Tutorial on Brain Storm Optimization

Tutorial on Brain Storm Optimization Junfeng Chen

Shi Cheng

Hohai University

Shaanxi Normal University

[email protected]

[email protected]

Yuhui Shi Southern University of Science and Technology [email protected]

06/02/2018

Outline 1.

Brainstorming Process

2.

BSO Algorithm

3.

Numerical Experiments

4.

Codes in MATLAB

5.

References

1. Brainstorming Process

1. Brainstorming Process

•Facilitator •Group of people •Problem owners

1. Brainstorming Process Osborn’s Original Rules for Idea Generation in a Brainstorming Process

Rule 1: Rule 2: Rule 3: Rule 4:

The more ideas, the better Withhold criticism for any idea Welcome unusual ideas Combine and improve ideas

1. Brainstorming Process

2. Brain Storm Optimization (BSO) Brain Storm Optimization (BSO) is a new swarm intelligence, which mimics the human brainstorming process. Clustering

Partition N ideas into M clusters.

Replacing

replace a random center with a new random idea.

Creating

produces new ideas in four patterns by using the Gaussian random strategy.

Selecting

Select those promising solutions into the next generation.

2. Brain Storm Optimization (BSO) Pseudo-code of BSO

Clustering

Replacing

2. Brain Storm Optimization (BSO)

Creating

Selecting

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2.1 Clustering Pseudo-code of k-means clustering Input: n points, distance function d(), number of clusters k. STEP NAME (1) Start with k centers (2) Compute d (each point x, each center c) (3) For each x, find closest center c(x)

“ALLOCATE”

(4) If no point has changed “owner” c(x), stop (5) Each c  mean of points owned by it (6) Repeat from 2

“LOCATE”

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2.1 Clustering K-means Clustering

Second Dimensional Value

5 The potential flaws of BSO

2.5

x9

x7 x x81

0

x4 -2.5

x5

x6 x10

-5 -5

x3 x 2 -2.5 0 2.5 First Dimensional Value

5

2.2 Replacing Replacing Operator

Second Dimensional Value

5

The potential flaws of BSO

2.5

xr

0

x9

x7 x x81

x4 -2.5

x5

x6 x10

-5 -5

x3 x 2 -2.5 0 2.5 First Dimensional Value

5

2.2 Replacing Peaks 0 Best -1

Fitness Values

-2

-3

-4

-5

-6

-7 0

20

40

60

80

100

120

Iterations

140

160

180

200

2.3 Creating Basic Creating

(A)

(B)

2.3 Creating Basic Creating

(C)

(D)

2.3 Creating The creating formulas for generating new candidate solutions are given as follows.

xnew  xold    G   ,  

xold

 x  d d 1  xi  2  x j d i

one cluster two clusters

 0.5  Itermax  Itercur   log sig  K 

   rand   

2.4 Selecting

(a)

competing selection

2.4 Selecting

(b) elites selection

2.4 Selecting

(c) proportional selection

3. Numerical Experiments Benchmark function

4. Codes

See Codes in MATLAB for Brain Storm Optimization

5. References 1.

2. 3.

4.

Shi, Y.: An optimization algorithm based on brainstorming process. International Journal of Swarm Intelligence Research (IJSIR) 2(4), 35–62 (2011) Cheng, S., Qin, Q., Chen, J., Shi, Y.: Brain storm optimization algorithm: A review. Artificial Intelligence Review 46(4), 445–458 (2016) Chen, J., Cheng, S., Chen, Y., Xie, Y., Shi, Y.: Enhanced brain storm optimization algorithm for wireless sensor networks deployment. In: Proceedings of 6th International Conference on Swarm Intelligence (ICSI 2015). pp. 373–381. Chen, J., Wang, J., Cheng, S., Shi, Y.: Brain storm optimization with agglomerative hierarchical clustering analysis. In: Proceedings of 7th International Conference on Swarm Intelligence (ICSI 2016). pp. 115–122.

Thank you!