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Path-planning research in radioactive environment based on particle swarm algorithm
Progress in Nuclear Energy 74 (2014) 184e192
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Path-planning research in radioactive environment based on particle swarm algorithm Yong-kuo Liu a, *, Meng-kun Li a, Chun-li Xie b, Min-jun Peng a, Fei Xie a a b
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin 150001, China Traffic College, Northeast Forestry University, Harbin 150040, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 January 2014 Received in revised form 3 March 2014 Accepted 6 March 2014
During the design, maintenance and decommissioning of nuclear facilities, nuclear radiation protection is an important part. In recent years, researchers have explored a lot of radiation protection approach, and some radiation protection approach have been applied in practice, such as visualization technique of radiation environment, path-planning method, robotics and etc., in these techniques the path-planning in radiation environment technology has become an important radiation protection measure. In this paper, we addressed a staff walking path-planning approach in radiation environment based on particle swarm algorithm and introduced some key technologies of path-planning in radiation environment. To obtain the optimal walking route to verify the operation of the proposed method, we carried out the simulation experiment in which dose and distance were as decision factors. The experiment results represented the probability and the effectiveness of path-planning in radiation environment based on particle swarm algorithm. 2014 Elsevier Ltd. All rights reserved.
Keywords: Radioactive environment Path-planning Particle swarm algorithm Simulation
1. Introduction It is the mission of engineers to design nuclear facilities and systems to be as safe as possible and to take necessary measures to preserve the safety and the health of personnel in nuclear power plant. However, no matter how sophisticated the designs, radiation exposure is unavoidable. According to statistics, the radiation dose that staff suffered during the daily activities of normal operation takes 20% of the total annual dose in Chinese nuclear power plant, and the radiation dose that staff suffered during the overhauling of nuclear power plant takes 80% of the total annual dose (Haixia Wan, 2012). As everyone knows, the basic ways of external irradiation protection are to reduce the time that personal stays in the radioactive room expand the distance between personal and radiation source, and take the shielding measures. So we can take the method of path-planning in radioactive environment as one of the measures of external irradiation protection. By path-planning we can control the time that personal stays in radiation environment and the distance between personal and radiation source, thereby to reduce the radiation exposure that personal suffered during work.
* Corresponding author. Tel.: þ86 (0) 451 82569302x458; fax:þ86 (0) 451 82569622. E-mail address: [email protected] (Y.-k. Liu). http://dx.doi.org/10.1016/j.pnucene.2014.03.002 0149-1970/ 2014 Elsevier Ltd. All rights reserved.
For the path-planning methods in radiation environment, domestic and foreign researchers have done a lot of research. For example, the Fugen Nuclear Power Station (NPS) in Japan was shut down permanently, Japanese developed Decommissioning Engineering Support System (DEXUS) to create a dismantling plan using state-of-the-art software such as 3-dimensional computer aided design (3D-CAD) and virtual reality (VR). In particular, an exposure dose evaluation system using VR has been developed and tested (Johnsen et al., 2004). The total system can be used to visualize radiation and evaluate the dose that personal suffered to optimize the walking route and the decommissioning plan. Mól et al. used a game engine for virtual reality simulations in emergency situations (Mól et al., 2008). Game engine’s open source code and existing functionalities are convenient for researchers and developers to simulate scenarios. The simulation platform collected dose rate data from radiation monitors installed in the real plant, then researchers assess dose for personnel (Mól et al., 2009). Further, Mól et al. used neural networks and virtual reality techniques for assessment of radiation dose exposition by nuclear plant’s personnel, to optimize working tasks for minimisation of received dose (Mól et al., 2011). South Korean developed simulation technology for prediction of radiation dose, which was developed by VRML and Java Applet. This simulation program can display radiation exposure levels in a virtual reality environment, represent high dose danger zones by
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graphically visualizing dose rates and predict the exposure dose of virtual workers (Kim and Park, 2004). This simulation program need specific dose calculation model to calculate the dose rate distribution, and then the workers should try and compare many paths to determine minimum radiation dose path. American L.S. Pachter and M. Pachter considered the problem of navigating between points in the plane so as to minimize the exposure to radiation source. In order to resolve this problem, L.S. Pachter and M. Pachter introduced a weighted exposure and path length optimization problem and applied requires a variational approach (Pachter and Pachter, 2001). L.S. Pachter has demonstrated the feasibility of this method that barrier-free environment theory in point source radiation field. The method may determine a minimum dose path, but the length of the path maybe too long and curved path is difficult to realize in practice. American M. Hage designed evolutionary software techniques based on sensor in radiation environments, and achieved the target which mobile vehicles avoid obstacle and reduce the continued radiation exploration (Hage and Couture, 1999). In the method, the genetic program was very complex and it need to be trained in known environments and then utilized in an unknown environment. The method was designed for the robot in radioactive environment, and not ensures the cumulative dose minimum on the optimized path, therefore maybe not suitable for walking pathplanning of staff. American Alzalloum (2009) addressed the least cost path problem for a radiological contaminated area and found optimal paths using Dijkstra’s and BellmaneFord algorithms, in these paths the total radiation exposure (cumulative dose) is minimum. In addressing this problem, Alzalloum took radioactive contamination area into vertices and edges, and respectively applied the point nuclear radiation model and Monte Carlo dose calculation model as the weights of each side of the edge. Dijkstra’s and BellmaneFord algorithms were modified and coded in Matlab, through simulation tests, and ultimately to find the optimize path which the total radiation exposure (cumulative dose) was the lowest. Alzalloum methods in the application process was too dependent on radiation field model, and ignored the actual environment of radioactive shielding, therefore, this method is only applicable to ideal radioactive environment, with some limitations. Khasawneh et al. in the University of Jordan addressed a localized navigation algorithm for radiation evasion. A well-designed and wireless sensor networks infrastructure that is distributed in radioactive environment, through sensors measure the radioactivity level and using wireless communication technology transfer the information, finally the use of local navigation algorithm based on graph coloring theory for radioactive evasion (Khasawneh and Al-Shboul, 2010; Khasawneh et al., 2013a,b). Khasawneh et al. who have some practical ways, but in some radioactive environment, the algorithm would be stalled or cycled so that the optimal path can’t be found, simultaneously, this method requires a lot of wireless sensors in practical applications, and it also increases the economic inputs. The researches of path-planning in radioactive environment are seldom in China. Haixia Wan in North China Electric Power University, who developed rapid calculation program for dose rate distribution in visualization platform of radiation field based on Monte Carlo method (Haixia Wan, 2012). The program combined the virtual reality technology and radiation protection techniques, applied the computer to simulate dose rate distribution in complex radiation field environment, did virtual experiments operation, and calculated and displayed the data in real-time, eventually the computer terminals provide the radiation exposure situations obviously to the user. It is thus clear that the radiation field
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visualization is an effective means to reduce radiation dose for nuclear workers. Currently, path-planning method in radioactive environment is mainly focused on searching the minimum total radiation exposure (cumulative dose) path. China has not yet a very perfect pathplanning technology for radiation environment in practical engineering tasks. In some simulation experiments and practical applications, it is not easy to find that distance and cumulative dose do not have explicit mathematical relationships. Due to the requirements for tasks are different, the requirements for the path may also be different. For example: equipment maintenance, decommissioning of nuclear facilities, nuclear emergency and other engineering tasks in the nuclear power plant, which require not only the low radiation doses, but also little travel time or low cost. Therefore, we proposed multi-objective path problem in radiation environment, and did research in this area using particle swarm algorithm and multi-objective decision-making techniques. On these bases, finally we addressed a multi-objective path-planning approach based on particle swarm algorithm in radiation environment, and did simulation experiments in a static radiation environment with dose and distance as two decision factors. The rest of this paper is organized as follows: path-planning strategy, particle swarm algorithm and decision-making techniques are introduced in Section 2. The mathematical model of path problem in radiation environment and the implementation of the proposed method are described in Section 3. Section 4 describes the simulation experiment. Section 5 analyzes the results of simulation experiment. Finally, Section 6 presents the concluding remarks for this paper. 2. Path-planning method The structure of path-planning method in radiation environment based on particle swarm algorithm is shown in Fig. 1. First, we get the geometry of radiation environment, distribution of dose rate and decision factors. Second, we set nodes in radiation environment, obtain weights of dose values between any two nodes, construct alternative road network. We transfer path-planning problem in radioactive environment into a variant TSP (traveling salesman problem), and then build the mathematical model of this problem. At last, we combine particle swarm optimization algorithm with multi-objective decision-making techniques to form the path-planning method in the radiation environment, and then implement the method by programming.
Fig. 1. The structure of multi-objective path-planning in radioactive environment based on PSO.
