CN110570018B - Planning and designing method for customized production workshop - Google Patents
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Abstract
A planning design method for a customized production workshop utilizes a binary space partition tree method to divide a workshop plane according to a key process path of a customized product, and analyzes a layout initial scheme of a production unit by using an isomorphic theory. Under the index constraint of the expected capacity and the order lead period of the production workshop, a trust domain-SQP algorithm embedded into a queuing network model is used for respectively solving equipment resource planning models corresponding to each production unit layer, wherein the equipment resource planning models comprise the number of processing machines, the number of industrial robots and the running speed of the industrial robots, and the equipment resource planning models corresponding to the production workshop layers comprise the number of AGVs and the running speed of the AGVs. And solving the overall layout of the production workshop and the equipment resource allocation scheme by a hierarchical optimization algorithm so as to minimize the investment cost.
Description
Technical Field
The invention relates to the technical field of manufacturing system planning and design, in particular to a planning and design method for a customized production workshop.
Background
Personalized customization is an important feature of intelligent manufacturing, and with the continuous advance of intelligent manufacturing strategies, the intelligent modification of factories becomes a main way for promoting intelligent manufacturing transformation in the current manufacturing industry. The intelligent workshop is an important link for realizing intelligent manufacturing by an intelligent factory, and for the planning design of the intelligent factory, the key step is to realize more reasonable intelligent workshop layout, can contain the layout of an automatic assembly line, automatic equipment, the Internet of things and the like in a production system, accords with the extended architecture of 'Chinese manufacturing 2025', and adapts to personalized customization requirements and future flexible rapid production. Meanwhile, because highly automated and intelligent production equipment is expensive, how to configure the equipment resources in a production workshop to ensure the expected capacity at the lowest cost and deliver orders on time and quickly is a problem to be solved by planning and designing a customized production workshop.
Disclosure of Invention
The invention aims to provide a planning and designing method for a customized production workshop aiming at the defects in the background technology, effectively solves the joint optimization problem of the layout of each production unit and the equipment resource allocation in the unit in the workshop by a hierarchical strategy, provides a scientific analysis method and a decision basis for enterprises to modify and upgrade the workshop or newly build a factory, and optimizes investment benefits.
In order to achieve the purpose, the invention adopts the following technical scheme:
a planning and designing method for a customized production workshop comprises the following specific steps:
step A: performing plane division on the workshop by using a binary difference space division tree method;
the method specifically comprises the following steps: dividing the workshop into blocks with the same number by using a binary space division tree method according to the operation number and the front-back relation of the key process path of the product, and matching corresponding operation, namely dividing the workshop into production units;
and B: analyzing an initial feasible scheme of unit layout by isomorphic theory;
the method comprises the following steps: analyzing the association among the schemes divided in the step A by utilizing an isomorphic theory, and screening out redundant schemes;
the method comprises the following specific steps:
step B1: screening out the architecture redundancy scheme before matching the operation corresponding to the block;
step B2: after the operation corresponding to the block is matched, constructing a corresponding adjacency graph by taking the central point of the block as a vertex, and screening out an adjacency redundancy scheme;
and C: b, according to the effective schemes left after the redundant schemes are screened out in the step B, a random nonlinear mixed integer programming model is established to respectively describe the equipment resource optimization configuration problems of the inter-vehicle layer and the unit layer;
step D: constructing a trust domain-sequence quadratic programming algorithm embedded into a queuing network model, judging the feasibility of the current resource allocation scheme by approximately solving the queuing network description model in the step C and obtaining the performance index of the system, then feeding back the feasibility to the subsequent quadratic programming subproblems, and promoting the iterative search process of the optimal solution, thereby solving the equipment allocation optimization scheme of each production unit from the effective scheme of each production unit in sequence;
step E: and D, constructing a unit-workshop hierarchical algorithm framework according to the equipment configuration optimal scheme of each production unit solved in the step D, solving an overall unit layout and equipment resource configuration optimization scheme of the workshop, and configuring the workshop layout according to the solved optimal scheme.
