1. A Tutorial (Complete) Yiming
Evolution Strategies
A Tutorial (Complete)
Yiming

2. Objectives For newly-coming students Get familiar with EC techniques
For senior students
Get inspired with some design principles in ES
For myself
Learn from all of audiences

3. Outline
Where
What
How
When/Why

4. Where
All fields of optimisation including continuous, discrete, combinatorial, with or without constraints
The objective function, i.e., f(y), can be represented in mathematical form, via simulations, or even in terms of measurements obtained from real objects.

5. Examples
…and more….

6. When

7. What A search paradigm Inspired by biological evolution
General EC algorithm

8. Mating Selection (fitness-independent
Main principles of ES
Mating Selection (fitness-independent
or fitness-based)
Recombination
Mutation
and Parameter control
Survivor Selection

9. ES Main Features Representation Real-valued vectors Recombination
Discrete, Intermediate, Weighted
Mutation
Gaussian Pertubation
Mating Selection
Fitness independent, Fitness-based
Survivor Selection
+ or ,
Special Feature
Parameter Control

10. Notations —Number of parents
—Number of parents are used for recombination
—Number of offspring
—“plus” selection selects the best of individuals without considering their ages
— “comma” selection selects the youngest individuals, parents die out
In this case of using comma selection , must hold.

11. Two Algorithm Templates

12. Recombination
Recombination combines information from several parents to generate a single new offspring
Discrete (Dominant)
Uniform select one parent to inherit values
Intermediate
Average values of values from all selected parents
Weighted
Weighted average of values from all selected parents
Others
One-point and two-point crossover, etc.
Note: ES allows multi-combination ( rho > 2)

13. Mutation
Mutation introduces (“small”) variations by adding a point symmetric perturbation to the result of recombination.
The perturbation is drawn from a multivariate normal distribution, We have
Spherical/isotropic (Uncorrelated)
with step size
Axis-parallel (Uncorrelated)
General (Correlated)

14. Mutation

15. Parameter Control The key of ES
Goal: drive the endogenous strategy parameters (e.g., step-size) close to their optimal values.

16. (1+1)-ES with 1/5th Success Rule

17. (1+1)-ES with 1/5th Success Rule

18. Sigma is IMPORTANT
Principle: Increasing it when the successful rate is high, decreasing it when the successful rate is low.
Other ways to adapt it via evolution
Self-adaptation
Derandomized Self-adaptation
Non-local derandomized step-size control

20. Address Dependencies
CMA-ES

21. Natural Evolutionary Strategy

22. Examples
1+1 ES (1/5 rules)
u+u ES
NES

23. Rastrigin Function

24. u+u ES

25. CMA-ES

26. NES

27. Travelling Salesman Problem

28. How do you solve the TSP problem?

29. Some possible ways Mathematical Programming - Google OR-tools
Memetic algorithms
Lin, S. (1965). Computer solutions of the traveling salesman problem. The Bell system technical journal, 44(10),
Ant colony algorithms
Simulated Annealing

30. Genetic Algorithms
Many can be found, I also implemented one.
Neural Networks
tsp/
And many more

31. Can this optimisation problem be solved by learning?

32. What about Deep Learning?

33. Some possible ways Deep Supervised learning ?
Deep Reinforcement learning
pytorch
et-salesman/

34. Skynet Salesman

35. CNN plays a game

36. Skynet Salesman

37. Can we expand this idea to other combinatorial optimisation problems?