adaptive comprehensive learning bacterial foraging optimization and its application on vehicle routing problem with time windows amirsh.nll@gmail.com seaman university - Msc. Artificial intelligence

1. Amir Shokri
‫الگوریتم‬ ‫در‬ ‫آن‬ ‫کاربرد‬ ‫و‬ ‫نقلیه‬ ‫وسایل‬ ‫مسیریابی‬ ‫مسئله‬ ‫در‬ ‫یادگیری‬ ‫جامع‬ ‫سازی‬ ‫بهینه‬Bacterial Foraging Optimization
Amirsh.nll@gmail.com
Dr. Kourosh Kiani

2. ‫مقدمه‬
2
‫الگوریتم‬ ‫از‬ ‫نوعی‬ ‫مقاله‬ ‫این‬ ‫در‬BFO‫با‬‫یادگیر‬ ‫سازی‬ ‫بهینه‬ ‫را‬ ‫آن‬ ‫ما‬ ‫که‬ ‫جامع‬ ‫یادگیری‬ ‫استراتژی‬ ‫و‬ ‫کموتاکسیس‬ ‫مختلف‬ ‫مرحله‬ ‫طول‬‫ی‬
‫باکتریایی‬ ‫جامع‬‫باکتریایی‬ALCBFO‫می‬‫دهد‬ ‫می‬ ‫ارائه‬ ، ‫نامیم‬.
‫یک‬‫استف‬ ‫پیشنهادی‬ ‫الگوریتم‬ ‫از‬ ‫برداری‬ ‫بهره‬ ‫و‬ ‫اکتشاف‬ ‫بین‬ ‫خوبی‬ ‫تعادل‬ ‫حفظ‬ ‫برای‬ ‫تطبیقی‬ ‫کاهش‬ ‫خطی‬ ‫غیر‬ ‫تعدیل‬ ‫مدل‬‫شود‬ ‫می‬ ‫اده‬.
‫مکانیسم‬‫دهد‬ ‫می‬ ‫کاهش‬ ‫را‬ ‫زودرس‬ ‫همگرایی‬ ‫بنابراین‬ ‫و‬ ‫کند‬ ‫می‬ ‫حفظ‬ ‫را‬ ‫ها‬ ‫باکتری‬ ‫جمعیت‬ ‫تنوع‬ ، ‫جامع‬ ‫یادگیری‬.

3. ‫مقدمه‬
3
‫در‬‫کالسیک‬ ‫الگوریتم‬ ‫با‬ ‫مقایسه‬GA،PSO،BFO‫اصلی‬‫یافته‬ ‫بهبود‬ ‫دو‬ ‫و‬BFO (BFO-LDC‫و‬BFO-NDC)،ACLBFO‫شده‬ ‫ارائه‬
‫دهد‬ ‫می‬ ‫نشان‬ ‫حالته‬ ‫چند‬ ‫مشکالت‬ ‫حل‬ ‫در‬ ‫بهتر‬ ‫توجهی‬ ‫قابل‬ ‫عملکرد‬.
‫ما‬‫روش‬ ‫عملکرد‬ ‫همچنین‬ACLBFO‫را‬‫ویندوز‬ ‫زمان‬ ‫با‬ ‫نقلیه‬ ‫وسایل‬ ‫مسیریابی‬ ‫مسئله‬ ‫در‬VRPTW‫ارزیابی‬‫کنیم‬ ‫می‬.
‫در‬‫الگوریتم‬ ‫سه‬ ‫با‬ ‫مقایسه‬BFO‫دیگر‬‫نقلی‬ ‫وسایل‬ ‫مسیریابی‬ ‫مسئله‬ ‫حل‬ ‫برای‬ ‫را‬ ‫آن‬ ‫پتانسیل‬ ‫و‬ ‫است‬ ‫برتر‬ ‫پیشنهادی‬ ‫الگوریتم‬ ،‫زمان‬ ‫با‬ ‫ه‬
‫ویندوز‬VRPTW‫تأیید‬‫کند‬ ‫می‬.

