Cluster Computing https://doi.org/10.1007/s10586-018-2195-y

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Optimal design of high-rise building wiring based on ant colony optimization Chunjiang Liu1 Received: 30 December 2017 / Revised: 2 February 2018 / Accepted: 14 February 2018  Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract With the continuous acceleration of the building process of urban modernization in China, the scale of buildings continues to expand, and more and more information equipment and electrical equipment are applied to high-rise buildings, which brings new challenges to the design of electricity for high-rise buildings. In order to ensure the normal operation of electric equipment and choose the reasonable electricity consumption and reduce the cost of investment and maintenance, it is necessary to discuss the wiring optimization problems of high-rise buildings. Therefore, this paper chooses the ant colony optimization to optimize the wiring design of the electrical equipment of the building intelligently. Based on the biological model of ant colony optimization, the traditional ant colony optimization is improved, and the ant colony optimization is proposed in the continuous space optimization problem. It optimizes the routing path of high-rise buildings by simulating the shortest path of the ant colony to find food. The computing results of power parameters show that, the improved ant colony optimization model proposed in this paper can shorten the length of high-rise building wiring, the control of voltage drop, line loss and other power parameters can improve the economic benefit of the algorithm, and it is feasible in the optimization of high-rise building wiring. Keywords Ant colony optimization  High-rise building  Wiring optimization  Load calculation

1 Introduction With the continuous development of the construction industry in China, the use of land resources is becoming more and more nervous, and more and more new buildings are chosen to develop in the direction of the high floor. The emergence of high floors makes the use of all kinds of electrical equipment more frequent, especially the development of computer network communication technology, buildings are more likely to use information-based electrical equipment. There is a sharp increase in power load [1]. To ensure the normal operation of all electrical equipment, avoid appearing the state of overloading operation, the line wiring and optimization of the cable and optical cable of the related electrical components have become the focus of attention. The ultimate objective of & Chunjiang Liu [email protected] 1

School of Economics and Management, Chang’an University, Xi’an 710064, Shaanxi, China

wiring optimization is to find a best way to connect electrical equipment and information equipment in the highrise building [2]. The wiring optimization is a multilevel optimization problem. It requires that the wiring path is as short as possible, the number of lines through wall as little as possible, line wiring as far as possible without turning and so on [3]. In the face of the optimal wiring and optimization of high-rise buildings, the theory of optimal method is usually adopted. Traditional optimization methods include: the derivative method of the gradient of the objective function and the non-derivative iterative method [4, 5]. The two types of methods have their own advantages and disadvantages. The former has a fast convergence rate, but it needs to calculate the gradient of the objective function, and the calculation is too complex [6]. The latter does not need to calculate the derivative of the objective function, and has a strong adaptability, but the speed of convergence is slow [7]. The American mathematician Dantzig proposed the simplex optimal solution method based on linear programming, which lays the foundation for the linear programming theory. After that,

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the India-American mathematician Karmakar, has proposed a polynomial time optimization algorithm based on linear programming, which has become the theoretical basis of operational research. Since the end of the 20th century, the typical representatives of intelligent optimization algorithms both at home and abroad are as follows: simulated Annealing (SA), Genetic Algorithm (GA), TabooSearch (TS), PaperSwarm Optimization (PSO), Pattern Extraction method (Alopex) and ant colony optimization (ACO) [8–11]. Based on all kinds of references, this paper uses ant colony optimization algorithm to complete the wiring optimization problem of high-rise buildings, and realizes the application of algorithm in continuous space optimization problem, achieves better global optimization effect, and meets the wiring demand of modern high-rise buildings.

length of BD path is 2, the length of AC path is 7, and the length of CD path is 8. In addition, the distance that the ant moves in a certain time is fixed value 1. Before ants find food, there is no resource on all paths. At the time of t = 0, 20 ants from the ant nest to A, at the same time, the probability of ants to choose the AB path or the AC path is equally possible. So, there are 10 ants walking the AB path, 10 ants walk the AC path. At the time of t = 5, the 10 ants on the AB path will return to the starting point when they reach the food source. In addition, 10 ants on the AC path are still on the path of finding food. As you can see, the amount of resources on the AB path is larger than the amount of resources on the AC path. As time goes on, more ants tend to choose the AB path.

