CN111881498B - Frame-shear structure wall layout optimization method based on improved particle swarm optimization - Google Patents
Frame-shear structure wall layout optimization method based on improved particle swarm optimization Download PDFInfo
- Publication number
- CN111881498B CN111881498B CN202010650657.8A CN202010650657A CN111881498B CN 111881498 B CN111881498 B CN 111881498B CN 202010650657 A CN202010650657 A CN 202010650657A CN 111881498 B CN111881498 B CN 111881498B
- Authority
- CN
- China
- Prior art keywords
- wall
- value
- shear
- particle swarm
- shear wall
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000002245 particle Substances 0.000 title claims abstract description 67
- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000005457 optimization Methods 0.000 title claims abstract description 38
- 238000013461 design Methods 0.000 claims abstract description 34
- 239000004567 concrete Substances 0.000 claims abstract description 15
- 239000013598 vector Substances 0.000 claims description 67
- 230000006870 function Effects 0.000 claims description 23
- 229910000831 Steel Inorganic materials 0.000 claims description 12
- 239000010959 steel Substances 0.000 claims description 12
- 230000035772 mutation Effects 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 7
- 230000008859 change Effects 0.000 claims description 5
- 230000001276 controlling effect Effects 0.000 claims description 5
- 230000006872 improvement Effects 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000010276 construction Methods 0.000 claims description 4
- 239000000203 mixture Substances 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 230000001105 regulatory effect Effects 0.000 claims description 3
- 239000000463 material Substances 0.000 abstract description 14
- 238000004540 process dynamic Methods 0.000 abstract description 3
- 230000009286 beneficial effect Effects 0.000 abstract 1
- 239000011159 matrix material Substances 0.000 description 9
- 230000009471 action Effects 0.000 description 4
- 239000011150 reinforced concrete Substances 0.000 description 4
- 230000008569 process Effects 0.000 description 3
- 238000010008 shearing Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000014509 gene expression Effects 0.000 description 2
- 239000010410 layer Substances 0.000 description 2
- 230000007246 mechanism Effects 0.000 description 2
- 239000000758 substrate Substances 0.000 description 2
- 230000001960 triggered effect Effects 0.000 description 2
- 230000001133 acceleration Effects 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000007123 defense Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000004134 energy conservation Methods 0.000 description 1
- 230000005484 gravity Effects 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 238000005192 partition Methods 0.000 description 1
- 238000012216 screening Methods 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 239000002344 surface layer Substances 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- General Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Life Sciences & Earth Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- Computational Linguistics (AREA)
- Biophysics (AREA)
- Mathematical Physics (AREA)
- Artificial Intelligence (AREA)
- Data Mining & Analysis (AREA)
- Architecture (AREA)
- Civil Engineering (AREA)
- Biomedical Technology (AREA)
- Health & Medical Sciences (AREA)
- Structural Engineering (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention provides a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, and provides a self-adaptive variation strategy and an overall process dynamic adjustment factor based on population diversity, which are used for improving a standard particle swarm algorithm. The technical scheme adopted by the invention is as follows: and (3) carrying out hierarchical coding on the position and the size of the shear wall in the structure, taking all performance index limit values in the specification as constraint conditions, taking the concrete dosage weighted by considering the tensile stress at the bottom of the shear wall as an objective function, and adopting an improved particle swarm algorithm to realize the optimization of the shear wall layout. The invention has the beneficial effects that: after the improved particle swarm optimization algorithm is adopted, a large number of individuals can be searched in a heuristic mode with high efficiency, analysis efficiency of the layout problem of the shear wall is greatly improved, the consumption of wall materials is obviously reduced compared with that of the traditional manual wall layout mode, and an optimization result can directly guide engineering design.
Description
Technical Field
The invention belongs to the technical field of frame-shear structure wall design, and particularly relates to a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm.
Background
The reinforced concrete frame-shear structure and the frame-barrel structure are one of the main structural forms of high-rise buildings in China, and the reinforced concrete frame-shear structure is widely applied. When the height of the frame-barrel structure exceeds 60m, the shear wall arranged at the periphery of the middle traffic core can present the stress characteristic of the core barrel, so that the frame-barrel structure can be regarded as a special frame-barrel structure, and the two structures are collectively called as a frame-barrel structure. Because the shear wall in the frame-shear structure is a first line of defense against side force, the layout of the shear wall has direct influence on the side force resistance of the structure. Therefore, shear wall layout optimization is a key step in determining the frame-shear structural scheme stage.
In the prior art, as the wall limbs in the frame-shear structure are provided with a plurality of layout modes such as a single wall, an even limb wall, an L shape, a T shape, a cross shape, a cylinder body and the like, the position, the length and the lateral rigidity resistance of the structure of the single wall are in a highly nonlinear relation. The number of feasible solutions of the shear wall layout optimization problem increases exponentially along with the increase of the number, the positions and the lengths of the limbs, and the optimization of the shear wall layout in the traditional design method mainly depends on conceptual design and manual adjustment, so that the working efficiency is low, the shear wall layout is different from person to person, the economy is difficult to ensure, and a large amount of unnecessary waste is caused. Therefore, aiming at the characteristics of the problem of optimizing the layout of the shear wall, an optimizing method for solving the problem of actual engineering is researched and developed, and the method has important significance for improving the working efficiency of the field, saving energy and saving materials.
Disclosure of Invention
The invention aims to provide a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, so as to improve design efficiency and achieve the purposes of energy conservation and material saving. In order to achieve the above purpose, the invention adopts the following technical scheme:
a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm comprises the following steps:
step1: design variable vector: constructing a frame-shear structure model, determining a wall distribution base point of the shear wall, and carrying out parameterization construction on position coordinates of the base point, the direction of the shear wall and the wall limb lengths in all directions;
step2: designing a first-stage code of position coordinates of each base point and a second-stage code of wall limb length in each direction based on a two-stage coding method;
step3: designing constraint conditions of the length of the wall limbs, and then constructing an upper limit value vector according to the sequence of the two-level codes in the step2 based on the two-level coding method in the step2, so that the upper limit value of the length of the wall limbs corresponds to the two-level codes in the step2 one by one;
step4: improving a particle swarm optimization algorithm;
step5: inputting the secondary code in the step2 into the improved particle swarm algorithm in the step4, and obtaining the wall length vector which can meet the constraint condition in the step3 and continuously optimize the fitness function value in the step4 through iteration.
