# Transit Route Optimization for Cable Crane Exposure Reduction Using NSGA-II Algorithm Based on Neural Networks

Authors: Shu Chen; Ya Tian; Yun Chen; Junbo Xi
Journal: Security and Communication Networks
 (2022)

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## Abstract

Owing to frequent man-machine interaction, cable crane operation during the dam construction becomes an intensive dangerous special equipment and easily enlarge exposure. In particular, high wind weather increases the risk of falling objects at high altitude and enhance the impact space of cable crane. These factors lead to space conflicts in the limited space, and prone to accidents. However, previous studies mainly focused on safety monitoring through various technologies, but lack of sufficient prior control, and current methods for searching the optimal transit route of cable crane are insecure and insufficient since the wind environment, complex construction process, and dense man-machine interaction are not simultaneously considered. Thus, in this article, a transit route optimization method for cable crane exposure considering dynamic wind loads during the dam construction is proposed to reduce hazard exposure risk. A comprehensive evaluation function is constructed to assess the cable crane transit route with taking the hazard exposure, efficiency, and operability and collision risk into consideration. The objective is to make use of the NSGA-II algorithm to optimize the transit route under different working situations based on neural networks. The model feasibility is validated by applying it to the Dagangshan hydropower station. A set of results show that the novel methodology is able to reduce exposure and assess the comprehensive performance of different transit route. This method provides an important objective and precise evaluation tool for the cable crane optimal transit route, and also promotes safety management in the project.


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## Body

## 1. Introduction

Cable crane refers to a flexible ropeway to support a hook to hoist material at any point of the track controlled from one of the stations. This device includes one or several track ropes, support towers, haul ropes, a haul winch, a carriage with hoisting tackle, and hoisting cable controls, and it can reach any position in the work zone [1]. Due to flexibility, as well as extended working period, high production efficiency, and large working range, cable crane adapts perfectly to the harsh construction environment and complex topography conditions [2, 3]. Therefore, it becomes an efficient transport machinery for large-scale civil projects and is widely applied to dams during the course of construction [4].However, cable crane is an intensive dangerous special equipment and is prone to accidents owing to complication of operation, complexity of instinct structure, and continuous changes in the external environment [5, 6], especially hydropower projects are built on narrow river valleys, where many workers and mechanical equipment are arranged in the dense construction site [7]. Inevitably, it will form a three-dimensional intersection and induce overlaps with construction equipment on the dam surface while cable crane transports concrete or other materials [8]. It means that the workers and equipment on the dam surface, unavoidable will often be exposed to the cable crane. The exposure to loss-of-control events of cable crane will impose a serious threat to cross operation on the dam surface and bring great challenges to the safety management of construction sites [9]. Therefore, the research about cable crane exposure reduction has been a hot topic in the field of construction safety.Exposure to the hazard as well as the possibility of an accident and the severity of the consequences is an important indicator of construction safety [10, 11]. Hence, exposure reduction is an indispensable part of safety management since it is an effective and essential measure to improve safety performance [12]. With the development of positioning technology, more and more equipment is designed to provide location services such as an early warning to reduce exposure [13]. Real-time locations are obtained to measure the distance between hazard and worker to minimize hazard exposure by various remote locating and tracking technologies, such as global positioning system [14], geographic information systems [15], positioning sensors [16], radio frequency [17, 18], and ultra-wideband technology [19]. However, previous research can be almost categorized as real-time control methods and are unable to meet the needs of prior control. Moreover, these locating and tracking systems are often subject to various interferences, resulting in many false alarms. After all, cable crane also requires planning guidance that improves operational efficiency with full consideration of safety in advance. Therefore, it is best to combine the two methods of precontrol and real-time control.The issue of transit route optimization for cable crane is a multiobjective planning problem, involving many factors such as safety, efficiency, and operability due to dynamic changes in the environment, intensive dam construction, and professional skill requirements [20]. An effective algorithm has been proposed to develop multievent area navigation trajectories to minimize the community noise exposure in terms of the number of people highly annoyed [21]. An efficient Dijkstra algorithm has been outlined to optimize the route for hazardous chemicals transportation based on population exposure as well as accident consequence and population density [22]. Both the motion characteristics for cable cranes are different from aircraft in the sky or vehicles on land, thus a variety of subfunction need to be fully considered to better optimize the transit route for exposure reduction.Transport distance, as well as transportation speed and load volume, was investigated to analyze the impact on cable crane productivity by using the methods of work and time study [2]. Another possible approach to optimize transit route for cable crane relies on GPS guidance and then seeking reasonable collision avoidance under different working situation types by using an artificial immune algorithm [20]. Despite these remarkable contributions to raising the operational performance of cable cranes, no substantial method has yet been presented to improve the work efficiency with full consideration of exposure reduction in the issue of transit route optimization for cable crane. Apart from the existence of various constraints, the transit route optimization for cable crane still needs to meet multiple requirements, involving transit route efficiency, manipulation convenience, collision risk, and hazard exposure. Since it is able to maintain a better spread of solutions and improve its convergence performance in the obtained Pareto-optimal front, the nondominating sorting genetic algorithm II (NSGA-II) has become widely used to solve multiobjective optimization [23]. This allows us to take full account of the numerous types of constraints at a construction site in accordance with the dynamic motion characteristics of a cable crane. In addition, the optimization method and NSGA-II are the basis of artificial intelligence. Therefore, in addition to ensuring the safety of the dam construction process, this article can also provide an important planning method for intelligent construction.To optimize the transit route for cable crane exposure reduction using the nondominating sorting genetic algorithm II (NSGA-II), we arrange the structure as follows: in the remainder of the article, we briefly analyze the motion characteristics of cable crane and parameterize for exposure frequency in Section1. Thereafter, in Section 2, we abstract the optimization of transit routes into a multiobjective planning problem including hazard exposure, efficiency, operability, and collision risk. In Section 3, we describe the NSGA-II algorithm to solve multiobjective optimization of the transit route in detail. Section 4 presents simulation results of NSGA-II and compares the results with another recently proposed transit route optimization method. Finally, we summarize the conclusions of this article.


## 2. Problem Description and Parameter Calculation

As the major construction machine for concrete transportation, the efficient operation of the cable crane is of great significance for dam construction [24]. Under the pressure of the construction period, it is necessary to excavate the working face at different elevations of the same three-dimensional space and arrange a large number of cross-operations to improve the construction efficiency and shorten the construction period. Hence, the exposure between vertical transport machinery and dam block surface machinery should be considered seriously. Therefore, it is essential to quantify the problem of cable crane with a mathematic model. Since the positioning and tracking technologies have been widely applied, the location information of various machines can be obtained conveniently. For the sake of optimizing the transit route, we mathematically define both the cable crane motion and its parameterization for potential exposure as follows.


