1. Introduction to Evolutionary Algorithms Lecture 2
Jim Smith
University of the West of England, UK
May/June 2012

2. Overview Recap of EC metaphor Recap of basic behaviour
Role of fitness function
Dealing with constraints
Representation as key to problem solving
Integer Representations
Permutation Representations
Continuous Representations
Tree-based Representations

3. Recap of EC metaphor
A population of individuals exists in an environment with limited resources
Competition for those resources causes selection of those fitter individuals that are better adapted to the environment
These individuals act as seeds for the generation of new individuals through recombination and mutation
The new individuals have their fitness evaluated and compete (possibly also with parents) for survival.
Over time Natural selection causes a rise in the fitness of the population

4. General Scheme of EAs

5. Typical behaviour of an EA
Phases in optimising on a 1-dimensional fitness landscape
Early phase:
quasi-random population distribution
Mid-phase:
population arranged around/on hills
Late phase:
population concentrated on high hills

6. Typical run: progression of fitness
Best fitness in population
Time (number of generations)
Typical run of an EA shows so-called “anytime behavior”

7. Are long runs beneficial?
Best fitness in population
Time (number of generations)
Progress in 1st half
Progress in 2nd half
Answer:
- how much do you want the last bit of progress?
- it may be better to do more shorter runs

8. Evolutionary Algorithms in Context
There are many views on the use of EAs as robust problem solving tools.
For most problems a problem-specific tool may:
perform better than a generic search algorithm on most instances,
have limited utility,
not do well on all instances
Goal is to provide robust tools that provide:
evenly good performance
over a range of problems and instances

9. What are the different types of EAs
Historically different flavours of EAs have been associated with different representations
Binary strings : Genetic Algorithms
Real-valued vectors : Evolution Strategies
Finite state Machines: Evolutionary Programming
LISP trees: Genetic Programming
These differences are largely irrelevant, best strategy
choose representation to suit problem
choose variation operators to suit representation
Selection operators only use fitness and so are independent of representation

10. Role of fitness function
The more fitness levels you have available, the more information is potentially available to guide search
EAs can cope with fitness functions that are:
Noisy,
Time dependant,
Discontinuous
and have Multiple optima,

11. Problems with Constraints
“Constrained Optimisation Problems”
Some problems inherently have constraints as well a fitness functions
Can incorporate into fitness functions (indirect)
Can also incorporate into representation (direct)
Constraint Satisfaction Problems
Seek solution which meets set of constraints
Transform to COP by minimising constraints (indirect method),
Might be able to use good representations (direct)

12. Feasible & Unfeasible Regions
Space will be split into two disjoint sets of spaces:
F (the feasible regions) –may be connected
U (the unfeasible regions). S X U F n s

13. Methods for constraint handling
Direct
Indirect

14. Direct vs Indirect Handling
Indirect (Penalty Functions)
Direct
Conceptually simple, transparent
it works well
reduces problem to ‘simple’ optimization
except simply eliminating all infeasible solutions
Pros
allows user to tune to his/her preferences by weights
allows EA to tune fitness function by modifying weights during the search
problem independent
Cons
loss of info by packing everything in a single number
problem specific
said not to work well for sparse problems
no guidelines

15. Example: N Queens 64*63*62*61*60*59*58*56 solutions for N=8
Place N queens on a chess board so they cannot take each other
64*63*62*61*60*59*58*56 solutions for N=8
=64!/ (56! * 8!)
= 4.4 * 109

16. Designing an EA Fitness function: N – num_vulnerable_queens
Transforms CSP to COP
Population and Selection?
Whatever we like, e.g:
Population size100,
tournament selection of 2 parents
Replace two least fit from population if better
Representation?

17. Possible Representations
Method 1: Based on the board
64-bit Binary string: 0/1 empty /occupied
264 possibilities –more than problem!
Introduces extra constraint that only 8 cells occupied
Repair function or specialised operators?
Or fractional penalty function
Based on the pieces
More natural and problem focussed
Avoids extra constraint

18. Operators for binary representations
Recombination
One point, N-point
Uniform
Randomly choose parent 1 or 2 for each gene
Mutation
Independent flip 0 1 for each gene

19. Integer Representations
Label cells 1-64
Method 2: one gene per piece encodes cell
64N = for 1.7 x 1014 for N=8 (potential duplicates)
1pt crossover, extended random mutation
Ok, but huge space with only 9 fitness levels
Could make think about constraints
Rows, columns, diagonals
Indirect – penalise all
Direct – can we avoid some?

