CN112085403B - Low-voltage transformer area topology identification method based on mixed integer programming - Google Patents
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Abstract
The invention relates to a low-voltage distribution area topology identification method based on mixed integer programming, which comprises the steps of firstly, combining user power consumption information acquisition system data and marketing system basic archive data, calculating to obtain line loss highly negative correlation and obviously abnormal distribution areas with user variation membership, then introducing binary variables into the abnormal distribution areas to accurately represent distribution area membership, constructing a distribution area user variation check mixed integer model by taking the line loss square sum minimum as an optimization target, and solving the model by adopting a branch-and-bound method; then, obtaining a station area topological relation with highest possibility of descending the most priority step by using an integer division method; and finally, establishing a reliability evaluation index, and performing reliability evaluation on checked and corrected abnormal users affiliated to the distribution area. The invention greatly reduces the dependency of the topology identification method on the sample data, thereby obtaining the correct membership relationship of the station area, and the accurate identification can be realized when more user variation exists.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to a low-voltage transformer area topology identification method based on mixed integer programming.
Background
Compared with the intelligent construction level of power transmission and medium-voltage distribution networks, the automation and intelligent construction level of the low-voltage distribution network falls behind, is the weakest link of the intelligent construction of the power network, and lacks intelligent means to carry out overall effective and accurate management. The low-voltage distribution network is a terminal power supply network directly facing users, is an important link for creating excellent power operator environment, and the accurate and reliable platform area electrical topological relation is an important premise for ensuring stable and reliable operation of the low-voltage distribution network, rapid fault first-aid repair and accurate platform area line loss management, and is a key for improving the intelligent level of the low-voltage distribution network. However, with the development of the power grid, such as the activities of migration, capacity expansion, addition of users, migration, account cancellation and the like, the problem that the records of the correspondence relationship between the user changes are not updated timely or the records are wrong is caused, which may cause a phenomenon of wrong topology membership of the distribution room.
The traditional maintenance and management work of the electrical topological relation of the transformer area mainly depends on manual on-site investigation, the problems of large workload, long time consumption, low efficiency, incapability of ensuring reliability and the like exist, and the efficient, accurate and automatic identification of the electrical topological relation of the transformer area cannot be realized. In order to realize the intellectualization and high efficiency of topology identification, research on the high-efficiency topology identification method is vigorously carried out by each unit, research institution and the like. Currently, the methods for identifying the power grid topology mainly include methods such as frame synchronization signal identification and carrier signal identification which are completely realized by hardware, and analysis and calculation based on different types of data. The hardware identification method has higher requirements on field communication conditions and hardware foundation, has more limited factors, and needs longer time for realizing efficient identification. With the construction of power consumption information acquisition systems (acquisition systems) of power consumers and the rise of big data technologies, data-based topology identification methods have a great breakthrough, and there are mainly methods based on the connection relation and the on-off state information of power-requiring network elements such as incidence matrixes or adjacent matrixes, network topology tracking and the like, and methods requiring a great amount of power data such as linear regression, CNN-LSTM deep learning neural networks and the like. The method requiring the connection relation of the power grid elements and the switch state information has referential significance for a newly added distribution area, but frequent switch switching is not practical and greatly influences the electricity consumption experience of residents for a storage distribution area; because the available sample amount of the stock area is limited, the algorithms such as machine learning, linear regression and the like cannot be effectively applied to analysis and calculation; the actual operation conditions of a few transformer areas are difficult to meet the goal of optimal line loss, and the optimal solution of the model obtained by only using the traditional planning algorithm sometimes does not accord with the actual transformer area topology. Therefore, an effective solution is difficult to obtain for the topology study and judgment of the low-voltage platform area with less samples.
Therefore, the traditional method for studying and judging the platform zone topology has certain difficulty in practical engineering application.
Disclosure of Invention
In view of the above, the present invention provides a low-voltage distribution area topology identification method based on mixed integer programming, which greatly reduces the dependency of the topology identification method on sample data, thereby obtaining a user variation relationship, and can accurately identify when there are many user variations.
