Column and constraint generation method for feasibility pump acceleration

Abstract

The invention discloses a feasible pump acceleration column and constraint generation method, and relates to the technical field of energy system planning, and the method comprises the steps: obtaining basic parameters of a three-layer mixed integer optimization problem, and constructing an original problem model based on the basic parameters; a column and constraint generation framework is adopted, an original problem model is decomposed into a main problem model and sub-problem models, dual processing is conducted on the sub-problem models, and a single-layer max model is obtained; calculating through a feasible pump accelerated column and constraint generation algorithm to obtain a main problem target solution and a sub-problem target solution, and updating the lower bound and the upper bound of an original problem model; judging whether a convergence condition is met or not, and if yes, directly outputting a target solution; and if not, iterative loop calculation is carried out until the convergence condition is met, and a target solution is obtained. According to the method, the global optimality of the solution can be guaranteed, the solving efficiency can be remarkably improved, and the method has good expandability and is suitable for solving the large-scale three-layer mixed integer optimization problem.

Description

Technical Field

[0001] This invention relates to the field of energy system planning, and more specifically to a method for generating columns and constraints for feasibility pump acceleration. Background Technology

[0002] In the field of energy system resilience enhancement planning, three-level optimization models are widely used to describe the game-theoretic behavior among planners, attackers, and schedulers. These models are typically mixed-integer three-level min-max-min optimization problems, exhibiting high non-convexity and combinatorial explosion properties, making them extremely difficult to solve. Currently, mainstream solution methods can be divided into two categories: heuristic algorithms and exact algorithms. Firstly, heuristic algorithms, such as genetic algorithms, particle swarm optimization, and simulated annealing, quickly obtain approximate solutions through search strategies and are commonly used methods for solving large-scale mixed-integer programming problems. However, because heuristic algorithms are usually based on probabilistic search or greedy strategies, they are prone to getting trapped in local optima and cannot guarantee the global optimality of the obtained solution. In three-level optimization problems, due to the complexity and nonlinearity of the problem, there may be a large gap between the local optimum and the global optimum, thus affecting the planning performance.

[0003] Secondly, there are exact algorithms, such as the column and constraint generation algorithm. By decomposing the original three-level problem into a main problem and subproblems, and iteratively adding variables and constraints, it can guarantee convergence to the global optimum. However, traditional column and constraint generation algorithms rely on branch and bound algorithms. If the initial solution obtained by the branch and bound algorithm is of poor quality, it will severely reduce the search efficiency for the optimal solution. In the column and constraint generation algorithm, each iteration needs to completely solve both the main problem and the subproblems. When both are mixed-integer linear programming problems, the solution time will increase exponentially as the problem size increases (e.g., the number of integer variables increases).

[0004] In summary, there is a significant contradiction between solution speed and solution quality in solving three-level mixed integer optimization problems. How to improve solution efficiency without sacrificing optimality is a core technical challenge that urgently needs to be addressed in this field.

[0005] Therefore, there is an urgent need for a feasible pump-accelerated column and constraint generation method to improve solution efficiency without sacrificing optimality. Summary of the Invention

[0006] This invention provides a feasible pump-accelerated column and constraint generation method, which aims to solve the problem that it is difficult to balance the solution speed and global optimality in traditional algorithms, and achieve efficient and accurate solution of three-level mixed integer optimization problems.

[0007] This invention provides a method for generating columns and constraints for feasible pump acceleration, which specifically includes the following steps: S1. Obtain the basic parameters of the three-level mixed integer optimization problem, and construct the original problem model based on the basic parameters; S2. Using a column and constraint generation framework, the original problem model is decomposed into a main problem model and sub-problem models, and the sub-problem models are dualized to obtain a single-layer max model. S3. Calculate the objective solution of the current main problem and the objective solution of the current subproblem using the column and constraint generation algorithm accelerated by the feasibility pump, and update the lower and upper bounds of the original problem model. S4. Determine whether the relative difference between the lower bound and the upper bound satisfies the convergence condition. If yes, output the final objective solution directly. If no, add the cut corresponding to the objective solution of the current subproblem to the main problem model, and re-execute S3 until the final objective solution is obtained.

