CN110826013A - Global optimization preprocessing method for intelligent manufacturing production scheduling - Google Patents
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Abstract
A global optimization preprocessing method for intelligent manufacturing production scheduling comprises the steps of pre-solving a mixed integer linear programming problem and reducing a search domain of the mixed integer nonlinear programming problem; the pre-solving of the mixed integer linear programming problem comprises the following steps: (1) selecting a variable based on a Fourier-Motzkin elimination method; (2) a redundant constraint elimination square based on a Fourier-Motzkin elimination method; (3) and (3) solving a linear programming problem based on Fourier-Motzkin elimination method. The global optimization preprocessing method for the intelligent manufacturing production scheduling aims at solving the difficult problem of large-scale engineering decision optimization problem in practice, two types of model preprocessing methods with universality are adopted, the solving performance is effectively improved, the method can directly act on the engineering decision problem with a complex structure, and the real-time performance and the resolving quality of the complex production scheduling decision are greatly improved.
Description
Technical Field
The invention belongs to the technical field of intelligent manufacturing, and particularly relates to a global optimization preprocessing method for intelligent manufacturing production scheduling.
Background
Under the background of intelligent manufacturing transformation oriented by a plurality of enterprises, manufacturing industry informatization, entity resource virtualization, production process intellectualization, industrial resource service and the like become popular research subjects and engineering propositions. Meanwhile, the manufacturing industry change taking informatization and industrialization integration as mainstream is being expanded all around, and the core problem is how to organically integrate advanced technologies and realize high integration of resources, services and production management and transformation and upgrading of production modes.
In the transformation process, the domestic and foreign business and academic circles respectively have rich explanations on the intelligent manufacturing production mode, wherein the mainstream ideas surround the China manufacturing 2025, the industry 4.0 and the intelligent manufacturing which are respectively proposed by China, Germany and the American three countries. In the strategy for transformation and upgrade of manufacturing industry, the ministry of industry and informatization of china proposes an intelligent manufacturing system architecture based on three dimensions of life cycle, system level and intelligent function in the national intelligent manufacturing standard system construction guidelines (2015); the german institute for the electrical and electronic industry determined a reference model architecture for industry 4.0 in month 4 of 2015, which again includes three dimensions: LifeCycle and Value flow (Life cycle & Value Stream), system level and function level. The strategy clearly shows that the model intelligent factory building plan mainly for automobile manufacturing in discrete industry is established, and clearly indicates that the exemplary application fields in the process industry comprise the industries of chemical industry, petrochemical industry, steel manufacturing, medicine and the like, and the mixed industry mainly comprises the food industry.
Therefore, the key technology and theoretical innovation, the development and implementation of engineering projects, and the construction and coordination of standard systems in the industry become the breakthrough points which are concerned by researchers and engineers at present.
The global optimization algorithm is used as a core of a computing engine of decision optimization services of each level of an enterprise, and the response capability, the processing scale and the decision quality of the enterprise to complex decision scenes in an intelligent manufacturing mode are determined. At present, most engineering decision models cannot be rapidly optimized through the existing commercial solver and heuristic algorithm due to the characteristics of integer variables, overlarge constraint scale, model nonlinearity, non-convexity and the like, so that the improvement of modeling complexity and precision is strictly limited, and the integrated research of planning, scheduling and operation level scheduling in the process industry cannot be implemented.
The Chinese patent application No. CN201611094736.5 discloses a hybrid global optimization method, which improves the calculation precision and convergence speed by providing a hybrid global optimization method combining a particle swarm algorithm, a chaotic search algorithm and a sequential quadratic programming algorithm, solves the related problems in the field of mechanical optimization design, and does not solve the technical problems of large-scale engineering decision models of intelligent manufacturing production scheduling due to integer variables, overlarge constrained scale or model nonlinearity and non-convex constraint modeling complexity and precision improvement.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects, the invention aims to provide a global optimization preprocessing method for intelligent manufacturing production scheduling, which adopts a pre-solving algorithm aiming at a mixed integer linear programming problem on the premise of ensuring global optimization, firstly deduces an optimality condition of the mixed integer nonlinear programming problem aiming at the mixed integer nonlinear programming problem, and applies the optimality condition to search domain reduction, thereby effectively improving the solving performance, being capable of directly acting on an engineering decision problem with a complex structure, and greatly improving the real-time performance and the resolving quality of a complex production scheduling decision.