20. Integer representations
Some problems naturally have integer variables, e.g. image processing parameters
Others take categorical values from a fixed set e.g. {blue, green, yellow, pink}
N-point / uniform crossover operators work
Extend bit-flipping mutation to make
“creep” i.e. more likely to move to similar value
Random choice (esp. categorical variables)
For ordinal problems, it is hard to know correct range for creep, so often use two mutation operators in tandem

21. Partially direct representations
Method 3
Row constraint <=> each queen on different row
Let value off gene I = column of queen in row I
Solution space size 8N = 1.67x107
One point crossover, extended randomised mutation
Method 4
As above but also meet column constraints
Permutation: N! = 40320
Now need specialised crossover and mutation

22. Permutation Representations
Ordering/sequencing problems form a special type.
Solution= arrangement objects in a certain order.
Example: sort algorithm: important thing is which elements occur before others (order),
Example: Travelling Salesman Problem (TSP) : important thing is which elements occur next to each other (adjacency),
These problems are generally expressed as a permutation:
if there are n variables then the representation is as a list of n integers, each of which occurs exactly once

23. Variation operators for permutations
Normal mutation operators don’t work:
e.g. bit-wise mutation : let gene i have value j
changing to some other value k would mean that k occurred twice and j no longer occurred
Therefore must change at least two values
Various mechanisms exist (swap, invert, ...).
Similar arguments mean specialised crossovers are needed.

24. Example mutation operators

25. Crossover operators for permutations
“Normal” crossover operators will often lead to inadmissible solutions
Many specialised operators have been devised which focus on combining order or adjacency information from the two parents

26. Another Example of Binary Encoding: Feature Selection for Machine Learning
Many successful Machine Learning / Data Mining algorithms use greedy search:
Decision trees add most informative nodes
Rule Induction: add most useful next rule
Bayesian networks: to identify co-related features
Distance-based methods measure difference along each axis
All these can be improved by using global search in the feature selection process
Use a binary coded GA: 0/1 : use/don’t use feature
M. Tahir and J.E. Smith. Creating Diverse Nearest Neighbour Ensembles using Simultaneous Metaheuristic Feature Selection Pattern Recognition Letters, 31(11):
Smith, M. & Bull, L. (2005) Genetic Programming with a Genetic Algorithm for Feature Construction and Selection. Genetic Programming and Evolvable Machines 6(3):

27. Schemata for Feature Selection
Binary string representing choice of features
Full Data Set
Reduced Data Set
Machine Learning Algorithm builds and evaluates model on reduced data
Fitness = accuracy EA

28. Example of Integer Encoding
Protein Structure Prediction:
Proteins are created as strings of amino acid “residues”
Behaviour of a protein is determined by its 3-D structure
Proteins naturally “fold” to lowest energy structure
Model as a fixed-length path through a 3D grid
Representation: sequence of “up/down/L/R/forward” to specify a path
Fitness based on pairwise interactions between residues
N. Krasnogor and W. Hart and J.E. Smith and D. Pelta . Protein Structure Prediction With Evolutionary Algorithms. Proc. GECCO 1999 , pages Morgan Kaufmann.
R. Santana, P. Larrañaga, and J. A. Lozano. Protein folding in simplified models with  estimation of distribution algorithms.   IEEE Transactions on Evolutionary Computation. Vol. 12. No. 4. Pp  

29. Example of 2D HP model Dark boxes represent hydrophobic residues (H):
H-H contacts add +1 to fitness

30. Example 2: Microprocessor Design Verification
Need to “drive” processor into a variety of states
to make sure it does the right thing in each.
Test = sequence of assembly code instructions
Traditional methods generate millions of random tests, weren’t reaching all states
UWE solution: evolve sequences of tests
Integer encoding (fixed number of instructions)
Specialised mutation: group instruction in classes,
more likely to move to similar type of instruction
J.E. Smith and M. Bartley and T.C. Fogarty. Microprocessor Design Verification by Two-Phase Evolution of Variable Length Tests. Proc IEEE Conference on Evolutionary Computation, pages IEEE Press

31. Summary
Fitness function should provide as much information as possible
Could penalise infeasible solutions
Selection / Population management is independent of representation
Representation should suit the problem
Can take constraints into account (direct)
Recombination/Mutation defined by representation
Could be problem specific (direct constraint handling)