The invention is realized by adopting the following scheme: a low-voltage transformer area topology identification method based on mixed integer programming specifically comprises the following steps:
combining the user power consumption information acquisition system data and marketing system basic archive data, calculating and screening a strong negative correlation area of line loss, determining the strong negative correlation area as an abnormal area of the household variable membership relationship, extracting power sample data from the system, and formulating a sample data cleaning rule to obtain cleaning data;
for the abnormal transformer subordination relation transformer area, introducing a binary variable to accurately represent the transformer area subordination relation, constructing a transformer area transformer check mixed integer model by taking the minimum sum of line loss squares as an optimization target, and solving the transformer area transformer check mixed integer model;
obtaining a station area topological relation with highest possibility of descending the most priority step by using an integer segmentation method;
and establishing a reliability evaluation index, and performing reliability evaluation on checked and corrected abnormal users affiliated to the distribution area.
Further, for the abnormal transformer subordination relationship transformer area, introducing a binary variable to accurately represent the transformer area subordination relationship, and constructing a transformer area transformer check mixed integer model with the minimum sum of line loss squares as an optimization target specifically comprises the following steps:
introduction of ak、bkTwo binary variables represent whether the kth electric energy meter belongs to a certain area, if yes, akA value of 1 indicates that the kth electric energy meter belongs to the region 1, if b k1 represents that the kth electric energy meter belongs to the station area 2; by constraining akAnd bkThe sum of (1) enables a certain sub-electric energy meter to be only affiliated to a certain area;
converting the line loss minimum solving problem into the following table area user variable check mixed integer model, wherein the optimization target is the minimum sum of the line loss squares in all time periods:
s.t.
ak+bk＝1,k＝1,2,......n
ak,bk∈[0,1]
in the formula, t is the total number of the collected time samples, and i is the ith time sample; n is the total number of the user tables belonging to 2 distribution areas in the file, and k is the kth user table; p is a radical ofk,iMetering the electric quantity for the kth user at the time i; y'1iThe total electric quantity of the 1 st distribution area at the time i is calculated according to the household meter data, and y 'is obtained'2iThe total electric quantity of the 2 nd distribution area is calculated according to the data of the household meter; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iAnd collecting a 2 nd station area total meter electric quantity sample in the system for time i.
And further, solving the transformer substation area household variable check mixed integer model by adopting a branch-and-bound solving algorithm.
Further, the step of obtaining the topology relationship of the station area with the highest probability of descending the most priority step by using the integer partition method specifically includes: and adding an integer partition in the solved integer programming optimal solution to make the previously solved optimal solution infeasible, solving the model again to find a suboptimal integer solution, and repeatedly executing the process to obtain a set number optimal solution in the integer programming.
Further, the establishing of the reliability evaluation index and the reliability evaluation of the checked and corrected users who are affiliated to the abnormal area specifically include: by calculation ofThe credibility evaluation index of each user is used for judging the possibility of abnormity of the user variable relationship of the user, and the checking sequence is arranged according to the credibility index, wherein the credibility index epsilon corresponding to the user kkIs calculated as follows:
in the formula, WlossThe method comprises the following steps of (1) according to marketing system files, summing the line loss squares of two distribution areas;
the electric quantity of the mth user belonging to the 1 st distribution area at the time i based on the marketing system file is m ' is 1,2,3, … n ', and n ' user tables are totally contained in the file belonging to the 1 st distribution area;
the electric quantity of the mth user at the time i, which belongs to the 2 nd distribution area, of the archive is m ' is 1,2,3, … n ', and n ' user tables are shared by the 2 nd distribution area in the archive;
the original marketing file belongs to the distribution area 2, and the user serial number k of the distribution area 1 is adjusted at the moment; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iCollecting a 2 nd station area total meter electric quantity sample in the system for time i; y'1iThe total electric quantity is calculated for the adjusted background area 1; y'2iThe total amount of electricity calculated for the adjusted background area 2.