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2.1. Particle swarm optimization algorithm The core of path-planning method is the design of pathplanning algorithm. There are many path-planning algorithms, but according to the different advantages and disadvantages of each algorithm, their suitable scopes and fields are different (Guanglin Zhang et al., 2011). The particle swarm optimization (PSO) is an evolutionary computation technique, which was developed by Kennedy and Eberhart (Eberhart and Kennedy, 1995; Kennedy and Eberhart, 1995). It is inspired by the social activity of flocks of animals, such as fish or birds. PSO algorithm is similar to genetic algorithm and is an optimum tool based on iteration, and PSO algorithm doesn’t have crossover and mutation of genetic algorithm, but particles search in solution space following optimal particle. At present PSO algorithm has been applied to solve pathplanning problem. Compared with other algorithms, PSO algorithm is simple, and easy to implement, and it has fast convergence speed, fewer adjustment parameters, etc. PSO algorithm has been applied to many areas of social production and life. Thereby, in this study, we used particle swarm optimization algorithm to solve the path-planning problem in the static radiation environment. PSO algorithm is first randomly initialized to a group of random particles (random solution), whose positions represent potential solutions, and then repeatedly updates the positions to the optimal one. In each iteration, the particles update themselves by tracking two “extremes”. The first extreme is the optimal solution that particle finds by itself, this optimal solution is called the personal best (pbest). The second extreme is the optimal solution that the whole population find, this optimal solution is called the group best (gbest). Alternatively, we also can take the neighbor particles’ optimal solution as the gbest which is local extreme, instead of the whole population’s optimal solution. Before we find these two optimal values, the update rules of the position and the velocity of the particle are shown as follows:
vkþ1 ¼ uvk þ c1 r1 ðpbestk xk Þ þ c2 r2 ðgbestk xk Þ
(1)
xkþ1 ¼ xk þ vkþ1
(2)
In the above formula, vk is current velocity of the particles; xk is current position of particles, and representing a candidate solution to the optimization problem. pbestk is personal best position of the particles, i.e., the best solution encountered by particle thus far. gbestk is global best particle, i.e., the best solution found by the entire swarm. u denotes the inertia weight, c1 and c2 are the acceleration constants, r1 and r2 are random numbers uniformly distributed within [0,1]. vkþ1 is the vector sum of vk, pbestk xk and gbestk xk, its diagram is shown in Fig. 2. PSO algorithm initially is used to solve continuous optimization problems, not to solve discrete optimization problems (Wenzhong
pbestk
xk
gbestk
vk Fig. 2. Weighted combination of three possible moving directions.
and Guolong, 2012). So we adopt the idea that the PSO algorithm is in combination with genetic algorithms (De Jong, 2005; Holland, 1973; Srinivas and Patnaik, 1994), in which crossover operator and mutation operator are adopted (Shang and Zhiyuan, 2005). Individual optimum crossover: the current path of each particle is crossed with its historical optimum path to generate a new path. Global optimum crossover: the current path of each particle is crossed with the group optimum path to generate a new path. The purpose of crossover operation is to influence the personal best and the group best, improve search capabilities of particles and increase the diversity of the population. Mutation: Mutation bits in the path of each particle are selected randomly, and then mutation bits are exchanged to generate a new path. The mutation purpose is to prevent particle swarm into local optimal solution, mutation increases the diversity of the population and improves the local search capabilities of particles. The improved algorithm is not only successfully used to solve discrete optimization problems, but also to accelerate the PSO algorithm’s convergence speed. When the PSO algorithm stagnates or falls into the local optimal solution, these genetic operators improve the diversity of population. The improved algorithm’s specific update formula is as follows.
Xit ¼ F3 F2 F1 Xit1 ; Pit1 ; Gt1 i
(3)
where, Xit is the tth iteration solution of ith particle, F1 is mutation operator, F2 is individual optimum crossover operator and F3 is global optimum crossover operator. Pit1 is individual optimal solution and Gt1 is group optimal solution. i 2.2. Dose calculation In this paper, we adopted PSO algorithm to combine the effective dose values between any two nodes to find the optimal walking path. Assuming that radiation environment is stable and limited. Select n nodes in radiation environment, and then use m edges that connect all possible pair of nodes. Each edge is associated with an effective dose value as its weight. We connect all nodes into a loop, and get n(n 1)/2 kinds of path. The total effective dose value is the sum of all of the weights of the edges in the path. Because of the actual equipment and obstructions in the radiation environment, some edges are not connected, and then the effective dose value between these nodes can be negligible. Supposing that effective dose value from the node A to node B is equal to the effective dose value from the node B to node A, the effective dose values between any two nodes is independent of the walking direction. Therefore we can simplify the entire radiation space and the scale of the problem. Effective dose value is calculated as follows: in practice, set up a sensor at each node in the radiation space for measuring the radioactivity at the node position. The dose rate is then averaged, and is calculated based on the length of the segment and the speed (assuming that the walking speed is constant throughout the path), time t that travels the segment. Effective dose is finally calculated by multiplying the average dose rate with the time t. 2.3. Decision-making factors and decision-making methods The path problem in radiation environment is different from the shortest path problem of everyday life. In most studies, the pathplanning in radiation environment basically focuses on solving the minimum total radiation exposure (effective dose) path problem. In this paper, we addressed multi-objective path-planning
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radiation environment. In simulation experiment, we selected effective dose and walking distance as decision factors, applied quantitative and qualitative analysis comparison methods to analyze the experimental results. 2.3.1. Quantitative analysis In quantitative analysis method, we add every criteria value of scheme up to a single numeric value, and then we evaluate these schemes based on these single numeric values to determine the optimal scheme. ICRP Publication No.55 (Hende Wang, 1995) described the method of multi-attribute utility analysis: quantify those factors which are difficult measured in monetary value, and then make quantitative judgments for those factors which usually can only be made a qualitative analysis, like this, the method of multi-attribute utility analysis can make decision-making more scientific. In this research, we borrowed ideas from multi-attribute utility analysis, and applied a quantitative analysis method to solve multi-objective path problem in radiation environment. First, we determine the reference value of every decision factor, which is selecting the minimum value of each decision factor as the reference value. Second, we consider the utility value of each decision factor, and the utility value is a dimensionless quantity which is that the value of each decision factor divides by its reference value. Utility value is greater than or equal to 1, if utility value is closer to 1, the corresponding path-planning’s effect is better in certain aspects. Finally, we calculate the total utility value of every path scheme according to formula (4):
Ui ¼
X
kj Uij
(4)
where, Ui is the total utility value of the ith scheme, Uij is utility value of the jth decision factor (j ¼ 1,2,.,n) in the ith scheme, kj is the attribute weight of the jth decision factor, and it is normalized, P i.e. kj ¼ 1. Attribute weight reflects the concern degree of decision factors which relate to the result of path-planning directly.
Fig. 3. Flowchart for multi- objective path-planning in radiation environment based on PSO algorithm.
2.3.2. Qualitative analysis Qualitative analysis method is complementary to quantitative analysis method. In qualitative analysis method, take one kind of decision factors as the main decision factor, and then select the scheme whose main decision factor is the best as the most optimal solution. In simulation experiment, we choose walk distance and effective dose as the main decision factor respectively. First, according to the main decision factor for path-planning, select and list the different and better path schemes. Second, if the rest of schemes are still in a dilemma, we can compare the rest of schemes based on the other decision factor. Finally, we get the optimal path scheme by comparison of the above. 3. Model building and algorithm implementation
problem in radiation environment. The optimal path is determined by multiple factors, such as safety, costs, mission requirements, etc. Safety factors include radiation exposure, additional risk or adverse effects to worker; Economic cost factors include costs of radiation protection, costs of occupational worker working, etc. Mission factors include object, constraint condition of the project, etc. Usually there is no clear mathematical relationship between these decision factors, so the paths can’t be directly compared and evaluated. Meanwhile, the PSO algorithm is mainly applied for solving the single objective problem. Therefore, in the study we combined quantitative and qualitative analysis comparison method with the PSO algorithm to achieve multi-objective path-planning in
3.1. The mathematical model of path-planning in radiation environment Assuming there are N nodes in radioactive environment. The coordinate of ith node is ðx; yÞ; i˛N; i is node number, Lij is the distance between any two points, Hij is the effective dose between any two points, attribute weights factors are k1 and k2. Distance matrix is ðLij ÞNN , dose matrix is ðHij ÞNN . L* is the reference value of the distance, H* is the reference value of the effective dose, where, i and j are node number, i; j˛C; C ¼ f1; 2; .; Ng. Mathematical models are as follows.
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Fig. 4. Main interface of path-planning in radiation environment based on PSO algorithm.
