JP2002189769A - Method for designing underground conduit structure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To objectively and quantitatively evaluate the balance between safety and economical efficiency. SOLUTION: In the designing method, when the method is started, examination conditions are inputted in S1. The examination conditions include a design condition, design variable and its examination range, alternative design preparation condition and limit state. In S2, a random number is generated, and n pieces of alternative designs are prepared. When the n pieces of alternative designs are prepared, fitness is respectively evaluated with respect to the n pieces of alternative designs in S3. In the fitness evaluation, the fitness evaluation for safety and the fitness evaluation for economical efficiency are handled on the same basis to each other, and a fitness evaluation by Pareto ranking is performed in order to evaluate the balance between the safety fitness evaluation and the economical efficiency fitness evaluation. In S4, n pieces of alternative designs based on genetic algorithm are updated, and in S5, local search is carried out. When it is decided that the number of generations reaches N in S6, a shift is made to S7. In the S7, an optimum alternative design is selected, results are outputted and the procedure is finished.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for designing an underground pipeline structure, and more particularly to a method for balancing the safety and economy of pipelines such as box culverts installed underground.
The present invention relates to a design method that can be evaluated objectively and quantitatively.

[0002]

2. Description of the Related Art When designing a pipe structure such as a reinforced concrete box culvert to be installed at a predetermined depth in the ground by an open-cutting method or the like, a designer generally performs the design in the following procedure. It is carried out.

That is, a normal design procedure is firstly performed by referring to the designer's own experience and the existing design conditions, etc., in order to always consider the limit state, pipe, The design variables such as the member thickness are determined based on the examination conditions such as the road installation level, the material properties of the pipeline, the geological composition and physical properties of the pipeline installation location, and the groundwater level.

[0004] Next, a structural design is performed based on the determined design variables, and the yield strength and the behavior of the skeleton are calculated by trial production experiments and simulations (structural analysis). Check if it does not meet the allowable value, if it does not satisfy the allowable value, slightly change the design variables set first, repeat the previous procedure, determine the structural specifications that satisfy the allowable value, The design has been completed.

[0005] However, such a conventional method of designing an underground pipeline structure has the following problems.

[0006]

That is, in the above-described conventional design method, the framework of the underground pipeline is designed based on the experience and acquired knowledge of the designer. For example, even if commercially available design software is used, an appropriate design can be performed with a relatively small number of repetitions, but it takes a lot of time if there is little experience.

[0007] Even if a design can be designed to a certain degree of efficiency, it is not objectively clear whether or not the safety and the economical efficiency of the designed structure are balanced. Even if it could be evaluated to some extent, there was a problem that the evaluation was not quantitative.

The present invention has been made in view of such conventional problems, and an object of the present invention is to provide an underground system capable of objectively and quantitatively evaluating the balance between safety and economy. An object of the present invention is to provide a method of designing a pipeline structure.

[0009]

SUMMARY OF THE INVENTION In order to achieve the above object, the present invention relates to a pipe installation level, a pipe material property, a stratum composition and a physical property value of a pipe installation location, a groundwater level, and a structure of a pipe. In a method of designing an underground pipeline structure based on study conditions including design conditions such as limit conditions to be considered in design, in the study conditions, a plurality of design variables set in advance are added, and A plurality of design alternatives are created by performing the combination based on random numbers, and the safety and economy of each of the created multiple design alternatives are respectively evaluated.The obtained evaluation result is referred to as the safety and economic efficiency. Is displayed on the two-dimensional coordinates as a parameter, a solution that does not include other evaluation results is set as a Pareto solution with high fitness in a quadrangle having the origin and the evaluation result as diagonals. Required and finally required Depending on the conditions, and to include the step of the final design plan can be selected from a plurality of the Pareto solutions in.

According to the method of designing an underground pipeline structure having the above-described configuration, a plurality of design variables set in advance are added to the study conditions, and a combination of the design variables is performed based on random numbers, so that a plurality of design proposals are formed. When the safety and economics of each of the created multiple design alternatives are evaluated, and the obtained evaluation results are displayed on the two-dimensional coordinates using the safety and economics as parameters, the origin and evaluation are evaluated. A solution that does not include other evaluation results is determined as a Pareto solution having a high degree of fitness in a quadrangle having the result as a diagonal, and a plurality of solutions are obtained. Since the final design plan can be selected from within the Pareto solution, the selected final design plan is evaluated as a balance between safety and economy,
Moreover, since the evaluation is selected from those obtained as Pareto solutions, the evaluation is objective and quantitative.