Preferably, step2 specifically includes:
step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X which is arranged corresponding to a base point in the first-stage code W and an orientation vector P which is in one-to-one correspondence with the second-stage code X are sequentially constructed d Vector of number of directions P n ；
The primary code W comprises coordinate vectors of all base points which are arranged according to a set sequence and can be provided with the shear wall; the secondary code X consists of shear wall information vectors S which are arranged in rows i Composition; s is S i The wall limb length corresponding to each direction;
step 22: based on orientation vector P d Removing invalid codes in the secondary code X, wherein the invalid codes cannot be distributed with walls;
step 23: based on the number of directions vector P n Decoding the optimized secondary code X into a plurality of shear wall information vectors S after block processing i 。
Preferably, the constraint in step3 is:
X L ＝(x j1,lim ,x j2,lim ,…,x jd,lim ,…,x jD,lim ) T ；
wherein x is jd,lim Is a length limit; j is the individual number; d is a dimension value; lim represents a limit value.
Preferably, the improvement of the particle swarm algorithm in the step4 comprises the design of inertia weight factors, the design of learning factors, the selection of fitness functions and the design of mutation strategies.
Preferably, the inertial weight factor ω and the learning factor c 1 、c 2 The models of (a) are respectively:
wherein T is max The maximum iteration number is set; t is the iteration number;
ω (T) is an inertial weight factor that dynamically changes with the number of iterations T;
ω start for initial value of inertial weight factor, ω end Setting a final value of the inertia weight factor of the iteration ending;
k 1 、k 2 respectively regulating factors;
c 1 、c 2 is a learning factor that dynamically changes with the number of iterations T;
c 1,start c is 1 An initial value of the iteration; c 1,end C is 1 Final value of iteration;
c 2,start c is 2 An initial value of the iteration; c 2,end C is 2 Final value of the iteration.
Preferably, the model of the fitness function is:
wherein F is the floor number, and F is the total number of floors;
i is the length grouping number of the shear wall member, and N is the total number of the arrangement number of all the shear walls;
L i the length value of the i-th shear wall is the length value of the i-th shear wall;
t f the thickness value of the shear wall of the f floor is that of the building, H is that of the buildingA layer height value;
j is the number of beam members, M is the total number of all beam members of a single floor;
B l is the width value of the beam section, B w Is the height value of the beam section, L b,j A length value for the j-th beam member;
k is the number of column members, and P is the total number of all column members on a single floor;
C l for the column section width value, C w Is the height value of the column section, L c,k A length value for the kth column member;
s is the number of the column or the wall component with the wall bottom tensile stress, S * The total number of columns or wall members for which wall bottom tensile stress exists;
γ s v is the conversion ratio of the steel bar to the concrete s The amount of steel bars to be arranged is required to take the wall bottom tensile stress into consideration.
Preferably, the functional model of the mutation strategy is:
wherein P is m Is a threshold for variation; d is the dimension; d (D) m Is a diversity threshold;
k is a control parameter, 0<K<1 for controlling P m The smoothness of the curve;
P m,start is the initial value of the variation; p (P) m,end Is the final value of the variation.
Preferably, the improved particle swarm algorithm in step4 specifically includes the following steps:
step1: initializing parameters in a particle swarm algorithm: omega start 、c 1,start 、c 2,start Maximum number of iterations T max The initial position variable of the particles and the initial speed variable of the particles are set as pbest, and the historical optimal value of the individual particles is set as gbest;
step2: in contemporary evolution, fitness function values for each particle are calculated
Step3: updating the pbest and gbest of the particle;
step4: updating the speed and position of the particles;
step5: checking population diversity: calculating the current population diversity, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step7; if the population diversity is smaller than the diversity threshold, executing Step6;
step6: randomly generating variation probability, and if the variation probability is larger than a variation threshold, executing variation operation to change the wall length according to the set probability;
step7: iterative calculation: judging whether the maximum iteration times are reached, if not, returning to Step4, and continuously executing Step4 to Step6; otherwise, the iteration is terminated and gbest is output.
Compared with the prior art, the invention has the advantages that:
(1) And determining performance constraint conditions and geometric dimension constraint conditions of the structure according to design conditions such as building functions, field environments and the like, performing secondary floating point number coding on the coordinates, the directions and the lengths of shear wall nodes in the frame-shear structure, taking the use amount of shear wall concrete weighted by wall bottom tensile stress as an objective function, improving a standard particle swarm algorithm by providing a self-adaptive variation strategy based on population diversity and an overall process dynamic adjustment factor, and optimizing the improved particle swarm algorithm to obtain the optimal layout of the shear wall, thereby remarkably improving the design efficiency and the economy of design results.
(2) The two-stage coding method is adopted, and the two-stage coding for optimization is simplified as much as possible through the index of the positioning vector, the directional vector and the direction number vector of the one-stage coding, so that the optimization workload is greatly reduced.
(3) Geometric constraint conditions such as room division, doors and window openings are introduced, so that an optimization result can adapt to building layout, and the method is high in practicability.
(4) The shear wall concrete consumption after the wall limb bottom tensile stress weighting correction is taken as an objective function, the wall limb stress and the material consumption are considered, and the optimized shear wall layout is more reasonable.
(5) The variation strategy based on population diversity is considered, and the probability of the shear wall layout falling into a local optimal solution is obviously reduced by adopting an improved particle swarm algorithm of a whole-process dynamic adjustment factor.