2 Related work

To illustrate the basic model of ant colony optimization, this paper first introduces the TSP algorithm [14]. The TSP problem model is as follows: There are n cities, and the cost of travel between each city is known, looking for a travel route that visits all the cities and costs the lowest. The mathematical definition of the TSP algorithm is: set up a city set C = {C1, C2, Cn}, the distance from each of the   cities of Ci ; Cj 2 C is d Ci ; Cj 2 Zþ . Finding a path (C(p1 ), C(p2 ),…, C(pn )) to access each city just once in C makes the result of the formula (1) is minimized.

2.1 The biological principle of ant colony optimization Ant colony optimization is a kind of simulation algorithm based on the resources, Dorigo [12] and other experts combine the process of searching for food by ant colony with the traveling salesman problem (TSP) [13], the problem is solved by the artificial simulation of ants in the process of finding food, they solve the problem by simulating ants in the process of searching for food. This paper takes Fig. 1 as an example to introduce the best path of ants from the nest to the food source. Ants encounter an obstacle in the process of finding food, assuming there is a path to the food source on both sides of the barrier at this time. The path length of AB is 3, the

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2.2 Basic model description of ant colony optimization

n¼1 X

dðC ðn1 Þ; Cðniþ1 ÞÞ þ dðC ðnn Þ; Cðn1 ÞÞ

ð1Þ

i¼1

In this, ðp1 ; p2 ; . . .; pn Þ is a replacement for (1,2,…,n). Based on the idea of graphics [15], the TSP problem can be described as: For graph G = (V, A), where V is a set of vertices, A is a set of arcs connected to each vertex, and D = (dij) is a cost matrix associated with a set A. The distance between each vertex is known, looking for a loop with the shortest length [16]. Set dij as the distance between the city I and the city J. Introducing decision variables [17]:  1; If the traveler visits the city j after the city i xij ¼ 0; Other ð2Þ

2EVWDFOH

&

% 

 ' )RRGVRXUFH Fig. 1 Ant colony search route

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The objective function of the TSP algorithm can define the formula (3): n X min Z ¼ xij dij ð3Þ i;j¼1

For any i; j 2 V dij = dji, then the algorithm is symmetric TSP algorithm; Otherwise, it is an asymmetric TSP algorithm. For any i; j; k 2 V; meet dij ? djk C dik, the cost matrix D conforms to the structure of the inverse

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trigonometric inequality [18]. When V 2 R2 and dij is a straight-line distance between j and i, it is called plane TSP algorithm. The basic model of ant colony optimization is illustrated with TSP algorithm. There are n cities in the plane (1, 2, 3,…, N), if we randomly put m ants in these n cities, set up dij (I, j = 1, 2, 3,… N) is the distance between the city I and the city J. sij ðtÞ is the amount of resources remaining on the city I and the city J path at t time, When t = 0, the amount of resources on each path is equal, sij ð0Þ ¼ c (C is constant). Ant k (k = 1, 2,… m) in the process of moving, select the cities that they have not passed, according to the amount of resources on each path, at the same time, after the completion of the inter-city visit, recalculate the residual resources in the entire path. The main variables for the visit to the next city are: sij ðtÞ is the remaining amount of resources in time t between city I and city J; gij is the expected value of the ant from city I to city j; Pij(t) is the probability that ant k is transferred from the city I to the target city J at t time. In the algorithm of this paper is usually take gij ¼ d1ij . The calculation formula of Pij(t) is as follows: 8 b a > < sij ðtÞ  gij ðtÞ ; j 2 allowedk k P Pij ¼ saij ðtÞ  gbij ðtÞ > : 0; else

coverage is represented by the parameter 1 - p. Dskij is the amount of resources that the K ant remains on the j path in this feeding cycle. Dsij is the increment in the amount of resources that all ants that may pass through the path (i, j) remain on the path i to the path j in the feeding cycle.

