The document discusses a modified brainstorming optimization algorithm that emphasizes generating a large quantity of ideas and clustering them using a k-means approach. It details the process of selecting, merging, and evaluating ideas to arrive at optimal solutions, highlighting the advantages and disadvantages of different strategies used. Experimental studies indicate that the modified method outperforms traditional approaches, particularly in its adaptability to environmental noise.

1. Modified Brain Storm Optimization
David Kuo

2. Osborn’s Original Rule
Suspend Judgment
There is no idea as bad idea.
1
Anything goes
Anything coming to your mind during process is an idea.
2
Cross-fertilize
Lots of ideas can and should be based on existed ideas.
3
Go for Quantity
It is necessary to generate as many ideas as possible.
4

3. Brain Storm Process
Generate ideas
(generate operation)
Cluster ideas
(cluster operation)
Select & Merge
ideas
Evaluate
cons & pros
Get good ideas
Hopefully to obtain a good
solution

4. Brain Storm Algorithm
1. Generate n potential solution (individuals)
2. Cluster n individuals into k clusters using k-means algorithm.
3. Evaluate the n individuals.
4. Rank individuals in each other cluster and record the best one as cluster center.
5. Select a cluster center or generate a individual to replace it (P5).
6. Generate new individuals from one or more (P6b) clusters:
a) Choose one cluster (P6ai) and choose cluster center or not (P6biii).
b) Choose more than one clusters and choose cluster center or not (P6c).
7. If n new individuals have been generated, go to step8, otherwise go back to step6.
8. Terminate if reached target, otherwise go back step2.

5. Generate new individual
Formula:
𝑋 𝑛𝑒𝑤 = 𝑋𝑠𝑒𝑙𝑒𝑐𝑡 +𝜉 ∗ 𝑛(𝜇, 𝜎)
𝜉 = 𝑙𝑜𝑔𝑠𝑖𝑔( 0.5 ∗ max_iteration − current_iternation) 𝑘 𝑥𝑖 ∗ 𝑟𝑎𝑛𝑑()
Weight
Gaussian Function
Logsig(n) is “Logarithmic sigmoid transfer function”

6. Experiments

7. Experiments

8. Modified Brain Strom Optimization
Using Simple Grouping replaced k-means1
Idea difference Strategy2

9. Simple Grouping Method
1. Randomly select M different ideas from current generation as the seeds of the M
groups and denoted as S𝑗 (1 ≤ j ≤ M)
2. For each ideas 𝑋𝑖(1 ≤ 𝑖 ≤ 𝑁) in the current generation, calculate its distance to each
group j as:
3. Compare all the M distance values and assign the idea 𝑋𝑖 into the nearest group,
but 𝑆𝑗unchanged.
4. Go to step2 for the next idea, otherwise all ideas have been assigned.
𝑑𝑖𝑗 = 𝑋𝑖, 𝑆𝑗 = (
𝑑=1
𝐷
(𝑋𝑖𝑑 − 𝑆𝑖𝑑)2)/𝐷

10. Idea Different Strategy
𝜉 𝑜𝑟𝑖𝑔𝑖𝑛 = 𝑙𝑜𝑔𝑠𝑖𝑔( 0.5 ∗ max_iteration − current_iternation) 𝑘 𝑥𝑖 ∗ 𝑟𝑎𝑛𝑑()
• In every generation, we use this FIXED value function.
No any feedback information from search process, we may not catch the search
characteristics.
• Commonly intuition
Noise is larger in early evolutionary phase and gradually become smaller during running
by the control of the logsig function.

11. Idea Different Strategy (cond)
𝜉 𝑜𝑟𝑖𝑔𝑖𝑛 = 𝑙𝑜𝑔𝑠𝑖𝑔( 0.5 ∗ max_iteration − current_iternation) 𝑘 𝑥𝑖 ∗ 𝑟𝑎𝑛𝑑()
• Range
1. Logsig function return value (0,1) and ξ is also in (0,1).
2. The value ξ multiplies Gaussian random value(μ=0,σ=1) is with high probability within
the range (-4,4).
𝑋 𝑛𝑒𝑤 = 𝑋𝑠𝑒𝑙𝑒𝑐𝑡 +𝜉 ∗ 𝑛(𝜇, 𝜎)

12. Idea Different Strategy (cond)
How to improve this operator?

13. Idea Different Strategy (cond)
𝑋 𝑛𝑒𝑤_d =
𝑟𝑎𝑛𝑑𝑜𝑚 𝐿 𝑑, 𝐻 𝑑 , 𝑖𝑓 𝑟𝑎𝑛𝑑𝑜𝑚 0,1 < 𝑝 𝑟
𝑋 𝑜𝑟𝑖_𝑑 + 𝑟𝑎𝑛𝑑𝑜𝑚 0,1 ∗ 𝑋 𝑎𝑑 − 𝑋 𝑏𝑑 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Discuss from two distinct ideas from all current
ideas.
Based on existed idea.
Find a new idea. Control new ideas created.
• Parameters setting
1. Experiments indicate that the value of 𝑝 𝑟 within [0.001,0.01] would be good.
2. In this paper, we choose 𝑝 𝑟=0.005.

14. Experimental Studies
300000 generations
30 times for each function.
Algorithms configurations

15. Experimental Studies
• MBSO is better than BSO.
This may be due to IDS can match the environment to provide
suitable noise.

16. Experimental Studies

17. Experimental Studies
• How to set 𝑝 𝑟?
a) Unimodal function
1. To observe this figure, we can find 𝑝 𝑟 is smaller, solution accuracy is more higher.
b) Multimodal function
1. Too much lower or higher is harmful for algorithm performance.
2. The results indicate that a 𝑝 𝑟 within [0.001,0.01].

18. Conclusion
Simple Grouping Method
• Advantages:
1. Simple to implement.
2. Lower computational burden.
• Disadvantages:
1. Can’t identify different peeks in multimodal function.
Idea Different Strategy
• Advantages:
1. Lower computation burden.
2. Should match environment of the evolutionary process.
• Disadvantages:
1. Can’t identify different peeks in multimodal function.
• MBSO using SGM and IDS has higher performance than BSO.

19. Question?