Drawings
FIG. 1 is a flow chart of a particle swarm algorithm in a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm according to an embodiment of the invention;
FIG. 2 is a schematic diagram of the relationship between the base points and the shear wall in step2 and the coding according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a two-stage encoding method in step2 according to an embodiment of the present invention;
FIG. 4 shows a simplified two-level coded X-transform block processed shear wall information vector S in step2 according to an embodiment of the present invention i Is a conversion schematic of (a);
fig. 5 is a variation curve of a moderate function value when the frame-shear structure wall layout optimization method based on the improved particle swarm algorithm is applied according to an embodiment of the present invention.
Detailed Description
The present invention will be described in more detail below with reference to the drawings, in which preferred embodiments of the invention are shown, it being understood that one skilled in the art can modify the invention described herein while still achieving the advantageous effects of the invention. Accordingly, the following description is to be construed as broadly known to those skilled in the art and not as limiting the invention.
The embodiment provides a frame-shear structure wall layout optimization method based on an improved particle swarm algorithm, which comprises the following steps of 1-5:
step1: design variable vector: and constructing a frame-shear structure model, determining a wall distribution base point of the shear wall, and carrying out parameterization construction on position coordinates of the base point, the direction of the shear wall and the wall limb lengths in all directions.
Step 11: according to building functions and field design conditions, intersection points of beam, column and wall axes are used as wall distribution base points, then base points of a plurality of shear walls are selected, and coordinate vectors of the base points are established. As shown in FIG. 2, the positions of the circles 1 to 6 are the foundation points of the wall layout.
Step 12: the direction and size of the shear wall at the base point is determined.
All the base points uniformly determine 4 directions, and the directions respectively correspond to 4 values. As shown in fig. 2, a plurality of base points where shear walls are to be arranged are selected, and the number of directions in which the shear walls can be arranged on each base point is different. If the foundation points No. 4 and No. 6 can be used for arranging the shear walls in 4 directions, the foundation points No. 2, no. 3 and No. 5 can be used for arranging the shear walls in 3 directions, the foundation point No. 1 can be used for arranging the shear walls in 2 directions, and each foundation point has a corresponding wall limb length value in each direction. Although the number of directions in which the shear walls can be arranged on the base points is different, if the number of the arrangement directions of all the base points is unified to be 4, that is, 4 directions are provided, each base point has 4 specific values uniformly, and the length values of the shear walls in the 4 directions are respectively represented. If the shear wall cannot be arranged in a certain direction of a certain base point, the length value in the direction is forcedly set to 0, and if the shear wall cannot be arranged in two directions of the base point 1 in fig. 2, the length value in the corresponding direction is set to 0.
Step 13: and determining a shear wall information matrix.
In order to facilitate the one-to-one correspondence between the length values and the directions in the subsequent parameterization process, the following provisions are made for each direction of the shear wall: taking the positive direction of the X direction of the floor plan (namely the length value increasing direction) as the 1 st direction, counting the other directions in turn according to the anticlockwise direction, and so on if the positive direction of the Y direction is the 2 nd direction. Taking the 6 th base point in fig. 2 as an example, the 4.5 m-long limb corresponds to the 1 st direction, the 4 m-long limb corresponds to the 2 nd direction, the 4.2 m-long limb corresponds to the 3 rd direction, the 3.2 m-long limb corresponds to the 4 th direction, and the other base points and so on. The length values of the shear wall in 4 directions of each base point correspond to 4 values, and the 4 values are arranged in order of 1-4 directions to form a vector. The vectors of the base points are combined to form a shear wall information matrix. Therefore, the position coordinates of the shear wall base points, the direction of the shear wall and the length information of the wall limbs in the frame-shear structure are all converted into rectangular forms, and parameterization of the shear wall is realized.
Step2: based on a two-stage coding method, a first-stage coding of the position coordinates of each base point and a second-stage coding of the wall limb length in each direction are designed. Based on floating point number coding, a two-stage coding method is proposed. The two-stage coding method is divided into 2 steps: firstly, according to building functions and limiting conditions, determining base points for arranging shear walls, ordering coordinates of the base points according to a certain number to obtain codes, and then sequentially distributing length values in four directions of each base point according to a floating point number coding method.
Step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X which is arranged corresponding to a base point in the first-stage code W and an orientation vector P which is in one-to-one correspondence with the second-stage code X are sequentially constructed d Vector of number of directions P n The method comprises the steps of carrying out a first treatment on the surface of the The primary code W comprises coordinate vectors of all base points which are arranged according to a set sequence and can be provided with the shear wall; the secondary code X consists of shear wall information vectors S which are arranged in rows i Composition; s is S i The length of the wall limb corresponding to each direction.
In this embodiment, as shown in fig. 2 to 4, the coordinates of the base points 1 to 6 are (0, 0), (0, 8), (8, 0), (24,0), (24, 32), respectively, and other positions are considered to be limited by the building and not allow the placement of the shear wall. The first-stage coding is to put 6 base points into a coordinate vector according to a self-defined sequence, and the sequence of each base point is defined so as to correspond to the second-stage coding of the next step, wherein the first-stage coding is as follows:
W＝((0，0),(0，8)，(8，0)，(8，8)，(24，0)，(24，32)) T ；
and (5) finishing the specification of the length of each wall limb by adopting a floating point coding method. The vectors at the above base points are S 1 ＝(3，3，0，0) T ，S 2 ＝(3，0，0，3) T ，S 3 ＝(0，3，3，0) T ，S 4 ＝(0，0，3，3) T ，S 5 ＝(4.8，4，4.2，0) T ，S 6 ＝(4.5，4，4.2，3.2) T Then the 6 vectors are combined into a line number of 4 lines6 columns of shear wall information matrix, namely:
X＝[S 1 ，S 2 ，S 3 ，S 4 ，S 5 ，S 6 ]
each row of X represents the length values of all base points in the same direction, and each column represents the length values of one point in all directions. In order to be unified with the form of the particle swarm algorithm, the matrix needs to be converted into a position vector, and the conversion method is as follows: changing 6 columns of the matrix to 1 column, i.e. putting the 2 nd column vector of the matrix under the first column vector, putting the 2 nd row vector immediately under, and so on, until all column vectors are converted to column vectors of only 1 column, thereby converting the matrix to vectors, at which point the position variable x= (3,3,0,0,3,0,0,3,0,3,3,0,0,0,3,3,4.8,4,4.2,0,4.5,4,4.2,3.2) T 。
Step 22: based on orientation vector P d And removing invalid codes which cannot be distributed in the secondary code X. During the shear wall parameterization (step 12), some base points are forced to be set to 0 because of building restrictions, and the shear wall cannot be arranged in some directions, resulting in some unchanged elements in the matrix, which are not in line with the concept of the design variables, and also increase the dimension value D. Therefore, the original position vector X needs to be set t i The redundant 0 element in the vector is removed, but for the element which is not taken as 0 due to the construction restriction, the element is not removed, so that all elements in the vector are ensured to be variable, and the specific improvement thinking is as follows: on the basis of one-stage coding in a two-stage coding method, improvement is carried out, a direction constraint condition is introduced, a directional vector is set, and all values in the directional vector correspond to the position vectors one by one.
