A security constrained unit commitment calculation method based on pre-solution-accurate solution double-layer iteration

Abstract

The application discloses a security constrained unit commitment calculation method based on pre-solution-accurate solution double-layer iteration, which comprises the following steps: acquiring power grid framework parameter data required by security constrained unit commitment calculation; constructing an original security constrained unit commitment problem according to power grid demand constraints; when the original security constrained unit commitment problem is feasible, processing power flow constraints according to the density of the original security constrained unit commitment problem, constraint coefficients and the connection between constraints, and according to whether the power flow constraints are easy to cross the boundary; solving a linear relaxation sub-problem of a relaxed Lagrange problem with an extension, and obtaining all linear relaxation solutions; simplifying integer variables and the number of power flow constraints in the original security constrained unit commitment problem by using the linear relaxation solutions, and obtaining a security constrained unit commitment result by solving the simplified original security constrained unit commitment problem.

Description

Technical Field

[0001] This invention belongs to the field of safety-constrained unit combination calculation, specifically involving a safety-constrained unit combination calculation method based on a two-level iterative method of pre-solution-exact solution. Background Technology

[0002] Safety-Constrained Unit Combination (SCUC) refers to the formulation of multi-period unit start-up and shutdown plans with the optimization objective of minimizing system power purchase costs while meeting power system safety constraints. SCUC is one of the most widely used models in grid clearing scenarios.

[0003] SCUC can be abstracted as a mixed integer programming model (MIP). In computer complexity theory, MIP is an NP-hard problem. Generally, SCUC is solved using commercial solvers. Designing a general-purpose, efficient algorithm framework based on commercial solvers to meet the needs of increasingly complex and large-scale clearing markets has become an important direction for technological breakthroughs.

[0004] For some difficult combinatorial optimization problems, all known algorithms require exponential time in the worst case. The basic principle of the Lagrange relaxation method is to incorporate the constraints that make solving the problem difficult into the objective function, resulting in a relatively easier-to-solve Lagrange relaxation problem. Its optimal value provides a bound to the optimal value of the original problem, and its quality will depend in part on the Lagrange multipliers chosen in the objective function.

[0005] The Lagrange relaxation method was proposed by Held and Karp in 1970. They designed a highly successful algorithm to solve the Traveling Salesman Problem (TSP) using the minimum spanning tree-based Lagrange relaxation problem. Since then, the application scope of the Lagrange relaxation method has continued to expand, including more than a dozen of the most difficult combinatorial optimization problems. For most of these problems, the Lagrange relaxation method provides the best existing algorithms and makes it possible to solve large-scale problems.

[0006] While linear Lagrange relaxation methods can circumvent complex constraints and accelerate solutions through iteration, they often suffer from convergence difficulties in large-scale complex problems, particularly exhibiting oscillations near the optimal solution. To address this issue, Guan et al. proposed introducing a quadratic term into the objective function of the Lagrange relaxation problem in 1995. Since the sequential quadratic programming problem (SQP) has stronger convergence, this method successfully solved the long-term convergence problem of traditional Lagrange methods.

[0007] Most existing technologies have two problems: First, the solution scale in actual production environments is nearly 8-10 times larger than that of standard datasets. For NP-hard problems like MIP, the solution results on standard datasets cannot meet the actual solution requirements. Second, many algorithms introduce quadratic term penalties to connect various subproblem modules, but quadratic terms are unacceptable in ultra-large-scale MIPs. Summary of the Invention

[0008] Purpose of the invention: In order to address the problem that the solution results on standard datasets cannot meet the actual solution requirements, and to address the problem that quadratic terms are unacceptable in ultra-large-scale MIPs, this invention proposes a solution method for ultra-large-scale SCUC problems based on a two-layer iteration of pre-solution and exact solution.