### 2.1. Description of Cable Crane Motion and Potential Exposure

The environment in which the cable crane operates is affected by many factors, while some parameters are different to obtain, the expression of cable crane motion should be simplified to an approximate model. According to the round-trip operation characteristics, the work breakdown structure (WBS) is used to decompose the concrete transportation cycle process into loading, transportation with full load, alignment, unloading, and return with empty load. Similarly, the bucket starts its motion from the feeding point to the dumping point, and then returns along the original path. In order to assure safe operations in restricted areas, it has to clearly avoid the collision risk with obstacles in the environment. Additionally, it forms a three-dimensional impact space when the cable crane works in the sky, which inevitably brings some risks to the people and machinery on the dam block surface.Owing to increasing pressure for shorter schedules and technical requirements of the construction process, some parallel activities with transportation of cable crane should be arranged on dam block surface simultaneously, mainly including concrete spreading, vibration, compaction, cutting, and concrete maintenance. As a result, a variety of machines, such as spreader, compactor, joint cutter, and so on, compete together and occupy the limited working space concurrently.In the concrete pouring process, when the bucket is close to the block surface, the impact space will overlap with the working space, as a result, there will be an exposure (shown in Figure1). Moreover, most of the hydropower projects under construction in China are located in hot and dry valleys, where foehn wind and valley wind effects are significant. High wind weather increases the risk of falling objects at high altitude and enhances the impact space of cable crane, in particular, this may lead to many serious accidents when the bucket touches the workers or machines.Figure 1
Schematic diagram of concrete placement during the dam construction.


### 2.2. Parameterization for Exposure Frequency

At present, most of the hydropower projects, under construction and proposed to be built in China, are located in the hot and dry valley, were frequently troubled by disastrous gale. However, owing to its uncertainly in speed and direction, gale is difficultly forecasting in construction projects. Additionally, the offsets of the cable crane, which is hugely relevant to the gale influence, are very diverse depending on the gale characteristics [20]. Therefore, it is necessary to count the meteorological materials near the dam site over the recent historical years, to obtain the probability of wind speed per scale PA.In the process of operation, the impact space of cable craneSI refers to the maximum envelope space range that the harmful energy can cover, namely, it can be defined as the bucket run on cable crane under a certain wind speed. In particular, the length of impact space Ix is the straight line distance from the feeding platform to a dumping point, the width of impact space Iy is regarded as the bucket deviation in the wind direction since it is affected by the gale. Therefore, the impact space can be described as follows:(1)SI=Ix⋅Iy.Considering the operation laws of the cable crane, when the operation heightH is the highest evaluation and the bucket under the action of wind load F, the offset Iy has the largest value, setting the duration of the entire drop process to t, Iy can be calculated as follows:(2)H=12gt2,Iy=Ft22m.Here, we employ an easy-to apply approach to obtain the wind loadF [25], and [26] has given the relationship between wind scale, wind speed vf, and wind pressure.(3)F=wφ=12ρvf2φ,where ρ = the air density, φ = windward area, φ = πrh, r = radius of bucket, and h = the physical height of bucket.The working space can be regarded as the boundary range of various construction machinery activities, specifically, refers to the dam block surface which is under construction. Set the length of the dam block surface asWx, the width as Wy, and the working space SW can be calculated as follows:(4)SW=Wx×Wy.The overlap that produces a wide variety of exposures represents the space occupied by the impact space and working space simultaneously. Considering the variation of the dam block surface, the length of the overlapOx refers to the distance from the left edge of the block surface to the dumping point. The width Oy of the overlap is determined compared the offset Iy with the length of the dumping point to the offset side Dy.(5)Oy=IyIy≤Dy,DyIy>Dy.Consequently, the length and width of the overlap space are determined, and overlap can be described as follows:(6)SO=Ox×Oy.According to the knowledge of probability theory, under certain wind speed conditions, the probability that the bucket appears in the overlapPB is equal to the ratio of the time that the bucket appears in the overlap tbucket to the possible exposure time of the cable crane Timpact. Notably, the compactor has a similar rule with the bucket. As a result, we have an unambiguous criterion:(7)PB=tbucketTimpact,PC=tcompactorTworking,where tcompactor = the time that the compactor appears in the overlap, Tworking = the total time that the compactor runs on a certain dam block surface.The possibility of the hazard occurring and/or the victim being exposed to danger is determined by the bucket and compactor relevant parameters. When the machines overlap in the same space, the source task is executed forPB, while the target task is performed for PC. Therefore, the probability of exposure of machines performing the target task to the undesired event occurring in the source task is PB⋅PC over the same wind loads. On this ground, exposure frequency expectation can be portrayed as the sum frequencies of bucket and compactor appear in the overlap where under various wind speed conditions. The following formula is a product of three independent factors:(8)E=∑PA⋅PB⋅PC,where E = the total exposure frequency under various wind speed conditions; PA = the frequency of wind speeds; PB = the probability of bucket appearing in overlap, it can be calculated explicitly based on round-trip route of cable crane; and PC = the probability of construction machinery on the dam surface presenting in the overlap.


## 2.1. Description of Cable Crane Motion and Potential Exposure

The environment in which the cable crane operates is affected by many factors, while some parameters are different to obtain, the expression of cable crane motion should be simplified to an approximate model. According to the round-trip operation characteristics, the work breakdown structure (WBS) is used to decompose the concrete transportation cycle process into loading, transportation with full load, alignment, unloading, and return with empty load. Similarly, the bucket starts its motion from the feeding point to the dumping point, and then returns along the original path. In order to assure safe operations in restricted areas, it has to clearly avoid the collision risk with obstacles in the environment. Additionally, it forms a three-dimensional impact space when the cable crane works in the sky, which inevitably brings some risks to the people and machinery on the dam block surface.Owing to increasing pressure for shorter schedules and technical requirements of the construction process, some parallel activities with transportation of cable crane should be arranged on dam block surface simultaneously, mainly including concrete spreading, vibration, compaction, cutting, and concrete maintenance. As a result, a variety of machines, such as spreader, compactor, joint cutter, and so on, compete together and occupy the limited working space concurrently.In the concrete pouring process, when the bucket is close to the block surface, the impact space will overlap with the working space, as a result, there will be an exposure (shown in Figure1). Moreover, most of the hydropower projects under construction in China are located in hot and dry valleys, where foehn wind and valley wind effects are significant. High wind weather increases the risk of falling objects at high altitude and enhances the impact space of cable crane, in particular, this may lead to many serious accidents when the bucket touches the workers or machines.Figure 1
Schematic diagram of concrete placement during the dam construction.