As shown in FIG. 3, an orientation vector, P, is added d ＝((1，2)，(1，4)，(2，3)，(3，4)，(1，2，3)，(1，2，3，4)) T The directions represented by the numbers in the orientation vectors are also in one-to-one correspondence with the new position variable, the modified position variable x= (3,3,3,3,3,3,3,3,4.8,4,4.2,4.5,4,4.2,3.2) T . It can be seen that No. 1The 1 direction and the 2 direction of the base point are both 3 in the position vector X, and the 6-th base point also corresponds to 4.5,4,4.2,3.2 in four directions respectively, which is consistent with the actual arrangement.
Step 23: as shown in fig. 4, based on the direction number vector P n Decoding the optimized secondary code X into a plurality of shear wall information vectors S after block processing i 。
Due to the above simplified operation, the individual position vector generated by each generation of iteration in the particle swarm algorithm cannot directly guide the shear wall parameterization modeling process, and the position vector generated by the two-stage encoding method must be decoded to convert the individual position into the form of a shear wall information matrix or vector.
P d ＝(d 1 ，d 2 ，…，d i ) T ，d i A direction array of the shear wall can be arranged for the ith base point;
P n ＝(k 1 ，k 2 ，…，k i ) T ，k i the number of directions in which the shear wall may be disposed at the i-th base point.
As shown in fig. 2,3 directions in which the shear wall can be arranged at the base point 5 are the first, second and third directions, i.e., d 5 ＝(1，2，3)；k 5 =3, then P d ＝((1，2)，(1，4)，(2，3)，(3，4)，(1，2，3)，(1，2，3，4)) T ，P n ＝(2，2，2，2，3，4) T 。
Step3: and (3) designing constraint conditions of the wall length, and then constructing an upper limit value vector according to the sequence of the two-level codes in the step (2) based on the two-level coding method in the step (2), so that the upper limit value of the wall length corresponds to the two-level codes in the step (2) one by one.
During the shear wall parameterization process, a length of shear wall may be deployed in a direction that allows for deployment of the shear wall. As shown in fig. 2, the maximum length value of the shear wall with the base point No. 5 in the 3 direction is 8m. At the base point 1 and the base point 2, since the 2 nd direction of the base point 1 is opposite to the 4 th direction of the base point 2, the sum of the values of the two directions cannot exceed the span between the two base points, soThe maximum value of the lengths of the shear walls in two directions of the two base points is half of the span, namely L i,2 ∈[0，l/2]Wherein L is i,2 The length of the wall limb of the ith base point in the 2 nd direction; l is the value of the span between the two base points.
Geometric constraint of the base point in each direction requires factors such as a total span value, building arrangement limitation of doors, windows, holes and the like, and takes smaller values, namely
The constraint conditions are as follows:
L 1 ＝{L 1,1 ,L 2,1 ,L 3,1 ,…,L N,1 },and L is i,1 ∈[0,l i,1,limit ]；
L 2 ＝{L 1,2 ,L 2,2 ,L 3,2 ,…,L N,2 },And L is i,2 ∈[0,l i,2,limit ]；
L 3 ＝{L 1,3 ,L 2,3 ,L 3,3 ,…,L N,3 },And L is i,3 ∈[0,l i,3,limit ]；
L 4 ＝{L 1,4 ,L 2,4 ,L 3,4 ,…,L N,4 },And L is i,4 ∈[0,l i,4,limit ]；
Wherein L is i,1,limit ，L i,2,limit ，L i,3,limit ，L i,4,limit The i-th base point is the geometric maximum in 4 directions due to building constraints, respectively.
Because of the vector expressions in four directions, which are inconsistent with the expression forms of the individual in the particle swarm algorithm, the execution of the particle swarm algorithm is inconvenientAnd (3) row. Therefore, the above-mentioned information vectors are firstly converted into several shear wall information vectors, and these vectors respectively obtain upper limit values, then according to two-stage coding method the above-mentioned information vectors are converted into a special position vector, and said position vector is the upper line value vector of solution space, i.e. X L ：
X L ＝(x j1 ,lim,x j2 ,lim,…,x jd ,lim,…,x jD,lim ) T
Wherein x is j1,lim Is a length limit and is unchanged; d is the dimension; j is the individual number; d is a dimension value; lim represents a limit value.
Step4: and (5) improving a particle swarm optimization algorithm. The improvement of the particle swarm algorithm comprises the design of inertia weight factors, the design of learning factors, the selection of fitness functions and the design of mutation strategies.