4. ‫کار‬ ‫شروع‬
4
‫هوشمند‬ ‫سازی‬ ‫بهینه‬ ‫های‬ ‫الگوریتم‬Swarm‫بیولوژیک‬ ‫سیستم‬ ‫در‬ ‫اجتماعی‬ ‫رفتارهای‬ ‫از‬ ‫ناشی‬ ‫محرک‬ ‫محاسبات‬ ‫از‬ ‫جدید‬ ‫نوعی‬ ‫عنوان‬ ‫به‬‫ی‬
‫است‬ ‫کرده‬ ‫جلب‬ ‫خود‬ ‫به‬ ‫را‬ ‫بسیاری‬ ‫دانشمندان‬.
‫بهینه‬‫ذرات‬ ‫سازی‬PSO،‫و‬ ‫کندی‬ ‫توسط‬ ‫شده‬ ‫پیشنهاد‬،‫ابرهارت‬‫است‬ ‫شده‬ ‫تحریک‬ ‫ماهی‬ ‫آموزش‬ ‫یا‬ ‫پرندگان‬ ‫های‬ ‫گله‬ ‫ازدحام‬ ‫رفتار‬ ‫با‬.
‫الگوریتم‬‫ماهی‬ ‫ازدحام‬‫مصنوعی‬AFSA‫است‬ ‫گرفته‬ ‫سرچشمه‬ ‫ماهی‬ ‫متالطم‬ ‫رفتار‬ ‫در‬.
‫بهینه‬‫ها‬ ‫مورچه‬ ‫کلونی‬ ‫سازی‬‫از‬ACO‫رفتار‬‫شد‬ ‫داده‬ ‫انگیزه‬ ‫ها‬ ‫مورچه‬ ‫ای‬ ‫علوفه‬.‫زنبورهای‬ ‫کلونی‬ ‫الگوریتم‬‫مصنوعی‬ABCA‫از‬
‫است‬ ‫شده‬ ‫گرفته‬ ‫الهام‬ ‫زنبورها‬ ‫اجتماعی‬ ‫تخصصی‬ ‫رفتار‬.
‫اینها‬‫می‬ ‫بهره‬ ، ‫کنند‬ ‫می‬ ‫تعامل‬ ‫خود‬ ‫محیط‬ ‫و‬ ‫یکدیگر‬ ‫با‬ ‫محلی‬ ‫افراد‬ ‫که‬ ‫جهانی‬ ‫رفتار‬ ‫از‬ ‫که‬ ‫هستند‬ ‫جمعیت‬ ‫بر‬ ‫مبتنی‬ ‫های‬ ‫تکنیک‬‫گیرند‬.

5. Bacterial Foraging Optimization
5
‫باکتریایی‬ ‫باکتریایی‬ ‫سازی‬ ‫بهینه‬ ‫الگوریتم‬BFO‫یک‬‫باکتریهای‬ ‫اجتماعی‬ ‫علوفه‬ ‫رفتار‬ ‫از‬ ‫که‬ ‫است‬ ‫تکاملی‬ ‫سازی‬ ‫بهینه‬ ‫جدید‬ ‫روش‬E.
coli‫کند‬ ‫می‬ ‫تقلید‬.
‫با‬‫ای‬ ‫علوفه‬ ‫رفتارهای‬ ‫اساسی‬ ‫فیزیک‬ ‫و‬ ‫شناسی‬ ‫زیست‬ ‫به‬ ‫توجه‬E. coli،Passino‫و‬Liu‫از‬‫و‬ ‫باکتریایی‬ ‫پرخاشگری‬ ‫رفتارهای‬ ‫انواع‬
‫کنترل‬ ‫سیستم‬ ‫چگونگی‬ ‫مورد‬ ‫در‬ ، ‫اند‬ ‫کرده‬ ‫سوءاستفاده‬ ‫اجتماعی‬ ‫رفتارهای‬E. coli‫کنید‬ ‫استفاده‬ ‫غذایی‬ ‫های‬ ‫برنامه‬ ‫اجرای‬ ‫بیانگر‬.
‫فرایند‬‫پراکند‬ ‫و‬ ‫حذف‬ ‫و‬ ‫مثل‬ ‫تولید‬ ، ‫ازدحام‬ ، ‫کموتاکسی‬ ‫یعنی‬ ، ‫کرد‬ ‫تقسیم‬ ‫بخش‬ ‫چهار‬ ‫به‬ ‫توان‬ ‫می‬ ‫را‬ ‫ها‬ ‫باکتری‬ ‫سازی‬ ‫علوفه‬‫گی‬.