## 2.2. Parameterization for Exposure Frequency

At present, most of the hydropower projects, under construction and proposed to be built in China, are located in the hot and dry valley, were frequently troubled by disastrous gale. However, owing to its uncertainly in speed and direction, gale is difficultly forecasting in construction projects. Additionally, the offsets of the cable crane, which is hugely relevant to the gale influence, are very diverse depending on the gale characteristics [20]. Therefore, it is necessary to count the meteorological materials near the dam site over the recent historical years, to obtain the probability of wind speed per scale PA.In the process of operation, the impact space of cable craneSI refers to the maximum envelope space range that the harmful energy can cover, namely, it can be defined as the bucket run on cable crane under a certain wind speed. In particular, the length of impact space Ix is the straight line distance from the feeding platform to a dumping point, the width of impact space Iy is regarded as the bucket deviation in the wind direction since it is affected by the gale. Therefore, the impact space can be described as follows:(1)SI=Ix⋅Iy.Considering the operation laws of the cable crane, when the operation heightH is the highest evaluation and the bucket under the action of wind load F, the offset Iy has the largest value, setting the duration of the entire drop process to t, Iy can be calculated as follows:(2)H=12gt2,Iy=Ft22m.Here, we employ an easy-to apply approach to obtain the wind loadF [25], and [26] has given the relationship between wind scale, wind speed vf, and wind pressure.(3)F=wφ=12ρvf2φ,where ρ = the air density, φ = windward area, φ = πrh, r = radius of bucket, and h = the physical height of bucket.The working space can be regarded as the boundary range of various construction machinery activities, specifically, refers to the dam block surface which is under construction. Set the length of the dam block surface asWx, the width as Wy, and the working space SW can be calculated as follows:(4)SW=Wx×Wy.The overlap that produces a wide variety of exposures represents the space occupied by the impact space and working space simultaneously. Considering the variation of the dam block surface, the length of the overlapOx refers to the distance from the left edge of the block surface to the dumping point. The width Oy of the overlap is determined compared the offset Iy with the length of the dumping point to the offset side Dy.(5)Oy=IyIy≤Dy,DyIy>Dy.Consequently, the length and width of the overlap space are determined, and overlap can be described as follows:(6)SO=Ox×Oy.According to the knowledge of probability theory, under certain wind speed conditions, the probability that the bucket appears in the overlapPB is equal to the ratio of the time that the bucket appears in the overlap tbucket to the possible exposure time of the cable crane Timpact. Notably, the compactor has a similar rule with the bucket. As a result, we have an unambiguous criterion:(7)PB=tbucketTimpact,PC=tcompactorTworking,where tcompactor = the time that the compactor appears in the overlap, Tworking = the total time that the compactor runs on a certain dam block surface.The possibility of the hazard occurring and/or the victim being exposed to danger is determined by the bucket and compactor relevant parameters. When the machines overlap in the same space, the source task is executed forPB, while the target task is performed for PC. Therefore, the probability of exposure of machines performing the target task to the undesired event occurring in the source task is PB⋅PC over the same wind loads. On this ground, exposure frequency expectation can be portrayed as the sum frequencies of bucket and compactor appear in the overlap where under various wind speed conditions. The following formula is a product of three independent factors:(8)E=∑PA⋅PB⋅PC,where E = the total exposure frequency under various wind speed conditions; PA = the frequency of wind speeds; PB = the probability of bucket appearing in overlap, it can be calculated explicitly based on round-trip route of cable crane; and PC = the probability of construction machinery on the dam surface presenting in the overlap.


## 3. Multiobjective Optimization Model

The focus of the article is to move the bucket from the initial position to the target point for the cable crane and finding the optimal path to reach the final position with exposure reduction. The bucket motion has to be accomplished by minimizing traveling time, obstacle avoidance, smooth steering, and less exposure frequency. The cable crane works in a changing and complex environment and the simultaneous participation of numerous resources on construction sites poses a significant challenge to access the comprehensive performance transit route. In addition to the hazard exposure, efficiency, operability, and collision risk should also be considered to find an optimal route. The optimal route will be significant for the construction of large-scale dam structures with casting, piece by piece [27]. Therefore, in this part, we will establish a comprehensive evaluation function to optimize the transit route from various angles, which guides the direction using (NSGA-II).


### 3.1. Space Exposure Assessment Subfunction

The space exposure assessment subfunction quantifies the hazard exposure between the cable crane and other construction machines on the dam block surface. Obviously, the higher the exposure frequency, the more dangerous to the construction machinery. Hence, the space exposure assessment functionfexposure is computed as:(9)fexposure=11+E.


### 3.2. Efficiency Assessment Subfunction

The efficiency assessment is related to the work cost of the cable crane. According to practical experience, it does not necessarily mean that the shorter the distance, the better the efficiency, but the longer the transit round-trip time the cable crane runs, the higher will be the cost and the lower the efficiency. Thus, the efficiency assessment function is computed as:(10)fefficiency=11+Tactual−Tplan/Tplan,where fefficiency is the efficiency assessment, Tactual is the actual running time that the cable crane takes to transport one can of concrete back and forth, and Tplan is the planned running time of the transit route. When the cable crane is working strictly on schedule, Tactual−Tplan is equal to 0 and fefficiency reaches a maximum value of 1. In other words, the longer the Tactual−Tplan is, the lower the efficiency is.


### 3.3. Operability Assessment Subfunction

Based on the actual experience, smoother steering contributes to avoiding collisions and is easier for the driver operation. Therefore, the average curvature of the steering process is used to evaluate the operability. As shown in Figure2, Δα refers to the change in the direction angle, ΔL is the distance of the steering process. When Δα/ΔL has a larger value, it means a larger swerve within a shorter distance. In this case, there will be a difficult operation for the cable crane drivers, the operability assessment foperability to be a lower value at this point. Hence, foperability is derived as equation (11):(11)foperability=11+Δα/ΔL.Figure 2
Schematic diagram of a cable crane transit route.


### 3.4. Collision Risk Assessment Subfunction

In order to reduce the collision risk during the operation of cable cranes, it is extremely important to determine the safe distance. Too much distance will seriously affect the construction progress, while too little distance will severely affect the avoidance effect. During their transit route, there may be two kinds of obstacle risks between cable cranes: static collision risk and dynamic collision risk.The static collision risk, including the dam block and slope, mainly determined by the minimum distancedstatic between bucket and obstacle, to avoid the collision, drivers need a buffer distance D1 to react. Suppose the location of the bucket is xi,yi,zi, i=1,2… and the coordinate of the dam block point is x0,y0,z0, the speed and normal braking acceleration of cable crane i is vi and ai, the minimum distance dstatic and the buffer distance D1 can be portrayed as follows:(12)dstatic=minxi−x02+yi−y02+zi−z02,D1=vi22ai.The dynamic collision risk of a transit route is associated with the distances between the buckets. As shown in Figure3, when the buckets are closest to each other, the distance between them is minimal and the dynamic collision risk becomes the most serious. This value is constantly changing as the position of the buckets changes. Obviously, if the value increases, it pulls the cable toward the safer operation. Setting vj and aj are the speed and normal braking acceleration of cable crane j, the location of another bucket is xj,yj,zj. The distances between the buckets ddynamic is calculated by:(13)ddynamic=xj−xi2+yj−yi2+zj−zi2.Figure 3
Collision risk descriptions.When the cable crane is in operation, there may be two kinds of motion between them: relative motion and catch-up motion. Therefore, the distance calculation formula is abstractly expressed as a linear motion [28].(14)Drelative=vi22ai+vit0+vj22aj+vjt0,(15)Dcatch−up=vi22ai+vit0−v1t1−a1ti22,where Drelative and Dcatch−up denote the critical safe distance of relative motion and catch-up motion. v1 and a1 represent the speed and acceleration of the cable crane being chased. t0 refers to the response time of drivers, t1 refers to the total braking time of chasing cable crane including operators’ reaction time and equipment braking time.Equations (14) and (15) are the general forms of distance calculation formulas. However, in practical application, the influence of operators’ response time k1, GPS error k2, system lag k3, rope swing k4, and wind pressure k5 on buffer distance should also be seriously considered [29]. Therefore, setting the margin of safety avoidance is K, the buffer distance D2 (relative movement: D2=Drelative; catch-up movement: D2=Dcatch−up) can be regarded as the critical condition for the collision risk.(16)D2=vi22ai+vit0+vj22aj+vjt0+Krelative,vi22ai+vit0−v3t1−a3ti22+Kcatch−up,K=k1+k2+k3+k4+k5.Combined with these two collision risks, we can determine their specific gravityμ1and1−μ1. Consequently, the collision risk subfunction fcollision can be revised as:(17)fcollision=μ1fstatic+1−μ1fdynamic=μ11+D1/dstatic−D1+1−μ11+D2/ddynamic−D2,fcollision=μ1fstatic+1−μ1fdynamic=μ11+D1/dstatic−D1+1−μ11+D2/ddynamic−D2.