(1) Inertia weight factor omega, learning factor c 1 、c 2 The models of (a) are respectively:
wherein T is max The maximum iteration number is set; t is the iteration number;
ω (T) is an inertial weight factor that dynamically changes with the number of iterations T;
ω start for initial value of inertial weight factor, ω end Setting a final value of the inertia weight factor of the iteration ending;
k 1 、k 2 respectively regulating factors; k (k) 1 The main control omega (T) varies between 0.4 and 0.9, k 2 The smoothness of the variation curves of omega (T) and T is mainly controlled;
c 1 、c 2 is a learning factor that dynamically changes with the number of iterations T;
c 1,start c is 1 Taking an initial value of iteration, and taking 2.75; c 1,end C is 1 Taking 1.25 as the final value of iteration;
c 2,start c is 2 Taking an initial value of iteration to be 0.5; c 2,end C is 2 The final value of the iteration is taken to be 2.25.
The main purpose of improving the inertial weighting factor ω is to trade-off local and global search capabilities when 0 < k 2 When the weight factor is less than 1, the algorithm has larger inertia weight factor in the early stage, but can be rapidly reduced along with the increase of iteration times, namely the search of the whole space can be rapidly completed, and then the search can be continuously completed by smaller inertia weight factor, so that the local search capability is enhanced, the convergence of the algorithm is improved, and meanwhile, the sinking of local optimal solution is effectively avoided; when k is 2 When the weight factor is more than 1, the inertia weight factor at the early stage of the algorithm is slower in descending speed, and the descending speed at the later stage is faster, so that the algorithm can fully ensure the global searching capability at the early stage, and meanwhile, the algorithm still has a larger inertia weight factor at the later stage, and can effectively avoid sinking into a local optimal solution on the basis of ensuring convergence.
Improved learning factor c 1 、c 2 The purpose of (2): initial pass delay c of algorithm 1 And accelerate c 2 The algorithm slowly enters local search and the global search capacity is enhanced, so that the situation of sinking into a local optimal solution is effectively avoided, and c which is more ideal than a linear change strategy is set at the later stage of the algorithm 1 、c 2 By accelerating c 1 And delay c 2 To accelerate convergence to some extent, thereby ensuring the convergence of the algorithm.
(2) The fitness function model is:
wherein F is the floor number, and F is the total number of floors;
i is the length grouping number of the shear wall member, and N is the total number of the arrangement number of all the shear walls;
L i the length value of the i-th shear wall is the length value of the i-th shear wall;
t f the thickness value of the shear wall of the f floor is the thickness value of the floor, and H is the height value of the floor;
j is the number of beam members, M is the total number of all beam members of a single floor;
B l is the width value of the beam section, B w Is the height value of the beam section, L b,j A length value for the j-th beam member;
k is the number of column members, and P is the total number of all column members on a single floor;
C l for the column section width value, C w Is the height value of the column section, L c,k A length value for the kth column member;
s is the number of the columns or wall members with the tensile stress of the wall bottom, and the total number of the columns or wall members with the tensile stress of the wall bottom is S * ；
γ s V is the conversion ratio of the steel bar to the concrete s The amount of steel bars to be arranged is required to take the wall bottom tensile stress into consideration.
In actual engineering, the shear wall bears most of the shear force of the seismic base, meanwhile, the earthquake overturning moment can generate tensile stress on the bottom section of the wall limb, and after the wall limb cracks due to the tensile stress, the shearing bearing capacity of the shear wall can be greatly reduced. Therefore, if the number of the wall limbs can meet the requirements of various indexes according to the elastic analysis result, but the tensile stress at the bottoms of the wall limbs is larger than the tensile strength of the concrete, the shearing resistance bearing capacity of the shear wall is required to be reinforced by adopting measures such as configuration steel and the like, and the analysis result shows that the arrangement of the shear wall is less and is not the optimal scheme. It is therefore necessary to introduce the wall limb bottom tensile stress into the objective function, with specific conversion weights being weighted by the amount of steel. The tensile stress at the bottom of the shear wall is assumed to be borne by the steel bars, and the additional steel bar cost caused by the tensile stress is converted into equal-value concrete according to the price, so that the material consumption of the steel bars is converted into the concrete material consumption, and the material consumption of the objective function-overall structure concrete is kept to be the smallest. Thus, the above objective function (fitness function) is actually composed of two parts: and one part of the concrete is not considered in the case of the tensile stress of the wall bottom (the total volume of the concrete of the beam column wall), and the other part of the concrete is considered in the case of the tensile stress of the wall bottom (the concrete is obtained by converting the value of the steel bar and the like).
(3) The function model of the mutation strategy is as follows:
wherein P is m Is a threshold for variation;
k is a control parameter, 0<K<1, 0.5 is taken for controlling P m The degree of smoothness of the curve and the change curve of D;
P m,start taking 0.8 as an initial value of variation; p (P) m,end The final value of the mutation was 0.3.
The values of the parameters related to the algorithm are as follows: population scale N is 25-40, diversity threshold D m Take the value of 2.25; the fine search coefficient takes 0.3, and the maximum speed ratio coefficient takes 0.4.
Step5: inputting the secondary code in the step2 into the improved particle swarm algorithm in the step4, and obtaining the wall length vector which can meet the constraint condition in the step3 and continuously optimize the fitness function value through iteration. As particularly shown in fig. 1.
Step1: initializing parameters in a particle swarm algorithm: omega start 、c 1 ,start、c 2,start Maximum number of iterations T max The initial position variable of the particles and the initial speed variable of the particles are set as pbest, and the historical optimal value of the individual particles is set as gbest;
step2: in contemporary evolution, fitness function values for each particle are calculatedScreening the generation pbest and gbest from the individuals; the individual optimal position variables for each generation are set as:
the global optimum position variable for each generation is set as:
step3: updating the particle's pbest and gbest.
Step4: updating the speed and the position of the particles, wherein the updating formula of the particles is as follows:
position variable
Speed variable
Wherein,position variable in the d dimension of the ith generation of the ith individual; />Speed variable in the d dimension of the ith generation of the ith individual; />An individual history optimal position of the ith individual in the d dimension of the th generation; />The global optimal position of the d dimension of the t generation;
r 1 ，r 2 is a random number uniformly distributed in the (0, 1) interval; c 1 ，c 2 Is a learning factor.