Preferably, in the step C, the random nonlinear mixed integer programming model is established to respectively comprise an inter-vehicle layer resource allocation optimization queuing network model and a unit layer resource allocation optimization queuing network description model;
the vehicle-level resource allocation optimization queuing network model is concretely as follows:
an objective function:
constraint conditions are as follows:
X1∈N+- - -formula four;
X2，Y∈R+- - -formula five;
formula one represents the minimum total investment cost;
the second formula represents the average capacity constraint;
representing average production cycle constraint in a formula;
formula four represents a non-negative integer vector;
formula five represents a non-negative real number vector;
wherein, X1: configuring vectors according to the number of the AGV; x2: configuring a vector for the AGV running speed; y: aggregating node processing rate configuration vectors; thetai min: a capacity demand prediction value; p is a radical ofi: capacity demand prediction probability; t isj max: predicting a production cycle demand; p is a radical ofj: a production cycle demand prediction probability;
the unit layer resource allocation optimization queuing network description model is concretely as follows:
an objective function:
constraint conditions are as follows:
Z1，R1∈N+- - -formula nine;
Z2，R2∈R+- - -equation ten;
formula six represents the minimum total investment cost;
formula seven represents the average capacity constraint;
formula eight represents the average production cycle constraint;
formula nine represents a non-negative integer vector;
formula ten represents a non-negative real number vector;
wherein Z is1: configuring vectors by the number of the processing machines; z2: configuring a vector for the running speed of the processing machine tool; r1: configuring a vector by the number of robots; r2: configuring a vector for the running speed of the robot; thetai min: delivery deviceCapacity requirements for stage conversion; tau isj min: the production cycle requirement of the step-by-step transformation;
the solutions of the vehicle-level resource allocation optimization queuing network model and the unit-level resource allocation optimization queuing network description model represent system performance indexes of effective schemes.
Preferably, in step D, the confidence domain-sequence quadratic programming algorithm for constructing the embedded queuing network model specifically includes
Step D1: decomposing a quadratic programming subproblem;
the method comprises the following steps of adopting an external approximation method to relax constraints in an inter-vehicle layer resource configuration optimization queuing network model and a unit layer resource configuration optimization queuing network description model, decomposing an original nonlinear constraint optimization problem into a series of quadratic programming subproblems with inequality constraints, and adopting a convex method if the relaxed quadratic programming subproblems are non-convex, so that the quadratic programming subproblems can calculate gradient of decision variables and determine the search direction of an iterative process, wherein the specific formula is as follows:
quadratic programming sub-problem:
wherein the content of the first and second substances,
for the objective function f (x) at the current iteration point xkP is the direction vector, H (x)k) Is f (x) at xkHessian matrix of (g)i(xk) Is a constraint function.
Step D2: solving a quadratic programming sub-problem by adopting a trust domain method;
after the search direction of the iterative process is determined, a small neighborhood of a current iteration point is given in each iteration as a confidence domain, then a subproblem is solved in the neighborhood to obtain a trial step length, then a queuing network model is called to calculate the actual descending quantity of a target function and the descending quantity of a quadratic model function, the ratio of the two is used as an evaluation function to determine whether to accept the trial step and determine the confidence domain of the next iteration, the process is iterated repeatedly until a satisfactory approximate optimal solution is obtained, and the specific formula is as follows:
trusted domain form:
wherein m isk(s) is an approximate quadratic model of the objective function f (x), s ═ x-xkIn order to be the step size vector,
is f (x) at the current iteration point xkTransposed matrix of gradients, H (x)k) Is f (x) at xkHessian matrix of (A) (. DELTA)kIs the confidence domain radius.
Preferably, the specific steps of constructing a unit-workshop hierarchical algorithm framework and solving the overall unit layout and equipment resource allocation optimization scheme of the workshop are as follows:
step E1: in a queuing network modeling solving link, namely in the step C, the production units are progressively aggregated into nodes of a queuing network model in a production workshop;
step E2: in the resource allocation optimization link, namely step D, the resource allocation result of the workshop layer node is converted into a performance constraint design index of the unit layer resource allocation optimization queuing network description model in a descending decomposition mode;
step E3: and obtaining the whole unit layout and the equipment resource allocation scheme of the production workshop according to the workshop area constraint coordination configuration result.