### 3.5. Comprehensive Evaluation Function

Based on the above analysis, these subfunctions are normalized and integrated into the comprehensive evaluation function. The function is given by(18)f=ω1fefficiency+ω2foperability+ω3fcollision+ω4fexposure,where ω1, ω2, ω3, and ω4 represent weighting factor of the fefficiency, foperability, fcollision, and fexposure, respectively. The weighting factor ωi (i = 1, 2, 3, 4) plays a vital role in the fitting process since these factors determine how much a control point influences locally the geometry of the transit route. The weight of these four indexes is calculated by the entropy weight method with strong objectivity. Some experts (q) will be invited to grade the four evaluation indicators in the form of a 100% system, so as to determine the weight of each indicator.


## 3.1. Space Exposure Assessment Subfunction

The space exposure assessment subfunction quantifies the hazard exposure between the cable crane and other construction machines on the dam block surface. Obviously, the higher the exposure frequency, the more dangerous to the construction machinery. Hence, the space exposure assessment functionfexposure is computed as:(9)fexposure=11+E.


## 3.2. Efficiency Assessment Subfunction

The efficiency assessment is related to the work cost of the cable crane. According to practical experience, it does not necessarily mean that the shorter the distance, the better the efficiency, but the longer the transit round-trip time the cable crane runs, the higher will be the cost and the lower the efficiency. Thus, the efficiency assessment function is computed as:(10)fefficiency=11+Tactual−Tplan/Tplan,where fefficiency is the efficiency assessment, Tactual is the actual running time that the cable crane takes to transport one can of concrete back and forth, and Tplan is the planned running time of the transit route. When the cable crane is working strictly on schedule, Tactual−Tplan is equal to 0 and fefficiency reaches a maximum value of 1. In other words, the longer the Tactual−Tplan is, the lower the efficiency is.


## 3.3. Operability Assessment Subfunction

Based on the actual experience, smoother steering contributes to avoiding collisions and is easier for the driver operation. Therefore, the average curvature of the steering process is used to evaluate the operability. As shown in Figure2, Δα refers to the change in the direction angle, ΔL is the distance of the steering process. When Δα/ΔL has a larger value, it means a larger swerve within a shorter distance. In this case, there will be a difficult operation for the cable crane drivers, the operability assessment foperability to be a lower value at this point. Hence, foperability is derived as equation (11):(11)foperability=11+Δα/ΔL.Figure 2
Schematic diagram of a cable crane transit route.


## 3.4. Collision Risk Assessment Subfunction

In order to reduce the collision risk during the operation of cable cranes, it is extremely important to determine the safe distance. Too much distance will seriously affect the construction progress, while too little distance will severely affect the avoidance effect. During their transit route, there may be two kinds of obstacle risks between cable cranes: static collision risk and dynamic collision risk.The static collision risk, including the dam block and slope, mainly determined by the minimum distancedstatic between bucket and obstacle, to avoid the collision, drivers need a buffer distance D1 to react. Suppose the location of the bucket is xi,yi,zi, i=1,2… and the coordinate of the dam block point is x0,y0,z0, the speed and normal braking acceleration of cable crane i is vi and ai, the minimum distance dstatic and the buffer distance D1 can be portrayed as follows:(12)dstatic=minxi−x02+yi−y02+zi−z02,D1=vi22ai.The dynamic collision risk of a transit route is associated with the distances between the buckets. As shown in Figure3, when the buckets are closest to each other, the distance between them is minimal and the dynamic collision risk becomes the most serious. This value is constantly changing as the position of the buckets changes. Obviously, if the value increases, it pulls the cable toward the safer operation. Setting vj and aj are the speed and normal braking acceleration of cable crane j, the location of another bucket is xj,yj,zj. The distances between the buckets ddynamic is calculated by:(13)ddynamic=xj−xi2+yj−yi2+zj−zi2.Figure 3
Collision risk descriptions.When the cable crane is in operation, there may be two kinds of motion between them: relative motion and catch-up motion. Therefore, the distance calculation formula is abstractly expressed as a linear motion [28].(14)Drelative=vi22ai+vit0+vj22aj+vjt0,(15)Dcatch−up=vi22ai+vit0−v1t1−a1ti22,where Drelative and Dcatch−up denote the critical safe distance of relative motion and catch-up motion. v1 and a1 represent the speed and acceleration of the cable crane being chased. t0 refers to the response time of drivers, t1 refers to the total braking time of chasing cable crane including operators’ reaction time and equipment braking time.Equations (14) and (15) are the general forms of distance calculation formulas. However, in practical application, the influence of operators’ response time k1, GPS error k2, system lag k3, rope swing k4, and wind pressure k5 on buffer distance should also be seriously considered [29]. Therefore, setting the margin of safety avoidance is K, the buffer distance D2 (relative movement: D2=Drelative; catch-up movement: D2=Dcatch−up) can be regarded as the critical condition for the collision risk.(16)D2=vi22ai+vit0+vj22aj+vjt0+Krelative,vi22ai+vit0−v3t1−a3ti22+Kcatch−up,K=k1+k2+k3+k4+k5.Combined with these two collision risks, we can determine their specific gravityμ1and1−μ1. Consequently, the collision risk subfunction fcollision can be revised as:(17)fcollision=μ1fstatic+1−μ1fdynamic=μ11+D1/dstatic−D1+1−μ11+D2/ddynamic−D2,fcollision=μ1fstatic+1−μ1fdynamic=μ11+D1/dstatic−D1+1−μ11+D2/ddynamic−D2.


## 3.5. Comprehensive Evaluation Function

Based on the above analysis, these subfunctions are normalized and integrated into the comprehensive evaluation function. The function is given by(18)f=ω1fefficiency+ω2foperability+ω3fcollision+ω4fexposure,where ω1, ω2, ω3, and ω4 represent weighting factor of the fefficiency, foperability, fcollision, and fexposure, respectively. The weighting factor ωi (i = 1, 2, 3, 4) plays a vital role in the fitting process since these factors determine how much a control point influences locally the geometry of the transit route. The weight of these four indexes is calculated by the entropy weight method with strong objectivity. Some experts (q) will be invited to grade the four evaluation indicators in the form of a 100% system, so as to determine the weight of each indicator.


