized field, the discretized configuration space of the group positions is calculated; Finally, within the configuration space within the group positions, the feasible positions of the group positions are calculated: Use the convolution formula to multiply the corresponding elements of the discrete matrices of the group and the site in turn and add them together. If the result is not equal to zero, it means that the position is not a feasible configuration point. H represents the matrix obtained after convolution, F is the sub-group discrete matrix, G is the site discrete matrix, i and j represent the matrix coordinates obtained after the convolution operation is completed, and m and n are the coordinates of the sub-group discrete matrix and the site discrete matrix.

4. A method for scheduling space for assembly work of a ship group according to claim 1, characterized in that: The performing of spatial scheduling optimization based on multiple rule selection based on the feasible position and the mathematical model includes: By adopting a multi-chromosome mixed coding method, two chromosomes are designed for each feasible solution individual of the mathematical model in the feasible position, so as to realize the coordinated optimization of the scheduling sequence and the spatial layout; On the basis of the collaborative optimization of the scheduling sequence and the spatial layout, a meta-heuristic method is adopted to achieve the final spatial optimization scheduling of the small group assembly.

5. A method for scheduling the space of a ship assembly operation according to claim 4, characterized in that: Each feasible solution individual designs two chromosomes, where: the first chromosome is the scheduling sequence of all sub-processes, and the length of the first chromosome is equal to the number of all sub-processes; each gene of the first chromosome corresponds to a sub-process number, and each sub-process number includes a sub-process number and a corresponding sub-process number; the first chromosome forms a sub-process number list; The second segment of the chromosome is the spatial layout rule called by all subgroups, and the length of the second segment of the chromosome is equal to the number of subgroups; each gene in the second segment of the chromosome is the spatial layout rule corresponding to a single subgroup.

6. A method for scheduling space for assembly work of a small ship group according to claim 5, characterized in that: The method of adopting multi-chromosome mixed coding to design two chromosomes for each feasible solution individual of the mathematical model in the feasible position to achieve the coordinated optimization of the scheduling sequence and the spatial layout includes: S31, initialize the list of scheduled group process numbers to be empty, initialize the scheduling time t=0, initialize the site occupancy status, and initialize the current number of remaining workers; S32, converting the subgroup independent process number list in the first chromosome into a subgroup independent process list; S33, traverse the group process list in sequence, if the process corresponding to the group process list is not included in the scheduled group process number list, go to S34, if all processes have been traversed, go to S39; S34: Determine whether all the preceding processes have been completed. If so, go to S35; otherwise, go to S33; S35: Determine whether the number of remaining workers at the current moment can meet the requirements of the considered process. If yes, go to S36, otherwise go to S33; S36: Determine whether the process is the first process of the group. If yes, go to S37; otherwise, go to S38; S37: If there is a feasible spatial position, go to S38, otherwise go to S33; S38: According to the corresponding rule of the process in the second segment of the chromosome, the process is mobilized, and the site occupancy status and the current number of remaining workers are updated; S39: Determine whether all processes have been scheduled. If yes, go to S311. If not, go to S10. S310: Select the minimum time greater than the current time from the completion time of the scheduled processes as the next scheduling time, update the site occupancy status, update the number of remaining workers, and go to S33; S311: Output the scheduling operation plan and site space layout.

7. A method for scheduling a space for a ship assembly operation according to claim 4, characterized in that: Based on the coordinated optimization of the scheduling sequence and the spatial layout, a meta-heuristic method is used to achieve the final spatial optimization scheduling of the small group assembly, including: After obtaining the scheduling sequence and spatial layout, that is, obtaining the feasible solution individuals of the mathematical model, the fitness function of each individual is calculated; Based on the fitness function of each individual, the probability of each individual in the roulette method is obtained, and the first n1 pairs of parents whose probabilities are sorted from large to small are selected from the population N composed of multiple individuals; The selected n1 pairs of parents are crossovered using an improved two-point crossover method to generate offspring; Select 1 / 5 individuals with the largest fitness function for mutation. For the first chromosome segment of these individuals, use the exchange mutation operator; for the second chromosome segment, use the Breeder Genetic Algorithm mutation operator for mutation. The offspring generated by the crossover operation, the offspring generated by the mutation operation, and the original population N are mixed, and the next generation population is generated using a population update operator based on an elite retention strategy.

8. A method for scheduling the space of a ship assembly operation according to claim 7, characterized in that: The scheduling goal based on the mathematical model is to minimize the maximum completion time, and the fitness function value adopts the maximum completion time of the group.

9. A method for scheduling ship assembly work space according to claim 7, characterized in that: The improved two-point intersection method comprises: Randomly generate crossover positions n1, n2, where n1 <n2; Fill the genes between the parent chromosomes n1 and n2 in each pair of parents to the corresponding positions of offspring 1; Traverse the maternal chromosomes in each pair of parents. If a process number of the maternal chromosome in offspring 1 has not reached the upper limit, fill the process number to a gene position in offspring 1. The gene position is the first blank gene position in the order from front to back. If the upper limit is reached, traverse the next process number. Fill the genes between maternal chromosomes n1 and n2 in each pair of parents to the corresponding positions of offspring 2; Traverse the parent chromosomes in each pair of parents. If a process number of the parent chromosome in offspring 2 has not reached the upper limit, fill the process number into a gene position of offspring 2. The gene position is the first blank gene position in the order from front to back. If the upper limit is reached, traverse the next process number.

10. A method for scheduling space for assembly work of a ship group according to claim 7, characterized in that: The meta-heuristic method adopts a genetic method or a particle swarm method.

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