Preferably, step E1 specifically includes:
firstly, a production unit queuing network model with resource synchronization constraint is established, and unit performance indexes are calculated by an approximate solving method. Then, according to the unit performance index, aggregating each production unit into a node of a production workshop queuing network model, then establishing a state-related random batch-handling production workshop queuing network model, and calculating the workshop performance index by an approximate solving method, wherein the specific formula is as follows:
{Θn，Tn}→{μn，sn 2}，
wherein, thetan: average production Rate, T, of production Unit nn: average production cycle, μ of production unit nn: processing Rate of polymerization, sn 2: the square coefficient of variation of the processing time of the polymerization.
Preferably, step E2 specifically includes:
firstly, establishing a random nonlinear mixed integer programming model for optimizing the resource allocation of a production workshop, solving a workshop resource allocation result by a trust domain algorithm embedded in a queuing network model, then converting the workshop resource allocation result into a performance index constraint requirement of a random programming model of a production unit according to the workshop resource allocation result, then establishing a random nonlinear mixed integer programming model for optimizing the resource allocation of the production unit, and solving a unit resource allocation result by the trust domain algorithm embedded in the queuing network model; the specific formula is as follows:
wherein, Y: aggregate node processing rate configuration vector, θi min: capacity requirement of step-wise conversion, τj min: the production cycle requirement of the step-by-step transformation.
Preferably, step E3 specifically includes:
coordinating and correcting the configuration result by the constraint condition of the workshop area, and finally verifying whether the total sum of the areas of all the production units after all the equipment is configured is required to be loosened or not; when the configuration result does not satisfy the total area constraint condition, performing necessary tightening on the performance index constraint of the vehicle interlayer, and then performing layered optimization; through repeated iteration processes, an optimal solution meeting global constraint conditions of the whole system is finally obtained; obtaining the whole unit layout and equipment resource allocation scheme of the production workshop according to the optimal solution; the constraint conditions of the workshop area are as follows:
wherein S isn: the sum of the areas of various devices configured by the unit n is as follows: coefficient of relaxation, S*: the area of a production workshop.
Has the advantages that: the invention provides a hierarchical strategy aiming at random production workshops of customized manufacturing enterprises, effectively solves the joint optimization problem of layout of each production unit in the workshop and equipment resource allocation in the unit, provides a scientific analysis method and a decision basis for the enterprises to improve and upgrade the workshops or newly build a factory, and optimizes investment benefits.
Drawings
FIG. 1 is an architectural redundancy block diagram of the partitioning scheme of the present invention;
FIG. 2 is a block diagram of contiguous redundant regions of the partitioning scheme of the present invention;
FIG. 3 is a framework diagram of the hierarchical optimization algorithm of the present invention;
FIG. 4 is a flow chart of the present invention for customizing the design of a manufacturing floor.
Detailed Description
The technical scheme of the invention is further explained by the specific implementation mode in combination with the attached drawings.
The planning and designing method for the customized production workshop, disclosed by the invention, comprises the following specific steps as shown in figure 4:
firstly, a binary space partition tree method is utilized to divide a workshop plane, and an isomorphic theory is used to analyze an initial feasible scheme of unit layout.
According to the operation quantity and the front-back relation of the product key process path, a production workshop is divided into blocks with the same quantity by using a binary space partition tree method, and the corresponding operation is matched to obtain a production unit. The number of partitioning schemes grows exponentially as the number of required partitioning blocks increases. Therefore, the isomorphic theory in the graph theory is used for analyzing the association between the division schemes, the redundancy scheme is screened out, and the scale of the feasible scheme can be effectively reduced. There are two main bases: (1) the architectural redundancy scheme is screened out before the operations corresponding to the blocks are matched. The two partitioning schemes shown in fig. 1 have a homogenous relationship. (2) After the operation corresponding to the block is matched, the adjacent redundancy scheme is screened out. As shown in fig. 2, A, B, C, D respectively represents four divided blocks, the left diagram represents the block division diagram, and the right diagram represents the adjacency diagram, although the three division schemes have different architectures, it can be seen that the three division schemes have an isomorphic relationship.
