A global optimization method for cycle time in flexible production line scheduling

Abstract

The present invention discloses a global optimization method for cycle time of flexible production line scheduling, the method comprising: converting the assembly line balance type II optimization problem into a discretized high-dimensional continuous domain optimization problem; using the Hilbert space filling curve method to simplify the discretized high-dimensional continuous domain optimization problem into a discretized one-dimensional continuous domain optimization problem; combining the multi-dimensional constraint characteristic factor global search algorithm of discrete grid technology to solve the one-dimensional continuous domain optimization problem. The present invention constructs an optimization method for the assembly line balance type II problem, combining Boolean network theory, Hilbert space filling curve technology, continuous domain model-free optimization method, and grid technology, so that the solution of the optimization problem is simpler, the solution efficiency is high, and it can ensure convergence to the global optimal solution, thereby shortening the processing cycle and improving the workstation utilization rate.

Description

Technical Field

[0001] The invention relates to workshop scheduling technology, and in particular to a global optimization method for cycle time of flexible production line scheduling. Background Art

[0002] In recent years, with the continuous expansion of the scale of my country's manufacturing industry, the production process and links have become increasingly complex, and the optimization management of the production process has gradually become one of the key factors in improving production capacity. Compared with the traditional dedicated fixed production process layout, the flexible production line, as a modular, adjustable and reconfigurable production line layout idea of ​​each component, has gradually become the mainstream of production line planning and design driven by the urgent needs of more types, shorter cycles and lower costs. Its highly elastic and flexible characteristics have brought greater challenges to the optimization management of the production process. As one of the typical propositions in the optimization management of the production process, the production line balance problem - also known as the assembly line balance (ALB) problem; assembly line balance is the planning strategy for the assembly line to produce a certain product at the desired productivity within a specific time frame. According to the specific optimization objectives, the assembly line balance problem can be divided into type I, type II, type E, type F, etc. Regardless of the type, the assembly line balance problem belongs to a mixed integer programming problem and has typical NP-hard characteristics. It is difficult to solve and is still one of the difficulties in optimization theory and application research.

[0003] The Type II assembly line balancing problem is a common problem in application scenarios such as automobile assembly lines, electrical appliance assembly lines, and clothing production lines. Its goal is to allocate the tasks in the production process to each workstation in a certain way under the premise of meeting certain constraints, so as to minimize the time of the entire production process - that is, to minimize the cycle time (CT). There have been many studies on the solution methods for the Type II assembly line problem. According to the idea of ​​constructing the optimization algorithm, it can be divided into two categories: exact method and heuristic method. The exact method aims to accurately find the global optimal solution of the assembly line problem. Representative algorithms include dynamic programming, branch and bound (B&B) method, lower bound search method, binary tree search method, etc. Heuristic methods construct algorithms based on intuition or experience, and give a feasible solution to the optimization problem under acceptable time and economic cost. However, the degree of closeness between the feasible solution and the global optimal solution is generally unpredictable. Representative algorithms are mainly natural-like algorithms, such as genetic algorithms, ant colony algorithms, simulated annealing algorithms, and taboo search. The above existing methods directly express the assembly line type II problem as a constrained, multi-variable mixed integer programming problem. In engineering application scenarios, the number of tasks to be assigned and the corresponding workstations is usually quite large (for example, the number of tasks to be assigned for a mixed-flow production line for door assembly is as high as more than 200), resulting in a large number of constraints and variables involved, making the problem difficult to solve and the solution efficiency extremely low. In addition, the mixed integer programming problem usually cannot guarantee the global optimal solution, resulting in a long processing cycle and low workstation utilization efficiency, which greatly limits the promotion and application of flexible production lines in actual industrial scenarios. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a global optimization method for cycle time of flexible production line scheduling to improve solution efficiency, shorten processing cycle and improve workstation utilization efficiency.

[0005] To achieve the above object, the technical solution of the present invention is:

[0006] A global optimization method for cycle time of flexible production line scheduling, the method comprising:

[0007] Transform the type II optimization problem of assembly line balance into a discretized high-dimensional continuous domain optimization problem;

[0008] Using the Hilbert space filling curve method, the discretized high-dimensional continuous domain optimization problem is simplified to a discretized one-dimensional continuous domain optimization problem.

[0009] The one-dimensional continuous domain optimization problem is solved by a multi-dimensional constrained characteristic factor global search algorithm combined with discrete grid technology.

[0010] Compared with the prior art, the present invention has the following beneficial effects:

[0011] The present invention constructs an optimization method for the type II assembly line balancing problem, which combines Boolean network theory, Hilbert space filling curve technology, continuous domain model-free optimization method, and grid technology to make the solution of the optimization problem simpler, improve the solution efficiency, and ensure convergence to the global optimal solution, thereby shortening the processing cycle and improving the workstation utilization rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flowchart of a method for global cycle time optimization of flexible production line scheduling provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0013] Example:

[0014] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0015] See also Figure 1 As shown, the global optimization method for cycle time of flexible production line scheduling provided in this embodiment mainly includes the following steps:

[0016] 101. Convert the assembly line balancing type II optimization problem into a discretized high-dimensional continuous domain optimization problem;

[0017] In this way, by transforming the difficult-to-solve mixed integer programming assembly line balancing type II optimization problem into a discretized high-dimensional continuous domain optimization problem, we can avoid solving the more difficult mixed integer programming problem, and make it possible to use a simpler continuous domain optimization algorithm, thereby reducing the difficulty of solving the problem from a methodological level and improving the efficiency of solving the problem.