Li ¼
n X n X
xij Lij
(5)
i¼1 j¼1
Hi ¼ Ui1 ¼
Ui2 ¼
n X n X
xij Hij
(6)
i¼1 j¼1 Li L*
(7)
Hi H*
(8)
Ui ¼ k1 Ui1 þ k2 Ui2 xij ¼
(9)
1 If the edge ijisin the path 0 otherwise:
(10)
where, formulas (5) and (6) are, respectively, distance and effective dose of the ith path scheme. Formulas (7) and (8) are, respectively, the distance utility value and the dose utility value of the ith path scheme. Formula (9) is the total utility value of the ith path scheme. Because the path consists of some edges from beginning to end, edge ij may be in the path. Formula (10) is the decision variable which represents whether the edge ij is in the path. If the edge ij belongs to the path, then xij is set to 1; if the edge ij doesn’t belongs to the path, then xij is set to 0. When using quantitative analysis, the fitness function of PSO algorithm is the formula (9). When using qualitative analysis, the fitness function of PSO algorithm is the formula (5) and (6) respectively. 3.2. Realization of path-planning method Because PSO algorithm doesn’t need too many parameters to be adjusted, it is fit to most users who don’t know about PSO algorithm. Normally, PSO algorithm can get satisfactory result as long as
Table 2 The location of point sources (m). Serial number
1
2
3
4
X coordinate Y coordinate
12 16
21 17
35 18
35 10
the iterations are adequate. So in the research, we take particle’s number and iterations as the adjustable parameters of PSO algorithm. When the algorithm reaches the maximum number of iterations, the loop iteration is terminated. However, if the number of particles and iterations are adjusted suitably, the PSO algorithm would get the better solution and run faster. The flowchart for multi-objective path-planning method in radiation environment based on PSO algorithm is shown in Fig. 3. Inside the PSO algorithm, we set up an external file to storage and screen the optimal path schemes in each generation. External file’s data includes utility value, distance, dose and path. The program outputs and saves the external file’s data for analysis. Fig. 4 shows the main interface of the program. Panel A: the optimal path display panel. Panel B: the room plane graph display panel. Panel C: the distribution of radioactivity display panel. Panel D: PSO’s fitness diagram panel . Panel E: data (location of nodes, distance data and dose data) input and parameters setting panel. Panel F: result display panel. The toolbar is used to output and save the different planned path’s result. 4. Simulation experiment test In the simulation experiment test, we set a case that workers make an inspection tour of radioactive nuclear facilities to verify the operation feasibility of the proposed method. In radiation environment we set 4 radiation sources which are of equal strength in 4 radioactive facilities separately, and select 14 nodes, plan workers’ walk path and determine the order of inspection. Here we ignore the radiation shielding, suppose the travel speed is constant, and take the distance and the effective dose as decision factors.
Table 1 The location of nodes (m). Serial number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X coordinate Y coordinate
30 0
30 10
30 20
35 27
26 17
16 26
21 21
10 21
2 25
1 8
10 14
21 13
25 24
3 14
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Table 3 Effective doses between any two nodes (mSv).
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1
2
3
4
5
6
7
8
9
10
11
12
13
14
999 4.88 13.81 39.27 9.24 327.36 29.92 28.4 682.79 6.08 13.62 6.83 13.97 10.04
4.88 999 8.95 21.03 6.22 24.66 17.79 35.36 37.13 11.77 21.83 7 10.5 20.61
13.81 8.95 999 4.85 3.84 7.88 7.39 18.06 15.05 79.24 179.93 12.67 3.51 1362.88
39.27 21.03 4.85 999 7.91 5.82 7.56 11.97 9.17 51.93 66.4 17.89 3.67 39.98
9.24 6.22 3.84 7.91 999 11.95 8.81 39.9 32.32 34.1 66.56 8.96 4.97 117.13
327.36 24.66 7.88 5.82 11.95 999 4.04 3.45 3.26 13.89 45.57 29.75 3.55 8.97
29.92 17.79 7.39 7.56 8.81 4.04 999 9.07 9.14 68.66 73.62 3415.27 3.38 36.07
28.4 35.36 18.06 11.97 39.9 3.45 9.07 999 2.59 7.12 14.88 20.38 8.94 4.99
682.79 37.13 15.05 9.17 32.32 3.26 9.14 2.59 999 2.81 8.94 26.21 7.71 2.17
6.08 11.77 79.24 51.93 34.1 13.89 68.66 7.12 2.81 999 4.94 11.32 88.61 1.11
13.62 21.83 179.93 66.4 66.56 45.57 73.62 14.88 8.94 4.94 999 18.52 83.8 4.69
6.83 7 12.67 17.89 8.96 29.75 3415 20.38 26.21 11.32 18.52 999 29.85 20.55
13.97 10.5 3.51 3.67 4.97 3.55 3.38 8.94 7.71 88.61 83.8 29.85 999 28.9
10.04 20.61 1362 39.98 117.13 8.97 36.07 4.99 2.17 1.11 4.69 20.55 28.9 999
In the simulation experiment test, distribution of radioactivity is calculated by point nuclear model. According to the principle of superposition, every node’s radiation strength is the accumulation of radioactivity that each radioactive source generates. The effective dose between any two nodes is calculated according to the method given in Section 2.2. Table 1 shows the number and the coordinates of nodes. Node 1 is assumed start and end of the path. Table 2 shows the number and the coordinates of radioactive source. Table 3 shows the effective dose for workers between any two nodes. Supposing that effective dose between any two nodes is independent of the walking direction, and then effective dose matrix is a symmetric matrix. Fig. 5 shows the room plane graph. Fig. 6 shows the distribution of radioactivity. In the setting case, after repeated tests, we found when the number of particles was set to 100, and the iterations of algorithm were set to 50, the improved PSO algorithm can get the best solution, meanwhile the program runs faster. When both the number of particles and the iterations are fewer, the algorithm may not get the best result. When both the number of particles and the iterations are larger, the algorithm can get the best results, but the program would take more time. If the number of nodes is more, we can increase the number of particle or iterations appropriately. 4.1. Quantitative analysis 4.1.1. Uncertain attribute weights In this experiment, we select four different sets of attribute weights ki1 and ki2 (ki1 and ki2 are, respectively, distance attribute
Fig. 5. Room plane graph.
weight and dose attribute weight, i ¼ 1, 2, 3, 4). We can get the minimum values of dose and distance through experiment, and take them as reference value. According to the quantitative analysis method, the reference value of dose is set to 63.75 mSv, the reference value of distance is set to 125.9738 m. Simulating the situation that the importance degree of distance and effective dose is different (i.e. the path of least utility value), the specific result is shown in Table 4, and these four path plane graphs are shown in Figs. 7e9. The experiment result shows that when the attribute weights are determined, path-planning method based on PSO algorithm can find the optimal path. The results in Table 4 show that different attributes weights may correspond to different optimal path, and some attribute weights in certain range may correspond to the same optimal path, such as the 3rd and the 4th path scheme. From Figs. 7e9 we can see that the proposed method can avoid obstacles or equipment and find the path to arrive at the specified location. The 1st scheme is the shortest path and can make occupational worker to travel the path with the minimum time. If the effective dose is too large, this scheme maybe no longer suitable. The 3rd scheme and the 4th scheme are all the minimum dose paths and contribute to the occupational worker’s safety. There are some path schemes of which dose and distance are close to the minimum values, such as the 2nd scheme. The 2nd scheme belongs to compromise solution that the dose and the distance are closer to the minimum value. We can select the path scheme based on special situation and decision-maker’s decision. 4.1.2. Certain attribute weights determined In this experiment, we select a set of attribute weights to observe the process of quantitative analysis. The distance attribute
Fig. 6. Distribution of radioactivity.
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Table 4 Simulation results of different attribute weights (ki1, ki2) Scheme number
1
2
3
4
Weight ki1 Weight ki2 All utility values Dose (mSv) Distance (m) Path
1 0 1 70.49 125.9738 1/2/5/3/4/13/7/6/8/ 9/14/10/11/12
0.4 0.6 1.0447 64.54 137.7034 1/10/11/14/9/8/6/7/ 13/4/3/5/12/2
0 1 1 63.75 145.1739 1/12/2/5/3/4/13/7/ 6/8/9/14/11/10
0.3 0.7 1.0305 63.75 145.1739 1/12/2/5/3/4/13/7/6/ 8/9/14/11/10
weight ki1 is set to 0.4 and the dose attribute weight ki2 is set to 0.6. Reference dose value is set to 63.75 mSv and reference distance value is set to 125.9738 m. Table 5 shows several different paths when ki1 ¼ 0.4 and ki2 ¼ 0.6. According to the proposed quantitative analysis method, the 1st scheme’s total utility value is the minimum, so we take the 1st scheme as the optimal path scheme. From the Fig. 10 we can see that the 1st scheme’s cumulative dose is less than the other path schemes’, and we find that the distance dose increase gradually, when the utility value increases. When the utility value is 1.044, the corresponding path is same to the least effective dose path in the quantitative analysis experiment, as shown in Fig. 7. When the utility value is 1.522, the corresponding path is shown in Fig. 11. Compare these two path schemes, we can clearly find that the path of which utility value is 1.522 is more complex and longer, the corresponding time in the radiation environment is longer. The experimental results show that once the attention degree of decision factors (attribute weights) is determined, this proposed method can quickly find out the optimal path which meets the requirements and expectation. As attribute weights depend on the attention degree of decision-maker to decision factors, it has a certain degree of subjectivity. In practical application, attribute weights can be set based on experience of decision-makers, or decision-makers set multiple sets of attribute weights and then select one scheme by comparing and analyzing the experiment results. 4.2. Qualitative analysis In this simulation experiment, we take effective dose and distance as the main decision factors respectively to plan path. We select 22 path schemes of which one decision factor’s values is less from many schemes, the 22 schemes are shown in Table 6.
Fig. 7. No. 1 scheme: the shortest distance walking path.
Fig. 8. No. 2 scheme: the distance and dose are close to the minimum.
From Fig. 12, we can see relative relationship between effective dose and distance in all path schemes. No. 2 path scheme’s effective dose is closer to 1st path scheme’s effective dose, but No. 2 scheme’s distance is less than No. 1 scheme’s distance. However, the other schemes’ distance and effective dose are more than No. 1 and No. 2 schemes’. Therefore, when the effective dose is taken as the main decision factor, we select 1st scheme or 2nd scheme as the optimal scheme. From Fig. 13, we can see relative relationship between effective dose and distance of all path schemes. No. 12 scheme’s distance is the shortest. In these 11 schemes, as the distance increases, the effective dose does not change significantly. Therefore, when the
Fig. 9. No. 3 and No. 4 schemes: the least dose walking path.
Y.-k. Liu et al. / Progress in Nuclear Energy 74 (2014) 184e192 Table 5 The simulation results when ki1 ¼ 0.4 and ki2 ¼ 0.6. Scheme number
All utility values
Distance/m
Dose/mSv
1 2 3 4 5 6 7 8 9 10 11
1.044 1.102 1.130 1.170 1.257 1.374 1.500 1.522 4.700 4.851 11.356
137.7034 139.2968 142.3459 145.4233 154.7892 164.6593 176.2579 177.7215 1140.169 1167.021 3178.405
64.54 70.06 72.01 75.2 81.31 90.4 99.93 101.71 114.67 121.67 134.23
Dose
Distance/m
3000 2500 2000
1
2
3
4
5
6
7
8
9
10
11
1500 1000 500 0
160 140 120 100 80 60 40 20 0
Distance as the main decision factor
Scheme number
Dose/mSv
Distance/m
Scheme number
Distance/m
Dose/mSv
1 2 3 4 5 6 7 8 9 10 11
63.75 64.54 68.89 69.54 69.69 69.98 73.94 74.33 76.42 80.58 82.06
145.1739 137.7034 151.3004 151.963 145.9688 158.007 151.6615 153.8288 152.717 160.7563 169.701
12 13 14 15 16 17 18 19 20 21 22
125.9738 128.1412 130.3902 131.2186 132.1003 132.9135 133.5252 142.4714 143.5828 144.7489 145.2351
70.49 70.88 74.4 74.07 75.63 73.89 68.89 80.04 89.75 83.94 83.88
5. Analysis of results
U lity value Fig. 10. The simulation results when ki1 ¼ 0.4 and ki2 ¼ 0.6.
distance is taken as the main decision factor, No. 12 scheme can be the optimal scheme. So far, we get the best schemes in the different decision factor analysis cases. If we continue to compare these best schemes from two analyses results, and then get the best scheme from them. No. 1 and No. 2 schemes are best schemes, when the effective dose is taken as the main decision factor. No. 12 scheme is best scheme, when the distance is taken as the main decision factor. We can see No. 1 and No. 2 schemes’ dose is less, No. 12 scheme’s distance is shorter. The result of this comparison indicates that decision factor is different, the result may be different, and the scheme’s advantage is also different. In the normal equipment inspections, taking into account of health, we select No. 1 scheme as the best scheme.
The result of simulation experiments represents that quantitative analysis is efficient and easier than qualitative analysis when the attribute weights are determined. On the contrary, when the attribute weights are not determined, qualitative analysis is better and easier than quantitative analysis to get the optimal path scheme. If the attribute weights are not determined, we can get the optimal scheme using quantitative analysis many times with different combinations of attribute weights, and then determine the final path scheme by comparing these ‘optimal’ schemes. In this study, this proposed method can not only be used to avoid the obstacles, but also solve single objective and multi-objective path problems. In practical application, by setting a small amount of sensor to measure the radioactivity in radiation environment, we can apply the proposed method to plan path. This method is economical and easily to implement. But the proposed method also has shortcomings, which is caused by the quantity and the location of nodes which are set artificially. Because set different quantity and location of nodes, we get the different optimal path and the corresponding value of decision factor may be different. So in this ongoing research work, we set out trying to solve this problem. 6. Conclusion In this paper, we introduced the innovative multi-objective path problem in radiation environment. At the beginning, we built the mathematical model of path problem in radiation environment and selected the decision factors. Secondly we applied the improved
Dose/,μSv
Dose
Distance
85 80 75 70 65 60 55 50 45 40
180 170 160 150 140 130 120 110 100 1
2
3
4
5
6
7
8
9
10
11
Path program number Fig. 11. The path that the total utility value is 1.522.
Fig. 12. Distance and dose curves for No. 1eNo. 11 schemes.
Distance/m
3500
Table 6 The simulation results when effective dose and distance are the main decision factor, respectively. Effective dose as the main decision factor
Dose/μSV
Distance
191
192
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References
Dose 95 90 85 80 75 70 65 60 55 50
Distance/m
145 140 135 130 125 120 115 12
13
14
15
16
17
18
19
20
21
Dose/μSv
Distance 150
22
Path program number Fig. 13. Distance and dose curves for No. 12eNo. 22 schemes.
PSO algorithm and multi-objective decision-making method to solve this problem, and coded the path-planning algorithm in Matlab (R2012a). Then we tested this method with distance and dose as decision factors by means of simulation experiment. At last, we got the optimal walking route in radiation environment. The research results show that the designed path-planning method is technically feasible, which has achieved initial progress. The path-planning method is not only used for searching the optimal path with minimum effective dose, but also used for solving the multi-objective path problem. In the simulation experiments, the method can get the optimal result quickly, and be applied for two situations: that is, significance of decision factors is certain and uncertain. The method is not limited to distance or dose as decision factors, we can also choose other decision factors (such as time, safety, cost and etc.) to plan path on the basis of particular situation and work. The planned path schemes are helpful for decision-maker to make decision, optimize and evaluate the program of work. Besides, this study can be a technical support means for working in radiation environment and development of radiation protection techniques. Acknowledgment This work is supported by Project (51379046) of the National Natural Science Foundation of China and Heilongjiang Postdoctoral Science Research Foundation of China (LBH-Q12119).