The purpose of the invention is realized by the following technical scheme:
a global optimization preprocessing method for intelligent manufacturing production scheduling is characterized by comprising the steps of pre-solving a mixed integer linear programming problem and reducing a search domain of the mixed integer nonlinear programming problem;
the pre-solving of the mixed integer linear programming problem comprises the following steps:
(1) selecting a variable based on a Fourier-Motzkin elimination method;
(2) a redundant constraint elimination square based on a Fourier-Motzkin elimination method;
(3) and (3) solving a linear programming problem based on Fourier-Motzkin elimination method.
Further, in the global optimization preprocessing method for intelligent manufacturing production scheduling, the search domain reduction of the mixed integer nonlinear programming problem includes the following steps:
(1) deriving an optimality condition: deducing an optimality condition through monotonicity characteristics of the objective function and the constraint;
(2) search domain reduction: and through the optimality condition, the optimal solution is used as a group of constraints which must be met, and solution domains meeting the constraints are screened and used as reduced search domains.
The global optimization method is used as a calculation engine core of decision optimization services of each level of an enterprise, and determines the response capability, processing scale and decision quality of the enterprise to complex decision scenes in an intelligent manufacturing mode. At present, most engineering decision models cannot be rapidly optimized by the existing method due to the characteristics of integral variables, overlarge constraint scale, model nonlinearity, non-convexity and the like, so that the improvement of modeling complexity and precision is strictly limited, and the integrated research of planning, scheduling and operation level scheduling in the process industry cannot be implemented on the ground.
In the global optimization process, the preprocessing of the model is more important than the links of real problem solving and branching, and the step determines the feasible domain range, the model scale, the model structure and even the convexity of the model of the problem solved by each node. For a general engineering decision problem, an optimization model of the method is mainly in the following two standard forms, one is a mixed integer linear programming model, and the other is a mixed integer non-linear programming model.
The global optimization preprocessing algorithm for the intelligent manufacturing production scheduling adopts a pre-solution algorithm aiming at a mixed integer linear programming problem on the premise of ensuring global optimization, can reduce the variable scale of a model before formal optimization, greatly reduces the problem scale and ensures the equivalence of an optimal solution, thereby simplifying the problem and reducing the optimization difficulty; aiming at the mixed integer nonlinear programming problem, the optimality condition of the mixed integer nonlinear programming problem is firstly deduced and applied to the reduction of a search domain, the search range can be shrunk in advance before each node is solved, the relaxation sub-problem of the nonlinear problem is enhanced, and the convergence of an upper and a lower boundary targets of the global optimization is accelerated.
Further, the global optimization preprocessing method for intelligent manufacturing production scheduling includes the following steps: estimating the quantity of non-zero elements of the model after the Fourier-Motzkin elimination method is executed, eliminating variables by applying the Fourier-Motzkin elimination method to reduce the non-zero elements, and sequencing the variables according to the quantity of the reduced non-zero elements, wherein the higher the reduced quantity is, the higher the priority of the variables is.
Further, the above global optimization preprocessing method for intelligent manufacturing production scheduling, the redundancy constraint elimination method based on Fourier-Motzkin elimination method, includes the following steps: after the selected variables are eliminated based on a Fourier-Motzkin elimination method, the judgment of constraint redundancy is carried out through boundary reasoning, and if the upper and lower bounds of the obtained constraint conflict or the original constraint boundary is violated through reasoning, the problem that the original linear programming is not feasible can be directly judged; if the upper bound of a new constraint is greater than or equal to the inference boundary, the constraint redundancy can be determined and can be discarded.
Further, the above global optimization preprocessing method for intelligent manufacturing production scheduling, the linear programming problem pre-solving based on Fourier-Motzkin elimination method, includes the following steps:
(1) after variable selection and a redundancy constraint elimination method based on a Fourier-Motzkin elimination method are combined, screening variables only appearing in inequality constraints, and defining a set;
(2) iteratively applying Fourier-Motzkin elimination method according to a certain sequence to eliminate the variables in the set, and equivalently transforming;
(3) and reconstructing an inequality constraint system.
Further, in the global optimization preprocessing method for intelligent manufacturing production scheduling, the search domain reduction includes single-constraint search domain reduction and multi-constraint search domain reduction.
Further, the above global optimization preprocessing method for intelligent manufacturing production scheduling, where the search domain reduction, includes the following steps:
(1) selecting a variable, forward-calculating an objective function and constraining a gradient boundary of the variable, and stopping the algorithm if the gradient boundary obtained by forward calculation meets an optimality condition;
(2) the method comprises the steps of performing reverse calculation on boundaries by limiting the gradient of an objective function and a constraint to be non-negative or non-positive, then keeping the boundaries of the gradient unchanged, and performing reverse calculation on all variable boundaries;
(3) the number of the boundaries obtained by reverse calculation under different limiting conditions is 4, and the intersection of the 4 bounded sets obtains the search domain after all variables are reduced.
