TWI491205B - Method for assigning transmission line of stochastic computer network - Google Patents

Description

Transmission line configuration method of random computer network

The present invention relates to a transmission line configuration method for a random computer network, and more particularly to an optimized transmission line configuration method for a random computer network that can simultaneously consider maximum network reliability and minimum total cost.

Computer network is an important tool for transmitting information in modern life. Whether it is a public agency, a profit-making organization or a non-profit organization or an individual, the transmission of information depends on the computer network. Therefore, the stability of the computer network will affect Execution of each job. At present, many research departments focus on the reliability evaluation and optimization of computer networks. Therefore, by establishing a network model to simulate a computer network, various evaluations can be facilitated. Among them, the arc on the network model represents the transmission line in the computer network, and the node on the network model is used to represent the server in the computer network.

For decision makers, how to achieve the optimization of network reliability and the minimization of total cost at the same time is the most difficult problem in the transmission line configuration of random computer networks. The so-called transmission line assignment (transmission line assignment) The pointer is placed on each side of the network model, and a transmission line is disposed thereon, and the same transmission line is not disposed on the other side. In order to construct a stable computer network, the conventional computer network can be regarded as a binary state network, that is, the edge or node in the network model considers only two states: a normal operation and a failure state. However, the actual transmission line in the computer network is composed of a plurality of physical lines (such as a fiber optic cable, a copper shaft cable or a twisted pair, etc.), and each physical line can contain two states. : providing a specific state of capacity or a failure state.

Since each transmission line has a plurality of states, and has a configuration cost corresponding to its unit length. Therefore, the computer network will have multiple states when configuring a set of transmission lines, so it can be called a stochastic computer network (SCN). For any set of transmission line configurations, network reliability can be defined as the probability that a particular amount of data will be successfully transmitted by a sender to a receiver in the set of transmission lines. The total cost is the sum of the configuration costs of all transmission lines on the computer network.

Therefore, how to configure an optimized transmission line on a computer network to construct a stable and economical computer network is an problem that the technical field is eager to solve.

An object of the present invention is to provide a transmission line configuration method for a random computer network, thereby finding a set of optimal transmission line configurations, so that a specific amount of data can be successfully transmitted from a transmitting end to a receiving end through a computer network. .

Another object of the present invention is to provide a transmission line configuration method for a random computer network, and at the same time consider the network reliability and total cost of the transmission line configuration to construct a reliable, stable and economical computer network.

Other objects and advantages of the present invention will be further understood from the technical features disclosed herein.

In order to achieve one or a part or all of the above or other objects, a method for configuring a transmission line of a random computer network according to an embodiment of the present invention is for evaluating a network reliability of a plurality of transmission line combinations in a computer network. Degree and total cost to select an optimal transmission line combination, the method includes: defining each A transmission line combination is a first independent solution; calculating a network unreliability and a total cost of each of the first independent solutions; performing an algorithm to generate a plurality of second independent solutions, and calculating each second One of the independent solutions is the network unreliability and a total cost; merge all the first independent solutions and the second independent solutions, and determine one of the first independent solutions according to the network unreliability and total cost. And a crowded distance, and a non-dominated level and a crowded distance of each second independent solution; performing a competitive selection according to the non-dominated level and the crowded distance, and the set formed by the first independent solution and In the set formed by the second independent solution, a plurality of third independent solutions are selected; the set formed by the third independent solution is converted into a matrix; a target weight vector is input; and the matrix is normalized to form a regular matrix; According to the target weight vector and the normal matrix, a weighted normalization matrix is constructed; one positive ideal solution and one negative ideal solution are calculated; a positive one of each third independent solution and positive ideal solution is calculated. Degree, and calculate the degree of negative separation of each of the third independent solution and the negative ideal solution; calculate the relative proximity of each of the third independent solutions according to the degree of positive separation and the degree of negative separation; and will have relative proximity The value is defined as the third independent solution that is closest to one, which is a best compromise solution, and the best compromise solution is an optimal transmission line combination.

Each transmission line combination includes a point, at least one relay point, an end point, and a plurality of transmission lines. The transmission line includes a first transmission line and a second transmission line, and the first transmission line is disposed between the start point and the relay point, and The second transmission line is disposed between the relay point and the end point to form one of the transmission line combinations, wherein the load state of the first transmission line is different from the load state of the second transmission line.