[0018] 102. The Hilbert space filling curve method is used to simplify the discretized high-dimensional continuous domain optimization problem into a discretized one-dimensional continuous domain optimization problem, which further reduces the difficulty of solving and improves the efficiency of solving.

[0019] 103. A multi-dimensional constrained characteristic factor global search algorithm combined with discrete grid technology is used to solve the one-dimensional continuous domain optimization problem to ensure that the solution process converges to one of the global optimal solutions of the problem.

[0020] It can be seen that this method constructs an optimization method for the type II assembly line balancing problem, which combines Boolean network theory, Hilbert space filling curve technology, continuous domain model-free optimization method, and grid technology to make the solution of the optimization problem simpler, improve the solution efficiency and ensure convergence to the global optimal solution, thereby shortening the processing cycle and improving the workstation utilization rate.

[0021] In a specific embodiment, the optimization objective of the assembly line balancing type II problem (ALB-II) is to minimize the cycle time CT. The specific mathematical expression of the problem is as follows:

[0022] minCT

[0023] st

[0024]

[0025]

[0026]

[0027] Among them, T i is the time required to execute task i, N is the number of tasks, M s is the number of workstations, F i is the set of tasks that follow task i in sequence. The above are all known conditions; x i,k is a Boolean variable to be optimized, with a value of 1 or 0. When task i is assigned to workstation k, x i,k =1, otherwise 0.

[0028] This method makes the following equivalent transformations on the three constraints contained in the above problem:

[0029] Constraint 1 This is equivalent to setting the specific form of the objective function CT to:

[0030]

[0031] Constraint 2 Equivalent transformation: specifies the sequence Only one element can be 1, and the rest are 0, which means that each task can only be assigned to one workstation for processing. From this observation, it can be seen that this sequence can actually be equivalent to M in Boolean network theory. s -valued logical vector, of the following form:

[0032]

[0033] in M s ×M s The identity matrix I Ms The kth column of M s The physical meaning of a -valued logical vector can be regarded as corresponding to an integer variable X i , when the logical vector is When (that is, when x i,k is 1, and the rest are 0), the corresponding integer variable X i= k-1. Constraint 2 can thus be equivalent to each task i corresponding to an integer variable X i , when workstation k is selected to process task i, X i =k-1.

[0034] Constraint Three (Priority constraint): Its corresponding equivalent can be:

[0035]

[0036] X 1 ,…,X N As the components of each dimension of an N-dimensional space, the value range of each dimension is [-0.5, M s -0.5], the N-dimensional space was originally continuous, but was discretized and approximated so that each component X i The value of can only be an integer. The solution of each ALB-II type problem corresponds to a certain X 1 ,…,X N Combination, that is, to form the N-dimensional space [-0.5, M s -0.5] N A point in the uniformly distributed lattice formed after discretization. The objective function CT can be regarded as X 1 ,…,X N Function

[0037] Therefore, the ALB-II type optimization problem is equivalent to the following multidimensional integer programming problem:

[0038]

[0039] st

[0040] X=[X 1 ,...,X N ]

[0041] X i ≤X j , j∈F i

[0042]

[0043] In order to reduce the difficulty of solving the above equivalent multidimensional integer programming problem, the N-dimensional integer programming problem is reduced to 1 dimension. The idea is to connect the points in the uniformly distributed lattice with the Hilbert space filling curve, and then "straighten" the curve so that these points form a 1-dimensional equidistant sequence, and finally achieve the purpose of dimensionality reduction.

[0044] According to the N-dimensional space [-0.5, M s -0.5]N By definition, each grid point can be regarded as the center of an N-dimensional square with a side length of 1, and the Hilbert curve approximation to N-dimensional space requires 2 MN The center of an N-dimensional square, where M is a positive integer (i.e., an M-order Hilbert curve). Since each dimension of this N-dimensional space can be 0, 1, …, M s -2,M s -1 Total M s The entire lattice has a total of M discrete points s N Therefore, the range of each dimension of the N-dimensional space equivalent to ALB-II is changed from [-0.5, M s -0.5] is expanded to [-0.5,2 M -0.5], where:

[0045] For the 2 in the above expanded lattice MN The points are reduced using the Hilbert space filling curve, and the points are placed along a straight line [0,2 MN -1] are arranged evenly with a spacing of 1. Define this straight line as the 1-dimensional p-axis, then the 1-dimensional coordinates of each point in the lattice on this axis can be expressed as p = 0, 1, ..., 2 MN -1. We only need to use the mapping relationship X(p) between the 1-dimensional coordinate p and the N-dimensional space coordinate X.