[0008] Preferably, in S1, the objective function of the original problem model is: ; in, For outer layer decision variables, and For mid-level attack variables, For inner-layer operating variables, 'a' represents the planning cost parameter and 'c' represents the system operating cost parameter. This is the matrix transpose symbol; The constraints of the original problem model include Feasible region constraints Attack capability constraints Attack capability constraints and system operation constraints; The The expression for the feasible region constraint is: ; The The expression for the attack capability constraint is: ; The The expression for the attack capability constraint is: ; The expression for the system operation constraints is: ; Where A, B, C, D, E, F, and G are the coefficient matrices in the constraints, and d, e, f, and is a constant vector in the constraints.

[0009] Preferably, the outer decision variable This represents system planning or investment decisions; it is a binary variable that takes the value 0 or 1. The mid-level attack variables represent the attacker's attack strategy, where, It is a binary variable, taking the value 0 or 1. For continuous variables; The inner layer running variables is a continuous variable, representing the system's target scheduling response when facing an attack.

[0010] Preferably, in S3, the main problem model makes a target investment decision based on the set of attack scenarios returned by the sub-problem models; The sub-problem model finds the attack scenario that maximizes the system's operating cost based on the target investment decision given by the main problem model.

[0011] Preferably, the objective function of the main problem model is: ; in, For continuous auxiliary variables, For the first k The second child problem returns the inner runtime variables under the worst-case attack scenario. The main problem model The expressions for the feasible region constraints are the same as those for the original problem model; The expression for the cost approximation constraint of the main problem model is: ; in, The index is the number of iterations. This is the current cycle number; The expressions for the system operation constraints of the main problem model are: ; in, and For the first k The second-child problem returns the mid-level attack variables under the worst-case attack scenario. The objective function of the sub-problem model is: ; Sub-problem model Attack capability constraints and The expression for the attack capability constraint is the same as that in the original problem model; The expressions for the system operation constraints of the subproblem model are: ; in, These are the outer-layer decision variables under the given target investment decision in the main problem model.

[0012] Preferably, in S2, the specific content of the dual processing includes: By using the Karush-Kuhn-Tucker condition, the inner-level min model of the subproblem is equivalently transformed into its dual form max model, and the overall subproblem is transformed into a single-level max model. The objective function of the single-layer max model is: ; Single-layer max model Attack capability constraints The expressions for attack capability constraints and system operation constraints are the same as those for the subproblem model; The formula for the dual stationarity condition of a single-layer max model is: ; The expression for the complementary relaxation linearization of a single-layer max model is: ; ; in, These are the numbers of the original constraints and their corresponding dual variables. As dual variables, The auxiliary binary variable introduced for linearization of large M. M This is a relatively large constant introduced for linearization using the Big M method.

[0013] Preferably, the specific content of S3 includes: S31. Set the iteration counter, the initial upper bound of the original problem model, and the initial lower bound of the original problem model; S32. Using the feasibility pump algorithm, the initial integer solution to the main problem is obtained; S33. Input the initial integer solution of the main problem into the branch and bound algorithm to solve the main problem, obtain the objective solution of the main problem, and update the lower bound of the original problem model; S34. Input the objective solution of the main problem into the subproblem, and use the feasibility pump algorithm to obtain the initial integer solution of the subproblem; S35. Input the initial integer solution of the subproblem into the branch and bound algorithm to solve the subproblem, obtain the objective solution of the subproblem, and update the upper bound of the original problem model.

[0014] Preferably, the specific process of the feasibility pump algorithm for solving the initial integer solution includes: S321. Convert the binary variables in the main problem model and the single-layer max model into continuous variables to obtain a linear model containing only continuous variables. S322. Solve the linear model to obtain the current continuous solution; S323. Round the initial continuous solution to obtain the current integer solution; S324. Determine whether the current integer solution satisfies all the constraints of the original problem model. If it does, output the current integer solution directly as the initial integer solution. If it does not, select a new continuous solution and continue to execute S325. S325. Round the new continuous solution to obtain a new integer solution; S326. Determine whether the new integer solution has appeared in the previous loop. If so, randomly flip a few bits and return to S324 to loop. If not, directly return to S324 to loop until an initial integer solution that satisfies all the constraints of the original problem model is output.