[0009] Technical solution: A method for calculating safety constraint unit combination based on a two-level iterative process of pre-solution and exact solution, comprising the following steps:

[0010] Step 1: Obtain the grid architecture parameter data required for safety-constrained unit combination calculation;

[0011] Step 2: Construct the original security-constrained unit combinatorial problem based on grid demand constraints; and determine whether the original security-constrained unit combinatorial problem is feasible. If the original security-constrained unit combinatorial problem is feasible, process the power flow constraints based on the density of the original security-constrained unit combinatorial problem, constraint coefficients, and relationships between constraints, as well as whether the power flow constraints are prone to exceeding limits; the processing of power flow constraints includes assigning linear penalty terms, quadratic penalties, aggregation addition, and removal;

[0012] Step 3: Following the power flow constraints processed in Step 2, solve the linear relaxed subproblem of the augmented relaxed Lagrange problem to obtain all linear relaxed solutions;

[0013] Step 4: Using the linear relaxation solution obtained in Step 3, simplify the number of integer variables and power flow constraints in the original safety-constrained unit combination problem. By solving the simplified original safety-constrained unit combination problem, obtain the safety-constrained unit combination result.

[0014] Furthermore, in step 2, the original safety-constrained unit combination problem is expressed as:

[0015]

[0016]

[0017] l s,t ≤G s,t (I t ,P t ,St )≤u s,t

[0018] Where I, P, and T represent the decision variables of the original safety-constrained unit combination problem, respectively, and G... s,t (·) represents a linear approximation of the power flow constraint, l s,t and u s,t Let represent the upper and lower bounds of section s at time t, respectively. Represents 01 variables, Let n represent the size of the 0 / 1 variable, and m and k represent the size of the continuous variable. I represents the non-power flow linear constraint of the SCUC problem. t ,P t ,S t Let I, P, and T represent the participating variables at time t, respectively.

[0019] Furthermore, the process of handling power flow constraints based on the density of the original safety-constrained unit combination problem, the constraint coefficients, and the relationships between constraints, as well as based on whether the power flow constraints are prone to exceeding limits, includes:

[0020] If the power flow constraints are dense and are judged to be prone to exceeding the limit, then the power flow constraints are given a linear penalty term;

[0021] If a power flow constraint is dense and is determined to be prone to out-of-bounds movement, then the power flow constraint is judged to be aggregated and added.

[0022] If the power flow constraint is not dense and is judged to be easy to exceed the limit, the power flow constraint will be judged as a second penalty;

[0023] If a current flow constraint is determined to be unlikely to exceed the limit, then the current flow constraint is removed.

[0024] Among them, dense power flow constraints refer to the number of constraint coefficients with absolute values ​​greater than zero that are greater than 20 and less than or equal to 50.

[0025] Among them, dense power flow constraints refer to the number of constraint coefficients with absolute values ​​greater than zero being greater than 50.

[0026] Among them, "not too dense current constraints" means that current constraints are relatively dense, but it does not belong to the category of dense current constraints.

[0027] Furthermore, step 3 includes:

[0028] Following the power flow constraints processed in step 2, solve the linear relaxation subproblem of the augmented relaxation Lagrange problem, expressed as:

[0029]

[0030] In the formula, λ1 and λ2 represent the Lagrange relaxation multiplier vectors for the upper and lower bounds of the power flow constraint exceeding the limits, respectively; u and l represent the upper and lower bound vectors of the cross section; and σ represents the augmented quadratic relaxation factor. express The linear relaxed feasible region;

[0031] λ1 and λ2 are updated according to the following update rules:

[0032]

[0033]

[0034]

[0035] in, and ρ represents the upper and lower limits of the cross-sectional power flow constraint; C is a constant term greater than 0. Let λ1 and λ2 represent the values ​​of the Lagrange multipliers corresponding to the interrupted surfaces s at time t in the k-th and k+1-th iterations, respectively.

[0036] And determine whether the following conditions are met:

[0037]

[0038] If satisfied, proceed to step 4; otherwise, proceed according to the updated... and Continue solving the linear relaxation subproblem of the augmented relaxation Lagrange problem.

[0039] Furthermore, the method of using the linear relaxation solution obtained in step 3 to simplify the number of integer variables and power flow constraints in the original safety-constrained unit combination problem includes:

[0040] Using step 3 and Determine the cross-sectional constraints for solving the unit combination problem by incorporating the original safety constraints;

[0041] Based on the relationship between the integer variable information and the boundary in the linear relaxation solution obtained in step 3, the integer variable information is processed. The processing includes: some integer variable information is fixed to the boundary, and the remaining integer variables participate in the solution of the original safety constraint unit combination problem.

[0042] Add the information of the last continuous variable in the linear relaxation solution obtained in step 3 to the hint interface of the commercial solver.

