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Bacterial Foraging Optimization Amir Shokri Amirsh.nll@gmail.com Dr. Kourosh Kiani

SLIDE 1

Amir Shokri

متیروگلا رد نآ دربراک و هیلقن لیاسو یبایریسم هلئسم رد یریگدای عماج یزاس هنیهب Bacterial Foraging Optimization

Amirsh.nll@gmail.com

Dr. Kourosh Kiani

SLIDE 2

همدقم

متیروگلا زا یعون هلاقم نیا رد BFO ابریگدای یزاس هنیهب ار نآ ام هک عماج یریگدای یژتارتسا و سیسکاتومک فلتخم هلحرم لوط ی ییایرتکاب عماج ییایرتکاب ALCBFO یمدهد یم هئارا ، میمان. کیفتسا یداهنشیپ متیروگلا زا یرادرب هرهب و فاشتکا نیب یبوخ لداعت ظفح یارب یقیبطت شهاک یطخ ریغ لیدعت لدمدوش یم هدا . مسیناکمدهد یم شهاک ار سردوز ییارگمه نیاربانب و دنک یم ظفح ار اه یرتکاب تیعمج عونت ، عماج یریگدای .

SLIDE 3

همدقم

رد کیسلبک متیروگلا اب هسیاقم GA ، PSO ، BFO یلصا هتفای دوبهب ود و BFO (BFO-LDC و BFO-NDC) ، ACLBFO هدش هئارا دهد یم ناشن هتلاح دنچ تلبکشم لح رد رتهب یهجوت لباق درکلمع. ام شور درکلمع نینچمه ACLBFO ار زودنیو نامز اب هیلقن لیاسو یبایریسم هلئسم رد VRPTW یبایزرامینک یم . رد متیروگلا هس اب هسیاقم BFO رگیدیلقن لیاسو یبایریسم هلئسم لح یارب ار نآ لیسناتپ و تسا رترب یداهنشیپ متیروگلا ، نامز اب ه زودنیو VRPTW دییأتدنک یم.

SLIDE 4

راک عورش

دنمشوه یزاس هنیهب یاه متیروگلا Swarm کیژولویب متسیس رد یعامتجا یاهراتفر زا یشان کرحم تابساحم زا دیدج یعون ناونع هب ی تسا هدرک بلج دوخ هب ار یرایسب نادنمشناد. هنیهب تارذ یزاس PSO ، و یدنک طسوت هدش داهنشیپ ،تراهرباتسا هدش کیرحت یهام شزومآ ای ناگدنرپ یاه هلگ ماحدزا راتفر اب . متیروگلا یهام ماحدزایعونصم AFSA تسا هتفرگ همشچرس یهام مطلبتم راتفر رد . هنیهب اه هچروم ینولک یزاس زا ACO راتفردش هداد هزیگنا اه هچروم یا هفولع . یاهروبنز ینولک متیروگلا یعونصم ABCA زا تسا هدش هتفرگ ماهلا اهروبنز یعامتجا یصصخت راتفر . اهنیایم هرهب ، دننک یم لماعت دوخ طیحم و رگیدکی اب یلحم دارفا هک یناهج راتفر زا هک دنتسه تیعمج رب ینتبم یاه کینکتدنریگ.

SLIDE 5

Bacterial Foraging Optimization

ییایرتکاب ییایرتکاب یزاس هنیهب متیروگلا BFO کی یاهیرتکاب یعامتجا هفولع راتفر زا هک تسا یلماکت یزاس هنیهب دیدج شور E. coli دنک یم دیلقت. اب یا هفولع یاهراتفر یساسا کیزیف و یسانش تسیز هب هجوت

E. coli

، Passino و Liu زا و ییایرتکاب یرگشاخرپ یاهراتفر عاونا لرتنک متسیس یگنوگچ دروم رد ، دنا هدرک هدافتساءوس یعامتجا یاهراتفر

E. coli دینک هدافتسا ییاذغ یاه همانرب یارجا رگنایب .

دنیارفدنکارپ و فذح و لثم دیلوت ، ماحدزا ، یسکاتومک ینعی ، درک میسقت شخب راهچ هب ناوت یم ار اه یرتکاب یزاس هفولعیگ.

SLIDE 6

Bacterial Foraging Optimization

𝜄𝑗 𝑘 + 1, 𝑙, 𝑚 = 𝜄𝑗 𝑘, 𝑙, 𝑚 + 𝐷 𝑗 Δ 𝑗 \√Δ𝑈 𝑗 Δ(i) 𝐾ℎ𝑓𝑏𝑚𝑢ℎ

𝑗

= Σ𝑘=1

𝑂𝑑 𝐾(𝑗, 𝑘, 𝑙, 𝑚)

Rep eproduction Chemotaxis

SLIDE 7

Adaptive Comprehensive Learning Bacterial Foraging Optimization

𝐷

𝑘 = 𝐷_ min + exp −𝑏 ∗

𝑙 𝑂𝑠𝑓

𝑜

∗ (𝐷_ max −𝐷_ min) 𝜄𝑒

𝑗 𝑘 + 1, 𝑙, 𝑚 = 𝜄𝑒 𝑗 + 𝐷 𝑗 Δ i

√Δ𝑈 𝑗 Δ(i) + 𝜇 ∗ 𝑠

1 ∗ 𝑞𝑐𝑓𝑡𝑢𝑗𝑒 − \tetha𝑒 𝑗 𝑘, 𝑙, 𝑚

+ 1 − 𝜇 ∗ 𝑠2 ∗ (𝑕𝑐𝑓𝑡𝑢𝑗𝑒 − 𝜄𝑒

𝑗 𝑘, 𝑙, 𝑚 )