## 4. Solution by NSGA-II Algorithm

Generally, traditional optimization methods yield suboptimal results, but intelligent optimization algorithms yield optimal solutions. Especially evolutionary algorithms, viz, genetic algorithm (GA), NSGA-II, DE, etc., give optimal solutions. Then, these optimal solutions can be converted into a global optimum. The effective and robust nature of these evolutionary algorithms makes them the best fit for multiobjective optimization problems. The outcome of the multiobjective optimization algorithm is the Pareto-optimal front. It gives more tradeoff solutions to users’ choices. A number of performance measures are available to find the effectiveness of a multiobjective optimization algorithm.NSGA-II has been widely employed in scientific research and engineering practice due to its various highly desirable properties like effective convergence and robustness [30]. This article introduces NSGA-II to optimize the transit route for cable crane by incorporating multiple objective functions into the system. The evaluation function quantifies the comprehensive performance of the transit route with respect to hazard exposure, efficiency, operability, and collision risk. The algorithm is implemented in a computerized model using MATLAB to facilitate automated computations. Figure 4 explains the procedure involved in this multiobjective optimal motion planning problem.Step 1 Input the required information of the cable crane, including bucket size, acceleration, deceleration, and uniform speed under various operating conditions. Set the driving parameters of the vibratory compactors, such as the size of the dam block surface.Step 2 Initialize the coordinates of the feeding point, target dumping point, maximum iteration, population size, crowding distance, and termination condition. Use these parameters to generate the initial route population.Step 3 For the route population, each subfunction and comprehensive evaluation function is calculated. The first generation subpopulation is obtained by nondominant sequencing and genetic manipulation.Step 4 Starting from the second generation, the parent population and the subpopulation are merged, and the crowding distance of each layer of individuals is calculated after a quick nondominant ranking. According to the nondominant relation and individual crowding distance, the appropriate individuals are selected to form a new parent population.Step 5 A new generation of the population is generated by genetic manipulation, and the subfunction and comprehensive evaluation function are calculated at the same time.Step 6 If the new route population converges to the maximum objective function, the optimal path is obtained and the whole path optimization should be terminated. Otherwise, return to Step 3 and continue optimizing. If the new population fails to converge after reaching the maximum iteration, go back to Step 2 for further adjustment.Figure 4
Flow chart of NSGA-II algorithm in the transit route optimization.


## 5. Case Study

The Dagangshan hydropower station, which is located in Shimian County, Szechwan Province, is selected to apply the methodology of the previous section. The 15 dam block 1,025 m elevation 25 m (Wx) × 44 m (Wy) is selected as an example. To assure the construction period, the dam has been poured with four cable cranes. The relevant data for cable crane are shown in Table 1.Table 1
The parameters of cable crane.
Construction machineryParametersValueLQP30t/677 m parallelly traveling cable craneThe distance between two neighboring cables11 mUniform speed7.5 m/sHoisting speed: loaded2.15 m/sLowering speed: loaded3 m/sLoad lifting acceleration0.75 m/s2Lateral traction acceleration0.75 m/s2


### 5.1. Results of Transit Route Optimization

It is indispensable to consider the configuration of construction machinery during dam construction so that each machine can achieve optimal efficiency. Taking the number of cable cranes into consideration, it is necessary to optimize the transit route of cable cranes under two conditions, namely, single cable crane transport and multiple cable cranes transport.During the optimization process by NSGA-II algorithm, to fix the maximum iteration, an analysis was made by varying the mix iteration value from 1 to 800. It is observed that when the value of iteration is 500, the value of each subfunction converges to a fixed value,fefficiency = 0.8178, foperability = 0.8182, fcollision = 0.8500, and fexposure = 0.9709. Therefore, the maximum iteration value is fixed as 500. Additionally, we set the max population size to 200, the distribution indices of crossover and mutation algorithms are 25 and 25.


#### 5.1.1. Single Cable Crane Transport

The feeding point and the dumping point of concrete transported are (0, 94.6) and (307.5, 2), respectively. Figure5(a) shows the initial route population is composed of six random routes, Figure 5(b) shows the final convergence result of the optimization procedure.Figure 5
Final convergence result of cable crane transit routes optimization under the single cable crane transport. (a) The initial route population. (b) The final convergence result.
(a)(b)


#### 5.1.2. Multiple Cable Cranes Transport

Compared with a cable crane, the simultaneous operation of multiple cables increases the collision risk between the cables making multiobjective optimization more complicated. Considering the problem of cooperative configuration and efficiency of construction machinery, two cable cranes are required to work at the same time. One of the feeding points and the dumping points of concrete transported is (0, 11, 94.6) and (307.5, 11, 2), and the other is (0, 33, 94.6) and (307.5, 33, 2). According to the size of the initial route population, we selected six typical pairs as initial routes, as shown in Figures6 and 7(a), and the pair of optimal transit routes is obtained when the initial route population converges to a stable state (shown in Figure 7(b)).Figure 6
Six typical pairs of initial cable crane transit routes.
(a)(b)(c)(d)(e)(f)Figure 7
Cable crane transit routes optimization under the multiple cable cranes transport. (a) The initial route pairs. (b) The final convergence route.
(a)(b)


### 5.2. Discussion

The methodology proposed is applied in the scenario described in the previous section. In this part, we will conduct a sensitivity analysis of the exposure effects on the optimal path of the cable crane. Furthermore, we will discuss the results of transit route optimization to illustrate the efficiency and performance of our proposed method.


#### 5.2.1. Hazard Exposure Sensitivity Analysis

In the canyons, wind is closely related to the environment and climate. The probability of different scales of wind appearing is various. Obviously, the higher the wind force level is, the higher the exposure frequency and the lower the safety. Based on this, five experts were invited to rate the impact of different objective functions and wind scales (7, 8, 9, 10, 11) on exposure. The methods of consulting experts are mainly through questionnaires and interviews. To ensure the accuracy of the evaluation data, these five experts are safety managers on the project site, and their working years have exceeded 20 years. The results are shown in Table2. As can be seen from Table 2, each expert gives different evaluation results according to his own experience. But the same thing is true: the higher the wind scale, the higher the exposure score. This is because the dynamic wind conditions of construction sites have a significant effect on the impact space, and then the variation of impact space leads to the change of overlap, thus affecting the exposure frequency.Table 2
The weight of each factor.
EfficiencyOperabilityCollision riskHazard exposure7891011Expert 19093988587909395Expert 29391978788909295Expert 38886959093959799Expert 48580938586889094Expert 58481988082859096Based on expert scores, the weighting factorsωi (i = 1, 2, 3, 4) were obtained by using the entropy weight method (described in Table 3). It can be seen that the proportion of exposure gradually increases with the increase of wind scale. According to the diversified weights, the objective functions of each wind scale were calculated strictly. The results showed that the transport routes of cable cranes were slightly different.Table 3
The weighting factor of different wind scale.
Wind scaleω1ω2ω3ω4fefficiencyfoperabilityfcollisionfexposuref70.2470.2410.2730.2380.81780.81820.85000.97090.862380.2460.2400.2720.2430.863790.2440.2380.2700.2490.8655100.2410.2360.2680.2560.8665110.2390.2330.2650.2640.8677