Further, in the present invention, a parameter of a genetic algorithm and the number of generations are added to the above-mentioned examination conditions, and storage, selection, selection, crossover, and mutation of elite pareto are set for a plurality of Pareto solutions. And a step of obtaining an improved Pareto solution each time the genetic algorithm is repeated for the set number of generations.

According to this configuration, by adopting the genetic algorithm, when there are a plurality of local solutions, or when design variables taking discrete values (reinforcing bar diameter, member thickness, etc. of a reinforced concrete skeleton of an underground pipeline). Effective measures can be taken, and a more suitable Pareto solution can be obtained.

Further, according to the present invention, for the improved solution, safety when the design variable is slightly changed is obtained.
If the safety does not change from before the change, the method may include a step of sequentially changing the design variables to the changed values.

According to this configuration, the calculation time when the genetic algorithm is employed can be reduced.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below in detail with reference to the accompanying drawings. 1 to 11 show an embodiment of a method of designing an underground pipeline structure according to the present invention.

FIG. 1 is an overall flowchart of the design method according to the present invention. In the design method of the present embodiment, a box culvert 10 having a shape as shown in FIGS. Designed.

In the design method of the present embodiment, first, when the design procedure starts, in step 1 the study conditions are input. The examination conditions input in this case are: Design condition,. Design variables and their study scope,. Design vs. drafting conditions,. This is a critical condition to be considered in the design of a structure.

Here,. The design conditions include the installation level of the box culvert 10, the material characteristics of the box culvert 10, the geological composition of the installation location and its physical properties, the groundwater level, and the like.

FIG. 2 shows more specific contents of the design conditions. The box culvert 10 shown in FIG.
The inner space has a roughly square section of 4.0m x 4.0m, and the upper end is buried at a location about 5m from the ground surface.

The ground layers around the burial site include backfill soil layers (cohesive soil: Bc layer, sandy soil: Bs layer), alluvial sandy soil layer (As layer) and sandy mudstone layer (Tm layer). Therefore, enter the numerical values of the physical properties corresponding to these strata, the depth value of the groundwater level, etc.

The material used for the box culvert 10 is concrete having a design standard strength of 24,40 N / mm ² , the main reinforcing bar is SD295, and the shear reinforcing bar is S.
D345 is used. Note that SD295 and SD345 are
It shows the type of deformed rebar, and each numerical value indicates that the yield point or 0.2% proof stress of the rebar is 295 (345) N / m.
m ² or more.

In addition,. The design variables were set as follows for each element forming the cross section of the box culvert 10. The frame of the box culvert 10 shown in FIGS. 2 and 3 includes a bottom plate 12, a pair of side walls 14 suspended at both ends of the bottom plate 12, and a top plate 16 installed between upper ends of the side walls 14.
And has a substantially square cross section.

The bottom plate 12 has a thickness of WD3, an upper main reinforcing bar of VL3, a lower main reinforcing bar of VU2, and a shear reinforcing bar of VS3. input.

Since the side wall 14 has a thickness of WD2, the main reinforcing bar is VL2, and the shear reinforcing bars are VS2 and VS3, these specific values are input.

The top plate 16 has a thickness of WD1, a lower main reinforcing bar of VL1, an upper main reinforcing bar of VU1, and a shear reinforcing bar of VS1. Enter each.

The study range of each member thickness is shown in Table 1 below.
As shown in FIG.

[0027]

[Table 1]

Further,. In the case of the present embodiment, since the analysis by the genetic algorithm is performed as described later and this is repeated a plurality of times, the parameters of the genetic algorithm, that is, the number of generations N (the number of repetitions) , The number of populations (the number of designs versus plans n), the number of elites saved, the mutation rate, and the like.

In addition,. The limit conditions to be considered in the design of the structure are shown in Table 2 below. The limit conditions to be considered and the checking method are described in the Concrete Standard Specifications (edited by the Japan Society of Civil Engineers, Concrete Standard Specifications, Heisei 8).
Yearly established, 1996).