In an embodiment, the step of calculating network unreliability further includes: The information demand is distributed in two transmission paths between the start point and the end point, wherein the two transmission paths are composed of transmission lines, each transmission line has a complex load quantity and a load upper limit value; defining an information flow vector, which is One of each transmission path is composed of information traffic, and the sum of the information flows is the information demand; finding all the information flows satisfying each transmission path is a relationship less than or equal to the load upper limit of each transmission line. Information flow vector; convert each information flow vector satisfying the above relationship into a corresponding load vector; compare the size of each two load vectors, and delete the larger one, and define the remaining load vectors as the lower bound Vector; evaluates the probability that each load vector is greater than or equal to the lower bound vector, and defines the probability as network reliability; and calculates network unreliability based on the network reliability.

In an embodiment, the algorithm is a non-dominated solution sorting algorithm, wherein the step of performing the algorithm further comprises: defining an evolution number and a number of times, wherein the starting value of the number of evolutions is one; each execution In one algorithm, the number of evolutions is increased by one; whether the number of evolutions is equal to the number of times of integration; when the number of evolutions is less than the number of times of integration, the set formed by the first independent solution and the set formed by the second independent solution are combined, and According to the network unreliability and the total cost, the non-domination level and the congestion distance are determined; and the competitive selection is performed according to the non-domination level and the congestion distance, and then the set formed by the third independent solution is selected. Wherein, when the number of evolutions is greater than or equal to the number of times of stacking, the algorithm is stopped.

In an embodiment, the step of performing a competitive selection further comprises: comparing two of the non-dominant levels, and deleting the larger one, the others being defined as a third independent solution; if the non-dominant level If the two are equal, compare the crowded distances corresponding to the two with equal non-dominated levels And the deleted ones are correspondingly smaller, and the rest are defined as the third independent solution.

The above and other technical contents, features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments. The directional terms mentioned in the following embodiments, such as upper, lower, left, right, front or rear, etc., are only used to refer to the directions of the accompanying drawings. Therefore, the directional terms are used for illustration only and are not intended to limit the invention.

The transmission line configuration method of the random computer network in the embodiment of the present invention uses a computer to execute a transmission line configuration software, and the computer has an input unit, an operation unit and an output unit. As for the transmission line configuration method, a non-dominated Sorting Genetic Algorithm II (NSGA-II) is combined with a Technology for Order Preference by Similarity to Ideal Solution (TOPSIS). To find the best combination of transmission lines with one of the greatest network reliability and the lowest total cost.

By non-dominated sorting gene algorithm, a non-dominated set, or a Pareto set, can be found, wherein the Pula diagram set has a Pareto solution. The so-called Pella diagram means that the solution has at least one criterion that outperforms other solutions. In addition, a best compromise solution, that is, an optimal transmission line combination, can be found in the set of non-dominated solutions according to the relative weight of each criterion given by the decision maker and in combination with the preference order evaluation method.

First, a network model (N, A) is built to simulate a computer network, where N stands for a complex node, A={ a _i |1 i n } represents n edges a _i on the network model, the distance of each side a _i is represented as l _i , and the node N includes a point O together, at least one relay point and one end point D. Wherein, P ₁ , P ₂ , . . . , P _q represent the q minimum path composed of the edge a _i and the node N in the network model. In addition, the computer network has a complex transmission line with V={ v _r |1 r z} represents the set consisting of the transmission line, v _r r transmission lines for the article transfer line set. Wherein, each transmission line v _r has a plurality of load states: 1, 2, ..., m _r , and each load state corresponds to a load capacity that can be carried as 0 = K _{r 1} < K _{r 2} <...< Load upper limit Is And its corresponding probability is Pr ( ), Pr ( ),...,Pr( ), Indicates the e- type load provided by the transmission line v _r , and the unit length cost of each transmission line is represented by c _r .

Referring to the first figure, the network model has a point O, an end point D, two relay points N ₁ , N ₂ and four sides a ₁ - a ₄ , and includes a first transmission line and a second transmission line, which will be a transmission line disposed on the origin O side and a relay point between N _{1 1,} a second transmission line disposed on a side of the relay point between the end point N ₁ and D ₂ to form a transmission line, or a combination The first transmission line is disposed on the side a ₃ between the starting point O and the relay point N ₂ , and the second transmission line is disposed on the side a ₄ between the relay point N ₂ and the ending point D to form another Transmission line combination. Wherein, the number of transmission lines to be configured is more than the number of edges between the two nodes to form a plurality of sets of transmission line combinations to find an optimal transmission line combination.