And secondly, improving a trust domain-SQP algorithm and solving an equipment configuration optimization scheme of each production unit.
Because the resource configuration variables have both integer variables and real variables, and the system performance index constraints have strong nonlinear association with the decision variables, a random nonlinear mixed integer programming model needs to be established to describe the equipment resource optimization configuration problem of the inter-vehicle layer and the unit layer respectively. The randomness of the stochastic programming model is described by two aspects: the probability distribution of the continuous type random variables describes the uncertainty of the production process. Random variables in the operation of a manufacturing system include: inter-arrival time of the workpiece, processing time, transport time, etc. By inputting the distribution model of the random variables into the queuing network model, the mathematical expectation of each performance index of the system is calculated, and whether the expected requirements are met can be judged. The probability distribution of the discrete random variables describes the uncertainty of the demand forecast. For the stochastic programming problem, the demand is uncertain, and the demand can be represented by a discrete random distribution generated according to a series of demand prediction scenes which are associated by occurrence probability, namely predicted values of product demands which can be realized in a certain time period in the future. Since the demands of the system capacity and the production cycle are described according to the prediction scenarios, such as the product yield and the order delivery date, the solution needs to be performed according to the combination of the two scenarios when the stochastic programming model is solved, and the optimization result of each combination is weighted according to the scenario probability to obtain the final optimization result.
The inter-vehicle layer resource allocation optimizing queuing network model comprises the following steps:
an objective function:
(minimizing the total investment cost)
Constraint conditions are as follows:
(average capacity constraint)
X1∈N+(non-negative integer vector)
X2，Y∈R+(non-negative real number vector)
Wherein, X1: configuring vectors according to the number of the AGV; x2: configuring a vector for the AGV running speed; y: aggregating node processing rate configuration vectors; thetai min: a capacity demand prediction value; p is a radical ofi: capacity demand prediction probability; t isj max: predicting a production cycle demand; p is a radical ofj: production cycle demand forecast probability.
Optimizing a queuing network model by using unit layer resource allocation:
an objective function:
(minimizing the total investment cost)
Constraint conditions are as follows:
(average capacity constraint)
Z1，R1∈N+(non-negative integer vector)
Z2，R2∈R+(non-negative real number vector)
Wherein Z is1: configuring vectors by the number of the processing machines; z2: configuring a vector for the running speed of the processing machine tool; r1: configuring a vector by the number of robots; r2: configuring a vector for the running speed of the robot; thetai min: capacity requirements for step-by-step conversion; tau isj min: the production cycle requirement of the step-by-step transformation.
As the queuing network description models of the manufacturing units and the manufacturing workshops do not have a product form solution, namely, a closed form expression does not exist between the system performance index and the optimization variable. Therefore, a trust domain-sequence quadratic programming algorithm embedded in a queuing network model is constructed, a performance index of a system is obtained by approximately solving the queuing network model, the feasibility of the current resource allocation scheme is judged and then fed back to a subsequent quadratic programming subproblem, and an iterative search process of an optimal solution is promoted. The method mainly comprises the following steps:
(1) and decomposing the quadratic programming subproblem. And (3) relaxing the constraint by adopting an external approximation method, and decomposing the original nonlinear constraint optimization problem into a series of quadratic programming subproblems with inequality constraints. Because the original problem has two performance index constraints and has partial order monotonicity, the relaxed problem may be non-convex, and a proper convex method is required to be adopted, so that the gradient of the decision variables can be solved, and the search direction of the iterative process can be determined.
Quadratic programming sub-problem:
wherein the content of the first and second substances,
for the objective function f (x) at the current iteration point xkP is the direction vector, H (x)k) Is f (x) at xkHessian matrix of (g)i(xk) Is a constraint function.
(2) And solving the quadratic programming subproblem by adopting a confidence domain method. And then, calling a queuing network model to calculate the actual descending quantity of the target function and the descending quantity of the quadratic model function, and taking the ratio of the actual descending quantity and the actual descending quantity as an evaluation function to determine whether to accept the tentative step and determine the trust domain of the next iteration. This process is iterated repeatedly until a satisfactory near-optimal solution is obtained.