Compared with the prior art, the invention has the following beneficial effects: the method specifically performs calculation on the transformer area with strong negative correlation suspected to be abnormal membership to the transformer station, introduces binary variables to the abnormal membership to the transformer station to accurately represent the membership of the user, has no mandatory requirement on the sample size, requires far lower sample size than other calculation methods such as linear regression and the like, greatly reduces the strong dependence of the identification of the transformer station on the large sample data, and simultaneously can still ensure the accuracy of algorithm study and judgment when more diversity exists to realize the topological identification of transformer station level. The invention obtains the station area topological relation with the optimality gradually decreased by using an integer segmentation method, provides various combinations with high possibility for the user-variant membership abnormal users, establishes a credibility index to judge the credibility of the checked membership abnormal users, and checks the abnormal users one by one according to the credibility priority, thereby having strong engineering practicability.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a diagram illustrating a branch-and-bound algorithm according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the present embodiment provides a low-voltage transformer area topology identification method based on mixed integer programming, which specifically includes the following steps:
step S1: combining the user electricity consumption information acquisition system data and the marketing system basic archive data, calculating and screening a station area with line loss having strong negative correlation, identifying the station area as an abnormal station area with a user variable membership, extracting electricity quantity sample data from the system, and formulating a sample data cleaning rule to obtain cleaning data;
step S2: for the abnormal transformer subordination relation transformer area, introducing a binary variable to accurately represent the transformer area subordination relation, and constructing a transformer area transformer check mixed integer model by taking the minimum sum of line loss squares as an optimization target;
step S3: solving the station area household variation check mixed integer model by adopting a branch-and-bound solving algorithm;
step S4: obtaining a station area topological relation with highest possibility of descending the most priority step by using an integer segmentation method;
step S5: and establishing a reliability evaluation index, and performing reliability evaluation on checked and corrected abnormal users affiliated to the distribution area.
Preferably, in the present embodiment, the step S1 specifically includes: because the abnormal situation of the station area household variable relationship membership mostly occurs in adjacent or similar station areas, in order to reduce the solving difficulty, two abnormal station areas with the household variable membership are accurately positioned by calculating the line loss negative correlation station areas of a plurality of station areas with similar names. When the line loss rate shows an obvious negative correlation distribution area, namely the line loss of the distribution area A is increased, the line loss of the distribution area B is reduced, and the increasing/decreasing amplitudes are close, so that the two distribution areas have complementary user variable membership abnormity, and the specific analysis is as follows.
Suppose user k*Belonging to the district A in the marketing archive, and actually belonging to the district B, the following relations hold for the district A:
in the formula, n +1 is the total number of the users in the distribution area A in the marketing file, i is the time sample serial number, and k is the user serial number; y isi,ACounting the total power consumption of the time i of the concentrator in the distribution area A; y isi，AThe actual total power consumption is the actual total power consumption of the time i of the distribution area A; p is a radical ofk,i,AMetering the electric quantity for the kth user at the time i; p'loss,i,AFor station area A true line loss, Ploss,i,AThe line loss of the distribution area A is obtained according to the marketing system file.
Then the line loss rate correlation calculation of the station area a is:
in the formula, ki,AIs the archive line loss rate, k 'of the time i station zone A'i,AIs the actual line loss rate of the station area A at the time i, due to the actual line loss rate k'i,AOnly related to fixed equipment such as district lines, therefore, the file line loss rate of district A and the electric quantity P with wrong membershipk*,i,AThere is a strong negative correlation.
Similarly, user k*The marketing file belongs to the area A and actually belongs to the area B, and the following relations are established for the area B.
Wherein n' -1 is the total number of B users in the region of the marketing file, yi,BCounting the total power consumption of the time i of the concentrator in the distribution room B; y'i，BThe actual total power consumption of the time i of the station area B; p is a radical ofk,i,BMetering the electric quantity for the kth user at the time i; p'loss,i,BFor station B true line loss, Ploss,i,BThe line loss of the distribution area B is obtained according to the marketing system file.