2.3 Improved ant colony optimization for improving performance The core application of ant colony optimization is method optimization. To make the algorithm better applied to the problem of function optimization, it is necessary to improve the basic ant colony optimization model [20]. This paper takes the application of ant colony optimization algorithm in continuous spatial function optimization. Based on the basic idea of ant colony optimization, the study of ant colony optimization for continuous spatial function optimization is carried out, then uses the improved ant colony optimization to solve optimization problem of high-rise building wiring. The basic form of the traditional function optimization problem with constraint, as shown in formula (7): min f ðxÞ s:t:Sð xÞ  0

ð4Þ

By the formula (1), it is known that ants will choose paths closer to yourself and have a greater concentration of resources, that is, the path of the maximum probability of   j ¼ max pkij . In formula (4): when variable allowedk ¼ f1; 2; . . .; ng  tabuk , it is the city that is not visited that ant k will choice. It is different from the real ant colony seeking method. The special expenditure of the ant colony optimization is a certain memory function [19]. This paper uses tabuk ðk ¼ 1; 2; . . .; mÞ to preserve the city that ants have already visited. In addition, after n cycles, the ant completes a feeding cycle, after the next round of feeding; we need to add new information remaining on each path that ants have visited to sij ðtÞ. The amount of resources needs to be adjusted according to the formula (5). sij ðt þ nÞ ¼ q  sij ðtÞ þ Dsij

ð5Þ

Among them: m X Dskij Dsij ¼

ð6Þ

ð7Þ

Each group of solutions in the formula (7) is selected as an ant in the ant colony. For example, for ant I, its function value is set to the corresponding target function value Zi, the objective function difference between ant I and the ant J is the formula (8): DZij ¼ Zi  Zj

ð8Þ

The moving probability of the ant I moving to the location of the ant J is as follows:  a  b sj  DZij Pij ¼ PM ð9Þ a b k¼1 ½sk  ½DZik  Among them, sj is the amount of resources in the neighborhood of ant j, and a and b are the weight wiping parameters of the algorithm, usually a ¼ b ¼ 1: After the replacement of ants, the algorithm immediately updates the amount of resources and calculates according to the formula (10). sk ¼ q  sk þ Dsk

ð10Þ

At this point, we can apply the basic model of ant colony optimization to the problem of function optimization, and then we can solve the optimization problem of high-rise building wiring.

k¼1

In the formula (5) and (6), P is the remaining coefficient of information. As time goes on, the information saved before will be covered, and the degree of information

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3 Application of ant colony optimization in high-rise building wiring 3.1 Main technology and engineering design of high rise building wiring

¶

3.1.1 Voltage drop

,5

žC

žC 8

,

The voltage quality has a great influence on the quality of power supply of electrical equipment. Voltage excursion is an important power parameter to evaluate the quality of the voltage [21]. If the voltage drop exceeds the rated range of the working voltage of the electrical equipment, the working efficiency of the electrical equipment and the life of the electrical equipment will be greatly reduced. In addition, the voltage drop will also cause the increase of distribution network line loss, especially in the case of complex high-rise building lines. Therefore, the voltage drop is a key power parameter in the optimal wiring of a high-rise building. In the design of the wiring, it is necessary to pay attention to the voltage loss of the line and ensure that the voltage loss of the line is within the allowable range. A line with an impedance of Z and a current of I, the voltage drop vector Ud can be calculated by formula Ud = IZ. In the equivalent line of a distribution line shown in Fig. 2, an approximate value of the voltage drop arithmetic difference can be introduced. In Fig. 2, the circuit impedance is set to Z = R ? jX, the delivery voltage port is U1, the end voltage port is U2, and the current I is lagging the voltage U2. Under normal conditions, the angle difference between the end voltage port U2 and the delivery voltage port U1 can be ignored. In practical application, the angle difference is /  /0 . Therefore, the relation of Angle difference can be written as formula (11): U1 ¼ U2 þ IR cos / þ IX sin /