[0043] Furthermore, the use of step 3 and Determine the cross-sectional constraints for solving the unit combination problem that incorporate the original safety constraints, including:

[0044] If a certain cross-section constraint never exceeds the limit during multiple iterations, then the cross-section is added as a constraint in the form of a linear penalty, and the result is obtained by selecting the relaxation solution of the corresponding Lagrange penalty multiplier.

[0045] If, during multiple iterations, the number of times a certain cross-section constraint exceeds half of the total number of iterations, then that cross-section constraint is treated as a hard constraint and added to the original safety constraints for solving the unit combination problem.

[0046] Furthermore, the process of processing the integer variable information based on the relationship between the integer variable information and the boundary obtained in step 3 includes:

[0047] If the integer variable information is always solved to its boundary in multiple iterations, then the integer variable information is fixed at the boundary.

[0048] In multiple iterations, if more than 90% of the total number of iterations of integer variable information are solved to its boundary, then the integer variable information is hot-started at this boundary.

[0049] Information on other integer variables that do not meet the above conditions is used to solve the original safety constraint unit combination problem.

[0050] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0051] (1) This invention uses the Lagrange relaxation method to add cross-sectional constraints to the objective function and simultaneously performs linear relaxation, transforming the original problem into a solvable problem within a reasonable time.

[0052] (2) The present invention can handle large-scale practical problems in a short time. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the structure of the present invention. Detailed Implementation

[0054] The technical solution of the present invention will now be further described in conjunction with the accompanying drawings and embodiments.

[0055] This invention discloses a method for solving the safety unit combination constraint problem (SCUC) of ultra-large scale using the Lagrange relaxation technique. The most significant feature of this method is that it uses the information obtained during the Lagrange relaxation process to construct a high-precision approximate model of the original SCUC problem. At the same time, it makes full use of the internal interface of commercial solvers to perform a hot start on the original problem, which enables it to converge to an extremely high-precision solution quickly and efficiently.

[0056] The method of this invention mainly includes the following steps:

[0057] Step 1: Pre-solution; The main purpose of pre-solution is to heuristically discover redundant constraints in the SCUC problem before the solution process and to optimize the problem structure; specifically:

[0058] After obtaining the structured power grid architecture parameter data, the primal SCUC problem is constructed based on the power grid demand constraints. This primal SCUC problem can be expressed as:

[0059]

[0060]

[0061] l s,t ≤G s,t (I t ,P t ,S t )≤u s,t

[0062] Where I, P, and T represent the decision variables of the original safety-constrained unit combination problem, respectively, and G... s,t (·) represents a linear approximation of the power flow constraint, l s,t and u s,t Let represent the upper and lower bounds of section s at time t, respectively. Represents 01 variables, Let n represent the size of the 0 / 1 variable, and m and k represent the size of the continuous variable. I represents the non-power flow linear constraint of the SCUC problem. t ,P t ,S t Let I, P, and T represent the participating variables at time t, respectively.

[0063] The first step, the pre-solution step, is responsible for determining whether the problem is feasible. If the original SCUC problem is infeasible, the pre-solution step will directly end the solution process and return a minimal infeasible set of the original SCUC problem.

[0064] If feasible, then based on the density of the original SCUC problem, constraint coefficients, relationships between constraints, and determining whether power flow constraints are prone to going out of bounds, whether constraints should be given linear penalties, quadratic penalties, and whether aggregation is necessary, the following four criteria are generally followed for constraint classification:

[0065] If the power flow constraints are dense and are judged to be prone to out-of-bounds, then the constraints are given a linear penalty term.

[0066] If the current flow constraint is dense and is judged to be prone to out-of-bounds, then the constraint is judged to be aggregated and joined.

[0067] If the current constraint is not dense and is judged to be easy to exceed the limit, the constraint is judged as a secondary penalty.

[0068] If a current flow constraint is determined to be unlikely to exceed the limit, then the constraint will be removed.

[0069] Among them, relatively dense constraints refer to constraints with more than 20 and less than or equal to 50 constraint coefficients whose absolute values ​​are greater than zero, and dense constraints are constraints with more than 50 constraint coefficients whose absolute values ​​are greater than zero. The rest are less dense constraints. Step 2: Relaxation solution; The main purpose of relaxation solution is to assist in obtaining the correct convergence situation and to obtain the feasible solution set of the original problem by solving simple subproblems; specifically including:

[0070] First, we solve a linear relaxation of an augmented relaxation Lagrange problem, expressed as:

[0071]

[0072] In the formula, λ1 and λ2 represent the Lagrange relaxation multiplier vectors for the upper and lower bounds of the power flow constraint exceeding the limits, respectively; u and l represent the upper and lower bound vectors of the cross section; and σ represents the augmented quadratic relaxation factor. express The linearly relaxed feasible region.

[0073] The reason for considering linear relaxation is that the difficulty of solving programming problems with commercial solvers lies in solving MILPs, where exact solutions often require a method called branch and bound, which is extremely time-consuming. Therefore, when solving the relaxation Lagrange problem, the integer form will be disregarded, and the linear relaxation form will be used instead. This will be considered in the subsequent solution steps of the original problem. The initial values ​​of the first and second level penalties will be added according to the information given in the pre-solution steps; currently, the main updates are to the two parameters λ1 and λ2.

[0074] Based on classical Lagrange duality theory, a closed-form update rule is proposed:

[0075]

[0076]

[0077]

[0078] in, and ρ represents the upper and lower limits of the cross-sectional power flow constraint; ρ is a coefficient ranging from [0,1]; C is a constant term greater than 0. Representing the k-th and k+1-th iterations respectively The value of the Lagrange multiplier corresponding to the midsection s at time t.

[0079] This update rule means that the step size gradually decreases during the Lagrange multiplication iteration, implying greater caution as we approach the optimal solution to the subproblem. Simultaneously, during the solution process, solutions obtained from the pre-solution steps are used as a warm-start for the problem via a commercial solver interface to reduce solution time. After solving each subproblem, all linearly relaxed solutions are saved as warm-start information for the final solution to the original SCUC problem.

[0080] Based on the updated multipliers, continue solving the relaxed Lagrange problem with augmentation, and after each update of the multipliers, make the following judgment:

[0081]

[0082] In the formula, ε represents a manually set small value, typically 10. -3 The significance of this judgment lies in determining whether the Lagrange relaxation problem has converged. If it has converged or the specified number of iterations has been reached, then the solution steps for the relaxation problem are exited, and the exact solution steps are entered.

[0083] Step 3: Exact Solution; Since SCUC is a large integer programming (MILP) problem, such problems are considered NP-hard problems and cannot be solved in polynomial time. In this embodiment, the solution information obtained by relaxation is used to cleverly construct a subproblem that is basically equivalent to the original problem but has a much smaller scale and a much lower difficulty to solve it. The solution scale is smaller, so it can be solved quickly.

[0084] Considering the original SCUC problem is:

[0085]

[0086]

[0087] l s,t ≤G s,t (I t ,P t ,S t )≤u s,t

[0088] Among them, G s,t (I t ,P t ,S t The constraints are mostly dense and unfriendly to the solver. Therefore, these constraints cannot be completely copied in the original SCUC problem solution. They need to be processed in a certain way. At this time, the problem needs to be simplified based on the information obtained from multiple Lagrange iterations.

[0089] The results obtained in the relaxation solution step and Information is used to determine whether each cross section should be included in the original SCUC problem solution. If the cross section does not exceed the bounds in multiple iterations, it is considered that the cross section will not exceed the bounds. In this case, the cross section is added as a constraint in the form of a linear penalty, and the corresponding Lagrange penalty multiplier is selected to obtain the result of relaxation. For cross section constraints that frequently exceed the bounds, they are added as hard constraints to the original SCUC problem solution. The criterion for frequently exceeding the bounds is that the number of times the bounds exceeds the bounds is greater than half of the total number of iterations.

[0090] The information about integer variables obtained during the relaxation process is the least considered but extremely valuable information in other techniques. This information plays a crucial role in accelerating the optimization of large problems by commercial solvers. This is because commercial solvers often use branch-and-bound methods that enumerate all possible solutions when the values ​​of a large number of 0-1 integer variables cannot be determined. However, if a portion of the integer variables can be determined beforehand, the solution bottleneck will be greatly improved, and the algorithm's search space will be reduced.