6. Bacterial Foraging Optimization
6
𝜃 𝑖 𝑗 + 1, 𝑘, 𝑙 = 𝜃 𝑖 𝑗, 𝑘, 𝑙 +
𝐶 𝑖 Δ 𝑖
√Δ 𝑇 𝑖 Δ(i)
𝐽ℎ𝑒𝑎𝑙𝑡ℎ
𝑖
= Σ𝑗=1
𝑁 𝑐
𝐽(𝑖, 𝑗, 𝑘, 𝑙)
Reproduction
Chemotaxis

7. Adaptive Comprehensive Learning Bacterial Foraging Optimization
7
𝐶𝑗 = 𝐶_ min + exp −𝑎 ∗
𝑘
𝑁𝑟𝑒
𝑛
∗ (𝐶_ max −𝐶_ min)
𝜃 𝑑
𝑖
𝑗 + 1, 𝑘, 𝑙 = 𝜃 𝑑
𝑖
+
𝐶 𝑖 Δ i
√Δ 𝑇 𝑖 Δ(i)
+ 𝜆 ∗ 𝑟1 ∗ 𝑝𝑏𝑒𝑠𝑡𝑖𝑑 − tetha 𝑑
𝑖
𝑗, 𝑘, 𝑙 + 1 − 𝜆 ∗ 𝑟2 ∗ (𝑔𝑏𝑒𝑠𝑡𝑖𝑑 − 𝜃 𝑑
𝑖
𝑗, 𝑘, 𝑙 )
Comprehensive Learning Mechanism
Chemotaxis step size
𝑝𝑏𝑒𝑠𝑡𝑖𝑑 = 𝜃 ∗ 𝑝𝑏𝑒𝑠𝑡 𝑐𝑜𝑚𝑝𝑒𝑟 + 1 − 𝜃 ∗ 𝑝𝑏𝑒𝑠𝑡𝑖𝑑
𝑝𝑏𝑒𝑠𝑡𝑖𝑑 = 𝑏𝑖 ∗ 𝑝𝑏𝑒𝑠𝑡 𝑛 + 1 − 𝑏𝑖 𝑝𝑏𝑒𝑠𝑡 𝑚
𝑝𝑐
𝑖 = 𝜖 + 0.5 − 𝜖 ∗
𝑒 𝑡 𝑖−𝑒 𝑡1
𝑒 𝑡 𝑠−𝑒 𝑡1
𝜆 = 𝑐𝑒𝑖𝑙(𝑟𝑎𝑛𝑑 − 1 + 𝑝𝑐)
𝑡𝑖 =
5 𝑖 − 1
𝑆 − 1
, 𝑡1 = 0 𝑎𝑛𝑑 𝑡 𝑆 = 5

8. Description of VRPTW
8
min 𝑧 = Σ𝑖=0
𝑁
Σ𝑗=0
𝑁
Σ 𝑘=1
𝐾
𝐶 ∗ 𝑥𝑖𝑗𝑘 + Σ𝑖=1
𝑁
max{𝑒 ∗ 𝐸𝑇𝑖 − 𝑡𝑖 ; 0 ; 𝑓 ∗ 𝑡𝑖 − 𝐿𝑇𝑖 }
𝑤ℎ𝑒𝑟𝑒 ∶ 𝑡𝑖𝑗 = Σ𝑥𝑖𝑗𝑘 𝑡𝑖 +
𝑑𝑖𝑗
𝑣
+ 𝑠𝑖 (𝑡0 = 0, 𝑠0 = 0)
Σ𝑗=1
𝑁
Σ 𝑘=1
𝐾
𝑥𝑗𝑖𝑘 = Σ𝑗=1
𝑁
Σ 𝑘=1
𝐾
= 𝑘 (𝑖 = 0)
Σ𝑗=0
𝑁
Σ 𝑘=1
𝐾
𝑥𝑖𝑗𝑘 = 1 (𝑖 ∈ 𝑁)
Σ𝑖=0
𝑁
Σ 𝑘=1
𝑘
𝑥𝑖𝑗𝑘 = 1 (𝑖 ∈ 𝑁)
Σ𝑗=1
𝑁
𝑥𝑖𝑗𝑘 = Σ𝑗=1
𝑁
𝑥𝑗𝑖𝑘 = 1 (𝑖 = 0, 𝑘 ∈ 𝐾)
Σ𝑖=0
𝑁
Σ𝑗=0
𝑁
𝑥𝑖𝑗𝑘 ∗ 𝑔𝑖 ≤ 𝑞