ð11Þ

In Fig. 3, the calculation formula of approximate value of the voltage arithmetic difference at both ends of the line is as follows: Ud  IR cos / þ IX sin /

8

M,;

=

ð12Þ

8

8 Fig. 3 Route suitable chart

According to the formula (12), the line voltage drop value in the three-phase power supply system can be calculated, and the formula is shown as (13). pffiffiffi PR þ QX ð13Þ Ud  3ðIR cos / þ IX sin /Þ ¼ U Among them, P is the total power of three-phase power, U is the line voltage, Q is the reactive power, meet the Q ¼ P tan /. 3.1.2 Line loss In the process of distribution wiring in high-rise buildings, we not only need to consider the quality of power supply of electric energy, but also need to analyze the economic benefits of its operation. Therefore, this paper not only considers the investment and land occupation of electrical equipment, but also calculates the operation cost of the equipment [22]. Line loss under normal operation of equipment is one of the most important contents in the plan and design of high-rise buildings wiring. Line loss includes fixed line loss and variable line loss. The loss of fixed line loss is caused by the excitation current of electrical elements such as transformers and reactors. The variable losses are due to the loss of the current through the irregularity of the equipment. This paper uses the number of the maximum load loss hour method to calculate the line loss [23]. The number of the maximum load loss hour is expressed by s. The power loss caused by the actual equipment load in a year corresponds to the time needed for the equipment line to produce the same loss when the device is working at the maximum load. The annual power loss value of the equipment is calculated as follows: DWy ¼ DPmax s ¼ 3I 2 Rs  103

, FRV¶

Fig. 2 Swith route equivalent circuit chart

123

ð14Þ

Among them, the I is the maximum load current, and the DPmax is the power loss corresponding to the maximum load.

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3.2 Optimal design of high-rise building wiring based on ant colony optimization The meaning of the wiring of high rise buildings is as follows: The obstacle set of the 3D wiring space, the set of electrical equipment to be connected, and the connection relation set of electrical equipment and other content are known to find a best path of electrical equipment wiring [24]. Wiring problem is a classic multilevel optimization problem. The main optimization objectives are as follows: the total line length of the routing path is as small as possible; the number of wiring paths through the wall as few as possible, the wiring path is as possible without turning. In order to avoid the obstacles of high-rise buildings, and make the line is beautiful after the installation of the equipment, the layout of the original line is often needed to be changed in a large range when wiring. Therefore, the problem of three-dimensional wiring can be considered as a multi-layer wiring problem of a two-dimensional plane figure [25]. The conventional wiring algorithm is completely NP problem, whether it is a layer wiring or a multilayer routing algorithm. In addition, with the further improvement of the complexity of the wiring problem, the time of solving is exponentially larger. At present, the problem of high-rise building wiring still lies in the experience of the installation and design personnel. Traditional wiring problem can not optimize the wiring strategy of the whole building three-dimensional space. For example, adding a new optimization function is easy to conflict with the existing optimization strategy. Therefore, it is urgent to adopt special method to optimize the cabling problem of high-rise building. Ant colony optimization is a new kind of simulation algorithm based on resource quantity, which belongs to random search algorithm category. It can be used to solve combinatorial optimization problems, such as TSP problem and scheduling problem, and get outstanding results. Therefore, this paper uses ant colony optimization to solve the problem of wiring optimization of high-rise buildings, and find the best wiring solution in the whole building three-dimensional space, and get the biggest economic benefits. The problem of high-rise building optimization needs to describe the wiring path first, and then solve the optimal wiring path on the wiring path. This paper is illustrated with Fig. 4 as the wiring path model. Let k be the minimum allowed wiring length. The wiring area is a rectangle with a length of L and a width of W, and L ¼ M  k,W ¼ Q  k.Taking the lower border, the left line and the lower left corner of the rectangular region as the X axis, the Y axis and co-ordinate origin to set up a