Step5: checking population diversity: calculating the current population diversity, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step7; if the population diversity is less than the diversity threshold, step6 is performed.
The calculation formula of population diversity is as follows:
m is the total number of particles x i Is the position variable of the particle, p c The position variable of the particle in the center position of the particle group is D, and the diversity of the particle group is defined.
Step6: and randomly generating variation probability, and if the variation probability is larger than a variation threshold, executing variation operation to change the wall length according to the set probability.
(1) Each particle randomly generates variation probability, if the variation probability is larger than a variation threshold value, a variation mechanism is triggered, and the position variable of the particle is updated according to the following formulaAnd checking whether the position variable is out of range, if so, setting the position value smaller than the minimum value and the position value larger than the maximum value as a preset position minimum value and a preset position maximum value respectively.
In the above, x id Position variable of the d dimension of the ith particle;
taking 0.3 as a fine search coefficient, and mainly controlling the variation degree of variation;
r is a random number between intervals [ -1,1] whose sign represents the direction of variation of the particles;
l max 、l min an upper limit and a lower limit representing a position variable of the particle in the d-th dimension;
p is the probability of currently producing variation; p (P) m Is the threshold for variation.
K is a control parameter, and must satisfy 0<K<1 for controlling P m Degree of smoothness of the curve with D, P m,start 、P m,end The initial and final values of the variation are respectively referred to as P m,start ＝0.8，P m,end ＝0.3。
The inequality on the right of the above equation indicates that the left equation can be executed only when the probability P of currently producing a variance is greater than the variance threshold. Until a maximum number of iterations is reached.
(2) If the mutation probability is not greater than the mutation threshold, the mutation mechanism is not triggered. The variation threshold varies with population diversity.
Step7: iterative calculation: judging whether the maximum iteration times are reached, if not, returning to Step4, and continuously executing Step4 to Step6; otherwise, the iteration is terminated and gbest is output.
The method of the invention is verified in connection with a certain build project case: the height from the outdoor ground to the main roof of 13 floors on the ground and 3 floors on the ground of a certain project is 57.85m, and the building belongs to a high-rise reinforced concrete building structure of A level. The plane arrangement of the project is regular, the length along the X direction is 67.20m, the length along the Y direction is 31.50m, and the main structure adopts a frame-shear wall structure. The service life of the structural design of the project is 50 years, the safety level of the main structure of the building is two levels, and the corresponding structural design importance coefficient gamma o The earthquake fortification intensity of the place is 7 degrees, the basic earthquake acceleration is designed to be 0.15g, the earthquake grouping is designed to be a second group, the earthquake fortification category is a third group, the site characteristic period is 0.55s, and the horizontal earthquake influence coefficient is 0.12. The basic wind pressure omega=0.45 kN/m, the basic snow pressure s=0.4 kN/m, the wind carrier type coefficient is 1.3, and the ground roughness is class B. Constant load design of 4.5kN/m 2 (constant load considers floorslab, surface layer, suspended ceiling),Partition wall equivalent weight, wherein floor thickness is calculated as 120 mm), roofing live load design is 3.5kN/m 2 . The reinforced concrete has the strength grade of C40, the design value of compressive strength of 19.1MPa and the elastic modulus of 3.25 multiplied by 10 4 The Poisson's ratio is 0.2. The main material dimensions in the model are as follows: the column is 700mm multiplied by 700mm, the beam is 400mm multiplied by 700mm, the secondary beam is 400mm multiplied by 600mm, and the thickness of the shear wall is 400mm. The design value of the shaft pressure considering the earthquake action combination is considered according to the load working condition which controls the bearing capacity, namely: 1.2× (constant load +0.5 live load) +1.4× seismic effort. The pressure design value of the shear wall is considered according to the pressure design value born by the wall limbs under the action of the gravity load representative value. Besides, the indexes are calculated according to standard values under the action of most earthquakes. The horizontal seismic action is applied by adopting a reaction spectrum method. Fig. 2 is a plan view of a standard layer structure of the project. And under the restriction of constraint conditions, taking the node and the length value of the shear wall as optimization variables, taking the minimum material consumption as an optimization target, adopting Python language to perform secondary development on the general finite element program, and performing optimization iteration through the developed program. FIG. 5 is a layout of a shear wall of an engineering after iteration, X is the number of iterations, Y is the material usage; table 1 shows the comparison results of the engineering example wall and the original design.
TABLE 1 comparison of design scheme of actual engineering and design scheme main mechanical Performance index generated by optimization algorithm iteration
As can be seen from fig. 5, the optimization of the method according to the present invention decreases the amount of concrete material as the number of iterations increases, and converges according to the constraint condition, which indicates that the method according to the present invention is truly effective.
It can be seen from table 1 that the original scheme has been subjected to many rounds of manual optimization adjustments in order to control the structure torsion, substrate shear, etc. But the optimization of the structural performance requires the cooperative consideration of the shear walls of all parts, and the optimization efficiency is low and the gap between the shear walls and the optimal solution is large through manual adjustment.
The meta-position angle is increased by 13% and 6.3% respectively in two directions, but the substrate shearing force is reduced by 24% and 16% respectively in two directions, and especially the surplus degree of the original scheme in the X direction is obviously reduced, so that the performances of the structure in the X, Y directions are as close as possible, and the optimization of the shear wall is realized under the condition that the structural performances are not obviously reduced, and the effect is good. The optimization algorithm can improve the material utilization efficiency of the shear wall, improve the plane arrangement of the shear wall of the frame-shear structure, reduce the material consumption of the structure and the wall distribution rate of floors, and improve the mechanical property of the structure.