[0030]

[Table 2]

In the design of a concrete structure using the limit state design method in the field of civil engineering, there is a high degree of recognition of the limit state described in the Standard Specification for Concrete and its checking method, and this is often used.

Therefore, in the present embodiment, the safety was evaluated using this. The Concrete Specification states that the design purpose of the structure is to have a moderate level of safety against the load applied to the structure during construction and during the design life. Therefore, the limit state here is defined for a proper safety of the structure.

When the input of each of the above examination conditions is completed, the process proceeds to step S2. In step 2,. A plurality (n) of design proposals are created corresponding to the design variables.

The results are shown in Table 1 above. In the design variables, there are six types of member thickness (WD1, 2, 3) and the main reinforcing bars (upper bar, VU
13), 13 main bars (lower bar, VL1,2,3)
13 types and 8 types of shear reinforcement (VS1, 2, 3, 4)
Because there is a way, the design countermeasure by these combinations,
^{(6 3) × (13 2} ) × (13 3) × (8 4) = become 328500000000 ways, considering all these, impractical takes a lot of time.

Therefore, in the present embodiment, in step 2, a random number is generated, a combination of these is randomly selected, and n design proposals are created. When n design alternatives are created, in the next step 3, fitness evaluation is performed on each of the n design alternatives.

FIG. 4 shows details of the fitness evaluation performed in step 3. In the fitness evaluation shown in the figure, the safety fitness evaluation shown in the sub-steps 3a to 3d and the economic fitness evaluation in the sub-steps 3e to 3f are treated in the same column in an associated state. I try to evaluate these balances.

That is, in the safety fitness evaluation, the safety is set as the maximum value (minimum value of the safety margin) in the check value for the limit state specified as the input condition, and the specified value is first specified in the sub-step 3a. An analysis model is created for each limit state.

FIG. 5 shows an example of the analysis model created in this embodiment. In the analysis model shown in this figure, the skeleton of the box culvert 10 is a beam element, and the outer peripheral ground contacting the skeleton is schematically represented by shear and horizontal ground springs.

When the setting of the analysis model is completed, in step 3b, an applied load is created. FIG. 6 shows Table 2.
3 shows an example of an acting load created when examining the level 2 ground motion in the limit state shown in FIG.

In the following sub-step 3c, the sectional force (moment, shear force, axial force, displacement) is calculated by structural analysis. For this calculation, for example, a two-dimensional frame analysis of a linear model is used for regular analysis, and a response displacement method is used for the analysis during an earthquake. Is applied to the frame model) to calculate the section force. FIG. 7 shows one mode of the sectional force obtained based on the analysis by the response displacement method.

In this case, the seismic external force used in the analysis at the time of the earthquake is calculated by, for example, performing a one-dimensional ground response analysis (total stress analysis for level 1 ground motion, effective stress analysis for level 2). (The input seismic motion used in this case is given as an acceleration time history waveform.) When the sectional force is calculated, in the following substep 3d, based on the calculation result, the limit state shown in Table 2 is checked, and n is checked. Safety is evaluated for each of the design alternatives.

In this case, the checking method is based on the above-mentioned concrete specification, and the regular examination is a. Ultimate limit state, b. In the investigation at the time of the earthquake, the use limit state is determined by: Study on level 1 ground motion (seismic performance 1), b. Level 2
Investigate seismic motion (seismic performance 2).

To explain this more concretely, first, in the regular examination, a. Ultimate limit state This is the limit state for the maximum load-carrying capacity, and typical examples include the ultimate limit state of section failure, rigid body stability, displacement and displacement. In this example, the safety was evaluated for the ultimate limit state of the cross-sectional fracture (the state in which the cross-section of the structure or the member is broken).

The inspection for safety was carried out for ultimate bending strength and shear strength. In these checks, the ratio of the design section force S calculated by the structural analysis to the design section strength R (check value = S / R) was determined to quantify safety.
Smaller values were considered safer. b. Service Limit State This is a limit state related to normal use or durability, and typical examples include a use limit state of cracking, deformation, displacement and vibration. In the present example, the safety was evaluated for the use limit state of the crack (whether the aesthetic appearance is impaired by the crack, or the durability or the watertightness or the airtightness is impaired).