Fig. 4 Disposal route create sketch map

Cartesian coordinate system. So let’s do the line X = 0, k, 2k…Qk and Y = 0, k, 2k,…Mk to carry out M  Q grid partition in the wiring area. Set O ¼ fO1 ; O2 ; . . .; Ok g as a set of obstacles, and E as an electrical connection set. And there is a h subset of E fE1 ; E2 ; . . .; Ek g. Each subset includes electrical equipment that needs to be connected.Eij is the j electrical connection of the I subset of the E. Therefore, the problem of wiring in this paper can be transformed into: A non-ring h subtree is formed along G = M  Q grid wiring in the wiring area. The vertex of the tree-shaped Tk (0 \ k\h ? 1) is a set of Ek. At this time, the h ant colony is walking in G, looking for the shortest path from the nest Ek1 to the food Ekj (i = 1). According to the previous article, each step of the ant is the same distance in Fig. 1, thus forming a virtual length 0 dij . The result of replacing the actual length of dij is as follows: (1) (2)

If there are obstacles such as wall or column that can 0 not be penetrated on the path, dij ¼ 1. If there is no invisible wall or column on the path, there are i penetrable walls, j pipes, wind pipes and 0 other wiring, it meets dij ¼ a  i þ b  jþ c  k þ d. Among them, a, b, c, and d are the control elements, which are used to represent different types of obstacles.

Usually, the wiring process consists of two types of wiring along the wall and parallel wiring [26]. The wiring along the wall only needs to modify the initial distribution of resources, increase the amount of resources along the path along the wall, and encourage the ants to continue along the wall. The control elements Cw is the amount of increased resources along the wall. If the path (i, j) belongs to the path along the wall wiring, the update process of the resource in the path is determined by formula (15): sij ðt þ nÞ ¼ sij ð0Þ  ð1 þ Cw Þ þ qsij ðtÞ

ð15Þ

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colony optimization automatically optimizes the way of rise or fall according to the actual situation. In order to reflect the effect of improved ant colony algorithm on the optimization of high-rise building wiring, based on the related electrical parameters, according to the results of the high-rise building wiring as shown in Fig. 5, the optimization results of the basement parameters of high-rise buildings are calculated, as shown in Table 1. After that, the optimization results of the odd-layer power parameters of the twenty-four storey building are shown in Table 2. Finally, the results of the optimization of the even layer power parameters of twenty-four storey building are shown as shown in Table 3. As can be seen from Tables 1, 2, and 3, the configuration parameters of the improved ant colony optimization are as follows: a ¼ 0:1; b ¼ 2:0; s0 ¼ 0:2; Cw ¼ 0:3; q ¼ 0:2; Q ¼ 0:1; a ¼ 0:05; b ¼ 0:2; c ¼ 0:2; d ¼ 0:1: It is found that the total length of wiring based on improved ant colony algorithm is reduced by 10–30% compared to the traditional line optimization method. The voltage drop and line loss can be controlled in a reasonable range, and the economic efficiency is considerable.

It is different from the wiring along the wall, and the parallel wiring is a dynamic change process. If the ant moves one step, it will increase the distribution of resources on the parallel path of its distance of dp, which is used to motivate the ants to wire in parallel direction. Control factor Cp is the increased amount of resources in parallel wiring. If the path (i, j) belongs to a parallel wiring path, the process of updating the amount of resources on the path is determined by formula (16).   sij ðt þ nÞ ¼ sij ð0Þ  1 þ Cp þ qsij ðtÞ þ Dsij ð16Þ

4 Analysis on experimental results and algorithm performance The improved ant colony algorithm was used to optimize and design the 24 storey high-rise buildings. Figure 5 shows the results of 2D wiring optimization for 30 storey tall buildings. The points in the figure are the electric points for the electrical equipment of the high-rise building, including the machine room, the office building, the house, the basement and so on. It can be seen that the intersection of lines is not completely intersected in Fig. 5, and the ant

