1. Evolutionary Computation: Advanced Algorithms and Operators
Chapter 1-6
Jang, HaYoung
March 28, 2011

2. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

3. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

4. Fitness Evaluation Optimization problem as follows:
Fitness evaluation function as follows:
In binary coding,

5. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

6. Binary Strings
N object variables x = (x1, x2, …, xn) into a binary string
Decoding scheme
Decoding function linearly maps the decoded integer value of the binary substring in the desired interval [ui, vi)

7. Gray Coded Strings Encoding binary string into Gray code
Decoding Gray code into binary string

8. Messy Coding
Gene position and the corresponding bit values are coded in a string

9. Floating Point Coding
Mantissa and exponent of a floating-point parameter
Decoding

10. Coding for … Binary Variables Permutation problems Control problems
Presence or absence
Permutation problems
TSP
Control problems
Time or frequency dependent function of some control variables

11. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

12. Competitive Fitness Evaluation
Objective Fitness
Is ‘absolute objective’ or complete ordering is always possible?
Relative Fitness
Direct comparison to some other solution either evolved or provided as a component of the environment
Competitive Fitness
Sensitive to the contents of the population

13. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

14. Model Selection Criteria
Minimal description length criterion
Tradeoff between residual error
Model complexity including a structure estimation term for the final model
Number of bits necessary to encode the observations
Number of bits needed to encode the parameters of the model

15. Model Selection Criteria
Akaike information criterion
Approximation of the idealized Kullback-Leibler distance between the true data and the model
Minimum message length
Inferred estimates of the unknown parameters
Data using an optimal code based on the data probability distribution

16. Minimum Descirption Legnth based Fitness Evaluation for Genetic Programming
Six multiplexor problem

17. Minimum Descirption Legnth based Fitness Evaluation for Genetic Programming

18. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

19. Contents Introduction to fitness evaluation
Encoding and decoding functions
Competitive fitness evaluation
Complexity-based fitness evaluation
Multiobjective optimization
Introduction to constraint-handling techniques

20. Search Space and Feasible and Infeasible Parts

21. Constraint Handling Techniques
Penalize infeasible individiuals
Change the topology of the search space
Repair infeasible solution
Start with an initial population of feasible individuals
Process solutions and constraints separately
Locate feasible solutions