Further, in the above global optimization preprocessing method for intelligent manufacturing production scheduling, the constraint of single-constraint search domain reduction is one, and the constraint of multi-constraint search domain reduction is multiple.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention discloses a global optimization preprocessing method for intelligent manufacturing production scheduling, which aims at solving the difficult problem of large-scale engineering decision optimization problem in practice, adopts two types of model preprocessing methods with universality, effectively improves the solving performance, can directly act on the engineering decision problem with a complex structure, and greatly improves the real-time performance and the resolving quality of complex production scheduling decisions;
(2) the invention discloses a global optimization preprocessing method for intelligent manufacturing production scheduling, which adopts a pre-solving algorithm aiming at a mixed integer linear programming problem, can reduce the variable scale of a model before formal optimization, greatly reduces the problem scale and ensures the equivalence of an optimal solution, thereby simplifying the problem and reducing the optimization difficulty; aiming at the mixed integer nonlinear programming problem, the optimality condition of the mixed integer nonlinear programming problem is firstly deduced and applied to the reduction of a search domain, the search range can be shrunk in advance before each node is solved, the relaxation sub-problem of the nonlinear problem is enhanced, and the convergence of an upper and a lower boundary targets of the global optimization is accelerated.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to specific embodiments, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The following embodiments provide a global optimization preprocessing method for intelligent manufacturing production scheduling, which includes pre-solving for a mixed integer linear programming problem, and reducing a search domain for a mixed integer non-linear programming problem.
Example 1
Pre-solving of mixed integer linear programming problem
The method comprises the following steps:
(1) variable selection based on Fourier-Motzkin elimination: estimating the quantity of non-zero elements of the model after the Fourier-Motzkin elimination method is executed, eliminating variables by applying the Fourier-Motzkin elimination method to reduce the non-zero elements, sequencing the variables according to the quantity of the reduced non-zero elements, and enabling the priority of the variables with higher reduced quantity to be higher;
(2) a redundancy constraint elimination square based on Fourier-Motzkin elimination method: after the selected variables are eliminated based on a Fourier-Motzkin elimination method, the judgment of constraint redundancy is carried out through boundary reasoning, and if the upper and lower bounds of the obtained constraint conflict or the original constraint boundary is violated through reasoning, the problem that the original linear programming is not feasible can be directly judged; if the upper bound of a new constraint is greater than or equal to the inference boundary, the constraint redundancy can be determined and discarded;
(3) linear programming problem pre-solving based on Fourier-Motzkin elimination method:
1) after variable selection and a redundancy constraint elimination method based on a Fourier-Motzkin elimination method are combined, screening variables only appearing in inequality constraints, and defining a set;
2) iteratively applying Fourier-Motzkin elimination method according to a certain sequence to eliminate the variables in the set, and equivalently transforming;
3) and reconstructing an inequality constraint system.
Example 2
Search domain reduction for mixed integer non-linear programming problem
The method comprises the following steps:
(1) deriving an optimality condition: deducing an optimality condition through monotonicity characteristics of the objective function and the constraint;
(2) search domain reduction: through the optimality condition, a group of constraints which must be satisfied by the optimal solution are used, solution domains satisfying the constraints are screened, and the solution domains are used as reduced search domains; the search domain reduction comprises single constraint search domain reduction and multi-constraint search domain reduction;
the search domain reduction comprises the following steps:
1) selecting a variable, forward-calculating an objective function and constraining a gradient boundary of the variable, and stopping the algorithm if the gradient boundary obtained by forward calculation meets an optimality condition;
2) the method comprises the steps of performing reverse calculation on boundaries by limiting the gradient of an objective function and a constraint to be non-negative or non-positive, then keeping the boundaries of the gradient unchanged, and performing reverse calculation on all variable boundaries;
3) the number of the boundaries obtained by reverse calculation under different limiting conditions is 4, and the intersection of the 4 bounded sets obtains the search domain after all variables are reduced.
Wherein, the single constraint search domain has one reduced constraint, and the multiple constraint search domain has multiple reduced constraints.
The invention has many applications, and the above description is only a preferred embodiment of the invention. It should be noted that the above examples are only for illustrating the present invention, and are not intended to limit the scope of the present invention. It will be apparent to those skilled in the art that various modifications can be made without departing from the principles of the invention and these modifications are to be considered within the scope of the invention.