Comprehensiv ive Le Learnin ing Mec echanism Chemotaxis step size 𝑞𝑐𝑓𝑡𝑢𝑗𝑒 = 𝜄 ∗ 𝑞𝑐𝑓𝑡𝑢𝑑𝑝𝑛𝑞𝑓𝑠 + 1 − 𝜄 ∗ 𝑞𝑐𝑓𝑡𝑢𝑗𝑒 𝑞𝑐𝑓𝑡𝑢𝑗𝑒 = 𝑐𝑗 ∗ 𝑞𝑐𝑓𝑡𝑢𝑜 + 1 − 𝑐𝑗 𝑞𝑐𝑓𝑡𝑢𝑛 𝑞𝑑

𝑗 = 𝜗 + 0.5 − 𝜗 ∗ 𝑓𝑢𝑗−𝑓𝑢1 𝑓𝑢𝑡−𝑓𝑢1

𝜇 = 𝑑𝑓𝑗𝑚(𝑠𝑏𝑜𝑒 − 1 + 𝑞𝑑) 𝑢𝑗 = 5 𝑗 − 1 𝑇 − 1 , 𝑢1 = 0 𝑏𝑜𝑒 𝑢𝑇 = 5

SLIDE 8

Description of VRPTW

min 𝑨 = Σ𝑗=0

𝑂

Σ𝑘=0

𝑂 Σ𝑙=1 𝐿

𝐷 ∗ 𝑦𝑗𝑘𝑙 + Σ𝑗=1

𝑂 max{𝑓 ∗ 𝐹𝑈𝑗 − 𝑢𝑗 ; 0 ; 𝑔 ∗ 𝑢𝑗 − 𝑀𝑈𝑗 }

𝑥ℎ𝑓𝑠𝑓 ∶ 𝑢𝑗𝑘 = Σ𝑦𝑗𝑘𝑙 𝑢𝑗 + 𝑒𝑗𝑘 𝑤 + 𝑡𝑗 (𝑢0 = 0, 𝑡0 = 0) Σ𝑘=1

𝑂

Σ𝑙=1

𝐿

𝑦𝑘𝑗𝑙 = Σ𝑘=1

𝑂 Σ𝑙=1 𝐿

= 𝑙 (𝑗 = 0) Σ𝑘=0

𝑂 Σ𝑙=1 𝐿

𝑦𝑗𝑘𝑙 = 1 (𝑗 ∈ 𝑂) Σ𝑗=0

𝑂 Σ𝑙=1 𝑙

𝑦𝑗𝑘𝑙 = 1 (𝑗 ∈ 𝑂) Σ𝑘=1

𝑂 𝑦𝑗𝑘𝑙 = Σ𝑘=1 𝑂 𝑦𝑘𝑗𝑙 = 1

(𝑗 = 0, 𝑙 ∈ 𝐿) Σ𝑗=0

𝑂 Σ𝑘=0 𝑂 𝑦𝑗𝑘𝑙 ∗ 𝑕𝑗 ≤ 𝑟

SLIDE 9

دک هبش Adaptive Comprehensive Learning

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)

SLIDE 10

دک هبش Adaptive Comprehensive Learning

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: End While

22. End

SLIDE 11

نومزآ عباوت یاهرتماراپ

Functioni=1 Mathematical Representation X* F(X*) R Sphere 𝑔

1 𝑦 = Σ𝑗=1 𝑜 𝑦𝑗 2

[0, 0, …, 0] [-100, 100]^n Rosenbrock 𝑔

2 𝑦 = Σ𝑗=1 𝑜 100 ∗ 𝑦𝑗+1 − 𝑦𝑗 2 2 + (1 − 𝑦𝑗 2)

[0, 0, …, 0] [-100. 100]^n Rastrigin 𝑔

3 𝑦 = Σ𝑗=1 𝑜 𝑦𝑗 2 − 10 cos 2𝜌𝑦𝑗 + 10

[0, 0, …, 0] [5.12, 5.12]^n Griewank 𝑔

4 𝑦 =

1 4000 Σ𝑗=1

𝑜 𝑦𝑗 2 − ෑ 𝑗=1 𝑜

cos 𝑦𝑗 𝑗 + 1 𝑔

5 𝑦 = Σ𝑗=1 𝑜 (Σ𝑙=0 𝑙max

𝑏𝑙 cos 2𝜌𝑐𝑙 𝑦𝑗 + 0.5 ) [0, 0, …, 0] [-600, 600]^n Weierstrass −𝐸Σ𝑙=0

𝑙max

𝑏𝑙 cos 2\pib𝑙. 0.5 𝑏 = 0.5, 𝑐 = 3, 𝑙_ max = 20 [0, 0, …, 0] [-0.5, 0.5]^n Ackley − exp 1 𝐸 Σ𝑗=1

𝐸

cos 2𝜌𝑦𝑗 + 20 + 𝑓 [0, 0, …, 0] [-32, 32]^n

SLIDE 12

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SLIDE 18

Thank You

Amir shokri Amirsh.nll@gmail.com

Dr. Kourosh Kiani