#### 5.2.2. Optimization Performance Analysis

The performance of the optimization results should satisfy four requirements, that is, hazard exposure, efficiency, operability, and collision risk so that it can better guide drivers following the optimal route. Figure8 shows the evaluation function values of six initial routes and the optimal route under the single machine work situation. Although there are some advantages for initial routes 1, 4, and 5, neither of them is the optimal route. It can be seen from Figure 8 that the exposure, efficiency, operability, and collision risk of the optimal route are 0.9836, 0.8178, 0.8182, and 0.8500, respectively, although not all of its four evaluation subfunction values are the highest. This indicates that the proposed optimization approach gives full consideration to the comprehensive performance rather than to a certain aspect.Figure 8
Evaluation function values of six initial routes and the optimal route.Regarding the exposure, under the condition that the feeding point and dumping point have been determined, the overlap will be fixed accordingly. Therefore, under the same wind force condition, the longer the running time of the bucket in the working space, the higher the exposure frequency. Regarding the efficiency, the initial route 5 has the highest value, routes 2 and 4 follow closely, this suggests that the route closer to the straight line is more efficient than those turning route. Additionally, the route, located in the middle, has a higher value than those on the top and bottom. From the operability perspective, initial route 4 has the highest value (0.9184), while initial route 1 has the lowest (0.4579). The manifests that the operability has an increasing tendency from the smoothness of the initial route. From the collision risk perspective, the route on the top has the highest safety, while that at the bottom has the lowest, which is in accordance with the working conditions on-site.Moreover, Figure9 shows the evaluation function value of six initial route pairs, as well as the optimal route pair, under the multiple-machine work situation. Similar to a single cable crane, the exposure frequency of multiple cable cranes depends on the time each bucket appears in the overlap space when the feeding and dumping points (the size of the overlap space) of the operation have been determined. Initial route pair c has the highest efficiency value (0.6209) but also low operability (76.53%). Similarly, initial route pair d has the highest security level (0.8837), but its efficiency is very low (0.5820). Unlike those route pairs, the optimal route pair has the best comprehensive performance (0.8565), although each index value of the optimal path is not the largest, it is the result of equilibrium of all aspects. Therefore, how to maintain the balance between various factors in the complex working environment is the key to realize the optimal transit route of cable crane GPS guidance.Figure 9
Evaluation function values of six initial pairs and the optimal route.


#### 5.2.3. Exposure Frequency Contrastive Analysis

The model proposed in this article shows that the optimal transit route can be obtained by solving the motion law of cable crane with NSGA-II algorithm in consideration of exposure, efficiency, operability, and collision risk, which is highly consistent with the previous model provided by [20] with the AIA algorithm. However, the previous model did not consider the influence of exposure on the transit routes. The optimal transit route of the two models for different situations is described in Table 4.Table 4
Optimal transit route of the two models for different situations.
fstaticfdynamicfefficiencyfoperabilityfexposurefThe previous methodSingle machine0.8654—0.90490.4156—0.8339Multiple machine0.80480.69110.86840.3883—0.7587The proposed modelSingle machine0.8178—0.91780.81820.97090.8525Multiple machine0.85120.39940.99710.88180.98500.8539Compared with the previous model, while there is a single cable machine is in operation, the collision risk between the bucket and the static obstacle such as the dam block increases with considering the exposure frequency. Additionally, the efficiency is improved slightly, the operability has a substantial increase, and the value of the comprehensive evaluation is increased. When multiple cables are working at the same time, the static collision risk is reduced but the dynamic collision risk is greatly increased, and meanwhile, the efficiency and operability of the cable crane are significantly improved. Similarly, the value of the comprehensive evaluation is increased.From the results, it can be seen that although the AIA algorithm has the ability to find the global optimal solution, the efficiency of optimization is lower than that of the NSGA-II algorithm. Therefore, if the problem requires a global optimal solution, the genetic algorithm is more beneficial to the solution of the problem.


## 5.1. Results of Transit Route Optimization

It is indispensable to consider the configuration of construction machinery during dam construction so that each machine can achieve optimal efficiency. Taking the number of cable cranes into consideration, it is necessary to optimize the transit route of cable cranes under two conditions, namely, single cable crane transport and multiple cable cranes transport.During the optimization process by NSGA-II algorithm, to fix the maximum iteration, an analysis was made by varying the mix iteration value from 1 to 800. It is observed that when the value of iteration is 500, the value of each subfunction converges to a fixed value,fefficiency = 0.8178, foperability = 0.8182, fcollision = 0.8500, and fexposure = 0.9709. Therefore, the maximum iteration value is fixed as 500. Additionally, we set the max population size to 200, the distribution indices of crossover and mutation algorithms are 25 and 25.


### 5.1.1. Single Cable Crane Transport

The feeding point and the dumping point of concrete transported are (0, 94.6) and (307.5, 2), respectively. Figure5(a) shows the initial route population is composed of six random routes, Figure 5(b) shows the final convergence result of the optimization procedure.Figure 5
Final convergence result of cable crane transit routes optimization under the single cable crane transport. (a) The initial route population. (b) The final convergence result.
(a)(b)


### 5.1.2. Multiple Cable Cranes Transport

Compared with a cable crane, the simultaneous operation of multiple cables increases the collision risk between the cables making multiobjective optimization more complicated. Considering the problem of cooperative configuration and efficiency of construction machinery, two cable cranes are required to work at the same time. One of the feeding points and the dumping points of concrete transported is (0, 11, 94.6) and (307.5, 11, 2), and the other is (0, 33, 94.6) and (307.5, 33, 2). According to the size of the initial route population, we selected six typical pairs as initial routes, as shown in Figures6 and 7(a), and the pair of optimal transit routes is obtained when the initial route population converges to a stable state (shown in Figure 7(b)).Figure 6
Six typical pairs of initial cable crane transit routes.
(a)(b)(c)(d)(e)(f)Figure 7
Cable crane transit routes optimization under the multiple cable cranes transport. (a) The initial route pairs. (b) The final convergence route.
(a)(b)


## 5.1.1. Single Cable Crane Transport

The feeding point and the dumping point of concrete transported are (0, 94.6) and (307.5, 2), respectively. Figure5(a) shows the initial route population is composed of six random routes, Figure 5(b) shows the final convergence result of the optimization procedure.Figure 5
Final convergence result of cable crane transit routes optimization under the single cable crane transport. (a) The initial route population. (b) The final convergence result.
(a)(b)


## 5.1.2. Multiple Cable Cranes Transport

Compared with a cable crane, the simultaneous operation of multiple cables increases the collision risk between the cables making multiobjective optimization more complicated. Considering the problem of cooperative configuration and efficiency of construction machinery, two cable cranes are required to work at the same time. One of the feeding points and the dumping points of concrete transported is (0, 11, 94.6) and (307.5, 11, 2), and the other is (0, 33, 94.6) and (307.5, 33, 2). According to the size of the initial route population, we selected six typical pairs as initial routes, as shown in Figures6 and 7(a), and the pair of optimal transit routes is obtained when the initial route population converges to a stable state (shown in Figure 7(b)).Figure 6
Six typical pairs of initial cable crane transit routes.
(a)(b)(c)(d)(e)(f)Figure 7
Cable crane transit routes optimization under the multiple cable cranes transport. (a) The initial route pairs. (b) The final convergence route.
(a)(b)


## 5.2. Discussion

The methodology proposed is applied in the scenario described in the previous section. In this part, we will conduct a sensitivity analysis of the exposure effects on the optimal path of the cable crane. Furthermore, we will discuss the results of transit route optimization to illustrate the efficiency and performance of our proposed method.