In this embodiment, each transmission line combination is defined as a separate solution, represented by X = ( x ₁ , x ₂ , . . . , x _n ). If a transmission line v _r is _disposed on the edge a _i , then x _i = r . When the computer network determines a transmission line combination X , the network is a random computer network, and the computer network can have an information flow vector F = ( f ₁ , f ₂ , ..., f _q ) and a load. The vector Y = ( y ₁ , y ₂ , ..., y _n ) is represented. In addition, a network reliability system is defined as the probability that a computer network under a combination of transmission lines can successfully transmit a d unit of information demand, expressed as R _d ( X ), and the total cost of configuring the transmission line is Expressed as C ( X ).

Please refer to the second figure, which is a flowchart for executing the above-mentioned transmission line configuration software, which can be used to evaluate the network reliability and total cost of a plurality of transmission line combinations in a computer network to select an optimal transmission line combination. Finished as follows:

Step (S1): First, each transmission line combination is defined as a first independent solution. At the same time, the input unit accepts the information demand quantity d of the input end of the user of the transmission line configuration software, and defines an initial parameter, including an evolution count count and a stacking number η, and the evolution count count is One. The number of times of stacking η is set by the user.

Step (S2): randomly generating a plurality of first independent solutions to generate θ initial groups: X ₁ , X ₂ , . . . , X _θ , and calculating a network unreliability of each of the first independent solutions And a total cost. The network unreliability can be calculated by the step (S20) of the third figure, and is represented by s ₁ =1 - R _d ( X ), and the total cost thereof is represented by s ₂ = C ( X ).

Step (S3): Perform an algorithm to generate a complex second independent solution. Wherein, each time an algorithm is executed, the number of evolutions is increased by one, that is, count = count + 1 , and the algorithm includes a competitive selection, a single point mating, and a mutation.

Step (S4): By the step (S20) of the third figure, one of the network unreliability s ₁ and the total cost s _{2 of} each of the second independent solutions can be calculated.

Step (S5): combining the set formed by the first independent solution and the set formed by the second independent solution, and according to their respective network unreliability and total Cost, to determine one of the first independent solutions, one non-dominant rank and one crowded distance, and one of each second independent solution, a non-dominated level and a crowded distance.

Step (S6): selecting a plurality of third independent solutions from the set formed by the first independent solution and the second independent solution according to the non-dominance level and the congestion distance to perform a competitive selection. . The step of performing a competitive selection further includes: comparing the non-dominated levels of all the first independent solutions and the second independent solutions, and deleting the larger ones, and the remaining ones are defined as the third independent solutions; If the second level of the sex rank is equal, then the crowded distance corresponding to both of the equal non-dominant grades is compared, and the corresponding crowded distances are deleted, and the rest are defined as the first Three independent solutions. In particular, the third independent solution is a so-called Pella diagram, so the non-dominance level of the third independent solution is the best non-dominated level, ie rank=1.

At this time, it is determined whether the count number is equal to the number of iterative evolution of a user with a set of η. When the count is less than the number of iterative times with evolution [eta], the process returns to step (S3); when the count is greater than or equal to the evolution of the number of iterative frequency and [eta], the algorithm is stopped, the output unit outputs the third set of separate solutions to the formed The next step (S7).

Step (S7): Converting the set formed by the third independent solution into a matrix S , wherein the matrix S represents the j- th target value of the i- th independent solution in the set formed by the third independent solution by the complex element s _ij .