Trusted domain form:
wherein m isk(s) is an approximate quadratic model of the objective function f (x), s ═ x-xkIn order to be the step size vector,
is f (x) at the current iteration point xkTransposed matrix of gradients, H (x)k) Is f (x) at xkHessian matrix of (A) (. DELTA)kIs the confidence domain radius.
And thirdly, solving the overall unit layout of the workshop and the optimization scheme of equipment resource allocation by using a hierarchical algorithm framework.
Adopting a unit-workshop hierarchical solving algorithm framework: in a queuing network modeling solving link, namely step C, the production units are progressively aggregated into nodes of a queuing network model in a production workshop; in the resource allocation optimization link, namely step D, the resource allocation results of the workshop layer nodes are decomposed and converted into performance constraint design indexes of the unit layer random optimization model in a descending mode, and finally the allocation results are coordinated according to the workshop area constraint to obtain the whole unit layout of the production workshop and the equipment resource allocation scheme. As shown in fig. 3, the algorithm framework is a schematic diagram of a hierarchical algorithm, and the algorithm mainly includes three stages:
(1) a method for modeling and solving a queuing network of ascending aggregation. Firstly, a production unit queuing network model with resource synchronization constraint is established, and unit performance indexes are calculated by an approximate solving method. Then, each production unit is aggregated into a node of the production workshop queuing network model according to the unit performance index. And then, establishing a state-related random batch-carrying production workshop queuing network model, and calculating the workshop performance index by an approximate solving method.
{Θn，Tn}→{μn，sn 2}，
Wherein, thetan: average production Rate, T, of production Unit nn: average production cycle, μ of production unit nn: processing Rate of polymerization, sn 2: the square coefficient of variation of the processing time of the polymerization.
(2) And (4) solving an algorithm by using a descending decomposition stochastic programming model. Firstly, establishing a random nonlinear mixed integer programming model for optimizing the resource allocation of the production workshop, and solving a workshop resource allocation result by a trust domain algorithm embedded into a queuing network model. And then, converting the configuration result into a performance index constraint requirement of the random planning model of the production unit according to the configuration result of the workshop resources. Then, a random nonlinear mixed integer programming model for optimizing the resource allocation of the production units is established, and the unit resource allocation result is solved by a trust domain algorithm embedded into the queuing network model.
Wherein, Y: aggregate node processing rate configuration vector, θi min: capacity requirement of step-wise conversion, τj min: the production cycle requirement of the step-by-step transformation.
(3) And coordinating and correcting the configuration result by the constraint condition of the workshop area. And finally, verifying whether the total sum of the required areas of all the production units after being configured with various devices after necessary relaxation meets the constraint of the total area of the production workshop. And when the configuration result does not meet the total area constraint condition, performing necessary tightening on the performance index constraint of the vehicle interlayer, and then performing layered optimization. And finally obtaining an optimal solution meeting global constraint conditions of the whole system through repeated iteration processes, and obtaining a production workshop whole unit layout and equipment resource allocation scheme according to the optimal solution. Constraint conditions of the workshop area:
wherein S isn: the sum of the areas of various devices configured by the unit n is as follows: coefficient of relaxation, S*: the area of a production workshop.
The technical principle of the present invention is described above in connection with specific embodiments. The description is made for the purpose of illustrating the principles of the invention and should not be construed in any way as limiting the scope of the invention. Based on the explanations herein, those skilled in the art will be able to conceive of other embodiments of the present invention without inventive effort, which would fall within the scope of the present invention.