9. ‫کد‬ ‫شبه‬Adaptive Comprehensive Learning
9
Begin
1: Initialize all the parameters and positions: S , c N , s N , re N , ed N , ed P ,C , c p , etc.
2: While (Terminate-condition is not met)
3: Evaluate fitness values of the initial population.
4: Figure out the gbest and the pbest of each bacterium
5: For (Elimination-dispersal loop)
6: For (Reproduction loop)
7: For (Chemotaxis loop)
8: Update the chemotaxis step size using Equation 3
9: Compute fitness function
10: Update the position using Equation 4
11: Boundary control(bacteria are not allowed to go out of bounds)

10. ‫کد‬ ‫شبه‬Adaptive Comprehensive Learning
10
12: Tumbleing, Swimming for s N steps
13: Update the gbest and the pbest
14: End For (Chemotaxis loop)
15: Compute the health values of each bacterium using Equation 2
16: Sort bacteria based on health values
17: Copy the best bacteria using health sorting approach
18: End For (Reproduction loop)
19: Eliminate and disperse each bacterium with probability ed P
20: End For (Elimination-dispersal loop)
21: EndWhile
22. End

11. ‫آزمون‬ ‫توابع‬ ‫امترهای‬‫ر‬‫پا‬
11
Functioni=1 Mathematical Representation X* F(X*) R
Sphere 𝑓1 𝑥 = Σ𝑖=1
𝑛
𝑥𝑖
2 [0, 0, …, 0] 0 [-100, 100]^n
Rosenbrock 𝑓2 𝑥 = Σ𝑖=1
𝑛
100 ∗ 𝑥𝑖+1 − 𝑥𝑖
2 2
+ (1 − 𝑥𝑖
2
) [0, 0, …, 0] 0 [-100. 100]^n
Rastrigin 𝑓3 𝑥 = Σ𝑖=1
𝑛
𝑥𝑖
2
− 10 cos 2𝜋𝑥𝑖 + 10 [0, 0, …, 0] 0 [5.12, 5.12]^n
Griewank
𝑓4 𝑥 =
1
4000
Σ𝑖=1
𝑛
𝑥𝑖
2
− ෑ
𝑖=1
𝑛
cos
𝑥𝑖
𝑖
+ 1
𝑓5 𝑥 = Σ𝑖=1
𝑛
(Σ 𝑘=0
𝑘max
𝑎 𝑘
cos 2𝜋𝑏 𝑘
𝑥𝑖 + 0.5 )
[0, 0, …, 0] 0 [-600, 600]^n
Weierstrass −𝐷Σ 𝑘=0
𝑘max
𝑎 𝑘
cos 2pib 𝑘
. 0.5 𝑎 = 0.5, 𝑏
= 3, 𝑘_ max = 20
[0, 0, …, 0] 0 [-0.5, 0.5]^n
Ackley
− exp
1
𝐷
Σ𝑖=1
𝐷
cos 2𝜋𝑥𝑖 + 20 + 𝑒
[0, 0, …, 0] 0 [-32, 32]^n

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17. ‫منابع‬
17
• [44] B. Niu, H. Wang, L.J. Tan, L. Li, J.W. Wang, Vehicle routing problem with time windows based on adaptive bacterial foraging optimization. Intell. Comput.
Theories Appl. Lect. Notes Comput. Sci., 7390(2012) 672–679.
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18. Thank You
Amir shokri
Amirsh.nll@gmail.com
Dr. Kourosh Kiani