[0015] Preferably, the new continuous solution is the continuous solution within the feasible region of the linear model that has the shortest Euclidean distance to the current integer solution.

[0016] Preferably, in S4, the formula for the convergence condition is: ; in, UB This represents the upper bound of the original problem model derived from the subproblems. LB This represents the lower bound of the original problem model derived from the main problem. This represents the set convergence condition value.

[0017] In summary, compared with traditional technologies, the beneficial effects of the feasible pump acceleration column and constraint generation method of the present invention are as follows: (1) Guaranteeing the global optimality of the solution: The feasibility pump-accelerated column and constraint generation method proposed in this invention can guarantee the global optimality of the solution. By continuously adding variables and constraints corresponding to the worst attack scenarios returned by subproblems to the main problem, it finally converges to the global optimal solution. The feasibility pump algorithm only provides the initial solution and does not intervene in the logic of the branch and bound algorithm for solving mixed integer optimization problems. Therefore, the convergence effect of the feasibility pump-accelerated column and constraint generation method can be guaranteed.

[0018] (2) Improve the efficiency of solving three-level mixed integer optimization problems: This invention introduces the feasibility pump algorithm into the traditional column and constraint generation algorithm to improve the efficiency of solving three-level mixed integer optimization problems. Before solving each round of mixed integer programming problems, the feasibility pump algorithm is used to quickly obtain high-quality integer initial solutions and warm-start the branch and bound algorithm, thereby accelerating the solution of mixed integer programming problems.

[0019] (3) The algorithm has good scalability: As the problem size and the dimension of integer variables increase, the column and constraint generation method based on feasibility pump shows a more significant acceleration effect. In problems with more complex integer structures and larger combinatorial spaces, this method can obtain feasible solutions more efficiently and promote convergence, demonstrating excellent scalability and engineering adaptability, and is particularly suitable for solving large-scale three-level mixed integer optimization problems. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the overall process framework of a feasible pump acceleration column and constraint generation method according to the present invention. Figure 2 This is a flowchart of the overall algorithm for generating columns and constraints for a feasible pump acceleration method according to the present invention. Figure 3 This is a flowchart of the feasibility pump algorithm for a feasibility pump acceleration column and constraint generation method according to the present invention. Detailed Implementation

[0021] This invention proposes a method for generating columns and constraints for feasible pump acceleration. The technical method of this invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application.

[0022] The following description of the embodiments is merely illustrative and is in no way intended to limit the scope of this application and its application or use.

[0023] Techniques, systems, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, they should be considered part of the instruction manual.

[0024] In the examples shown and discussed herein, any specific values ​​should be interpreted as exemplary only and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0025] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0026] Example 1 This embodiment presents an overall process framework for a feasible pump acceleration column and constraint generation method, such as... Figure 1 As shown, the specific steps are as follows: S1. Obtain the basic parameters of the three-level mixed integer optimization problem, and construct the original problem model based on the basic parameters; S2. Using a column and constraint generation framework, the original problem model is decomposed into a main problem model and sub-problem models, and the sub-problem models are dualized to obtain a single-layer max model. S3. Calculate the objective solution of the current main problem and the objective solution of the current subproblem using the column and constraint generation algorithm accelerated by the feasibility pump, and update the lower and upper bounds of the model. S4. Determine whether the difference between the lower bound and the upper bound of the model satisfies the convergence condition. If yes, output the final target solution directly. If no, add the cut corresponding to the worst attack scenario of the current subproblem target solution to the main problem, and re-execute S3 until the final target solution is obtained.

[0027] Example 2 This embodiment uses a column and constraint generation framework to decompose the original problem model into a main problem model and sub-problem models, and performs dual processing on the sub-problem models to obtain a single-layer max model. The calculation process based on the feasibility pump is also demonstrated, as follows: The original problem model of the three-level mixed integer optimization problem solved in this embodiment has a general and compact expression, and its objective function is as follows: ; in, This is the matrix transpose symbol. This is an outer-layer decision variable, representing system planning or investment decisions, and takes the value 0 or 1. and This is a mid-level attack variable, representing the attacker's attack strategy. A 0 / 1 variable, such as the variable used to select the target of the attack. For continuous variables, such as the attack vector in a fake data injection attack. These are the inner-layer operational variables, which are continuous variables representing the system's optimal scheduling response when facing attacks, such as unit output and load reduction. 'a' represents the planning cost parameter, and 'c' represents the system operating cost parameter.