A check for safety was performed on the width of the bending crack. From the sectional force calculated by structural analysis,
The crack width w was calculated and the ratio of the crack width w to the allowable crack width wa (check value = w / wa) was determined. It was considered that the smaller the check value, the safer.

In the investigation at the time of the earthquake, a. Examination of Level 1 ground motion Level 1 ground motion is a ground motion that occurs several times within the useful life of the structure. The safety of the structure against the seismic motion (the seismic performance to be kept) is that the function is healthy even after the earthquake, and that the structure can be used without repair (seismic performance 1).

The safety was checked for the yield strength and shear strength of the rebar. In these checks, the ratio of the design section force S calculated by the structural analysis to the design section strength R (check value = S / R) was determined to quantify safety. b. Examination of Level 2 earthquakes Level 2 ground motions are strong ground motions that have a very low probability of occurring within the useful life of the structure. The safety of the structure against the seismic motion (seismic performance to be possessed) is that the function can be recovered in a short time after the earthquake, and a condition that does not require reinforcement (seismic performance 2) is satisfied.

Inspection for safety was carried out with respect to mode judgment (guaranteed prior to bending fracture) and deformation performance. The mode is determined by comparing the designed shear strength Vyd with the shear force Vmu when the bending strength is reached.

If Vmu / Vyd is smaller than 1.0, it is determined that the mode is the bending fracture mode and Vmu / Vyd is 1.0.
If it is larger than this, the mode is determined to be the shear failure mode. Flexural failure is more ductile than shear failure,
In the design of the structure, there is a tendency to be as much as possible to the type of bending failure.

In the deformation performance check, the plasticity factor μrd is calculated from the sectional force calculated from the structural analysis, and the design toughness factor μd
(Control value = μrd / μd), and the smaller the ratio, the safer the product.

On the other hand, in the evaluation of the adaptability of economy, the frame cost of the box culvert 10 is obtained for each of n design alternatives by the type of the reinforcing steel and concrete.

For this reason, first, in sub-step 3e, quantity calculation such as the amount of rebar and concrete is performed, and in the following sub-step 3f, the unit price is multiplied to calculate the frame cost. Table 3 below shows an example of the unit price of the reinforcing bar and the concrete in this case.

[0053]

[Table 3]

As described above, when the evaluation of the fitness of each of the n design alternatives and the evaluation of the fitness of the economy corresponding thereto are obtained, in the sub-step 3g, the adaptation by the Pareto ranking is performed. A degree evaluation is performed.

The fitness evaluation based on the Pareto ranking was introduced in order to evaluate the balance between the economic value and the safety of the reference value obtained in the above evaluation. Is a method of ranking by the number of solutions existing in a quadrilateral having the origin and each solution as a diagonal line in the two objective space.

More specifically, sub-step 3
When the evaluation results obtained up to f are displayed on two-dimensional coordinates using safety and economy as parameters, other evaluation results are included in a quadrilateral having the origin and the evaluation results as diagonals. This is an evaluation method in which the solution that is not determined is the Pareto solution with the highest fitness.

For example, as shown in FIG. 8, the evaluation result obtained by the execution up to the sub-step 3f is shown in two-dimensional coordinates where the vertical axis represents economy and the horizontal axis represents safety. Then, the evaluation result of the 0 black circle in the figure, that is, each of these solutions does not include other solutions in the rectangle, so that a total of three solutions are Pareto solutions.

After the fitness evaluation based on the Pareto ranking is performed as described above, the process proceeds to step 4 shown in FIG. In this step 4, update of n design alternatives based on the genetic algorithm (setting of an improved solution)
Is performed.

FIG. 9 shows a detailed procedure of this updating.
In the update by the genetic algorithm, first, in sub-step 4a, an elite to be saved is selected by selecting one having a large fitness during Pareto solution, and the next sub-step 4a is set.
In b, selection and selection, and in the next substep 4c, a new design alternative is created by crossover and mutation.

When such a genetic algorithm is applied to a design proposal, respective improved solutions can be obtained. In other words, the genetic algorithm leaves the best-fit design alternative (Pareto solution) according to the fitness evaluation result,
For other design alternatives, operations such as selection, selection, crossover, and mutation are performed to improve and create a new design alternative.

In this case, since the optimal solution may fall into a local solution, the possibility is prevented by mutation. For some design alternatives according to the set mutation rate, for example, the wall thickness of the box culvert 10, the diameter of the reinforcing bar, and the like are forcibly changed by random numbers, and a next-generation design alternative is created.