Step (S8): input a target weight vector W , wherein the target weight vector W has a plurality of weights w _j , w _j represents the weight of the jth target value, and the sum of the weights is one, that is, the W must satisfy

Step (S9): normalizing the matrix S to form a regular matrix , its expression is as follows: , where i =1, 2, ..., τ and j =1, 2 (1)

Step (S10): according to the target weight vector W and the normal matrix To construct a weighted normalization matrix , its expression is as follows: , where i =1, 2, ..., τ and j =1, 2 (2)

Step (S11): Calculating a weighted normalization matrix One positive ideal solution S ⁺ and one negative ideal solution S ^- , the expression is as follows:

Step (S12): calculating a degree of positive separation between each of the third independent solution and the positive ideal solution And calculating the degree of negative separation of each of the third independent solution and the negative ideal solution , its expression is as follows: , where i =1, 2,..., τ (5)

, where i =1, 2,..., τ (6)

Step (S13): according to the degree of positive separation And negative separation To calculate the relative closeness H _{i of} each of the third independent solutions, the expression is as follows: , where i = 1, 2, ..., τ and 0 < H _i <1 (7)

Step (S14): defining a third independent solution having a relative proximity H _i that is closest to one, which is an optimal compromise solution, and step (S15): defining the best compromise solution as the best one. The transmission lines are combined and displayed by combining the output transmission unit with the output optimal transmission line on a display unit.

As shown in the third figure, it is a flowchart of a method for calculating network unreliability in the process of performing the above step (S20). Through the network reliability evaluation algorithm (NREA), and with the minimum path (MP) and Recursive Sum of Disjoint Products (RSDP) method to calculate the network The road is unreliable. The detailed steps are as follows: Step (S21): A information demand is distributed in two transmission paths between the start point and the end point, wherein the two transmission paths are composed of a plurality of transmission lines.

Step (S22): defining an information flow vector F = ( f ₁ , f ₂ , ..., f _m ), which is composed of one of the information flow vectors transmitted by each transmission path configuration, wherein each An information flow is information transmitted via a transmission path between a start point and an end point.

Step (S23): Find all the information flow F that satisfies the information flow of each transmission path, which is less than or equal to the load upper limit value of each transmission line, that is, whether it satisfies the following relationship: , where a _i A. The sum of the information traffic in all transmission paths is the information demand and must be met. . If at least one information flow vector F is obtained , step (S23) is performed; otherwise, the network reliability R _{d of the} transmission line combination is defined to be zero, and step (S27) is performed to obtain network unreliability s ₁ =1- R _d ( X ), and the value of the network unreliability s _{1 is} transmitted to the step (S2) or (S4) in the second figure.

Step (S24): converting, by the operation unit, each information flow vector satisfying the above relationship into a corresponding load vector Y =( y ₁ , y ₂ , . . . , y _n ), and the load vector Y = ( y ₁ , y ₂ ,..., y _n ) is composed of one of the transmission lines of each transmission line, which can be converted by using the following relation: y _i = , where e {1,2,..., }, and meet , where a _i A.

Step (S25): comparing the size of each of two load vectors, delete greater, the rest of the load vector is defined as the lower bound vector d - MPs (lower boundary vector for d).

Step (S26): Evaluate the probability that each load vector is greater than or equal to the lower bound vector, and define the probability as the network reliability R _d .

Step (S27): Calculate the network unreliability s ₁ =1- R _d ( X ) according to the network reliability R _d . Finally, after the loop of the step (S20) is finished, the value of the network unreliability s ₁ is transmitted to the step (S2) or (S4) in the second figure.

In the following, in a preferred embodiment, how to use a transmission line configuration method of a random computer network to implement a dominating solution algorithm to find a Plato set, that is, by using the step (S1) in the second figure. (S6) to find a third independent solution set. In addition, in combination with the implementation of the preference order evaluation method, a best compromise solution can be selected from the above-mentioned Plato set, that is, steps (S7) to (S15) in the second figure to find the maximum network reliability and minimum. An optimal transmission line configuration for total cost.

At the same time, refer to the fourth figure, Table 1 and Table 2. The fourth picture is a schematic diagram of the network model of the computer network of Taiwan universities and colleges. The 80 transmission lines in Table 1 and Table 2 are the existing transmission lines of the computer network company. . Among the 80 transmission lines, the transmission line is selected and deployed in the computer network of Taiwanese colleges and universities, and the unit length cost of each transmission line is calculated by NTD, and it is composed of a plurality of first physical wires. OC-36 (Optical Carrier 36) and a plurality of second physical wires OC-18 lines (Optical Carrier 18). Each of the first physical wires OC-36 has two load states: one can provide a bandwidth of 2 Gbps (giga bits per second) under normal conditions, and the other provides a bandwidth of 0 Gbps in the case of failure. ;with Each second physical wire OC-18 has two load states: one that provides 1 Gbps of bandwidth speed under normal conditions and the other provides 0 Gbps bandwidth speed in the event of a failure.