Compared with actual engineering, the method for optimizing the design has the advantages that the accuracy of size selection of the shear wall is higher, the material consumption is better, automatic optimization adjustment can be realized, the optimization adjustment of the shear wall can be realized rapidly after the adjustment of the building scheme, and the working efficiency is improved.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any person skilled in the art will make any equivalent substitution or modification to the technical solution and technical content disclosed in the invention without departing from the scope of the technical solution of the invention, and the technical solution of the invention is not departing from the scope of the invention.
Claims (3)
1. The frame-shear structure wall layout optimization method based on the improved particle swarm optimization is characterized by comprising the following steps of:
step1: design variable vector: constructing a frame-shear structure model, determining a wall distribution base point of the shear wall, and carrying out parameterization construction on position coordinates of the base point, the direction of the shear wall and the wall limb lengths in all directions;
step2: designing a first-stage code of position coordinates of each base point and a second-stage code of wall limb length in each direction based on a two-stage coding method;
step3: designing constraint conditions of the length of the wall limbs, and then constructing an upper limit value vector according to the sequence of the two-level codes in the step2 based on the two-level coding method in the step2, so that the upper limit value of the length of the wall limbs corresponds to the two-level codes in the step2 one by one;
step4: improving a particle swarm optimization algorithm;
the improvement of the particle swarm algorithm comprises the design of inertia weight factors, the design of learning factors, the selection of fitness functions and the design of mutation strategies;
inertia weight factor omega, learning factor c 1 、c 2 The models of (a) are respectively:
wherein T is max The maximum iteration number is set; t is the iteration number;
ω (T) is an inertial weight factor that dynamically changes with the number of iterations T;
ω start for initial value of inertial weight factor, ω end Setting a final value of the inertia weight factor of the iteration ending;
k 1 、k 2 respectively regulating factors;
c 1 、c 2 is a learning factor that dynamically changes with the number of iterations T;
c 1,start c is 1 An initial value of the iteration; c 1,end C is 1 Final value of iteration;
c 2,start c is 2 An initial value of the iteration; c 2,end C is 2 Final value of iteration;
the fitness function model is:
wherein F is the floor number, and F is the total number of floors;
i is the length grouping number of the shear wall component;
n is the total number of the arrangement numbers of all the shear walls;
L i the length value of the i-th shear wall is the length value of the i-th shear wall; the position variable of the particles is
t f The thickness value of the shear wall of the f floor is the thickness value of the floor, and H is the height value of the floor;
j is the number of beam members, M is the total number of all beam members of a single floor;
B l is the width value of the beam section, B w Is the height value of the beam section, L b,j A length value for the j-th beam member;
k is the number of column members, and P is the total number of all column members on a single floor;
C l for the column section width value, C w Is the height value of the column section, L c,k A length value for the kth column member;
s is the number of the column or the wall component with the wall bottom tensile stress, S * The total number of columns or wall members for which wall bottom tensile stress exists;
γ s v is the conversion ratio of the steel bar to the concrete s The amount of the steel bars to be configured is used for considering the tensile stress of the wall bottom;
the function model of the mutation strategy is as follows:
wherein P is m Is a threshold for variation; d is the dimension; d (D) m Is a diversity threshold;
k is a control parameter, 0<K<1 for controlling P m The smoothness of the curve;
P m,start is the initial value of the variation; p (P) m,end Is the final value of the variation;
the improved particle swarm algorithm specifically comprises the following steps:
step1: initializing parameters in a particle swarm algorithm: omega start 、c 1,start 、c 2,start Maximum number of iterations T max The initial position variable of the particles and the initial speed variable of the particles are set as pbest, and the historical optimal value of the individual particles is set as gbest;
step2: in contemporary evolution, fitness function values for each particle are calculated
Step3: updating the pbest and gbest of the particle;
step4: updating the speed and position of the particles;
step5: checking population diversity: calculating the current population diversity, if the population diversity is greater than the diversity threshold, skipping Step6, and executing Step7; if the population diversity is smaller than the diversity threshold, executing Step6;
step6: randomly generating variation probability, and if the variation probability is larger than a variation threshold, executing variation operation to change the wall length according to the set probability;
step7: iterative calculation: judging whether the maximum iteration times are reached, if not, returning to Step4, and continuously executing Step4 to Step6; otherwise, the iteration is terminated, and the gbest is output;
step5: inputting the secondary code in the step2 into the improved particle swarm algorithm in the step4, and obtaining the wall length vector which can meet the constraint condition in the step3 and continuously optimize the fitness function value in the step4 through iteration.