By executing such a genetic algorithm, the design alternative is updated, and a local search is performed in the next step 5 in order to search for a better design alternative.

The reason that the local search is employed in the present embodiment is that, in recent years, the computing capability of a computer has been dramatically improved, but as a search method in a large solution area, a relatively efficient optimal method is employed. It takes an enormous amount of time to search for an optimal design alternative using only a genetic algorithm that is considered to be an optimization method.

Therefore, in the present embodiment, a local search is employed in the process of searching for an optimal design alternative by a genetic algorithm in order to perform a search more efficiently and reduce the operation time.

FIG. 10 shows an example of the execution flow of the local search. In the local search flow shown in the figure, for each of a plurality of design alternatives (Pareto solutions) evaluated as having high fitness, operations are performed to change each design variable little by little, and the economics remain unchanged without changing the security. Is better, the changed value is adopted and the design variable is set to the value after the change.

In the flow shown in FIG. 10, a member thickness (WD), a main reinforcing bar (upper bar, VU),
In order of main reinforcement (lower reinforcement, VL) and shear reinforcement (VS), lower by one rank one by one and check the safety,
When the safety changes, the procedure is returned to the original state, and when the security does not change, the procedure is lowered by one rank and the same operation is repeated.

If the result obtained by repeating such an operation is taken as a new design proposal, without lowering the safety,
By lowering the rank, it is possible to change to a design variable that is more economical, so that the search for the optimal solution is made more efficient.

When the above local search is completed, it is determined in step 6 whether or not the number of generations has reached the set N. If the number of generations has not reached N, the flow returns to step 3. , And the above procedure is sequentially repeated.

On the other hand, if it is determined in step 6 that the number of generations has reached N, the flow shifts to step 7 to select an optimal design proposal, output the result, and end the procedure. For example, as shown in FIG. 11, the design proposal output here ultimately requires, from among the Pareto solutions, the highest priority on economy or the priority on safety regardless of economy. Depending on the conditions, a final design plan can be selected from among a plurality of Pareto solutions.

FIG. 12 shows the result of searching for a Pareto solution according to the procedure of this embodiment. FIG. 12A shows the first generation, FIG. 12B shows the seventh generation, and FIG. (C) is the first
Two generations. In addition, this search result is an example in the case where the compressive strength of concrete is set to 24 N / mm ² .

In this specific example,. The design conditions are as shown in FIG. The design variables are as shown in Table 1.
. Table 2 shows the limit conditions to be considered in the design of the structure.
The conditions were set as shown in (1). Also,. The parameters of the genetic algorithm which are the conditions for creating the design proposal were set to 100 design proposals, 12 generations, 10 elite conservations, and 0.1 mutation rate.

Table 4 below shows the cross-sectional data of six design alternatives among the selected optimal design alternatives.

[0073]

[Table 4]

As can be seen from the Pareto solution for each generation shown in FIG. 12, as the generation progresses, the degree of the set of Pareto solutions is improved, and the Pareto solution related to economy and security is improved.

The final design plan is, for example, the design plan E if the designer satisfies the check value ≦ 1.0 and selects a plan with a low skeleton cost.

According to the underground pipeline structure designing method configured as described above, a plurality of design variables set in advance are added to the study conditions, and the combination of the design variables is performed based on random numbers. When creating multiple design alternatives, evaluating the safety and economy of each of the created multiple design alternatives, and displaying the obtained evaluation results in two dimensions with the safety and economics as parameters, A plurality of Pareto solutions that do not include other evaluation results are found in a quadrilateral with the origin and the evaluation results as diagonals, and the final design is made from among the multiple Pareto solutions according to the finally required conditions. Since the alternatives are selectable, the final design alternative selected will be a balance between safety and economics, and the evaluation will:
Since it is selected from the ones obtained as Pareto solutions, it is objective and quantitative.

In this embodiment, the parameters of the genetic algorithm are added to the examination conditions, and the storage, selection, selection, crossover, and mutation of elite pareto are set for a plurality of Pareto solutions. The method includes a step of obtaining an improved Pareto solution by repeating the genetic algorithm by a number.