The following is an example of the transmission line and its probability distribution: assuming that a transmission line consists of two first physical wires OC-36, the probability of each first physical wire OC-36 being in the event of failure is 0.1, and the transmission line has three loads. Status: 0Gbps, 2Gbps and 4Gbps. If both first physical wires OC-36 are in a failure condition and the load state of the transmission line is 0 Gbps, the probability of corresponding to the load state is (0.9) ⁰ (0.1) ² = 0.01. If the load status provided by the transmission line is 2 Gbps, the probability of corresponding to the load status is (0.9) ¹ (0.1) ¹ =0.18. If the load status provided by the transmission line is 4 Gbps, the probability of corresponding to the load status (0.9) ² (0.1) ⁰ = 0.81.

The architecture of the network model in the fourth figure is a network of servers from a number of colleges, high schools, and countries. Each network server is represented by a node and is used by Taiwan University. NTU is used as the starting point O, and NSYSU of Zhongshan University is used as the ending point D. Considering that different information needs d = 3Gb, d = 4Gb and d = 5Gb, before finding a Platonic set by dominating the solution sorting algorithm, we need to define an initial parameter, including an initial group θ=100. The number of times of laps is η=3000, a mating rate α=0.8, and a mutation rate β=0.1. In addition, the length information of the complex side in the network model is summarized in Table 3.

The results of the various combinations of transmission lines under different information requirements are listed in Table 4 by the set of Platos obtained by the steps in the second and third figures, and the fifth figure depicts the information demand d = 5Gb. The distribution of the complex best compromise solution, that is, the distribution of the best transmission line combinations with different network reliability and their corresponding total cost.

In this embodiment, three schemes are provided for the decision maker to select the most appropriate combination of transmission lines: the network reliability of the transmission line combination is used as a main criterion, the total cost of the transmission line combination is used as a main criterion, or there is no specific criterion. . If the network reliability is used as the main criterion, the target weight vector W = (0.8, 0.2) is set, and the network reliability of the transmission line combination is 0.95436, as shown in the fifth and fourth tables. The total cost is $65385 (NTD); if there is no specific criterion, the target weight vector W = (0.5, 0.5) is set, and the network reliability of this transmission line combination is 0.93487, and the total cost is $62450 (NTD). If the total cost is used as the main criterion, the target weight vector W = (0.2, 0.8) is set, and the network reliability of the transmission line combination is 0.92895, and the total cost is $62360 (NTD). According to the different weights in the target weight vector, an optimal compromise solution can be selected from the Plato set by the preference order evaluation method. Therefore, the decision maker can select a combination of the most appropriate transmission lines from a plurality of optimal transmission line combinations according to different criteria.

In summary, the present invention provides a transmission line configuration method for a random computer network, which can consider network reliability or total cost to find an optimal transmission line combination, so that the supply end of the computer network can meet the demand side. Specific information needs to ensure that information can be distributed to the demand side.

The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent. In addition, any of the objects or advantages or features of the present invention are not required to be achieved by any embodiment or application of the invention. In addition, the abstract sections and headings are only used to assist in the search of patent documents and are not intended to limit the scope of the invention.

The first picture is a simplified diagram of the network model.

The second figure is a transmission line of a random computer network in the embodiment of the present invention. Flow chart of the configuration method.

The third figure is a flow chart of the method for calculating network unreliability.

The fourth picture is a schematic diagram of the network model of the computer network of Taiwanese colleges and universities.

The fifth figure is a schematic diagram of the best transmission line combination obtained by the network model in the fourth figure, and distributed according to its network reliability and total cost.