Claims (8)
1. A global optimization preprocessing method for intelligent manufacturing production scheduling is characterized by comprising the steps of pre-solving a mixed integer linear programming problem and reducing a search domain of the mixed integer nonlinear programming problem;
the pre-solving of the mixed integer linear programming problem comprises the following steps:
(1) selecting a variable based on a Fourier-Motzkin elimination method;
(2) a redundant constraint elimination square based on a Fourier-Motzkin elimination method;
(3) and (3) solving a linear programming problem based on Fourier-Motzkin elimination method.
2. The global optimization pre-processing method for intelligent manufacturing production scheduling of claim 1, wherein the search domain reduction of the mixed integer non-linear programming problem comprises the following steps:
(1) deriving an optimality condition: deducing an optimality condition through monotonicity characteristics of the objective function and the constraint;
(2) search domain reduction: and through the optimality condition, the optimal solution is used as a group of constraints which must be met, and solution domains meeting the constraints are screened and used as reduced search domains.
3. The global optimization preprocessing method for intelligent manufacturing production scheduling as claimed in claim 1, wherein the variable selection based on Fourier-Motzkin elimination method comprises the following steps: estimating the quantity of non-zero elements of the model after the Fourier-Motzkin elimination method is executed, eliminating variables by applying the Fourier-Motzkin elimination method to reduce the non-zero elements, and sequencing the variables according to the quantity of the reduced non-zero elements, wherein the higher the reduced quantity is, the higher the priority of the variables is.
4. The global optimization preprocessing method for intelligent manufacturing production scheduling as claimed in claim 3, wherein the redundancy constraint elimination method based on Fourier-Motzkin elimination method comprises the following steps: after the selected variables are eliminated based on a Fourier-Motzkin elimination method, the judgment of constraint redundancy is carried out through boundary reasoning, and if the upper and lower bounds of the obtained constraint conflict or the original constraint boundary is violated through reasoning, the problem that the original linear programming is not feasible can be directly judged; if the upper bound of a new constraint is greater than or equal to the inference boundary, the constraint redundancy can be determined and can be discarded.
5. The global optimization preprocessing method for intelligent manufacturing production scheduling as claimed in claim 4, wherein the linear programming problem pre-solving based on Fourier-Motzkin elimination method comprises the following steps:
(1) after variable selection and a redundancy constraint elimination method based on a Fourier-Motzkin elimination method are combined, screening variables only appearing in inequality constraints, and defining a set;
(2) iteratively applying Fourier-Motzkin elimination method according to a certain sequence to eliminate the variables in the set, and equivalently transforming;
(3) and reconstructing an inequality constraint system.
6. The global optimization pre-processing method for intelligent manufacturing production scheduling of claim 1, wherein said search domain reduction comprises single constraint search domain reduction and multi-constraint search domain reduction.
7. The global optimization preprocessing method for intelligent manufacturing production scheduling as claimed in claim 6, wherein the search domain reduction comprises the following steps:
(1) selecting a variable, forward-calculating an objective function and constraining a gradient boundary of the variable, and stopping the algorithm if the gradient boundary obtained by forward calculation meets an optimality condition;
(2) the method comprises the steps of performing reverse calculation on boundaries by limiting the gradient of an objective function and a constraint to be non-negative or non-positive, then keeping the boundaries of the gradient unchanged, and performing reverse calculation on all variable boundaries;
(3) the number of the boundaries obtained by reverse calculation under different limiting conditions is 4, and the intersection of the 4 bounded sets obtains the search domain after all variables are reduced.
8. The global optimization pre-processing method for intelligent manufacturing production scheduling of claim 7, wherein the constraint of single constraint search domain reduction is one, and the constraint of multi-constraint search domain reduction is multiple.
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| CN113661510A (en) * | 2020-02-28 | 2021-11-16 | 京东方科技集团股份有限公司 | Non-linear programming model-based production planning system, production planning method, and computer-readable storage medium |
| CN118295344A (en) * | 2024-03-26 | 2024-07-05 | 广东省科学院智能制造研究所 | Circulation time global optimization method for flexible production line scheduling |
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| CN113661510A (en) * | 2020-02-28 | 2021-11-16 | 京东方科技集团股份有限公司 | Non-linear programming model-based production planning system, production planning method, and computer-readable storage medium |
| CN118295344A (en) * | 2024-03-26 | 2024-07-05 | 广东省科学院智能制造研究所 | Circulation time global optimization method for flexible production line scheduling |
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