Then the correlation calculation of the line loss rate of the station area B is:
in the formula, ki,BIs the archive line loss rate, k 'of the time i station zone B'i,BIs the actual line loss rate of the station zone B at the time i, due to the actual line loss rate k'i,BOnly relating to fixed equipment such as district lines, therefore, the file line loss rate of district B and the electric quantity P with wrong membershipk*,i,BThere is a strong positive correlation. In summary, when the user-variant membership error occurs, the line loss rates of the two regions a and B with complementary membership relationship have strong negative correlation relationship.
Based on the user electricity information data of the acquisition system and the basic archive data of the marketing system, a cleaning rule is formulated: for the table area general tables and the household meters under the two table areas, the electric quantity data of the acquisition system in the last 1 year is obtained through arrangement, and 1 group of data each day is 1 sample (the sample comprises 2 table area general tables and date and electric quantity data of all household meters under the table areas). And if any sample in the user table or the general table fails to be acquired, the sample is regarded as an invalid sample, and the sample is eliminated completely.
In this embodiment, the specific content of step S2 is: and for the abnormal transformer subordination relation transformer area, introducing a binary variable to accurately represent the transformer area subordination relation, and constructing a transformer area transformer check mixed integer model by taking the minimum sum of line loss squares as an optimization target.
On the premise that the marketing system file is correct, the low-voltage distribution area should satisfy the electric quantity balance relationship, namely, the total electric quantity of each distribution area should be equal to the sum of the electric quantities of all household meters in the distribution area, and the line loss rate is low. And converting the topology studying and judging problem into a planning problem by adopting a mixed integer optimization model, and solving the model by using a specific algorithm. Introduction of ak、bkTwo binary variables (only can take 0 or 1) represent whether the kth electric energy meter belongs to a certain area, if yes, akA value of 1 indicates that the kth electric energy meter belongs to the region 1, if b k1 represents that the kth electric energy meter belongs to the station area 2; by constraining akAnd bkThe sum of (1) enables a certain sub-electric energy meter to be only affiliated to a certain area; i.e., akWhen the value is 1, it means that the sub-electric energy meter belongs to the station area 1, and b is set to bekIs 0; in the same way, bkWhen 1, it means that the sub-electric energy meter belongs to the station area 2, and a is in this casekIs 0.
Converting the line loss minimum solving problem into the following table area user variable check mixed integer model, wherein the optimization target is the minimum sum of the line loss squares in all time periods:
s.t.
ak+bk＝1,k＝1,2,......n
ak,bk∈[0,1]
in the formula, t is the total number of the collected time samples, and i is the ith time sample; n is the total number of the user tables belonging to 2 distribution areas in the file, and k is the kth user table; p is a radical ofk,iMetering the electric quantity for the kth user at the time i; y'1iThe total electric quantity of the 1 st distribution area at the time i is calculated according to the household meter data, and y 'is obtained'2iThe total electric quantity of the 2 nd distribution area is calculated according to the data of the household meter; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iAnd collecting a 2 nd station area total meter electric quantity sample in the system for time i.
In this embodiment, the specific content of step S3 is: and solving the station area user variable check mixed integer model by adopting a branch-and-bound solving algorithm. The branch-and-bound method is an effective method for solving integer programming problems. The method is based on 'relaxation', 'branching', 'delimiting' and 'clipping', and starts from the optimal solution of the original relaxation problem, discrete variables are branched layer by layer, feasible domains are subdivided step by step, and finally the discrete variables are approximated to integer solutions.
The basic principle of the method is as follows: the model to be solved is a mixed integer convex programming model shown as the following formula, wherein x is a binary integer variable containing 0 or 1, f (eta) is an objective function, h (eta) is an equality constraint, and g (eta) is an inequality constraint.
min f(x)
s.t.h(x)＝0
If the solution is started by taking 0 or 1 from the 1 st integer variable by building a binary tree until the last integerNumber variable, then the original model has 2mThe scale is solved, and the problem of dimension disaster is easily caused. The model boundary is determined through a branch-and-bound algorithm, and branches which are obviously impossible to be superior to the current feasible solution are removed, so that the solving scale is greatly reduced, and the optimal solution of the mixed integer is obtained.
