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CN-121996876-A - Papermaking mixed integer nonlinear optimization method, device, equipment and storage medium

CN121996876ACN 121996876 ACN121996876 ACN 121996876ACN-121996876-A

Abstract

The invention relates to the technical field of papermaking process optimization, and discloses a papermaking mixed integer nonlinear optimization method, a device, equipment and a storage medium. The method comprises the steps of receiving a mixed integer nonlinear programming model to be optimized, calling a feasible pump to perform initial iterative optimization on the mixed integer nonlinear programming model to be optimized to obtain a preliminary optimization result, obtaining a plurality of behavior state quantities in the initial iterative optimization process, calling an external approximation main loop to perform external approximation main loop iterative optimization on the preliminary optimization result when an optimization switching condition is met until a convergence condition is met, outputting a target optimization result, and determining optimization operation parameters of the papermaking process based on the target optimization result. According to the scheme, the starting time is dynamically switched based on the iteration characteristics of the feasible pump stage, and the invalid iteration caused by fixed stage division is reduced through the global optimization solving concept of staged and collaborative optimization, so that the solving efficiency and the robustness of the complex industrial MINLP problem are improved.

Inventors

  • MAN YI
  • CHEN HAOZHOU

Assignees

  • 华南理工大学

Dates

Publication Date
20260508
Application Date
20260410

Claims (10)