2. The method for optimizing a layout of a frame-shear structure wall based on an improved particle swarm algorithm according to claim 1, wherein the step2 specifically comprises:
step 21: based on a two-stage floating point number coding method, a first-stage code W, a second-stage code X which is arranged corresponding to a base point in the first-stage code W and an orientation vector P which is in one-to-one correspondence with the second-stage code X are sequentially constructed d Vector of number of directions P n ；
The primary code W comprises coordinate vectors of all base points which are arranged according to a set sequence and can be provided with the shear wall; the secondary code X consists of shear wall information vectors S which are arranged in rows i Composition; s is S i The wall limb length corresponding to each direction;
step 22: based on orientation vector P d Removing invalid codes in the secondary code X, wherein the invalid codes cannot be distributed with walls;
step 23: based on the number of directions vector P n Decoding the optimized secondary code X into a plurality of shear wall information vectors S after block processing i 。
3. The method for optimizing a frame-shear structure wall layout based on an improved particle swarm optimization according to claim 1, wherein the constraint conditions in step3 are:
X L ＝(x j1,lim ,x j2,lim ,…,x jd,lim ,…,x jD,lim ) T ；
wherein x is jd,lim Is a length limit; j is the individual number; d is a dimension value; lim represents a limit value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010650657.8A CN111881498B (en) | 2020-07-08 | 2020-07-08 | Frame-shear structure wall layout optimization method based on improved particle swarm optimization |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010650657.8A CN111881498B (en) | 2020-07-08 | 2020-07-08 | Frame-shear structure wall layout optimization method based on improved particle swarm optimization |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111881498A CN111881498A (en) | 2020-11-03 |
| CN111881498B true CN111881498B (en) | 2024-01-19 |
Family
ID=73151430
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010650657.8A Active CN111881498B (en) | 2020-07-08 | 2020-07-08 | Frame-shear structure wall layout optimization method based on improved particle swarm optimization |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111881498B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004046303A (en) * | 2002-07-09 | 2004-02-12 | Fuji Electric Holdings Co Ltd | Optimum structure design method of electromagnet |
| JP2014206813A (en) * | 2013-04-11 | 2014-10-30 | 株式会社神戸製鋼所 | Optimum solution search method and optimum solution search device |
| CN106599467A (en) * | 2016-12-14 | 2017-04-26 | 哈尔滨工业大学 | Building construction design method in severe cold areas based on multi-objective optimization algorithm |
| CN107085640A (en) * | 2017-04-19 | 2017-08-22 | 青岛腾远设计事务所有限公司 | The simulation algorithm of the non-stiffened steel plate shear wall of circular-arc cut |
| CN107169558A (en) * | 2017-05-25 | 2017-09-15 | 河海大学 | A kind of Modified particle swarm optimization method for realizing engineering rock mass mechanics parameter inverting |
| CN109871600A (en) * | 2019-01-30 | 2019-06-11 | 宁波工程学院 | A kind of prefabricated prestressing without bondn shear wall structure fast optimal design method |
| CN110427722A (en) * | 2019-08-09 | 2019-11-08 | 安徽水利开发股份有限公司 | Complex heat-preservation non-dismantling formwork support system design method based on construction time reliability |
-
2020
- 2020-07-08 CN CN202010650657.8A patent/CN111881498B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004046303A (en) * | 2002-07-09 | 2004-02-12 | Fuji Electric Holdings Co Ltd | Optimum structure design method of electromagnet |
| JP2014206813A (en) * | 2013-04-11 | 2014-10-30 | 株式会社神戸製鋼所 | Optimum solution search method and optimum solution search device |
| CN106599467A (en) * | 2016-12-14 | 2017-04-26 | 哈尔滨工业大学 | Building construction design method in severe cold areas based on multi-objective optimization algorithm |
| CN107085640A (en) * | 2017-04-19 | 2017-08-22 | 青岛腾远设计事务所有限公司 | The simulation algorithm of the non-stiffened steel plate shear wall of circular-arc cut |
| CN107169558A (en) * | 2017-05-25 | 2017-09-15 | 河海大学 | A kind of Modified particle swarm optimization method for realizing engineering rock mass mechanics parameter inverting |
| CN109871600A (en) * | 2019-01-30 | 2019-06-11 | 宁波工程学院 | A kind of prefabricated prestressing without bondn shear wall structure fast optimal design method |
| CN110427722A (en) * | 2019-08-09 | 2019-11-08 | 安徽水利开发股份有限公司 | Complex heat-preservation non-dismantling formwork support system design method based on construction time reliability |
Non-Patent Citations (3)
| Title |
|---|
| 基于WDO的无人机全局路径规划方法;宋宇;王志明;;长春工业大学学报(第06期);全文 * |
| 基于粒子群算法的钢管混凝土减震框架优化研究;梁健伟;中国优秀硕士学位论文全文数据库;全文 * |
| 基于粒子群算法的预制构件生产调度优化应用研究;孟旭;祝连波;石振群;;价值工程(第03期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111881498A (en) | 2020-11-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Aldwaik et al. | Advances in optimization of highrise building structures | |
| Saka et al. | Mathematical and metaheuristic applications in design optimization of steel frame structures: an extensive review | |
| Liang et al. | Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization | |
| Chen et al. | Analysis of outrigger numbers and locations in outrigger braced structures using a multiobjective genetic algorithm | |
| Zhou et al. | Sensor placement optimization in structural health monitoring using cluster-in-cluster firefly algorithm | |
| Saka et al. | Harmony search algorithms in structural engineering | |
| CN111622369A (en) | Optimal design method for anti-buckling restrained brace steel frame structure | |
| Nouri et al. | Weight and topology optimization of outrigger-braced tall steel structures subjected to the wind loading using GA | |
| Hadidi et al. | A new hybrid algorithm for simultaneous size and semi-rigid connection type optimization of steel frames | |
| Akın et al. | Optimum design of steel space frames by hybrid teaching-learning based optimization and harmony search algorithms | |
| Hosseinaei et al. | Optimal design of passive and active control systems in seismic-excited structures using a new modified TLBO | |
| Talatahari et al. | Shear wall layout optimization of tall buildings using Quantum Charged System Search | |
| Kookalani et al. | Shape optimization of GFRP elastic gridshells by the weighted Lagrange ε-twin support vector machine and multi-objective particle swarm optimization algorithm considering structural weight | |
| CN111881498B (en) | Frame-shear structure wall layout optimization method based on improved particle swarm optimization | |
| Kazemzadeh Azad et al. | Computationally efficient optimum design of large scale steel frames | |
| Yousif et al. | Optimum design of post-tensioned flat slabs with its columns to ACI 318-11 using population based beetle antenna search algorithm | |
| Whitworth et al. | Embodied energy optimization of steel-concrete composite beams using a genetic algorithm | |
| Schnellenbach-Held et al. | Bionic optimization of concrete structures by evolutionary algorithms | |
| Edemskaya et al. | Rethinking Complexity: Vladimir Shukhov's Steel Lattice Structures | |
| Shen et al. | Optimal Building Frame Column Design Based on the Genetic Algorithm. | |
| Desai | Structural Optimization Using Genetic Algorithm | |
| Shi | Research on the optimisation of complex models of large-scale building structures dependent on adaptive grey genetic algorithms | |
| Prabhavati et al. | Optimization of RCC dome using genetic algorithm | |
| Sun et al. | The optimum design of high-rise building structure based on the strength and stiffness of genetic algorithm | |
| Aldwaik | Cost Optimization of Reinforced Concrete Highrise Building Structures |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |