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Radioactive source search problem and optimisation model based on meta-heuristic algorithm

Min Zhang

Min Zhang

  • School of Math and Physics, University of South ChinaHengyang, China
  • School of Mathematics, Physics and Energy EngineeringHengyang, China
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Zhang, Min
, 
Xuewen Lu

Xuewen Lu

Department of Mathematics and Statistics, University of CalgaryCalgary, Canada
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Lu, Xuewen
, 
Ettiene Hoffman

Ettiene Hoffman

Canadian University DubaiDubai United Arab Emirates, Dubai
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Hoffman, Ettiene
, 
Radwan Kharabsheh

Radwan Kharabsheh

Business Administration Economics and Administrative Science, Applied Science University BahrainAl Hidd, Bahrain
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Kharabsheh, Radwan
 and 
Qianghua Xiao

Qianghua Xiao

School of Math and Physics, University of South ChinaHengyang, China
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Xiao, Qianghua
  
Mar 31, 2022
Radioactive source search problem and optimisation model based on meta-heuristic algorithm's Cover Image
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Published Online: Mar 31, 2022
Page range: 601 - 630
Received: May 05, 2021
Accepted: Jul 29, 2021
DOI: https://doi.org/10.2478/amns.2021.2.00159
Keywords
© 2021 Min Zhang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Division of the search area
Division of the search area

Fig. 2

Random Searching for Radiation Sources
Random Searching for Radiation Sources

Fig. 3

Misreading variable large correction diagram of radiation dosage maximum
Misreading variable large correction diagram of radiation dosage maximum

Fig. 4

Schematic diagram of K-level hierarchical random search
Schematic diagram of K-level hierarchical random search

Fig. 5

A sketch of overlapping radiation
A sketch of overlapping radiation

Fig. 6

Schematic diagram of fields from two near sources radiation superposition field
Schematic diagram of fields from two near sources radiation superposition field

Fig. 7

Diagram of two-point Radiation Source Division
Diagram of two-point Radiation Source Division

Fig. 8

Schematic diagram of improved markup random search algorithm
Schematic diagram of improved markup random search algorithm

Fig. 9

Schematic diagram of the selection of random probability extreme points and when y=d2 y = {d \over 2} , let p*=(x−d)22d2 {p^*} = {{{{\left({x - d} \right)}^2}} \over {2{d^2}}} . For 0 ≤ x ≤ d, so 0≤p*≤12 0 \le {p^*} \le {1 \over 2}
Schematic diagram of the selection of random probability extreme points and when y=d2 y = {d \over 2} , let p*=(x−d)22d2 {p^*} = {{{{\left({x - d} \right)}^2}} \over {2{d^2}}} . For 0 ≤ x ≤ d, so 0≤p*≤12 0 \le {p^*} \le {1 \over 2}

Fig. 10

Starting point for escape from radioactive source
Starting point for escape from radioactive source

Fig. 11

Multiple point random search
Multiple point random search

Fig. 12

Schematic diagram of radius selection for escaping
Schematic diagram of radius selection for escaping

Fig. 13

Orphan radiation sources out of control in the area
Orphan radiation sources out of control in the area

Fig. 14

Algorithm flow chart
Algorithm flow chart

The relationship between the increase in random search times and the probability of successful search

K k=3 k=4 k=5
P 0.182 0.588 0.959

Radiation dosage at the grid nodes

x1 x2 x3 … xn
y1 f11 f21 f31 … fn1
y2 f12 f22 f32 … fn2
⋮ ⋮ ⋮ ⋮ ⋮
ym f1m f2m f3m … fnm

Probability relationship between two times of independent random search and search success

K K=2 K=3 K=4 K=10
P 0.95 0.0475 2.375*10−3 <=3.71*10−11

The number of random searches and the size of pseudo-regions

|D1| |D1|<=0.5|D| |D1|<=0.2|D| |D1|<=0.05|D| |D1|=0
P >=0.5 >=0.8 >=0.95 1
K <=3 <=2.25 <=2.053 2

The influence of the size of pseudo-region in the whole search area on the probability of search success

D1 |D1|<=0.5|D| |D1|<=0.2|D| |D1|<=0.05|D| |D1|=0
P >=0.5 >=0.8 >=0.95 1

Random search to find the average search step for the source

Experiment Number of staring point Number of searches The average number of steps for a successful search
1 1000 1000 494
2 10000 10000 497
3 100000 100000 499
Language:
English
Publication timeframe:
1 times per year
Journal Subjects:
Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other
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