  1. 1. A method for mixed integer nonlinear optimization of papermaking, the method comprising: receiving a mixed integer nonlinear programming model to be optimized, wherein the mixed integer nonlinear programming model to be optimized is determined based on a target problem to be optimized; Invoking a feasible pump to initialize iterative optimization of the mixed integer nonlinear programming model to be optimized to obtain a preliminary optimization result; Acquiring a plurality of behavior state quantities in an initialization iterative optimization process; Determining whether an optimized switching condition is met or not based on state quantity comparison thresholds corresponding to the behavior state quantities; When the optimization switching condition is met, an external approximation main loop is called to carry out external approximation main loop iterative optimization on the preliminary optimization result until the convergence condition is met, and then a target optimization result is output; And determining the optimized operation parameters of the papermaking process based on the target optimization result.
  2. 2. The method for optimizing mixed integer nonlinear optimization of papermaking according to claim 1, wherein the step of calling a feasible pump to perform initial iterative optimization on the mixed integer nonlinear programming model to be optimized, and the step of obtaining a preliminary optimization result comprises the following steps: Determining the viable pump configuration parameters; Carrying out continuous relaxation problem solving on the mixed integer nonlinear programming model to be optimized by combining the feasible pump configuration parameters to obtain a relaxation solution result, Based on the relaxation solution result, initial iteration input data of feasible pump initialization iteration optimization is obtained; And carrying out initial iterative optimization on the mixed integer nonlinear programming model to be optimized based on the initial iterative input data to obtain a preliminary optimization result.
  3. 3. The method of claim 1, wherein the performing a continuous relaxation problem solution on the mixed integer nonlinear programming model to be optimized in combination with the feasible pump configuration parameters to obtain a relaxation solution result comprises: Relaxing integer constraint of the mixed integer nonlinear programming model to be optimized, and changing integer variables From the feasible domain of (2) Relaxed into Obtaining a continuous relaxation nonlinear programming problem; Wherein, the Is that Is the original feasible domain of (1) Is a set of integers of (c), Is after relaxation Is used in the constraint of (a), At the position of Any real number is taken from the interval, For the lower bound of the two-dimensional space, As a variable Is defined by the lower bound vector of (c), As an upper bound of the two-dimensional space, As a variable Upper bound vector of (2); solving the continuous relaxation nonlinear programming problem by combining a relaxation formula to obtain a relaxation solution result; wherein, the relaxation formula is as follows: ; Wherein, the To be as an objective function A minimized optimization objective; As an objective function, i.e. , As a continuous variable, the number of the variables, As a function of the integer variable(s), As corresponding variable And Is a transpose of the objective function coefficient vector; as a result of the non-linear constraint, Index of what nonlinear constraint is; As a result of the linear constraint, As corresponding continuous variable Is used for the coefficient matrix of (a), Is a corresponding integer variable Is used for the coefficient matrix of (a), Is a constant vector.
  4. 4. The method for non-linear optimization of a papermaking mixed integer according to claim 3, wherein the performing initial iterative optimization on the to-be-optimized mixed integer non-linear programming model based on the initial iterative input data to obtain a preliminary optimization result comprises: And carrying out feasible pump iteration main circulation on the mixed integer nonlinear programming model to be optimized by adopting an internal and external double-layer circulation structure based on the initial iteration input data, wherein each internal iteration comprises the following steps: Based on the projection point obtained by the previous iteration, adding the external approximation cutting of the nonlinear constraint at the point to the current linearization model, constructing and solving a feasible pump nonlinear programming sub-problem with the minimum norm distance from the previous projection point as a target, and obtaining an integer solution; Fixing the initial integer solution, solving a feasible pump nonlinear sub-problem with the square of the Euclidean distance between the minimum and the last projection point as a target, and obtaining a continuous solution; Determining a projection distance between the current continuous solution and the previous projection point; If the projection distance is smaller than the convergence tolerance, ending iteration, and determining a current feasible solution as the preliminary optimization result, wherein the current feasible solution is determined based on the integer solution and the continuous solution; And if the projection distance is not smaller than the convergence tolerance, determining the current feasible solution as initial iteration input data and returning to a main loop step of performing feasible pump iteration on the mixed integer nonlinear programming model to be optimized.
  5. 5. The method of claim 4, wherein the obtaining a plurality of behavior state quantities in an iterative optimization process comprises: in initializing the iterative optimization process, performing behavior monitoring and state quantity calculation synchronously to determine a plurality of behavior state vectors, comprising: recording an integer solution of each external iteration, and marking the integer solution as an integer solution stable state if the integer solution in the external iteration is unchanged under the continuous preset times; Recording the projection distance of each internal iteration, and marking as a stable state of the projection process if the current projection distance is smaller than a preset distance; And recording the solving result of the nonlinear programming problem in each projection stage, and marking the nonlinear programming problem as a continuous feasible state if solutions meeting all constraints exist in the nonlinear programming sub-problem under the continuous solving times.
  6. 6. The method according to claim 4, wherein when the optimization switching condition is satisfied, invoking the external approximation main loop to perform the external approximation main loop iterative optimization on the preliminary optimization result until the convergence condition is satisfied, and outputting the target optimization result comprises: Constructing an initial mixed integer linear programming main problem based on the initial optimization result, an objective function upper bound and an initial linearization cutting set, wherein the initial linearization cutting set is determined based on the external approximation cutting of adding nonlinear constraint at the point to a corresponding linearization model in each round of iteration; determining a candidate integer solution and a current lower bound based on the mixed integer linear programming main problem; Fixing the candidate integer solution, and solving a nonlinear programming sub-problem to obtain a solving result; outputting the target optimization result when the solving result meets all constraint conditions and iteration conditions; The main problems of the mixed integer linear programming are as follows: ; Wherein, the By a variable A minimized optimization objective; an upper bound variable which is an objective function and is used for linearizing the objective function; at the point for the objective function A function value at the location; at the point for the objective function Gradient vector at, representing the objective function The direction of the rate of change at that point; the inner product of the gradient vector and the difference vector is the objective function At the position of A first order taylor expansion linear approximation term at; As a variable Point of attachment Is a difference vector of (a); The cutting points generated in the FP stage; And Respectively the continuous variable at the cutting point And integer variable Is used for the value of (a) and (b), The cutting points; to cut all indexes in a collection ; The generated cutting set for the FP stage comprises index sets of all linearization cutting; Is the first At the point of the nonlinear constraint function Gradient vector at representing constraint function The direction of the rate of change at that point; the inner product of the gradient vector and the difference vector is a constraint function At the position of A first order taylor expansion linear approximation term at; The nonlinear programming sub-problem is: ; Wherein, the For a fixed integer solution A post objective function; For a fixed integer solution A nonlinear constraint is performed; For a fixed integer solution The linear constraint of the latter.
  7. 7. The method of claim 6, wherein when there is an unsatisfied constraint on the solution, the method comprises: solving a feasibility restoration problem and forming feasibility cutting; Adding new cuts to the linearization master problem, generating optimality cuts, constrained by linear inequality Is taken to be such that Always greater than or equal to objective function To approach the real objective function in a successive approximation; Wherein, the ; Generating a feasibility cutting, and determining and excluding a region which causes infeasibility through the feasibility cutting when the nonlinear programming sub-problem is infeasible; wherein when present When the nonlinear programming sub-problem is determined to be infeasible, the infeasible point is taken as a new cutting point And performing first-order Taylor expansion on the corresponding nonlinear constraint function at the point, and converting the linear approximation constraint into a linear approximation constraint, wherein the linear approximation constraint is as follows: ; Wherein, the Is the opposite number of constraint function values.
  8. 8. A papermaking mixed integer nonlinear optimization apparatus, the apparatus comprising: The receiving module is used for receiving a mixed integer nonlinear programming model to be optimized, and the mixed integer nonlinear programming model to be optimized is determined based on a target problem to be optimized; the preliminary optimization result determining module is used for calling a feasible pump to perform initial iterative optimization on the mixed integer nonlinear programming model to be optimized to obtain a preliminary optimization result; The behavior state quantity acquisition module is used for acquiring a plurality of behavior state quantities in the initialization iterative optimization process; The switching condition determining module is used for determining whether the optimized switching condition is met or not based on state quantity comparison thresholds corresponding to the behavior state quantities; The target optimization result output module is used for calling an external approximation main loop to perform external approximation main loop iterative optimization on the preliminary optimization result when the optimization switching condition is met, and outputting a target optimization result after the convergence condition is met; And the optimized operation parameter determining module is used for determining the optimized operation parameters of the papermaking process based on the target optimized result.
  9. 9. An electronic device comprising a memory and at least one processor, the memory having instructions stored therein, the at least one processor invoking the instructions in the memory to cause the electronic device to perform the steps of the papermaking hybrid integer nonlinear optimization method recited in any one of claims 1-7.
  10. 10. A computer readable storage medium having instructions stored thereon, which when executed by a processor, perform the steps of the papermaking hybrid integer nonlinear optimization method recited in any one of claims 1-7.