Alzalloum, A., 2009. In Application of Shortest Path Algorithms to Find Paths of Minimum Radiation Dose. Dissertation. Illinois, Urbana. De Jong, K., 2005. Genetic algorithms: a 30 year perspective. Perspect. Adapt. Nat. Artif. Syst. 11. Eberhart, R., Kennedy, J., 1995. A new optimizer using particle swarm theory, micro machine and human science, 1995. In: MHS’95, IEEE Proceedings of the Sixth International Symposium, pp. 39e43. Guanglin, Zhang, Xiaomei, Hu, Jianfei, Chai, Lei, Zhao, Tao, Yu, 2011. Summary of path-planning algorithm and its application. Mod. Machin., 85e90. Hage, M., Couture, S., 1999. Evolutionary Software for Autonomous Path-Planning. Haixia, Wan, 2012. Development of Rapid Calculation Code for Dose Rate Distribution in Visualization Platform of Radiation Field. Dissertation. North China Electric Power University. Hende, Wang, 1995. Procedure and methodology of radiation protection optimization. Radiat. Prot. 15, 147e157. Holland, J.H., 1973. Genetic algorithms and the optimal allocation of trials. SIAM J. Comput. 2, 88e105. Johnsen, T., Edvardsen, S.T., Mever, G., Rindahl, G., Lee, S.A., Sivertsen, E.R., 2004. The VRdose Software System: User Manual, Report and Design Documentation for R5. Kakunenryo Saikuru Kaihatsu Kiko Kokai Shiryo, p. 184. Kennedy, J., Eberhart, R., 1995. Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942e1948. Khasawneh, M., Al-Shboul, Z., 2010. Localized navigation algorithm for radiation evasion at nuclear facilities. In: Proceedings of the First International Conference on Nuclear and Renewable Energy, Amman, Jordan. Khasawneh, M.A., Al-Shboul, Z.A.M., Jaradat, M.A., 2013a. A localized navigation algorithm for radiation evasion for nuclear facilities: optimizing the “radiation evasion” criterion: part I. Nucl. . Des. 259, 240e257. Khasawneh, M.A., Al-Shboul, Z.A.M., Jaradat, M.A., Malkawi, M.I., 2013b. A localized navigation algorithm for radiation evasion for nuclear facilities. Part II: optimizing the “nearest exit” criterion. Nucl. Eng. Des. 259, 258e 277. Kim, Y.H., Park, W.M., 2004. Use of simulation technology for prediction of radiation dose in nuclear power plant. Lect. Not. Comput. Sci. 3314, 413e418. Mól, A.C.A., Jorge, C.A.F., Couto, P.M., 2008. Using a game engine for VR simulations in evacuation planning. IEEE Comput. Graph. Appl. 28 (3), 6e12. Mól, A.C.A., Aghina, M.A.C., Jorge, C.A.F., Lapa, C.M.F., Couto, P.M., 2009. Nuclear plant’s virtual simulation for on-line radioactive environment monitoring and dose assessment for personnel. Ann. Nucl. Energy 36, 1747e1752. Mól, A.C.A., Pereira, C.M.N.A., Freitas, V.G.G., Jorge, C.A.F., 2011. Radiation dose rate map interpolation in nuclear plants using neural networks and virtual reality techniques. Ann. Nucl. Energy 38, 705e712. Pachter, L., Pachter, M., 2001. Optimal paths for avoiding a radiating source, decision and control. In: Proceedings of the 40th IEEE Conference, pp. 3581e3586. Shang, Gao, Zhiyuan, Hu, 2005. Particle Swarm Optimization Algorithm for Set Partition Problem. Jiangsu University of Science and Technology, pp. 41e44. Srinivas, M., Patnaik, L.M., 1994. Genetic algorithms: a survey. IEEE Comput. 27, 17e26. Wenzhong, Guo, Guolong, Chen, 2012. Discrete Particle Swarm Optimization Algorithm and Its Application. Tsinghua University Press, pp. 27e35.
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Path-planning research in radioactive environment based on particle swarm algorithm Yong-kuo Liu a, *, Meng-kun Li a, Chun-li Xie b, Min-jun Peng a, Fei Xie a a b
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin 150001, China Traffic College, Northeast Forestry University, Harbin 150040, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 January 2014 Received in revised form 3 March 2014 Accepted 6 March 2014
During the design, maintenance and decommissioning of nuclear facilities, nuclear radiation protection is an important part. In recent years, researchers have explored a lot of radiation protection approach, and some radiation protection approach have been applied in practice, such as visualization technique of radiation environment, path-planning method, robotics and etc., in these techniques the path-planning in radiation environment technology has become an important radiation protection measure. In this paper, we addressed a staff walking path-planning approach in radiation environment based on particle swarm algorithm and introduced some key technologies of path-planning in radiation environment. To obtain the optimal walking route to verify the operation of the proposed method, we carried out the simulation experiment in which dose and distance were as decision factors. The experiment results represented the probability and the effectiveness of path-planning in radiation environment based on particle swarm algorithm. 2014 Elsevier Ltd. All rights reserved.
Keywords: Radioactive environment Path-planning Particle swarm algorithm Simulation
1. Introduction It is the mission of engineers to design nuclear facilities and systems to be as safe as possible and to take necessary measures to preserve the safety and the health of personnel in nuclear power plant. However, no matter how sophisticated the designs, radiation exposure is unavoidable. According to statistics, the radiation dose that staff suffered during the daily activities of normal operation takes 20% of the total annual dose in Chinese nuclear power plant, and the radiation dose that staff suffered during the overhauling of nuclear power plant takes 80% of the total annual dose (Haixia Wan, 2012). As everyone knows, the basic ways of external irradiation protection are to reduce the time that personal stays in the radioactive room expand the distance between personal and radiation source, and take the shielding measures. So we can take the method of path-planning in radioactive environment as one of the measures of external irradiation protection. By path-planning we can control the time that personal stays in radiation environment and the distance between personal and radiation source, thereby to reduce the radiation exposure that personal suffered during work.
* Corresponding author. Tel.: þ86 (0) 451 82569302x458; fax:þ86 (0) 451 82569622. E-mail address: [email protected] (Y.-k. Liu). http://dx.doi.org/10.1016/j.pnucene.2014.03.002 0149-1970/ 2014 Elsevier Ltd. All rights reserved.
For the path-planning methods in radiation environment, domestic and foreign researchers have done a lot of research. For example, the Fugen Nuclear Power Station (NPS) in Japan was shut down permanently, Japanese developed Decommissioning Engineering Support System (DEXUS) to create a dismantling plan using state-of-the-art software such as 3-dimensional computer aided design (3D-CAD) and virtual reality (VR). In particular, an exposure dose evaluation system using VR has been developed and tested (Johnsen et al., 2004). The total system can be used to visualize radiation and evaluate the dose that personal suffered to optimize the walking route and the decommissioning plan. Mól et al. used a game engine for virtual reality simulations in emergency situations (Mól et al., 2008). Game engine’s open source code and existing functionalities are convenient for researchers and developers to simulate scenarios. The simulation platform collected dose rate data from radiation monitors installed in the real plant, then researchers assess dose for personnel (Mól et al., 2009). Further, Mól et al. used neural networks and virtual reality techniques for assessment of radiation dose exposition by nuclear plant’s personnel, to optimize working tasks for minimisation of received dose (Mól et al., 2011). South Korean developed simulation technology for prediction of radiation dose, which was developed by VRML and Java Applet. This simulation program can display radiation exposure levels in a virtual reality environment, represent high dose danger zones by
Y.-k. Liu et al. / Progress in Nuclear Energy 74 (2014) 184e192
graphically visualizing dose rates and predict the exposure dose of virtual workers (Kim and Park, 2004). This simulation program need specific dose calculation model to calculate the dose rate distribution, and then the workers should try and compare many paths to determine minimum radiation dose path. American L.S. Pachter and M. Pachter considered the problem of navigating between points in the plane so as to minimize the exposure to radiation source. In order to resolve this problem, L.S. Pachter and M. Pachter introduced a weighted exposure and path length optimization problem and applied requires a variational approach (Pachter and Pachter, 2001). L.S. Pachter has demonstrated the feasibility of this method that barrier-free environment theory in point source radiation field. The method may determine a minimum dose path, but the length of the path maybe too long and curved path is difficult to realize in practice. American M. Hage designed evolutionary software techniques based on sensor in radiation environments, and achieved the target which mobile vehicles avoid obstacle and reduce the continued radiation exploration (Hage and Couture, 1999). In the method, the genetic program was very complex and it need to be trained in known environments and then utilized in an unknown environment. The method was designed for the robot in radioactive environment, and not ensures the cumulative dose minimum on the optimized path, therefore maybe not suitable for walking pathplanning of staff. American Alzalloum (2009) addressed the least cost path problem for a radiological contaminated area and found optimal paths using Dijkstra’s and BellmaneFord algorithms, in these paths the total radiation exposure (cumulative dose) is minimum. In addressing this problem, Alzalloum took radioactive contamination area into vertices and edges, and respectively applied the point nuclear radiation model and Monte Carlo dose calculation model as the weights of each side of the edge. Dijkstra’s and BellmaneFord algorithms were modified and coded in Matlab, through simulation tests, and ultimately to find the optimize path which the total radiation exposure (cumulative dose) was the lowest. Alzalloum methods in the application process was too dependent on radiation field model, and ignored the actual environment of radioactive shielding, therefore, this method is only applicable to ideal radioactive environment, with some limitations. Khasawneh et al. in the University of Jordan addressed a localized navigation algorithm for radiation evasion. A well-designed and wireless sensor networks infrastructure that is distributed in radioactive environment, through sensors measure the radioactivity level and using wireless communication technology transfer the information, finally the use of local navigation algorithm based on graph coloring theory for radioactive evasion (Khasawneh and Al-Shboul, 2010; Khasawneh et al., 2013a,b). Khasawneh et al. who have some practical ways, but in some radioactive environment, the algorithm would be stalled or cycled so that the optimal path can’t be found, simultaneously, this method requires a lot of wireless sensors in practical applications, and it also increases the economic inputs. The researches of path-planning in radioactive environment are seldom in China. Haixia Wan in North China Electric Power University, who developed rapid calculation program for dose rate distribution in visualization platform of radiation field based on Monte Carlo method (Haixia Wan, 2012). The program combined the virtual reality technology and radiation protection techniques, applied the computer to simulate dose rate distribution in complex radiation field environment, did virtual experiments operation, and calculated and displayed the data in real-time, eventually the computer terminals provide the radiation exposure situations obviously to the user. It is thus clear that the radiation field
185
visualization is an effective means to reduce radiation dose for nuclear workers. Currently, path-planning method in radioactive environment is mainly focused on searching the minimum total radiation exposure (cumulative dose) path. China has not yet a very perfect pathplanning technology for radiation environment in practical engineering tasks. In some simulation experiments and practical applications, it is not easy to find that distance and cumulative dose do not have explicit mathematical relationships. Due to the requirements for tasks are different, the requirements for the path may also be different. For example: equipment maintenance, decommissioning of nuclear facilities, nuclear emergency and other engineering tasks in the nuclear power plant, which require not only the low radiation doses, but also little travel time or low cost. Therefore, we proposed multi-objective path problem in radiation environment, and did research in this area using particle swarm algorithm and multi-objective decision-making techniques. On these bases, finally we addressed a multi-objective path-planning approach based on particle swarm algorithm in radiation environment, and did simulation experiments in a static radiation environment with dose and distance as two decision factors. The rest of this paper is organized as follows: path-planning strategy, particle swarm algorithm and decision-making techniques are introduced in Section 2. The mathematical model of path problem in radiation environment and the implementation of the proposed method are described in Section 3. Section 4 describes the simulation experiment. Section 5 analyzes the results of simulation experiment. Finally, Section 6 presents the concluding remarks for this paper. 2. Path-planning method The structure of path-planning method in radiation environment based on particle swarm algorithm is shown in Fig. 1. First, we get the geometry of radiation environment, distribution of dose rate and decision factors. Second, we set nodes in radiation environment, obtain weights of dose values between any two nodes, construct alternative road network. We transfer path-planning problem in radioactive environment into a variant TSP (traveling salesman problem), and then build the mathematical model of this problem. At last, we combine particle swarm optimization algorithm with multi-objective decision-making techniques to form the path-planning method in the radiation environment, and then implement the method by programming.