[0028] The original problem model must satisfy the following constraints: ; ; ; ; ; Where A, B, C, D, E, F, and G are the coefficient matrices in the constraints, and d, e, f, and The constant vector in the constraints. Programming variables. The feasible domain constraints include investment budget, upper limit on the number of constructions, etc., attack variables and Attack capability constraints include attack quantity limits and attack logic, while system operation constraints include power balance, device capacity, and power flow constraints. The variable type definition explicitly distinguishes between integer and continuous variables. It is a real number.

[0029] Since the original problem model belongs to a three-level optimization structure of min-max-min mixed integers, it cannot be directly solved by commercial solvers. Therefore, the implementation method adopts a column and constraint generation framework to decompose the original problem into a main problem and sub-problems. By iteratively solving the problem and updating the upper and lower bounds, the optimal solution is gradually approached.

[0030] The main problem is responsible for making the optimal investment decision based on the set of attack scenarios returned by the subproblems. The objective function of the main problem model is: ; The main problem model must satisfy the following constraints: ; ; ; ; in, As an auxiliary variable, This is the matrix transpose symbol. For the first k The inner runtime variables returned by the second child problem under the worst-case attack scenario and For the first The second-child problem returns the mid-level attack variable under the worst-case attack scenario.

[0031] The objective function of the main problem model is used to determine the planning scheme that minimizes the sum of the total investment cost and the system's operating cost under the worst-case scenario. The constraints include investment decision variables. Constraints; through auxiliary variables By progressively approximating the system operating cost under the worst-case attack scenario, we ensure that the target value of the main problem is not lower than the actual cost of any exposed scenario; k The worst-case attack scenario and investment decision variables returned by the second child problem Coupling is implemented to ensure that the system's operating variables satisfy operational constraints such as power balance, capacity, and power flow under this attack. In each iteration, a new set of variables and constraints is added to the main problem, forming a mechanism for the simultaneous generation of columns and constraints, gradually updating and tightening the lower bound of the original problem model.

[0032] The decomposed subproblems are responsible for finding attack scenarios that maximize the system's operating cost, given the investment decision options provided by the main problem. The objective function of the subproblem model is: ; The sub-problem model must satisfy the following constraints: ; ; ; ; in, These are the outer-layer decision variables under the given target investment decision in the main problem model.

[0033] The objective function of the sub-problem is used to determine the investment plan. The attack strategy aims to maximize system operating costs. Constraints include attack variables. and Attack capability constraints and investment decisions Lower system operation constraints.

[0034] Because the subproblem has a max-min two-layer structure, existing commercial solvers cannot handle it directly. This embodiment uses the Karush-Kuhn-Tucker (KKT) conditions to equivalently transform the inner min model into its dual max model, thus rewriting the overall subproblem as a single-layer max model, making it solvable. ; In a single-layer max model and The attack capability constraints and system operation constraints are the same as those in the sub-problem model; The formula for the dual stationarity condition of a single-layer max model is: ; The formula for the complementary relaxation linearization condition of the single-layer max model after linearization by the Big M method is: ; ; in, i These are the numbers of the original constraints and their corresponding dual variables. As dual variables, The auxiliary binary variable introduced for linearization of large M. M This is a relatively large constant introduced for linearization using the Big M method.

[0035] After decomposition and duality, both the main problem and its subproblems become mixed-integer linear programming models. Due to the large number of integer variables, solving them using the branch and bound algorithm is time-consuming.

[0036] Therefore, this embodiment proposes a feasibility pump-accelerated column and constraint generation method. It embeds a feasibility pump acceleration module into the traditional column and constraint generation framework to quickly generate high-quality integer initial solutions to warm-start the branch and bound algorithm, thus significantly shortening the solution time while ensuring optimality. Figure 2 As shown, the steps of the algorithm for generating columns and constraints for feasibility pump acceleration include: S1: Set the iteration counter, initial upper bound, initial lower bound, and convergence tolerance.

[0037] S2: Use the feasibility pump algorithm to quickly generate the initial integer solution to the main problem.