[0091] Since a linear approximation of the relaxation of the original SCUC problem has been solved in multiple rounds, the following judgment is made based on the information of the integer variables:

[0092] If a variable is always solved to near its boundary (0 or 1) during the solution process, then the variable will be fixed on the boundary. Note that this fixing will only lose a small amount of the optimality of the original problem, but will not affect the feasibility of the original problem (such a solution has been proven to be feasible in the relaxation solution step).

[0093] If a variable spends most of its time near its boundary during the solution process, then this variable will be warm-started with that boundary at the beginning of the exact solution. "Most of its time" is defined as more than 90% of the total number of iterations.

[0094] The remaining variables will be freely optimized.

[0095] For the continuous variable information obtained in the relaxation step, all commercial solvers provide a "hint" interface that is weaker than a warm start. This "hint" interface aims to provide a reliable optimization direction for the heuristic algorithm during branch and bound operations within the commercial solver. Generally, commercial solver branch and bound algorithms spend 50% of their time running a large number of built-in heuristic algorithms. If the confidence level of the continuous variable information is high enough, it will greatly reduce the time spent by the heuristic algorithm in finding a feasible solution. The information of the last continuous variable solution obtained in the relaxation step will be added to the "hint" interface to help the heuristic algorithm achieve better performance. The reason for choosing the last solution is that the last solution is generally considered to be closest to the global optimum, and therefore will be more helpful in solving the problem.

[0096] There is a very small chance that the fixed variable information obtained in the relaxation solution step will make the problem infeasible. Therefore, to prevent infeasibility, it is necessary to pre-solve the approximate problem. If the approximate problem is infeasible after fixing the variables, a portion of the variables are randomly selected for unfixation. This proportion increases by 10% with each pre-solution until 100% of them are unfixed. This logic has not been triggered in daily calculations so far.

[0097] With the acceleration of the above three parts of information, the original problem can generally reduce the number of integer variables by nearly 60% and the number of power flow constraints by nearly 50%, so that the original ultra-large-scale SCUC problem is optimized from an unsolvable state to a stable solution within 1000s with an output of 0.1% accuracy (the difference from the current lower bound of branch and bound is one-thousandth, which is different from the optimal solution).

[0098] This implementation relaxes the power flow constraints that are difficult to solve in the original SCUC problem through linear and quadratic penalties. At the same time, it uses the information obtained in the process of solving the relaxed SCUC problem to stably construct a strictly feasible solution to the original problem, which is used as the preferred solution for hot start of ultra-large-scale MILP.

[0099] By comparing direct solutions with solutions obtained through patents, it can be found that Lagrange iteration can greatly accelerate the solution of the original problem, thereby significantly improving the solution speed of large-scale cross-sectional constraint optimization problems.

[0100] Table 2 Comparison of solution times

[0101]

[0102]

[0103] Experiments have shown that the method of this invention effectively solves the problem that commercial solvers cannot directly solve large-scale SCUC problems, and can stably and efficiently output high-quality clearing solutions in practical production applications.

Claims

1. A method for calculating safety constraint unit combination based on a two-level iterative process of pre-solution and exact solution, characterized in that: Includes the following steps: Step 1: Obtain the grid architecture parameter data required for safety-constrained unit combination calculation; Step 2: Construct the original security-constrained unit combinatorial problem based on grid demand constraints; and determine whether the original security-constrained unit combinatorial problem is feasible. If the original security-constrained unit combinatorial problem is feasible, process the power flow constraints based on the density of the original security-constrained unit combinatorial problem, constraint coefficients, and relationships between constraints, as well as whether the power flow constraints are prone to exceeding limits; the processing of power flow constraints includes assigning linear penalty terms, quadratic penalties, aggregation addition, and removal; Step 3: Following the power flow constraints processed in Step 2, solve the linear relaxed subproblem of the augmented relaxed Lagrange problem to obtain all linear relaxed solutions; Step 4: Using the linear relaxation solution obtained in Step 3, simplify the number of integer variables and power flow constraints in the original safety-constrained unit combination problem. By solving the simplified original safety-constrained unit combination problem, obtain the safety-constrained unit combination result. In step 2, the original safety-constrained unit combination problem is expressed as: （1）； in, Let each represent a decision variable in the original safety-constrained unit combination problem. This represents a linear approximation of the power flow constraints. as well as Representing cross-sections exist The upper and lower bounds of time, Represents 01 variables, Represents continuous variables, Indicates the size of the 01 variable. , Indicates the size of a continuous variable. Represents the non-power flow linear constraint of the SCUC problem. They represent exist The variable involving time.