Fig. 1. The structure of multi-objective path-planning in radioactive environment based on PSO.
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2.1. Particle swarm optimization algorithm The core of path-planning method is the design of pathplanning algorithm. There are many path-planning algorithms, but according to the different advantages and disadvantages of each algorithm, their suitable scopes and fields are different (Guanglin Zhang et al., 2011). The particle swarm optimization (PSO) is an evolutionary computation technique, which was developed by Kennedy and Eberhart (Eberhart and Kennedy, 1995; Kennedy and Eberhart, 1995). It is inspired by the social activity of flocks of animals, such as fish or birds. PSO algorithm is similar to genetic algorithm and is an optimum tool based on iteration, and PSO algorithm doesn’t have crossover and mutation of genetic algorithm, but particles search in solution space following optimal particle. At present PSO algorithm has been applied to solve pathplanning problem. Compared with other algorithms, PSO algorithm is simple, and easy to implement, and it has fast convergence speed, fewer adjustment parameters, etc. PSO algorithm has been applied to many areas of social production and life. Thereby, in this study, we used particle swarm optimization algorithm to solve the path-planning problem in the static radiation environment. PSO algorithm is first randomly initialized to a group of random particles (random solution), whose positions represent potential solutions, and then repeatedly updates the positions to the optimal one. In each iteration, the particles update themselves by tracking two “extremes”. The first extreme is the optimal solution that particle finds by itself, this optimal solution is called the personal best (pbest). The second extreme is the optimal solution that the whole population find, this optimal solution is called the group best (gbest). Alternatively, we also can take the neighbor particles’ optimal solution as the gbest which is local extreme, instead of the whole population’s optimal solution. Before we find these two optimal values, the update rules of the position and the velocity of the particle are shown as follows:
vkþ1 ¼ uvk þ c1 r1 ðpbestk xk Þ þ c2 r2 ðgbestk xk Þ
(1)
xkþ1 ¼ xk þ vkþ1
(2)
In the above formula, vk is current velocity of the particles; xk is current position of particles, and representing a candidate solution to the optimization problem. pbestk is personal best position of the particles, i.e., the best solution encountered by particle thus far. gbestk is global best particle, i.e., the best solution found by the entire swarm. u denotes the inertia weight, c1 and c2 are the acceleration constants, r1 and r2 are random numbers uniformly distributed within [0,1]. vkþ1 is the vector sum of vk, pbestk xk and gbestk xk, its diagram is shown in Fig. 2. PSO algorithm initially is used to solve continuous optimization problems, not to solve discrete optimization problems (Wenzhong
pbestk
xk
gbestk
vk Fig. 2. Weighted combination of three possible moving directions.
and Guolong, 2012). So we adopt the idea that the PSO algorithm is in combination with genetic algorithms (De Jong, 2005; Holland, 1973; Srinivas and Patnaik, 1994), in which crossover operator and mutation operator are adopted (Shang and Zhiyuan, 2005). Individual optimum crossover: the current path of each particle is crossed with its historical optimum path to generate a new path. Global optimum crossover: the current path of each particle is crossed with the group optimum path to generate a new path. The purpose of crossover operation is to influence the personal best and the group best, improve search capabilities of particles and increase the diversity of the population. Mutation: Mutation bits in the path of each particle are selected randomly, and then mutation bits are exchanged to generate a new path. The mutation purpose is to prevent particle swarm into local optimal solution, mutation increases the diversity of the population and improves the local search capabilities of particles. The improved algorithm is not only successfully used to solve discrete optimization problems, but also to accelerate the PSO algorithm’s convergence speed. When the PSO algorithm stagnates or falls into the local optimal solution, these genetic operators improve the diversity of population. The improved algorithm’s specific update formula is as follows.
Xit ¼ F3 F2 F1 Xit1 ; Pit1 ; Gt1 i
(3)
where, Xit is the tth iteration solution of ith particle, F1 is mutation operator, F2 is individual optimum crossover operator and F3 is global optimum crossover operator. Pit1 is individual optimal solution and Gt1 is group optimal solution. i 2.2. Dose calculation In this paper, we adopted PSO algorithm to combine the effective dose values between any two nodes to find the optimal walking path. Assuming that radiation environment is stable and limited. Select n nodes in radiation environment, and then use m edges that connect all possible pair of nodes. Each edge is associated with an effective dose value as its weight. We connect all nodes into a loop, and get n(n 1)/2 kinds of path. The total effective dose value is the sum of all of the weights of the edges in the path. Because of the actual equipment and obstructions in the radiation environment, some edges are not connected, and then the effective dose value between these nodes can be negligible. Supposing that effective dose value from the node A to node B is equal to the effective dose value from the node B to node A, the effective dose values between any two nodes is independent of the walking direction. Therefore we can simplify the entire radiation space and the scale of the problem. Effective dose value is calculated as follows: in practice, set up a sensor at each node in the radiation space for measuring the radioactivity at the node position. The dose rate is then averaged, and is calculated based on the length of the segment and the speed (assuming that the walking speed is constant throughout the path), time t that travels the segment. Effective dose is finally calculated by multiplying the average dose rate with the time t. 2.3. Decision-making factors and decision-making methods The path problem in radiation environment is different from the shortest path problem of everyday life. In most studies, the pathplanning in radiation environment basically focuses on solving the minimum total radiation exposure (effective dose) path problem. In this paper, we addressed multi-objective path-planning
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radiation environment. In simulation experiment, we selected effective dose and walking distance as decision factors, applied quantitative and qualitative analysis comparison methods to analyze the experimental results. 2.3.1. Quantitative analysis In quantitative analysis method, we add every criteria value of scheme up to a single numeric value, and then we evaluate these schemes based on these single numeric values to determine the optimal scheme. ICRP Publication No.55 (Hende Wang, 1995) described the method of multi-attribute utility analysis: quantify those factors which are difficult measured in monetary value, and then make quantitative judgments for those factors which usually can only be made a qualitative analysis, like this, the method of multi-attribute utility analysis can make decision-making more scientific. In this research, we borrowed ideas from multi-attribute utility analysis, and applied a quantitative analysis method to solve multi-objective path problem in radiation environment. First, we determine the reference value of every decision factor, which is selecting the minimum value of each decision factor as the reference value. Second, we consider the utility value of each decision factor, and the utility value is a dimensionless quantity which is that the value of each decision factor divides by its reference value. Utility value is greater than or equal to 1, if utility value is closer to 1, the corresponding path-planning’s effect is better in certain aspects. Finally, we calculate the total utility value of every path scheme according to formula (4):
Ui ¼
X
kj Uij
(4)
where, Ui is the total utility value of the ith scheme, Uij is utility value of the jth decision factor (j ¼ 1,2,.,n) in the ith scheme, kj is the attribute weight of the jth decision factor, and it is normalized, P i.e. kj ¼ 1. Attribute weight reflects the concern degree of decision factors which relate to the result of path-planning directly.
Fig. 3. Flowchart for multi- objective path-planning in radiation environment based on PSO algorithm.