### 5.2.1. Hazard Exposure Sensitivity Analysis

In the canyons, wind is closely related to the environment and climate. The probability of different scales of wind appearing is various. Obviously, the higher the wind force level is, the higher the exposure frequency and the lower the safety. Based on this, five experts were invited to rate the impact of different objective functions and wind scales (7, 8, 9, 10, 11) on exposure. The methods of consulting experts are mainly through questionnaires and interviews. To ensure the accuracy of the evaluation data, these five experts are safety managers on the project site, and their working years have exceeded 20 years. The results are shown in Table2. As can be seen from Table 2, each expert gives different evaluation results according to his own experience. But the same thing is true: the higher the wind scale, the higher the exposure score. This is because the dynamic wind conditions of construction sites have a significant effect on the impact space, and then the variation of impact space leads to the change of overlap, thus affecting the exposure frequency.Table 2
The weight of each factor.
EfficiencyOperabilityCollision riskHazard exposure7891011Expert 19093988587909395Expert 29391978788909295Expert 38886959093959799Expert 48580938586889094Expert 58481988082859096Based on expert scores, the weighting factorsωi (i = 1, 2, 3, 4) were obtained by using the entropy weight method (described in Table 3). It can be seen that the proportion of exposure gradually increases with the increase of wind scale. According to the diversified weights, the objective functions of each wind scale were calculated strictly. The results showed that the transport routes of cable cranes were slightly different.Table 3
The weighting factor of different wind scale.
Wind scaleω1ω2ω3ω4fefficiencyfoperabilityfcollisionfexposuref70.2470.2410.2730.2380.81780.81820.85000.97090.862380.2460.2400.2720.2430.863790.2440.2380.2700.2490.8655100.2410.2360.2680.2560.8665110.2390.2330.2650.2640.8677


### 5.2.2. Optimization Performance Analysis

The performance of the optimization results should satisfy four requirements, that is, hazard exposure, efficiency, operability, and collision risk so that it can better guide drivers following the optimal route. Figure8 shows the evaluation function values of six initial routes and the optimal route under the single machine work situation. Although there are some advantages for initial routes 1, 4, and 5, neither of them is the optimal route. It can be seen from Figure 8 that the exposure, efficiency, operability, and collision risk of the optimal route are 0.9836, 0.8178, 0.8182, and 0.8500, respectively, although not all of its four evaluation subfunction values are the highest. This indicates that the proposed optimization approach gives full consideration to the comprehensive performance rather than to a certain aspect.Figure 8
Evaluation function values of six initial routes and the optimal route.Regarding the exposure, under the condition that the feeding point and dumping point have been determined, the overlap will be fixed accordingly. Therefore, under the same wind force condition, the longer the running time of the bucket in the working space, the higher the exposure frequency. Regarding the efficiency, the initial route 5 has the highest value, routes 2 and 4 follow closely, this suggests that the route closer to the straight line is more efficient than those turning route. Additionally, the route, located in the middle, has a higher value than those on the top and bottom. From the operability perspective, initial route 4 has the highest value (0.9184), while initial route 1 has the lowest (0.4579). The manifests that the operability has an increasing tendency from the smoothness of the initial route. From the collision risk perspective, the route on the top has the highest safety, while that at the bottom has the lowest, which is in accordance with the working conditions on-site.Moreover, Figure9 shows the evaluation function value of six initial route pairs, as well as the optimal route pair, under the multiple-machine work situation. Similar to a single cable crane, the exposure frequency of multiple cable cranes depends on the time each bucket appears in the overlap space when the feeding and dumping points (the size of the overlap space) of the operation have been determined. Initial route pair c has the highest efficiency value (0.6209) but also low operability (76.53%). Similarly, initial route pair d has the highest security level (0.8837), but its efficiency is very low (0.5820). Unlike those route pairs, the optimal route pair has the best comprehensive performance (0.8565), although each index value of the optimal path is not the largest, it is the result of equilibrium of all aspects. Therefore, how to maintain the balance between various factors in the complex working environment is the key to realize the optimal transit route of cable crane GPS guidance.Figure 9
Evaluation function values of six initial pairs and the optimal route.


### 5.2.3. Exposure Frequency Contrastive Analysis

The model proposed in this article shows that the optimal transit route can be obtained by solving the motion law of cable crane with NSGA-II algorithm in consideration of exposure, efficiency, operability, and collision risk, which is highly consistent with the previous model provided by [20] with the AIA algorithm. However, the previous model did not consider the influence of exposure on the transit routes. The optimal transit route of the two models for different situations is described in Table 4.Table 4
Optimal transit route of the two models for different situations.
fstaticfdynamicfefficiencyfoperabilityfexposurefThe previous methodSingle machine0.8654—0.90490.4156—0.8339Multiple machine0.80480.69110.86840.3883—0.7587The proposed modelSingle machine0.8178—0.91780.81820.97090.8525Multiple machine0.85120.39940.99710.88180.98500.8539Compared with the previous model, while there is a single cable machine is in operation, the collision risk between the bucket and the static obstacle such as the dam block increases with considering the exposure frequency. Additionally, the efficiency is improved slightly, the operability has a substantial increase, and the value of the comprehensive evaluation is increased. When multiple cables are working at the same time, the static collision risk is reduced but the dynamic collision risk is greatly increased, and meanwhile, the efficiency and operability of the cable crane are significantly improved. Similarly, the value of the comprehensive evaluation is increased.From the results, it can be seen that although the AIA algorithm has the ability to find the global optimal solution, the efficiency of optimization is lower than that of the NSGA-II algorithm. Therefore, if the problem requires a global optimal solution, the genetic algorithm is more beneficial to the solution of the problem.