[0038] S3: Use this solution as the input branch and bound algorithm to solve the main problem.

[0039] S4: Obtain the optimal solution to the main problem and update the lower bound of the model.

[0040] S5: Input the investment decision obtained from the main problem into the subproblem, and use the feasibility pump algorithm to quickly generate the initial integer solution of the subproblem.

[0041] S6: Use this solution as a warm-start input branch-bound algorithm to solve the subproblem.

[0042] S7: Obtain the optimal solution to the subproblem and update the upper bound.

[0043] S8: Determine if convergence has occurred. If convergence has occurred, output the optimal solution. If convergence has not occurred, add the cut corresponding to the worst-case attack scenario obtained from solving the subproblem to the main problem, and execute the next iteration of the solution.

[0044] The formula for determining whether a convergence has occurred is: ; in, UB This represents the upper bound of the original problem model derived from the subproblems. LB This represents the lower bound of the original problem model derived from the main problem. This represents the set convergence condition value.

[0045] To avoid the lengthy computations caused by the branch-and-bound algorithm starting with low-quality solutions when solving mixed-integer programming models, this embodiment embeds a feasibility pump algorithm before each solution to the main problem and subproblems to obtain high-quality initial integer solutions, thereby accelerating the solution of mixed-integer programming problems. For example... Figure 3 As shown, the feasibility pump algorithm flow includes: S11: Relax all binary variables in the mixed integer programming model to continuous variables, resulting in a linear model containing only continuous variables.

[0046] S12: Solve the relaxed linear model to obtain the current continuous solution.

[0047] S13: Round the current continuous solution to obtain the current integer solution.

[0048] S14: Determine if the current integer solution satisfies all constraints of the original problem model. If it does, output the solution directly as the initial integer solution for the warm start of the branch and bound algorithm. If there is a constraint violation, find the continuous solution with the shortest Euclidean distance to the current integer solution within the feasible region of the relaxed linear model, and use it as the new continuous solution.

[0049] S15: Round the new continuous solution to obtain a new integer solution.

[0050] S16: Determine if the new integer solution has appeared in the previous loop. If so, randomly flip a small number of bits and return to step S14 to avoid an infinite loop. Otherwise, directly return to step S14 and loop until an initial integer solution that satisfies all the constraints of the original problem model is output.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical methods of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical methods of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical methods to deviate from the spirit and scope of the technical methods of the present invention.

Claims

1. A method for generating columns and constraints for feasible pump acceleration, characterized in that, Includes the following steps: S1. Obtain the basic parameters of the three-level mixed integer optimization problem, and construct the original problem model based on the basic parameters; S2. Using a column and constraint generation framework, the original problem model is decomposed into a main problem model and sub-problem models, and the sub-problem models are dualized to obtain a single-layer max model. S3. Calculate the objective solution of the current main problem and the objective solution of the current subproblem using the column and constraint generation algorithm accelerated by the feasibility pump, and update the lower and upper bounds of the original problem model. S4. Determine whether the relative difference between the lower bound and the upper bound satisfies the convergence condition. If so, directly output the final target solution. If not, add the cut corresponding to the objective solution of the current subproblem to the main problem model, and re-execute S3 until the final objective solution is obtained.

2. The method for generating columns and constraints for feasible pump acceleration according to claim 1, characterized in that, In S1, the objective function of the original problem model is: ; in, For outer layer decision variables, and For mid-level attack variables, For inner-layer operating variables, 'a' represents the planning cost parameter and 'c' represents the system operating cost parameter. This is the matrix transpose symbol; The constraints of the original problem model include Feasible region constraints Attack capability constraints Attack capability constraints and system operation constraints; The The expression for the feasible region constraint is: ; The The expression for the attack capability constraint is: ; The The expression for the attack capability constraint is: ; The expression for the system operation constraints is: ; Where A, B, C, D, E, F, and G are the coefficient matrices in the constraints, and d, e, f, and is a constant vector in the constraints.

3. The method for generating columns and constraints for feasible pump acceleration according to claim 2, characterized in that, The outer decision variables This represents system planning or investment decisions; it is a binary variable that takes the value 0 or 1. The mid-level attack variables represent the attacker's attack strategy, where, It is a binary variable, taking the value 0 or 1. For continuous variables; The inner layer running variables z is a continuous variable, representing the system's target scheduling response when facing an attack.