2.3.2. Qualitative analysis Qualitative analysis method is complementary to quantitative analysis method. In qualitative analysis method, take one kind of decision factors as the main decision factor, and then select the scheme whose main decision factor is the best as the most optimal solution. In simulation experiment, we choose walk distance and effective dose as the main decision factor respectively. First, according to the main decision factor for path-planning, select and list the different and better path schemes. Second, if the rest of schemes are still in a dilemma, we can compare the rest of schemes based on the other decision factor. Finally, we get the optimal path scheme by comparison of the above. 3. Model building and algorithm implementation
problem in radiation environment. The optimal path is determined by multiple factors, such as safety, costs, mission requirements, etc. Safety factors include radiation exposure, additional risk or adverse effects to worker; Economic cost factors include costs of radiation protection, costs of occupational worker working, etc. Mission factors include object, constraint condition of the project, etc. Usually there is no clear mathematical relationship between these decision factors, so the paths can’t be directly compared and evaluated. Meanwhile, the PSO algorithm is mainly applied for solving the single objective problem. Therefore, in the study we combined quantitative and qualitative analysis comparison method with the PSO algorithm to achieve multi-objective path-planning in
3.1. The mathematical model of path-planning in radiation environment Assuming there are N nodes in radioactive environment. The coordinate of ith node is ðx; yÞ; i˛N; i is node number, Lij is the distance between any two points, Hij is the effective dose between any two points, attribute weights factors are k1 and k2. Distance matrix is ðLij ÞNN , dose matrix is ðHij ÞNN . L* is the reference value of the distance, H* is the reference value of the effective dose, where, i and j are node number, i; j˛C; C ¼ f1; 2; .; Ng. Mathematical models are as follows.
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Fig. 4. Main interface of path-planning in radiation environment based on PSO algorithm.
Li ¼
n X n X
xij Lij
(5)
i¼1 j¼1
Hi ¼ Ui1 ¼
Ui2 ¼
n X n X
xij Hij
(6)
i¼1 j¼1 Li L*
(7)
Hi H*
(8)
Ui ¼ k1 Ui1 þ k2 Ui2 xij ¼
(9)
1 If the edge ijisin the path 0 otherwise:
(10)
where, formulas (5) and (6) are, respectively, distance and effective dose of the ith path scheme. Formulas (7) and (8) are, respectively, the distance utility value and the dose utility value of the ith path scheme. Formula (9) is the total utility value of the ith path scheme. Because the path consists of some edges from beginning to end, edge ij may be in the path. Formula (10) is the decision variable which represents whether the edge ij is in the path. If the edge ij belongs to the path, then xij is set to 1; if the edge ij doesn’t belongs to the path, then xij is set to 0. When using quantitative analysis, the fitness function of PSO algorithm is the formula (9). When using qualitative analysis, the fitness function of PSO algorithm is the formula (5) and (6) respectively. 3.2. Realization of path-planning method Because PSO algorithm doesn’t need too many parameters to be adjusted, it is fit to most users who don’t know about PSO algorithm. Normally, PSO algorithm can get satisfactory result as long as
Table 2 The location of point sources (m). Serial number
1
2
3
4
X coordinate Y coordinate
12 16
21 17
35 18
35 10
the iterations are adequate. So in the research, we take particle’s number and iterations as the adjustable parameters of PSO algorithm. When the algorithm reaches the maximum number of iterations, the loop iteration is terminated. However, if the number of particles and iterations are adjusted suitably, the PSO algorithm would get the better solution and run faster. The flowchart for multi-objective path-planning method in radiation environment based on PSO algorithm is shown in Fig. 3. Inside the PSO algorithm, we set up an external file to storage and screen the optimal path schemes in each generation. External file’s data includes utility value, distance, dose and path. The program outputs and saves the external file’s data for analysis. Fig. 4 shows the main interface of the program. Panel A: the optimal path display panel. Panel B: the room plane graph display panel. Panel C: the distribution of radioactivity display panel. Panel D: PSO’s fitness diagram panel . Panel E: data (location of nodes, distance data and dose data) input and parameters setting panel. Panel F: result display panel. The toolbar is used to output and save the different planned path’s result. 4. Simulation experiment test In the simulation experiment test, we set a case that workers make an inspection tour of radioactive nuclear facilities to verify the operation feasibility of the proposed method. In radiation environment we set 4 radiation sources which are of equal strength in 4 radioactive facilities separately, and select 14 nodes, plan workers’ walk path and determine the order of inspection. Here we ignore the radiation shielding, suppose the travel speed is constant, and take the distance and the effective dose as decision factors.
Table 1 The location of nodes (m). Serial number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
X coordinate Y coordinate
30 0
30 10
30 20
35 27
26 17
16 26
21 21
10 21
2 25
1 8
10 14
21 13
25 24
3 14
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Table 3 Effective doses between any two nodes (mSv).
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1
2
3
4
5
6
7
8
9
10
11
12
13
14
999 4.88 13.81 39.27 9.24 327.36 29.92 28.4 682.79 6.08 13.62 6.83 13.97 10.04
4.88 999 8.95 21.03 6.22 24.66 17.79 35.36 37.13 11.77 21.83 7 10.5 20.61
13.81 8.95 999 4.85 3.84 7.88 7.39 18.06 15.05 79.24 179.93 12.67 3.51 1362.88
39.27 21.03 4.85 999 7.91 5.82 7.56 11.97 9.17 51.93 66.4 17.89 3.67 39.98
9.24 6.22 3.84 7.91 999 11.95 8.81 39.9 32.32 34.1 66.56 8.96 4.97 117.13
327.36 24.66 7.88 5.82 11.95 999 4.04 3.45 3.26 13.89 45.57 29.75 3.55 8.97
29.92 17.79 7.39 7.56 8.81 4.04 999 9.07 9.14 68.66 73.62 3415.27 3.38 36.07
28.4 35.36 18.06 11.97 39.9 3.45 9.07 999 2.59 7.12 14.88 20.38 8.94 4.99
682.79 37.13 15.05 9.17 32.32 3.26 9.14 2.59 999 2.81 8.94 26.21 7.71 2.17
6.08 11.77 79.24 51.93 34.1 13.89 68.66 7.12 2.81 999 4.94 11.32 88.61 1.11
13.62 21.83 179.93 66.4 66.56 45.57 73.62 14.88 8.94 4.94 999 18.52 83.8 4.69
6.83 7 12.67 17.89 8.96 29.75 3415 20.38 26.21 11.32 18.52 999 29.85 20.55
13.97 10.5 3.51 3.67 4.97 3.55 3.38 8.94 7.71 88.61 83.8 29.85 999 28.9
10.04 20.61 1362 39.98 117.13 8.97 36.07 4.99 2.17 1.11 4.69 20.55 28.9 999
In the simulation experiment test, distribution of radioactivity is calculated by point nuclear model. According to the principle of superposition, every node’s radiation strength is the accumulation of radioactivity that each radioactive source generates. The effective dose between any two nodes is calculated according to the method given in Section 2.2. Table 1 shows the number and the coordinates of nodes. Node 1 is assumed start and end of the path. Table 2 shows the number and the coordinates of radioactive source. Table 3 shows the effective dose for workers between any two nodes. Supposing that effective dose between any two nodes is independent of the walking direction, and then effective dose matrix is a symmetric matrix. Fig. 5 shows the room plane graph. Fig. 6 shows the distribution of radioactivity. In the setting case, after repeated tests, we found when the number of particles was set to 100, and the iterations of algorithm were set to 50, the improved PSO algorithm can get the best solution, meanwhile the program runs faster. When both the number of particles and the iterations are fewer, the algorithm may not get the best result. When both the number of particles and the iterations are larger, the algorithm can get the best results, but the program would take more time. If the number of nodes is more, we can increase the number of particle or iterations appropriately. 4.1. Quantitative analysis 4.1.1. Uncertain attribute weights In this experiment, we select four different sets of attribute weights ki1 and ki2 (ki1 and ki2 are, respectively, distance attribute
Fig. 5. Room plane graph.
weight and dose attribute weight, i ¼ 1, 2, 3, 4). We can get the minimum values of dose and distance through experiment, and take them as reference value. According to the quantitative analysis method, the reference value of dose is set to 63.75 mSv, the reference value of distance is set to 125.9738 m. Simulating the situation that the importance degree of distance and effective dose is different (i.e. the path of least utility value), the specific result is shown in Table 4, and these four path plane graphs are shown in Figs. 7e9. The experiment result shows that when the attribute weights are determined, path-planning method based on PSO algorithm can find the optimal path. The results in Table 4 show that different attributes weights may correspond to different optimal path, and some attribute weights in certain range may correspond to the same optimal path, such as the 3rd and the 4th path scheme. From Figs. 7e9 we can see that the proposed method can avoid obstacles or equipment and find the path to arrive at the specified location. The 1st scheme is the shortest path and can make occupational worker to travel the path with the minimum time. If the effective dose is too large, this scheme maybe no longer suitable. The 3rd scheme and the 4th scheme are all the minimum dose paths and contribute to the occupational worker’s safety. There are some path schemes of which dose and distance are close to the minimum values, such as the 2nd scheme. The 2nd scheme belongs to compromise solution that the dose and the distance are closer to the minimum value. We can select the path scheme based on special situation and decision-maker’s decision. 4.1.2. Certain attribute weights determined In this experiment, we select a set of attribute weights to observe the process of quantitative analysis. The distance attribute
Fig. 6. Distribution of radioactivity.
