Evolutionary Computation

Transcription

1 Evolutionary Computation Evolution and Intelligent Besides learning ability, intelligence can also be defined as the capability of a system to adapt its behaviour to ever changing environment. Evolutionary computation simulates evolution on a computer. The result of such a simulation is a series of optimisation algorithms, usually based on a simple set of rules. Optimisation iteratively improves the quality of solutions until an optimal, or at least feasible, solution is found. The behaviour of an individual organism is an inductive inference about some yet unknown aspects of its environment. Week 4 Lecture Notes page 1 of 1

2 If, over successive generations, the organism survives, we can say that this organism is capable of learning to predict changes in its environment. The evolutionary approach is based on computational models of natural selection and genetics. It is call evolutionary computation, an umbrella term that combines genetic algorithms, evolution strategies and genetic programming. Evolution can be seen as a process leading to the maintenance of a population s ability to survive and reproduce in a specific environment. This ability is called evolutionary fitness. Evolutionary fitness can also be viewed as a measure of the organism s ability to anticipate changes in its environment. Week 4 Lecture Notes page 2 of 2

3 The fitness, or the quantitative measure of the ability to predict environment changes and respond adequately, can be considered as the quality that is optimised in natural life. How is a population with increasing fitness generated? Let us consider a population of rabbits. Some rabbits are faster than others, and we may say that these rabbits posses superior fitness, because they have a greater chance of avoiding foxes, surviving and then breeding. If two parents have superior fitness, there is a good chance that a combination of their genes will produce an offspring with even higher fitness. Over time the entire population of rabbits becomes faster to meet their environment challenges in the face of foxes. Week 4 Lecture Notes page 3 of 3

4 Genetic Algorithms Genetic Algorithm (GA) is a sub branch of Evolutionary Algorithm (EA) GA was introduced in 1970s by John Holland with the aim to make computes do what nature does He was concerned with algorithms that manipulate strings of binary digits Each artificial chromosomes consists of a number of genes, and each gene is represented by 0 or 1: Nature has an ability to adapt and learn without being told what to do. In other words, nature finds good chromosomes blindly, and GAs do the same. Two mechanisms link a GA to the problem it is solving: encoding and evaluation. Week 4 Lecture Notes page 4 of 4

5 The GA uses a measure of fitness of individual chromosomes to carry out reproduction. As reproduction takes place, the crossover operator exchanges parts of two single chromosomes, and the mutation operator changes the gene value in some randomly chosen location of the chromosome. Basic Genetic Algorithms Step 1: Represent the problem variable domain as a chromosome of a fixed length, choose the size of a chromosome population N, the crossover probability p c, and the mutation probability p m. Step 2: Define a fitness function to measure the performance, or fitness, of an individual chromosome in the problem domain. The fitness function establishes the basis for selecting chromosomes that will be mated during reproduction. Week 4 Lecture Notes page 5 of 5

6 Step 3: Randomly generate an initial population of chromosomes of size N: x x,..., 1, 2 x N Step 4: Calculate the fitness of each individual chromosome: f ( x ), f ( x 2),..., f ( x 1 N ) Step 5: Select a pair of chromosomes for mating from the current population. Parent chromosomes are selected with a probability related to their fitness. Step 6: Create a pair of offspring chromosomes by applying the genetic operators crossover and mutation. Step 7: Place the created offspring chromosomes in the new population. Week 4 Lecture Notes page 6 of 6

7 Step 8: Repeat Step 5 until the size of new chromosome population becomes equal to the size of the initial population, N. Step 9: Replace the initial (parent) chromosome population with the new (offspring) population. Step 10: Go to Step 4, and repeat the process until the termination criterion is satisfied. GA represents an iterative process. Each iteration is called a generation. Week 4 Lecture Notes page 7 of 7

8 A typical number of generations for a simple GA can range from 50 to over 500. The entire of set of generation is called a run. Chromosomes could be: o Bit strings ( ) o Real numbers ( ) o Permutations of element (E11 E3 E7... E1 E15) o Lists of rules (R1 R2 R3... R22 R23) o Program elements (genetic programming)... any data structure... An Example: The Travelling Salesman Problem Find a tour of a given set of cities so that o each city is visited only once o the total distance travelled is minimized Representation is an ordered list of city numbers known as an order-based GA 1) London 3) Dunedin 5) Beijing 7) Tokyo 2) Venice 4) Singapore 6) Phoenix 8) Victoria CityList1 ( ) CityList2 ( ) Week 4 Lecture Notes page 8 of 8

9 Crossover combines inversion and recombination: * * Parent1 ( ) Parent2 ( ) Child ( ) This operator is called the Order 1 crossover. Mutation involves reordering of the list: * * Before: ( ) After: ( ) Example of 30 cities: Week 4 Lecture Notes page 9 of 9

10 Solution i (Distance = 941) Solution j (Distance = 800) Week 4 Lecture Notes page 10 of 10

11 Solution k (Distance = 652) Best solution (Distance = 420) Week 4 Lecture Notes page 11 of 11

12 Overview of Performance Benefits of using GA Concept is easy to understand Supports multi-objective optimization Good for noisy environments Always an answer; answer gets better with time Easy to exploit previous or alternate solutions Many ways to speed up and improve a GA-based application as knowledge about problem domain is gained Easy to exploit previous or alternate solutions Week 4 Lecture Notes page 12 of 12

13 Flexible building blocks for hybrid applications Substantial history and range of use When GA can be use? Alternate solutions are too slow or overly complicated Need an exploratory tool to examine new approaches Problem is similar to one that has already been successfully solved by using a GA Want to hybridise with an existing solution Benefits of the GA technology meet key problem requirements Week 4 Lecture Notes page 13 of 13