4. The method for generating columns and constraints for feasible pump acceleration according to claim 1, characterized in that, In S3, the main problem model makes a target investment decision based on the set of attack scenarios returned by the sub-problem models; The sub-problem model finds the attack scenario that maximizes the system's operating cost based on the target investment decision given by the main problem model.

5. The method for generating columns and constraints for feasible pump acceleration according to claim 4, characterized in that, The objective function of the main problem model is: ; in, η For continuous auxiliary variables, For the first The second child problem returns the inner runtime variables under the worst-case attack scenario. The main problem model x The expressions for the feasible region constraints are the same as those for the original problem model; The expression for the cost approximation constraint of the main problem model is: ; in, The index is the number of iterations. K This is the current cycle number; The expressions for the system operation constraints of the main problem model are: ; in, and For the first k The second-child problem returns the mid-level attack variables under the worst-case attack scenario. The objective function of the sub-problem model is: ; Sub-problem model Attack capability constraints and The expression for the attack capability constraint is the same as that in the original problem model; The expressions for the system operation constraints of the subproblem model are: ; in, These are the outer-layer decision variables under the given target investment decision in the main problem model.

6. The method for generating columns and constraints for feasible pump acceleration according to claim 1, characterized in that, In S2, the specific content of the dual processing includes: By using the Karush-Kuhn-Tucker condition, the inner-level min model of the subproblem is equivalently transformed into its dual form max model, and the overall subproblem is transformed into a single-level max model. The objective function of the single-layer max model is: ; Single-layer max model Attack capability constraints The expressions for attack capability constraints and system operation constraints are the same as those for the subproblem model; The formula for the dual stationarity condition of a single-layer max model is: ; The expression for the complementary relaxation linearization of a single-layer max model is: ; ; in, i These are the numbers of the original constraints and their corresponding dual variables. As dual variables, The auxiliary binary variable introduced for linearization of large M. M This is a relatively large constant introduced for linearization using the Big M method.

7. The method for generating columns and constraints for feasible pump acceleration according to claim 1, characterized in that, The specific content of S3 includes: S31. Set the iteration counter, the initial upper bound of the original problem model, and the initial lower bound of the original problem model; S32. Using the feasibility pump algorithm, the initial integer solution to the main problem is obtained; S33. Input the initial integer solution of the main problem into the branch and bound algorithm to solve the main problem, obtain the objective solution of the main problem, and update the lower bound of the original problem model; S34. Input the objective solution of the main problem into the subproblem, and use the feasibility pump algorithm to obtain the initial integer solution of the subproblem; S35. Input the initial integer solution of the subproblem into the branch and bound algorithm to solve the subproblem, obtain the objective solution of the subproblem, and update the upper bound of the original problem model.

8. The method for generating columns and constraints for feasible pump acceleration according to claim 7, characterized in that, The specific process of the feasibility pump algorithm for finding the initial integer solution includes: S321. Convert the binary variables in the main problem model and the single-layer max model into continuous variables to obtain a linear model containing only continuous variables. S322. Solve the linear model to obtain the current continuous solution; S323. Round the initial continuous solution to obtain the current integer solution; S324. Determine whether the current integer solution satisfies all the constraints of the original problem model. If it does, output the current integer solution directly as the initial integer solution. If it does not, select a new continuous solution and continue to execute S325. S325. Round the new continuous solution to obtain a new integer solution; S326. Determine whether the new integer solution has appeared in the previous loop. If so, randomly flip a few bits and return to S324 to loop. If not, directly return to S324 to loop until an initial integer solution that satisfies all the constraints of the original problem model is output.

9. The method for generating columns and constraints for feasible pump acceleration according to claim 8, characterized in that, The new continuous solution is the continuous solution within the feasible region of the linear model that has the shortest Euclidean distance to the current integer solution.

10. The method for generating columns and constraints for feasible pump acceleration according to claim 1, characterized in that, In S4, the formula for the convergence condition is: ; in, UB This represents the upper bound of the original problem model derived from the subproblems. LB This represents the lower bound of the original problem model derived from the main problem. This represents the set convergence condition value.

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