Therefore, by adopting the genetic algorithm, when there are a plurality of local solutions, or when design variables taking discrete values (rebar diameter of reinforced concrete frame of underground pipeline,
(E.g., member thickness) can be effectively dealt with, and a more suitable Pareto solution can be obtained.

In the above-described embodiment, as shown in the overall flow of FIG. 1, a case is shown in which, following evaluation of fitness based on Pareto ranking, improvement of a design proposal by a genetic algorithm and execution of a local search are performed. However, the genetic algorithm and the local search need not be executed successively.

In the design method shown in the above embodiment,
Although the box culvert 10 having a square cross section is exemplified as the underground pipeline structure, the embodiment of the present invention is not limited to this, and can be applied to, for example, a tunnel constructed by a shield method. The cross-sectional shape is not limited to a square.

[0081]

As described above, according to the method of designing an underground pipeline structure according to the present invention, the balance between safety and economy can be objectively and quantitatively evaluated.

[Brief description of the drawings]

FIG. 1 is an overall flowchart showing one embodiment of a method of designing an underground pipeline structure according to the present invention.

FIG. 2 is an explanatory diagram of an installation stratum of an underground pipeline structure (box culvert) to be designed by the method of FIG. 1;

FIG. 3 is a detailed sectional view of the underground pipeline structure (box culvert) shown in FIG. 2;

FIG. 4 is a detailed flowchart of step 3 in FIG. 1;

FIG. 5 is an explanatory diagram of an analysis model of the underground pipeline structure (box culvert) shown in FIG. 2;

6 is an action load diagram of the analysis model shown in FIG.

FIG. 7 is an explanatory view showing a design sectional force by the response displacement method shown in FIG. 5;

FIG. 8 is an explanatory diagram of the Pareto ranking shown in FIG. 4;

FIG. 9 is a detailed flowchart of step 4 in FIG. 1;

FIG. 10 is a detailed flowchart of step 5 in FIG. 1;

FIG. 11 is an explanatory diagram of a diagram output by the procedure shown in FIG. 1;

12 is an explanatory diagram for each generation of a Pareto search result obtained when the procedure shown in FIG. 1 is specifically executed.

[Explanation of symbols]

 10 Box culvert 12 Bottom plate 14 Side wall 16 Top plate

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Mitsuo Harada, 1-3-1, Uchisaiwaicho, Chiyoda-ku, Tokyo Inside Tokyo Electric Power Company (72) Ikumasa Yoshida 3-3-1, Higashi-Ueno, Taito-ku, Tokyo Inside TEPCO Design Co., Ltd. (72) Shuichi Suzuki 3-3-3 Higashi Ueno, Taito-ku, Tokyo Tokyo Inside (72) Inventor Atsuo Takahashi 3-3-1 Higashi Ueno, Taito-ku, Tokyo TEPCO Design F term in reference (reference) 2D063 BA00 5B046 AA03 DA01 JA08

Claims (3)

[Claims] 1. Consideration conditions including design conditions such as pipeline installation level, pipeline material characteristics, geological composition of the pipeline installation location and its physical properties, groundwater level, and critical conditions to be considered in structural design. In the method of designing an underground pipeline structure based on the above, a plurality of design variables set in advance are added to the study conditions, and a plurality of design alternatives are created by performing a combination of the design variables based on random numbers. The safety and economics of each of the plurality of design proposals created are evaluated, and the obtained evaluation result is displayed on the two-dimensional coordinates using the safety and economics as parameters. A solution that does not include other evaluation results in a quadrilateral with the result as a diagonal is determined as a Pareto solution with high fitness, and a plurality of solutions are obtained. From the Pareto solution Design method of underground pipeline structure, characterized in that it comprises a step of enabling selected a final design plan. 2. A method in which a parameter of a genetic algorithm and the number of generations are added to the examination conditions, and elite pareto storage, selection, selection, crossover, and mutation are set for a plurality of the Pareto solutions. 2. The underground pipeline structure design method according to claim 1, further comprising a step of obtaining an improved solution of the Pareto solution every time the genetic algorithm is repeated for the number of generations. 3. With respect to the improved solution, a security when the design variable is slightly changed is obtained. If the safety is not changed from before the change, the design variable is changed to a value after the change. 3. The method according to claim 2, further comprising the step of sequentially changing.
The design method of the underground pipeline structure described in the above.