5 Conclusion Based on the ant colony optimization, this paper studies the optimization of the wiring of high-rise buildings, this paper studies the optimal wiring design of high-rise buildings, seeks a most economical and efficient wiring way, and proposes a new practical engineering calculation method for load calculation. According to the existing literature, it is found that the traditional route optimization method cannot effectively solve the complex combinatorial optimization problem such as wiring optimization. Through the study of the basic model of ant colony optimization, the ant colony optimization is creatively introduced into the optimization of continuous space function, and the basic model of ant colony optimization is improved, so that the improved algorithm can be successfully applied to the layout optimization of high-rise buildings. The feasibility and correctness of the algorithm are tested by an example

Fig. 5 Disposal route result planar lay match

Table 1 basement parameters of electrical parameters

123

Node i

Node j

Line length L (m)

Active power P (kW)

Reactive power Q (kVAR)

Resistance R (X)

Reactance X (X)

Voltage loss DUðVÞ

E21

E24

17.1

15

12

0.00072

0.00156

2.42

E31

E32

11.96

5

4

0.00096

0.00208

3.23

E41

E42

9.42

10

4.8

0.0012

0.0026

4.04

E51

E25

31.74

629

503.2

0.00144

0.00312

4.85

E11

E12

10.69

667

433.6

0.00168

0.00365

5.66

Cluster Computing Table 2 Electrical parameters of the data in odd-layers building

Table 3 Electrical parameters of the data in even-layers building

Node i

Node j

Line length L (m)

Active power P (kW)

Reactive power Q (kVAR)

Resistance R (X)

Reactance X (X)

Voltage loss DUðVÞ

0

1

16.8

624

302.2

0.00072

0.00156

0

3

22.4

624

302.2

0.00096

0.00208

3.23

0

5

28

624

302.2

0.0012

0.0026

4.04

0

7

33.6

624

302.2

0.00144

0.00312

4.85

0

9

39.2

624

302.2

0.00168

0.00365

5.66

0

11

44.8

624

302.2

0.00192

0.00417

6.47

0

13

50.4

624

302.2

0.00216

0.00469

7.28

0

15

56

624

302.2

0.00241

0.00521

8.09

0

17

61.6

624

302.2

0.00265

0.00573

8.9

0

19

67.2

624

302.2

0.00289

0.00625

9.72

0 0

21 23

72.8 78.4

624 624

302.2 302.2

0.00313 0.00337

0.00677 0.00729

10.52 11.33

1

3

5.6

624

302.2

0.00024

0.00052

0.81

Line length L (m)

Active power P (kW)

Reactive power Q (kVAR)

Resistance R (X)

Reactance X (X)

Node i

Node j

2.42

Voltage loss DUðVÞ

0

2

19.6

576

278.96

0.00084

0.00182

2.61

0

4

25.2

576

278.96

0.00108

0.00234

3.35

0 0

6 8

30.8 36.4

576 576

278.96 278.96

0.00132 0.00156

0.00286 0.00339

4.1 4.85

0

10

42

576

278.96

0.0018

0.00391

5.6

0

12

47.6

576

278.96

0.00204

0.00443

6.34

0

14

53.2

576

278.96

0.00228

0.00495

7.09

0

16

58.8

576

278.96

0.00253

0.00547

7.85

0

18

64.4

576

278.96

0.00277

0.00599

8.6

0

20

70

576

278.96

0.00301

0.00651

9.34

0

22

75.6

576

278.96

0.00325

0.00703

10.09

0

24

81.2

576

278.96

0.00349

0.00755

10.83

2

4

5.6

576

278.96

0.00024

0.00052

0.75

and the relevant power parameters. The experimental results show that the routing optimization method based on ant colony optimization can greatly improve the economic efficiency and reduce the power load pressure, and has practical application value in the optimal wiring of highrise buildings.

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Chunjiang Liu Ph.D. of Control Science and Engineering, Lecturer. Graduated from Northwestern Polytechnical University in 2010. His research interests include Construction Management, and Land Use and Environmental Management.