Claims (10)

A transmission line configuration method for a random computer network, which is used for evaluating network reliability and total cost of a plurality of transmission line combinations in a computer network to select an optimal transmission line combination, the method comprising: The transmission line combination is defined as a first independent solution; calculating one of the first independent solutions for network unreliability and a total cost; performing an algorithm to generate a complex second independent solution, and calculating each of the second Independently solving a network unreliability and a total cost; combining the set formed by the first independent solutions and the set formed by the second independent solutions, and according to the network unreliability and the And a total cost, to determine a non-dominated level and a crowded distance of each of the first independent solutions, and a non-dominated level and a crowded distance of each of the second independent solutions; according to the non-dominant level And the crowded distances to perform a competitive selection, and wherein the set of the first independent solutions and the set of the second independent solutions select a complex third independent solution; Three independent Converting the formed set into a matrix; inputting a target weight vector, wherein the target weight vector has a plurality of weights, and the sum of the weights is one; normalizing the matrix to form a regular matrix; a target weight vector and the normal matrix to construct a weighted normalization matrix; calculating a positive ideal solution and a negative ideal solution of the weighted normalization matrix; calculating each of the third independent solution and the positive ideal solution Degree of separation, And calculating a degree of negative separation of each of the third independent solution and the negative ideal solution; calculating a relative proximity of each of the third independent solutions according to the degree of positive separation and the degree of negative separation; and The value of the relative proximity is the third independent solution closest to one, defined as an optimal compromise solution, and the best compromise solution is an optimal transmission line combination. The method for configuring a transmission line of a random computer network according to claim 1, wherein each of the transmission line combinations includes a point, at least one relay point, an end point, and a plurality of transmission lines, wherein the transmission line includes a first transmission line and a second transmission line, the first transmission line is disposed between the starting point and the relay point, and the second transmission line is disposed between the relay point and the end point to form a combination of the transmission lines In one case, the load state of the first transmission line is not the same as the load state of the second transmission line. The method for configuring a transmission line of a random computer network according to claim 2, wherein the step of calculating the network unreliability further comprises: distributing an information demand amount to the two transmission paths between the starting point and the end point. Wherein the two transmission paths are composed of the transmission lines, each of the transmission lines having a complex load amount and a load upper limit value; defining an information flow vector, which is an information flow rate of each of the transmission paths Composed, and the sum of the information flows is the information demand; finding all the information flows satisfying each of the transmission paths is less than or equal to the relationship of the load upper limit of each of the transmission lines Information flow vector Each of the information flow vectors satisfying the above relationship is converted into a corresponding load vector; the size of each of the load vectors is compared, and the larger one is deleted, and the remaining load vectors are defined as a lower bound vector; Evaluating the probability that each of the load vectors is greater than or equal to the lower bound vector, and defining the probability as the network reliability; and calculating the network unreliability according to the network reliability. For example, the transmission line configuration method of the random computer network described in claim 1 is a non-dominated solution sorting algorithm. The method for configuring a transmission line of a random computer network according to claim 1, wherein the step of executing the algorithm further includes: defining an evolution number and a number of times, wherein the initial value of the evolution number is one Each time the algorithm is executed, the number of evolutions is increased by one; whether the number of evolutions is equal to the number of times of the overlap; and when the number of evolutions is less than the number of times of the overlap, the set formed by the first independent solutions and The sets formed by the second independent solutions are combined, and the non-dominated levels and the crowded distances are determined according to the network unreliability and the total cost; and according to the non-dominant levels And the crowded distances to perform the competitive selection, and then select the set formed by the third independent solution. The method for configuring a transmission line of a random computer network according to claim 5, wherein the number of times of the connection is set by a user. The method for configuring a transmission line of a random computer network according to claim 5, wherein the step of determining whether the number of evolutions is equal to the number of times of the overlap further comprises: stopping the number of times when the number of evolutions is greater than or equal to the number of times of the overlap Algorithm. The method for configuring a transmission line of a random computer network according to claim 1, wherein the step of performing the competitive selection further comprises: comparing the two non-dominant levels, and deleting the larger one. The rest are defined as the third independent solution. The method for configuring a transmission line of a random computer network according to claim 1, wherein the step of performing the competitive selection further comprises: comparing the two non-dominant levels; and if the If the second level of dominance is equal, the crowded distances corresponding to the two having equal non-dominant levels are compared, and the corresponding crowded distances are deleted, and the rest are Defined as this third independent solution. The method for configuring a transmission line of a random computer network according to claim 1, further comprising: executing a transmission line configuration software by using a computer, the computer having an input unit, an operation unit and an output unit; Receiving one of the information demand input by the user of the transmission line configuration software, the complex load state of each of the transmission lines, and a load upper limit value; the optimal transmission line combination is calculated by the operation unit; The optimal transmission line combination is displayed on the output unit.