The number of integer variables is 3, i.e. the integer variable in the model is x1,x2,x3As shown in FIG. 2, the binary tree starts to be built, and the root node is numbered "0", at which time the model lower boundfIs + INF (plus infinity):
(1) relaxation and branching: generate x1Take a branch of 0 or 1 and relax other binary integer variables to [0,1]Continuous variable solving model;
(2) delimitation: solving one by one from left to right, firstly solving until the leaf node of the 1 st branch, and carrying out the 2 nd branch solution to obtain the 1 st feasible solution x under the assumption that no feasible solution exists1,x2,x3If the value of the objective function f' is smaller than the lower bound of the original model + INF, the lower bound of the model is updated by ffContinuing to solve the 3 rd branch;
(3) cutting branches: when assuming the 3 rd branch is solved, when x2The relaxation solution of the model when taking 1 is already larger than the current lower bound of the modelfThe condition of solving the model downwards is more rigorous, and the target value is worse, so that the branch has no need of solving downwards, and the 3 rd branch and the 4 th branch are cut off;
(5) determining an optimal solution: repeating the processes of delimiting and pruning until all branches are traversed, assuming that the 5 th branch has no solution, and the 6 th branch updates the lower bound of the modelfAnd 7 th and 8 th branches are cut without solving. At this time, the optimal solution of the model is the lower bound of the modelfInteger solution x of corresponding branch 61,x2,x3And (4) obtaining the optimal solution of the model.
In this embodiment, the specific content of step S4 is: in reality, the operation is performed under the condition that the distribution room is not in the optimal solution of the model (that is, the line loss is not the minimum), so that a plurality of distribution room membership relations with decreasing optimality need to be obtained. The method for obtaining the topological relation of the station area with the highest possibility of descending the most priority step by applying the integer segmentation method specifically comprises the following steps: adding an integer partition in the solved integer programming optimal solution to make the previously solved optimal solution infeasible, solving the model again to find a suboptimal integer solution, repeatedly executing the process to obtain the set number optimal solution in the integer programming, and finding the optimal, suboptimal and third optimal … … solutions of the model by the method.
In this embodiment, the specific content of step S5 is: and establishing a reliability evaluation index, and performing reliability evaluation on checked and corrected abnormal users affiliated to the distribution area. The method comprises the steps of judging the possibility of abnormity of user variable relations by calculating the credibility evaluation index of each user, and arranging a checking sequence according to the credibility index, wherein the credibility index epsilon corresponding to a user kkIs calculated as follows:
in the formula, WlossThe method comprises the following steps of (1) according to marketing system files, summing the line loss squares of two distribution areas;
the electric quantity of the mth user belonging to the 1 st distribution area at the time i based on the marketing system file is m ' is 1,2,3, … n ', and n ' user tables are totally contained in the file belonging to the 1 st distribution area;
the electric quantity of the mth user at the time i, which belongs to the 2 nd distribution area, of the archive is m ' is 1,2,3, … n ', and n ' user tables are shared by the 2 nd distribution area in the archive;
the original marketing file belongs to the distribution area 2, and the user serial number k of the distribution area 1 is adjusted at the moment; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iCollecting a 2 nd station area total meter electric quantity sample in the system for time i;y”1ithe total electric quantity is calculated for the adjusted background area 1; y'2iThe total amount of electricity calculated for the adjusted background area 2.
If only the kth user has the user-to-user relationship error and other users do not have the user-to-user relationship error, only the user electric quantity with the abnormal single user-to-user relationship is adjusted at the moment
At this moment, the
And (4) counting the total electric quantity of the platform area 1, and removing the total electric quantity from the platform area 2, namely adjusting the total electric quantity from the 2 nd platform area to the 1 st platform area by the file. The line loss square sum P of the original platform arealossAnd adjusting the difference of the square sum of line losses of the background area of the user k as an abnormal user reliability index epsilonk. The greater the confidence index, the greater the likelihood that the user becomes abnormal.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.
Claims (3)
1. A low-voltage transformer area topology identification method based on mixed integer programming is characterized by comprising the following steps:
combining the user electricity consumption information acquisition system data and the marketing system basic archive data, calculating and screening a station area with line loss having strong negative correlation, identifying the station area as an abnormal station area with a user variable membership, extracting electricity quantity sample data from the system, and formulating a sample data cleaning rule to obtain cleaning data;
for the abnormal transformer subordination relation transformer area, introducing a binary variable to accurately represent the transformer area subordination relation, constructing a transformer area transformer check mixed integer model by taking the minimum sum of line loss squares as an optimization target, and solving the transformer area transformer check mixed integer model;
obtaining a station area topological relation with highest possibility of descending the most priority step by using an integer segmentation method;
establishing a reliability evaluation index, and performing reliability evaluation on checked and corrected abnormal users affiliated to the distribution room;
for the abnormal transformer subordination relation transformer area, introducing a binary variable to accurately represent the transformer area subordination relation, and constructing a transformer area transformer check mixed integer model by taking the minimum sum of line loss squares as an optimization target specifically comprises the following steps:
introduction of ak、bkTwo binary variables represent whether the kth electric energy meter belongs to a certain area, if yes, akA value of 1 indicates that the kth electric energy meter belongs to the region 1, if bk1 represents that the kth electric energy meter belongs to the station area 2; by constraining akAnd bkThe sum of (1) enables a certain sub-electric energy meter to be only affiliated to a certain area;
converting the line loss minimum solving problem into the following table area user variable check mixed integer model, wherein the optimization target is the minimum sum of the line loss squares in all time periods:
in the formula, t is the total number of the collected time samples, and i is the ith time sample; n is the total number of the user tables belonging to 2 distribution areas in the file, and k is the kth user table; p is a radical ofk,iMetering the electric quantity for the kth user at the time i; y'1iIs the total electric quantity of the 1 st distribution room at the time i, similarly, y 'calculated according to the user table data'2iThe total electric quantity of the 2 nd distribution area is calculated according to the data of the household meter; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iFor time i the 2 nd in the system is acquiredA table area total meter electric quantity sample;
the establishing of the credibility evaluation index and the reliability evaluation of the checked and corrected abnormal users belonging to the distribution area specifically comprise the following steps: the method comprises the steps of judging the possibility of abnormity of user variable relations by calculating the credibility evaluation index of each user, and arranging a checking sequence according to the credibility index, wherein the credibility index epsilon corresponding to a user kkIs calculated as follows:
in the formula, WlossThe method comprises the following steps of (1) according to marketing system files, summing the line loss squares of two distribution areas;
the electric quantity of the mth user belonging to the 1 st distribution area at the time i based on the marketing system file is m ' is 1,2,3, … n ', and n ' user tables are totally contained in the file belonging to the 1 st distribution area;
the electric quantity of the mth user at the time i, which belongs to the 2 nd distribution area, of the archive is m ' is 1,2,3, … n ', and n ' user tables are shared by the 2 nd distribution area in the archive;
the original marketing file belongs to the distribution area 2, and the user serial number k of the distribution area 1 is adjusted at the moment; y is1iCollecting a 1 st station area total meter electric quantity sample, y, in the system for time i2iCollecting a 2 nd station area total meter electric quantity sample in the system for time i; y ″)1iThe total electric quantity is calculated for the adjusted background area 1; y ″)2iThe total amount of electricity calculated for the adjusted background area 2.
2. The method for identifying the low-voltage transformer area topology based on the mixed integer programming as claimed in claim 1, wherein a branch-and-bound solution algorithm is adopted to solve the transformer area household variation check mixed integer model.
3. The method for identifying the low-voltage transformer area topology based on the mixed integer programming as claimed in claim 1, wherein the step of obtaining the transformer area topology relation with the highest possibility of the highest priority progressive reduction by using the integer partition method specifically comprises: and adding an integer partition in the solved integer programming optimal solution to make the previously solved optimal solution infeasible, solving the model again to find a suboptimal integer solution, and repeatedly executing the process to obtain a set number optimal solution in the integer programming.
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