2. The method for calculating safety constraint unit combination based on a pre-solution-exact solution two-level iteration as described in claim 1, characterized in that: The aforementioned processing of power flow constraints based on the density of the original safety-constrained unit combination problem, constraint coefficients, and relationships between constraints, as well as based on whether power flow constraints are prone to exceeding limits, includes: If the power flow constraints are dense and are judged to be prone to exceeding the limit, then the power flow constraints are given a linear penalty term; If a power flow constraint is dense and is determined to be prone to out-of-bounds movement, then the power flow constraint is judged to be aggregated and added. If the power flow constraint is not dense and is judged to be easy to exceed the limit, the power flow constraint will be judged as a second penalty; If a current flow constraint is determined to be unlikely to exceed the limit, then the current flow constraint is removed. Among them, dense power flow constraints refer to the number of constraint coefficients with absolute values ​​greater than zero that are greater than 20 and less than or equal to 50. Among them, dense power flow constraints refer to the number of constraint coefficients with absolute values ​​greater than zero being greater than 50. Among them, "not too dense current constraints" means that current constraints are relatively dense, but it does not belong to the category of dense current constraints.

3. The method for calculating safety constraint unit combination based on a pre-solution-exact solution two-level iteration as described in claim 2, characterized in that: Step 3 includes: Following the power flow constraints processed in step 2, solve the linear relaxation subproblem of the augmented relaxation Lagrange problem, expressed as: （2）； In the formula, and Let represent the Lagrange relaxation multiplier vectors for the upper and lower bounds of the power flow constraints, respectively. and for and transpose, , The vectors representing the upper and lower bounds of the cross-section. Represents the augmenting secondary relaxation factor. express The linear relaxed feasible region; and Update according to the following update rules: （3）； in, and The upper and lower limits of cross-sectional power flow constraints; For coefficients, A constant term that is greater than 0; , , , They represent the first , Second iteration and Section exist The values ​​of the Lagrange multipliers corresponding to time; And determine whether the following conditions are met: （4）； If satisfied, proceed to step 4; otherwise, proceed according to the updated... and Continue to solve the linear relaxation subproblem with augmented relaxation Lagrange problem.

4. The method for calculating safety constraint unit combination based on a pre-solution-exact solution two-level iteration as described in claim 3, characterized in that: The method of using the linear relaxation solution obtained in step 3 to simplify the number of integer variables and power flow constraints in the original safety-constrained unit combination problem includes: Using step 3 and Determine the cross-sectional constraints for solving the unit combination problem by incorporating the original safety constraints; Based on the relationship between the integer variable information and the boundary in the linear relaxation solution obtained in step 3, the integer variable information is processed. The processing includes: some integer variable information is fixed to the boundary, and the remaining integer variables participate in the solution of the original safety constraint unit combination problem. Add the information of the last continuous variable in the linear relaxation solution obtained in step 3 to the hint interface of the commercial solver.

5. The method for calculating safety constraint unit combination based on a pre-solution-exact solution two-level iteration as described in claim 4, characterized in that: The use of step 3 and The cross-sectional constraints for solving the unit combination problem, which incorporate the original safety constraints, are determined, including: If a certain cross-section constraint never exceeds the limit during multiple iterations, then the cross-section is added as a constraint in the form of a linear penalty, and the result is obtained by selecting the relaxation solution of the corresponding Lagrange penalty multiplier. If, during multiple iterations, the number of times a certain cross-sectional constraint exceeds the limit is greater than half of the total number of iterations, then that cross-sectional constraint is treated as a hard constraint and added to the original safety constraints for solving the unit combination problem.

6. The method for calculating safety constraint unit combination based on a pre-solution-exact solution two-level iteration as described in claim 5, characterized in that: The process of processing the integer variable information based on the relationship between the integer variable information and the boundary obtained in step 3 includes: If the integer variable information is always solved to its boundary in multiple iterations, then the integer variable information is fixed at the boundary. In multiple iterations, if more than 90% of the total number of iterations of integer variable information are solved to its boundary, then the integer variable information is hot-started at this boundary. Information on other integer variables that do not meet the above conditions is used to solve the original safety constraint unit combination problem.

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