Description

Papermaking mixed integer nonlinear optimization method, device, equipment and storage medium Technical Field The invention belongs to the technical field of papermaking process optimization, and particularly relates to a papermaking mixed integer nonlinear optimization method, a device, equipment and a storage medium. Background SCIP solver is one of the currently globally leading non-commercial universal mixed integer nonlinear programming (MINLP) solvers. The core adopts a Branch-and-Bound (B & B) framework, and fuses a cutting plane (Cutting Planes) and various heuristic algorithms to accelerate solving. The typical process for solving the MINLP problem comprises the steps of simplifying an original model through a pre-solving stage, removing redundant constraint, fixing partial variable values, and tightening the variable value range through constraint propagation technology, so that the complexity of the problem is reduced. In a continuous relaxation stage, an algorithm ignores integer constraint to obtain a nonlinear programming relaxation problem, and a lower bound estimation of the original problem is obtained by solving the relaxation problem. The branching operation is a core mechanism of SCIP, when the integer variable value in the relaxation solution is a fraction, the algorithm selects the branching variable and creates two child nodes, and corresponding boundary constraints are respectively added to exclude the current fraction solution. To accelerate convergence SCIP integrates a cut plane generation technique, tightening the feasible region of the relaxation problem by adding effective linear or convex constraints. Meanwhile, the algorithm adopts various heuristic strategies to search for a high-quality feasible solution in the searching process so as to provide an upper bound reference. The pruning mechanism then uses the upper and lower bound information to exclude branches that are unlikely to contain the optimal solution, and the algorithm terminates when all nodes are processed or a convergence condition is reached. SCIP adopts a modularized design architecture, supports integration of various external solvers (such as IPOPT is used for processing nonlinear sub-problems, CPLEX is used for solving linear programming problems), and has strong problem adaptability and expansibility. SCIP has perfect solving function, but certain remarkable limitations still exist when dealing with the specific complex MINLP problems of papermaking production. First, it is difficult to guarantee global optimality for non-convex problems, whose branch-and-bound solution framework is theoretically suitable for global optimization, but whose efficiency depends on the quality of the relaxation technique. For strong non-convex and nonlinear production process constraints commonly existing in papermaking production, such as reaction dynamics engineering in pulping process, mass and heat transfer models in paper drying process and the like, the convex relaxation of the constraint structure is difficult, so that model calculation is difficult, and timeliness requirements of actual production scheduling or real-time optimization are difficult to meet. Secondly, the papermaking production optimization model has large scale and multiple variables, and when facing such high-dimensional problems, the branch tree becomes extremely huge, and is difficult to satisfactorily solve in a feasible time. Particularly when dealing with multi-time-period production scheduling problems, the problem size grows linearly with increasing time periods, making the solution process more difficult. The difficulty in acquiring the initial feasible solution is also a significant defect of SCIP, the algorithm efficiency is seriously dependent on the high-quality initial upper bound for effective pruning, but the complex constraint characteristic of the papermaking production problem makes the initial feasible solution difficult to acquire. Although various heuristic methods are built in, when a papermaking model with complex process constraints is processed, the success rate of the methods is low, so that effective upper bound information is lacking in the initial stage of searching, and pruning efficiency is low. Finally, as a general solver, the algorithm of the general solver comprises a large number of general strategies and parameters designed for coping with various problem types, but lacks of stage division and adaptive solving strategies aiming at the characteristics of papermaking production models, such as identification and utilization of specific constraint structures, searching strategy adjustment aiming at process characteristics and the like, and the solving efficiency is not as good as that of a custom algorithm specially designed for the papermaking industry. The traditional Outer approximation algorithm (Outer-Approximation) is a class of classical algorithms for solving convex MINLP problems, the basic idea of which is to