Claims (7)
1. A planning and designing method for a customized production workshop is characterized by comprising the following steps: the method comprises the following specific steps:
step A: performing plane division on the workshop by using a binary space division tree method;
the method specifically comprises the following steps: dividing the workshop into blocks with the same number by using a binary space division tree method according to the operation number and the front-back relation of the key process path of the product, and matching corresponding operation, namely dividing the workshop into production units;
and B: analyzing an initial feasible scheme of unit layout by isomorphic theory;
the method comprises the following steps: analyzing the association among the schemes divided in the step A by utilizing an isomorphic theory, and screening out redundant schemes;
the method comprises the following specific steps:
step B1: screening out the architecture redundancy scheme before matching the operation corresponding to the block;
step B2: after the operation corresponding to the block is matched, constructing a corresponding adjacency graph by taking the central point of the block as a vertex, and screening out an adjacency redundancy scheme;
and C: b, according to the effective schemes left after the redundant schemes are screened out in the step B, a random nonlinear mixed integer programming model is established to respectively describe the equipment resource optimization configuration problems of the inter-vehicle layer and the unit layer;
step D: constructing a trust domain-sequence quadratic programming algorithm embedded into a queuing network model, judging the feasibility of the current resource allocation scheme by approximately solving the queuing network description model in the step C and obtaining the performance index of the system, then feeding back the feasibility to the subsequent quadratic programming subproblems, and promoting the iterative search process of the optimal solution, thereby solving the equipment allocation optimization scheme of each production unit from the effective scheme of each production unit in sequence;
step E: and D, constructing a unit-workshop hierarchical algorithm framework according to the equipment configuration optimal scheme of each production unit solved in the step D, solving an overall unit layout and equipment resource configuration optimal scheme of the workshop, and configuring the workshop layout according to the solved optimal scheme.
2. The method of claim 1, wherein the step of:
in the step C, establishing a random nonlinear mixed integer programming model respectively comprising an inter-vehicle layer resource allocation optimization queuing network model and a unit layer resource allocation optimization queuing network description model;
the vehicle-level resource allocation optimization queuing network model is concretely as follows:
an objective function:
constraint conditions are as follows:
X1∈N+- - -formula four;
X2，Y∈R+- - -formula five;
formula one represents the minimum total investment cost;
the second formula represents the average capacity constraint;
representing average production cycle constraint in a formula;
formula four represents a non-negative integer vector;
formula five represents a non-negative real number vector;
wherein, X1: configuring vectors according to the number of the AGV; x2: configuring a vector for the AGV running speed; y: aggregating node processing rate configuration vectors; thetai min: a capacity demand prediction value; p is a radical ofi: capacity demand prediction probability; t isj max: predicting a production cycle demand; p is a radical ofj: a production cycle demand prediction probability;
represents the minimum investment cost of the inter-vehicle layer; theta { X }1，X2Y represents the average capacity constraint value of the vehicle interlayer; t { X1，X2Y represents the average production cycle constraint value of the vehicle interlayer;
the unit layer resource allocation optimization queuing network description model is concretely as follows:
an objective function:
constraint conditions are as follows:
Z1，R1∈N+- - -formula nine;
Z2，R2∈R+- - -equation ten;
formula six represents the minimum total investment cost;
formula seven represents the average capacity constraint;
formula eight represents the average production cycle constraint;
formula nine represents a non-negative integer vector;
formula ten represents a non-negative real number vector;
wherein Z is1: configuring vectors by the number of the processing machines; z2: configuring a vector for the running speed of the processing machine tool; r1: configuring a vector by the number of robots; r2: configuring a vector for the running speed of the robot; thetai min: capacity requirements for step-by-step conversion; tau isj min: the production cycle requirement of the step-by-step transformation;
represents the minimum total investment cost of the unit layer; formula seven: theta { Z1，Z2，R1，R2Representing the average capacity constraint value of the unit layers; formula eight: t { Z1，Z2，R1，R2Represents the average production cycle constraint value of the unit layer;
the solutions of the vehicle-level resource allocation optimization queuing network model and the unit-level resource allocation optimization queuing network description model represent system performance indexes of effective schemes.