[0046] Based on the above problem deconstruction and dimensionality reduction methods, the present invention equates the ALB-II type problem to the following discretized continuous domain optimization problem final form:

[0047]

[0048] st

[0049] X=[X 1 ,...,X N ]

[0050] 0≤p≤2 M -1

[0051] 0≤X i (p)≤M s -1

[0052] X i (p)≤X j (p),j∈ F

[0053]

[0054] For the above equivalent form, the present invention uses a multi-dimensional constraint characteristic factor global search algorithm combined with discrete grid technology ∑GT-MI-GSA Searching for the global optimal solution can theoretically ensure that it will eventually converge to one of the global optimal solutions.

[0055] In summary, the present invention is aimed at the type II optimization problem of assembly line balance in flexible production line scheduling, and proposes a grid-based constrained model-free optimization method based on dimensionality reduction of Hilbert space filling curve. The solution idea is relatively simple, the solution efficiency is high, and it can ensure that the solution process converges to one of the global optimal solutions of the problem, thereby shortening the processing cycle and improving the utilization rate of the workstation.

[0056] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A global optimization method for cycle time of flexible production line scheduling, characterized in that: The method comprises: Transform the type II optimization problem of assembly line balance into a discretized high-dimensional continuous domain optimization problem; Using the Hilbert space filling curve method, the discretized high-dimensional continuous domain optimization problem is simplified to a discretized one-dimensional continuous domain optimization problem. A multi-dimensional constraint characteristic factor global search algorithm combined with discrete grid technology is used to solve the one-dimensional continuous domain optimization problem; The purpose of the assembly line balancing type II optimization problem is to minimize the cycle time CT. The specific mathematical expression of the problem is as follows: min CT st Among them, T i is the time required to execute task i, N is the number of tasks, M s is the number of workstations, F i is the set of tasks that follow task i in sequence; x i,k is a Boolean variable to be optimized, with a value of 1 or 0. When task i is assigned to workstation k, x i,k =1, otherwise 0, The prefix means "any"; The Hilbert space filling curve method is used to simplify the discretized high-dimensional continuous domain optimization problem into a discretized one-dimensional continuous domain optimization problem, including: The range of each dimension of the N-dimensional space equivalent to the type II optimization problem of assembly line balance is changed from [-0.5, M s -0.5] is expanded to [-0.5,2 M -0.5], where: M s is the number of possible values ​​for each dimension of the N-dimensional space; For the 2 in the expanded lattice MN The Hilbert space filling curve is used to reduce the dimension of the points and place them along a straight line [0,2 MN -1] are evenly arranged with a spacing of 1, and the straight line is defined as the 1-dimensional p-axis. Then the 1-dimensional coordinates of each point in the lattice on this axis are expressed as p = 0, 1, ..., 2 MN -1.

2. The method for global optimization of cycle time for flexible production line scheduling according to claim 1, characterized in that: Constrain the problem The equivalent is: transform the objective function CT into the following specific form:

3. The method for global optimization of cycle time for flexible production line scheduling according to claim 2, characterized in that: The constraint two Do the following conversion: Specify sequence Only one element can be 1, and the rest are 0, which means that each task can only be assigned to one workstation for processing. The sequence is actually equivalent to M in Boolean network theory. s -valued logical vector, of the following form: in, M s ×M s The identity matrix The kth column of M s The physical meaning of a -valued logical vector is considered to correspond to an integer variable X i , when the logical vector is When its corresponding integer variable X i = k-1; Constraint 2 is thus equivalent to an integer variable X corresponding to each task i i , when workstation k is selected to process task i, X i =k-1.

4. The method for global optimization of cycle time for flexible production line scheduling according to claim 3, characterized in that: The constraint three of the problem The corresponding equivalent is: in is a set of natural numbers.

5. The method for global optimization of cycle time for flexible production line scheduling according to claim 4, characterized in that: X1,...,X N As the components of each dimension of an N-dimensional space, the value range of each dimension is [-0.5, M s -0.5], the N-dimensional space was originally continuous, but was discretized and approximated so that each component X i The value of can only be an integer; the solution of each assembly line balance type II optimization problem corresponds to a certain X1,...,X N Combination, that is, to form the N-dimensional space [-0.5, M s -0.5] N A point in the uniformly distributed lattice formed after discretization; and the objective function CT is regarded as X1,...,X N Function 6. The method for global optimization of cycle time for flexible production line scheduling according to claim 5, characterized in that: The assembly line balancing type II optimization problem is equivalent to the following multidimensional integer programming problem: st X=[X1,...,X N ] X i ≤X j ,j∈F i 7. The method for global optimization of cycle time for flexible production line scheduling according to claim 6, characterized in that: The assembly line balancing type II optimization problem is equivalent to the following discretized continuous domain optimization problem in the final form: st X=[X1,..,X N ] 0≤p≤2 M -1 0≤X i (p)≤M s -1 X i (p)≤X j (p),j∈F i 8. The method for global optimization of cycle time for flexible production line scheduling according to claim 1, characterized in that: The global optimal solution is searched by using a global search algorithm of multi-dimensional constrained characteristic factors combined with discrete grid technology, so as to theoretically ensure that it will eventually converge to one of the global optimal solutions.

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