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Table 4 Simulation results of different attribute weights (ki1, ki2) Scheme number
1
2
3
4
Weight ki1 Weight ki2 All utility values Dose (mSv) Distance (m) Path
1 0 1 70.49 125.9738 1/2/5/3/4/13/7/6/8/ 9/14/10/11/12
0.4 0.6 1.0447 64.54 137.7034 1/10/11/14/9/8/6/7/ 13/4/3/5/12/2
0 1 1 63.75 145.1739 1/12/2/5/3/4/13/7/ 6/8/9/14/11/10
0.3 0.7 1.0305 63.75 145.1739 1/12/2/5/3/4/13/7/6/ 8/9/14/11/10
weight ki1 is set to 0.4 and the dose attribute weight ki2 is set to 0.6. Reference dose value is set to 63.75 mSv and reference distance value is set to 125.9738 m. Table 5 shows several different paths when ki1 ¼ 0.4 and ki2 ¼ 0.6. According to the proposed quantitative analysis method, the 1st scheme’s total utility value is the minimum, so we take the 1st scheme as the optimal path scheme. From the Fig. 10 we can see that the 1st scheme’s cumulative dose is less than the other path schemes’, and we find that the distance dose increase gradually, when the utility value increases. When the utility value is 1.044, the corresponding path is same to the least effective dose path in the quantitative analysis experiment, as shown in Fig. 7. When the utility value is 1.522, the corresponding path is shown in Fig. 11. Compare these two path schemes, we can clearly find that the path of which utility value is 1.522 is more complex and longer, the corresponding time in the radiation environment is longer. The experimental results show that once the attention degree of decision factors (attribute weights) is determined, this proposed method can quickly find out the optimal path which meets the requirements and expectation. As attribute weights depend on the attention degree of decision-maker to decision factors, it has a certain degree of subjectivity. In practical application, attribute weights can be set based on experience of decision-makers, or decision-makers set multiple sets of attribute weights and then select one scheme by comparing and analyzing the experiment results. 4.2. Qualitative analysis In this simulation experiment, we take effective dose and distance as the main decision factors respectively to plan path. We select 22 path schemes of which one decision factor’s values is less from many schemes, the 22 schemes are shown in Table 6.
Fig. 7. No. 1 scheme: the shortest distance walking path.
Fig. 8. No. 2 scheme: the distance and dose are close to the minimum.
From Fig. 12, we can see relative relationship between effective dose and distance in all path schemes. No. 2 path scheme’s effective dose is closer to 1st path scheme’s effective dose, but No. 2 scheme’s distance is less than No. 1 scheme’s distance. However, the other schemes’ distance and effective dose are more than No. 1 and No. 2 schemes’. Therefore, when the effective dose is taken as the main decision factor, we select 1st scheme or 2nd scheme as the optimal scheme. From Fig. 13, we can see relative relationship between effective dose and distance of all path schemes. No. 12 scheme’s distance is the shortest. In these 11 schemes, as the distance increases, the effective dose does not change significantly. Therefore, when the
Fig. 9. No. 3 and No. 4 schemes: the least dose walking path.
Y.-k. Liu et al. / Progress in Nuclear Energy 74 (2014) 184e192 Table 5 The simulation results when ki1 ¼ 0.4 and ki2 ¼ 0.6. Scheme number
All utility values
Distance/m
Dose/mSv
1 2 3 4 5 6 7 8 9 10 11
1.044 1.102 1.130 1.170 1.257 1.374 1.500 1.522 4.700 4.851 11.356
137.7034 139.2968 142.3459 145.4233 154.7892 164.6593 176.2579 177.7215 1140.169 1167.021 3178.405
64.54 70.06 72.01 75.2 81.31 90.4 99.93 101.71 114.67 121.67 134.23
Dose
Distance/m
3000 2500 2000
1
2
3
4
5
6
7
8
9
10
11
1500 1000 500 0
160 140 120 100 80 60 40 20 0
Distance as the main decision factor
Scheme number
Dose/mSv
Distance/m
Scheme number
Distance/m
Dose/mSv
1 2 3 4 5 6 7 8 9 10 11
63.75 64.54 68.89 69.54 69.69 69.98 73.94 74.33 76.42 80.58 82.06
145.1739 137.7034 151.3004 151.963 145.9688 158.007 151.6615 153.8288 152.717 160.7563 169.701
12 13 14 15 16 17 18 19 20 21 22
125.9738 128.1412 130.3902 131.2186 132.1003 132.9135 133.5252 142.4714 143.5828 144.7489 145.2351
70.49 70.88 74.4 74.07 75.63 73.89 68.89 80.04 89.75 83.94 83.88
5. Analysis of results
U lity value Fig. 10. The simulation results when ki1 ¼ 0.4 and ki2 ¼ 0.6.
distance is taken as the main decision factor, No. 12 scheme can be the optimal scheme. So far, we get the best schemes in the different decision factor analysis cases. If we continue to compare these best schemes from two analyses results, and then get the best scheme from them. No. 1 and No. 2 schemes are best schemes, when the effective dose is taken as the main decision factor. No. 12 scheme is best scheme, when the distance is taken as the main decision factor. We can see No. 1 and No. 2 schemes’ dose is less, No. 12 scheme’s distance is shorter. The result of this comparison indicates that decision factor is different, the result may be different, and the scheme’s advantage is also different. In the normal equipment inspections, taking into account of health, we select No. 1 scheme as the best scheme.
The result of simulation experiments represents that quantitative analysis is efficient and easier than qualitative analysis when the attribute weights are determined. On the contrary, when the attribute weights are not determined, qualitative analysis is better and easier than quantitative analysis to get the optimal path scheme. If the attribute weights are not determined, we can get the optimal scheme using quantitative analysis many times with different combinations of attribute weights, and then determine the final path scheme by comparing these ‘optimal’ schemes. In this study, this proposed method can not only be used to avoid the obstacles, but also solve single objective and multi-objective path problems. In practical application, by setting a small amount of sensor to measure the radioactivity in radiation environment, we can apply the proposed method to plan path. This method is economical and easily to implement. But the proposed method also has shortcomings, which is caused by the quantity and the location of nodes which are set artificially. Because set different quantity and location of nodes, we get the different optimal path and the corresponding value of decision factor may be different. So in this ongoing research work, we set out trying to solve this problem. 6. Conclusion In this paper, we introduced the innovative multi-objective path problem in radiation environment. At the beginning, we built the mathematical model of path problem in radiation environment and selected the decision factors. Secondly we applied the improved
Dose/,μSv
Dose
Distance
85 80 75 70 65 60 55 50 45 40
180 170 160 150 140 130 120 110 100 1
2
3
4
5
6
7
8
9
10
11
Path program number Fig. 11. The path that the total utility value is 1.522.
Fig. 12. Distance and dose curves for No. 1eNo. 11 schemes.
Distance/m
3500
Table 6 The simulation results when effective dose and distance are the main decision factor, respectively. Effective dose as the main decision factor
Dose/μSV
Distance
191
192
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References
Dose 95 90 85 80 75 70 65 60 55 50
Distance/m
145 140 135 130 125 120 115 12
13
14
15
16
17
18
19
20
21
Dose/μSv
Distance 150
22
Path program number Fig. 13. Distance and dose curves for No. 12eNo. 22 schemes.
PSO algorithm and multi-objective decision-making method to solve this problem, and coded the path-planning algorithm in Matlab (R2012a). Then we tested this method with distance and dose as decision factors by means of simulation experiment. At last, we got the optimal walking route in radiation environment. The research results show that the designed path-planning method is technically feasible, which has achieved initial progress. The path-planning method is not only used for searching the optimal path with minimum effective dose, but also used for solving the multi-objective path problem. In the simulation experiments, the method can get the optimal result quickly, and be applied for two situations: that is, significance of decision factors is certain and uncertain. The method is not limited to distance or dose as decision factors, we can also choose other decision factors (such as time, safety, cost and etc.) to plan path on the basis of particular situation and work. The planned path schemes are helpful for decision-maker to make decision, optimize and evaluate the program of work. Besides, this study can be a technical support means for working in radiation environment and development of radiation protection techniques. Acknowledgment This work is supported by Project (51379046) of the National Natural Science Foundation of China and Heilongjiang Postdoctoral Science Research Foundation of China (LBH-Q12119).
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