## 5.2.1. Hazard Exposure Sensitivity Analysis

In the canyons, wind is closely related to the environment and climate. The probability of different scales of wind appearing is various. Obviously, the higher the wind force level is, the higher the exposure frequency and the lower the safety. Based on this, five experts were invited to rate the impact of different objective functions and wind scales (7, 8, 9, 10, 11) on exposure. The methods of consulting experts are mainly through questionnaires and interviews. To ensure the accuracy of the evaluation data, these five experts are safety managers on the project site, and their working years have exceeded 20 years. The results are shown in Table2. As can be seen from Table 2, each expert gives different evaluation results according to his own experience. But the same thing is true: the higher the wind scale, the higher the exposure score. This is because the dynamic wind conditions of construction sites have a significant effect on the impact space, and then the variation of impact space leads to the change of overlap, thus affecting the exposure frequency.Table 2
The weight of each factor.
EfficiencyOperabilityCollision riskHazard exposure7891011Expert 19093988587909395Expert 29391978788909295Expert 38886959093959799Expert 48580938586889094Expert 58481988082859096Based on expert scores, the weighting factorsωi (i = 1, 2, 3, 4) were obtained by using the entropy weight method (described in Table 3). It can be seen that the proportion of exposure gradually increases with the increase of wind scale. According to the diversified weights, the objective functions of each wind scale were calculated strictly. The results showed that the transport routes of cable cranes were slightly different.Table 3
The weighting factor of different wind scale.
Wind scaleω1ω2ω3ω4fefficiencyfoperabilityfcollisionfexposuref70.2470.2410.2730.2380.81780.81820.85000.97090.862380.2460.2400.2720.2430.863790.2440.2380.2700.2490.8655100.2410.2360.2680.2560.8665110.2390.2330.2650.2640.8677


## 5.2.2. Optimization Performance Analysis

The performance of the optimization results should satisfy four requirements, that is, hazard exposure, efficiency, operability, and collision risk so that it can better guide drivers following the optimal route. Figure8 shows the evaluation function values of six initial routes and the optimal route under the single machine work situation. Although there are some advantages for initial routes 1, 4, and 5, neither of them is the optimal route. It can be seen from Figure 8 that the exposure, efficiency, operability, and collision risk of the optimal route are 0.9836, 0.8178, 0.8182, and 0.8500, respectively, although not all of its four evaluation subfunction values are the highest. This indicates that the proposed optimization approach gives full consideration to the comprehensive performance rather than to a certain aspect.Figure 8
Evaluation function values of six initial routes and the optimal route.Regarding the exposure, under the condition that the feeding point and dumping point have been determined, the overlap will be fixed accordingly. Therefore, under the same wind force condition, the longer the running time of the bucket in the working space, the higher the exposure frequency. Regarding the efficiency, the initial route 5 has the highest value, routes 2 and 4 follow closely, this suggests that the route closer to the straight line is more efficient than those turning route. Additionally, the route, located in the middle, has a higher value than those on the top and bottom. From the operability perspective, initial route 4 has the highest value (0.9184), while initial route 1 has the lowest (0.4579). The manifests that the operability has an increasing tendency from the smoothness of the initial route. From the collision risk perspective, the route on the top has the highest safety, while that at the bottom has the lowest, which is in accordance with the working conditions on-site.Moreover, Figure9 shows the evaluation function value of six initial route pairs, as well as the optimal route pair, under the multiple-machine work situation. Similar to a single cable crane, the exposure frequency of multiple cable cranes depends on the time each bucket appears in the overlap space when the feeding and dumping points (the size of the overlap space) of the operation have been determined. Initial route pair c has the highest efficiency value (0.6209) but also low operability (76.53%). Similarly, initial route pair d has the highest security level (0.8837), but its efficiency is very low (0.5820). Unlike those route pairs, the optimal route pair has the best comprehensive performance (0.8565), although each index value of the optimal path is not the largest, it is the result of equilibrium of all aspects. Therefore, how to maintain the balance between various factors in the complex working environment is the key to realize the optimal transit route of cable crane GPS guidance.Figure 9
Evaluation function values of six initial pairs and the optimal route.


## 5.2.3. Exposure Frequency Contrastive Analysis

The model proposed in this article shows that the optimal transit route can be obtained by solving the motion law of cable crane with NSGA-II algorithm in consideration of exposure, efficiency, operability, and collision risk, which is highly consistent with the previous model provided by [20] with the AIA algorithm. However, the previous model did not consider the influence of exposure on the transit routes. The optimal transit route of the two models for different situations is described in Table 4.Table 4
Optimal transit route of the two models for different situations.
fstaticfdynamicfefficiencyfoperabilityfexposurefThe previous methodSingle machine0.8654—0.90490.4156—0.8339Multiple machine0.80480.69110.86840.3883—0.7587The proposed modelSingle machine0.8178—0.91780.81820.97090.8525Multiple machine0.85120.39940.99710.88180.98500.8539Compared with the previous model, while there is a single cable machine is in operation, the collision risk between the bucket and the static obstacle such as the dam block increases with considering the exposure frequency. Additionally, the efficiency is improved slightly, the operability has a substantial increase, and the value of the comprehensive evaluation is increased. When multiple cables are working at the same time, the static collision risk is reduced but the dynamic collision risk is greatly increased, and meanwhile, the efficiency and operability of the cable crane are significantly improved. Similarly, the value of the comprehensive evaluation is increased.From the results, it can be seen that although the AIA algorithm has the ability to find the global optimal solution, the efficiency of optimization is lower than that of the NSGA-II algorithm. Therefore, if the problem requires a global optimal solution, the genetic algorithm is more beneficial to the solution of the problem.


## 6. Conclusion

The environment of dam concrete pouring is extremely complicated, and under the influence of wind, the cable crane bucket will change dynamically during the operation of transporting concrete. Hazard exposure reduction for hydropower station dam concrete placement is an essential procedure in safety management. To seek the optimal transit route for cable crane, this article presents a transit route optimization method to reduce cable crane exposure. In contrast to previous research, this study makes two theoretical and practical contributions. First, the hazard exposure between vertical transport machinery and dam block surface machinery is quantified by a mathematic model. The complex construction process of dam construction, the conflict of man-machine interaction, and dynamic wind loads are considered comprehensively. Second, a multiobjective optimization model, including the hazard exposure, efficiency, operability, and collision, is proposed and the NSGA-II algorithm is used to solve multiobjective optimization.The conclusions made from this research work are: (1) the numerical results of the experience proved that the NSGA-II is a good algorithm for optimal trajectory planning for derivers. It is feasible to use the NSGA-II algorithm to achieve cable crane transit route optimization under a complex environment. (2) Various random conditions of cable crane running in different situations were simulated respectively. Comparative analysis shows that the optimization results fully consider various factors to achieve the best comprehensive performance. (3) The exposure changes with the location of the dumping point and the various transit route of cable crane.Even though the model presented in this article brings a reference and many benefits in the optimization of the transit route of the cable crane, it still has some deficiencies: to name only a few, the work environment for cable cranes will become more complicated when more machines are put into use in the sky or on the dam block surface, such as tower cranes, portal cranes, and pavers. These situations will present more unknown risk factors and potential obstacles to drivers. Therefore, researchers need to pay more attention to these complex conditions to ensure the operation of cable crane is more secure. Moreover, this research is mainly to provide some algorithm basis for intelligent construction. Thus, the combination of locating and tracking technology and transit route optimization method will be an important topic in the future.



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*Source: 4743706-2022-05-16.xml*