Zorica StanimirovićFaculty of Mathematics, University of Belgrade

zoricast@matf.bg.ac.rs

offspring-chromosomes decoding

EvaluationFitness

calculation

Variation operators (crossover, mutation, inversion, deletion,…).

Selection

operator

Population(chromosomes)

parent-chromosomes

Basic GA scheme

Types of encoding

Vectors: • usually of fixed length• usually implemented as arrays or lists• often represented as n-tuples of binary, integer or real values

Trees:• size usually not fixed• usually implemented as lists, or list-based structures• often represent symbolic expressions (for example, formulae)

Other types:• matrices, generalized graphs, etc.• hybrid representations may also be used (for example, binary vector + matrix)

Example: Tree structure encoding

0.48*Z1 + (Z2 – 0.56)

(1.1-Z1 )+ (Z2 – 0.56)

Individuals (mathematical equations) are represented as treesThe branching nodes of the tree correspond to functions(operators)The end-nodes(leaves) of the tree correspond to input data

Equation modeling:

f= number of incorrect properties such as: no coffee contained, no milk contained, no foam

on the top,…

GA population

• GA works over the population of individuals, usually numbering 10-200 • Each individual is represented by a genetic code (chromosome) ,

which corresponds to one solution of the problem

• Initial population is usually randomly generated

• A fitness value is assigned to each individual, measuring its quality

• Individuals in the population then pass through the process of “simulated evolution”

• Genetic operators are iteratively applied and the sequence of GA generations is created until certain stopping criterion is satisfied

Selection operator

• As in nature, the selection operator provides necessary mechanism for better individuals to survive

• The probability that a individual will take part in producing offspring individual(s) depends on its fitness

• The higher fitness value of an individual provides higher chances for its survival and reproduction

• There are different ways for the selection of best fitted individuals: roulette selection, rang-based selection, tournament selection,fine-grained tournament selection, etc.

Variation = Crossover + Mutation

• Selected individuals are subject to Variation operators

• Usually, two types of variation operators are used:

Crossover

Mutation

But, keep in mind that:

The choice of variation operators depends on the problem under consideration and the chosen encoding of individuals

However,

There are some operators that are applicable to wider set of problems and tailored to standard encodings, such as vectors, trees,…

Various stopping criteria may be used for forcing the GA to finish its run• maximal number of GA generations

• high similarity of individuals in the population

• the best individual is repeated maximal times

• GA has reached global optimum or the best GA solution is good enough (according to some criterion)

• limited time of the GA run….

But:

the combination of two or more stopping criteria gives the best results in practice...

1. Generation GA: all individuals from the population are replaced in each GA generation

2. Stationary GA: only one part of the population is replaced in each generation

3. Elitistic GA: elite individuals are directly passing in the next genaration, while the remaining individuals are replaced

Most used: stationary GA with elitist strategy

• GA implementation has numerous parameters:

selection, crossover, mutation rates, population size, stopping criteria parameters ….

• There is NO unique combination of GA parameters that guarantees successful GA implementation for all problems

• Parameter values may be fixed in advance or they can change during the GA run

- fixed parameter change

- adaptive parameter change

Hybridization: general considerations

Idea: to combine a general search strategy such as GA with a problem specific heuristic or exact method

Some examples:

Evolutionary approach + Local search = Memetic algorithm

Evolutionary approach + Variable Neighborhood Search

Evolutionary approach + Tabu Search

Evolutionary approach + Linear programming method= Matheuristics

Questions?