1. Real-valued Optimization Algorithms
Peng Chun-Jen Taiwan Evolutionary Intelligence Laboratory 2017/05/15 Group Meeting Presentation

2. Outline Covariance Matrix Adaptation Evolution Strategy
Standard Particle Swarm Optimization
Ant Colony Optimization on Real Domain
Progress Report

3. CMA-ES
Covariance Matrix Adaptation Evolution Strategy

4. CMA-ES
Sampling

5. CMA-ES
Covariance

6. CMA-ES
Covariance Matrix Adaptation Evolution Strategy

7. SPSO 2011 Standard Particle Swarm Optimization
SPSO2006, SPSO2007, SPSO2011
Not intend to be the best on the market
Common ground for future comparison

8. SPSO 2011 Components Update position & fitness position velocity
previous best position & fitness
Best of previous best in neighborhood position & fitness
Update

9. SPSO 2011 Update Update velocity Update position
Update previous best and best of previous best

10. SPSO 2006 and 2007
Update
Update velocity

11. SPSO 2006 and 2007

12. SPSO 2006 and 2007
Update

13. SPSO 2011
Update
Update velocity
SPSO 2006
SPSO 2011

14. SPSO 2011
Construct a hypersphere s.t. velocity update does not depend on system coordinates
𝒙 𝒊 ′ ∈

15. SPSO vs. SPSO2006
𝒙 𝒊 ′ ∈

16. PSO topologies

17. SPSO 2011
Random topology (K = 3)
Stochastic Star

18. SPSO 2011
Standard Particle Swarm Optimization

19. ACOR
Ant Colony Optimization

20. ACOR
Solution Construction
Pheromone Update

21. ACOR
Ant Colony Optimization for Continuous Domain

22. ACOR
Ant Colony Optimization for Continuous Domain

23. ACOR
Solution archive

24. ACOR
Solution archive

25. ACOR
Solution archive

26. Progress Report Where to focus? Decide number of clusters
max( 50 *dim, n_points * max_n_clusters)
Decide number of clusters
K-Means & silhouette score

27. Bandit Initialization
Break down multi model search space
Magnify possible regions

28. Multi-armed bandit Bandit: Arm: Concern ranks, and f_left
Transformation + Algorithm

29. Multi-armed bandit Bandit Arm1 Algo1 Linear Transformation by Matrix
Nonlinear Transformation by Neurons

30. Bandit Initialization
Initial population
max( 50 *dim, n_points * max_n_clusters)
Decide number of clusters
K-Means & silhouette score

31. Bandit Initialization
Initial Transformation Matrix
Sample 50 * dimension points from each arm
Update matrix with gradient descent

32. Bandit Initialization
Uniform distribution vs. Beta distribution
Overlapped detection

33. Bandit Initialization
Initial Transformation Matrix
Transformation
Update matrix with gradient descent

34. Affine Transformation

35. Projection Transformation

36. Bandit Initialization
The new bandit technique
What should we do if optimum is not in border?

37. Bandit Initialization
Recluster criteria
Translate borders
Recluster

38. Problems What is a educated guess for initial population
Better idea for collision detection in high dimension
How to design loss function for simple optimizers
Projection matrix => nonlinear neurons
Original data for SPSO2011 on CEC2005 benchmarks

39. Reference
Socha, K., & Dorigo, M. (2008). Ant colony optimization for continuous domains. European journal of operational research, 185(3),
Clerc, M. (2007). Back to random topology. Relatório Técnico, mar.
Hansen, N. (2006). The CMA evolution strategy: a comparing review. Towards a new evolutionary computation,