3. The method of claim 2, wherein the step of:
in step D, constructing a confidence domain-sequence quadratic programming algorithm embedded in the queuing network model specifically comprises
Step D1: decomposing a quadratic programming subproblem;
the method comprises the following steps of adopting an external approximation method to relax constraints in an inter-vehicle layer resource configuration optimization queuing network model and a unit layer resource configuration optimization queuing network description model, decomposing an original nonlinear constraint optimization problem into a series of quadratic programming subproblems with inequality constraints, and adopting a convex method if the relaxed quadratic programming subproblems are non-convex, so that the quadratic programming subproblems can calculate gradient of decision variables and determine the search direction of an iterative process, wherein the specific formula is as follows:
quadratic programming sub-problem:
wherein the content of the first and second substances,
for the objective function f (x) at the current iteration point xkP is the direction vector, H (x)k) Is f (x) at xkHessian matrix of (g)i(xk) Is a constraint function;
step D2: solving a quadratic programming sub-problem by adopting a trust domain method;
after the search direction of the iterative process is determined, a small neighborhood of a current iterative point is given in each iteration as a trust domain, then a subproblem is solved in the neighborhood to obtain a trial step length, then a queuing network model is called to calculate the actual descending quantity of a target function and the descending quantity of a quadratic model function, the ratio of the two is used as an evaluation function to determine whether the trial step length is accepted or not and determine the trust domain of the next iteration, the process is iterated repeatedly until a satisfactory approximate optimal solution is obtained, and the specific formula is as follows:
trusted domain form:
wherein m isk(s) is an approximate quadratic model of the objective function f (x), s ═ x-xkIn order to be the step size vector,
is f (x) at the current iteration point xkTransposed matrix of gradients, H (x)k) Is f (x) at xkHessian matrix of (A) (. DELTA)kIs the confidence domain radius.
4. The method of claim 1, wherein the step of:
the specific steps of constructing a unit-workshop hierarchical algorithm framework and solving the overall unit layout and equipment resource allocation optimization scheme of the workshop are as follows:
step E1: in a queuing network modeling solving link, namely in the step C, the production units are progressively aggregated into nodes of a queuing network model in a production workshop;
step E2: in the resource allocation optimization link, namely step D, the resource allocation result of the workshop layer node is converted into a performance constraint design index of the unit layer resource allocation optimization queuing network description model in a descending decomposition mode;
step E3: and obtaining the whole unit layout and the equipment resource allocation scheme of the production workshop according to the workshop area constraint coordination configuration result.
5. The method of claim 4, wherein the step of:
step E1 specifically includes:
firstly, establishing a production unit queuing network model with resource synchronization constraint, and calculating unit performance indexes by an approximate solving method; then, according to the unit performance index, aggregating each production unit into a node of a production workshop queuing network model, then establishing a state-related random batch-handling production workshop queuing network model, and calculating the workshop performance index by an approximate solving method, wherein the specific formula is as follows:
{Θn，Tn}→{μn，sn 2}，
wherein, thetan: average production Rate, T, of production Unit nn: average production cycle, μ of production unit nn: processing Rate of polymerization, sn 2: the square coefficient of variation of the processing time of the polymerization; → represents approach: infinitely close, and do not coincide with each other.
6. The method of claim 5, wherein the step of:
step E2 specifically includes:
firstly, establishing a random nonlinear mixed integer programming model for optimizing the resource allocation of a production workshop, solving a workshop resource allocation result by a trust domain algorithm embedded in a queuing network model, then converting the workshop resource allocation result into a performance index constraint requirement of a random programming model of a production unit according to the workshop resource allocation result, then establishing a random nonlinear mixed integer programming model for optimizing the resource allocation of the production unit, and solving a unit resource allocation result by the trust domain algorithm embedded in the queuing network model; the specific formula is as follows:
wherein, Y: aggregate node processing rate configuration vector, θi min: capacity requirement of step-wise conversion, τj min: the production cycle requirement of the step-by-step transformation; → represents approach: infinitely close, and do not coincide with each other.
7. The method of claim 6, wherein the step of:
step E3 specifically includes:
coordinating and correcting the configuration result by the constraint condition of the workshop area, and finally verifying whether the total sum of the areas of all the production units after all the equipment is configured is required to be loosened or not; when the configuration result does not satisfy the total area constraint condition, performing necessary tightening on the performance index constraint of the vehicle interlayer, and then performing layered optimization; through repeated iteration processes, an optimal solution meeting global constraint conditions of the whole system is finally obtained; obtaining the whole unit layout and equipment resource allocation scheme of the production workshop according to the optimal solution; the constraint conditions of the workshop area are as follows:
wherein S isn: the sum of the areas of various devices configured by the unit n is as follows: coefficient of relaxation, S*: the area of a production workshop.
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