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A lecture note from a university course on intelligent systems and soft computing. The lecture focuses on genetic algorithms, a method used in evolutionary computation. The basics of genetic algorithms, including the simulation of natural evolution, the concept of chromosomes and genes, and the use of roulette wheel selection, crossover, and mutation operators. The document also includes a case study on maintenance scheduling using genetic algorithms.
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Can evolution be intelligent?
ļ® Intelligence can be defined as the capability of a system to adapt its behavior to ever-changing environment. According to Alan Turing, the form or appearance of a system is irrelevant to its intelligence.
ļ® Evolutionary computation simulates evolution on a computer. The result of such a simulation is a series of optimization algorithms, usually based on a simple set of rules. Optimization iteratively improves the quality of solutions until an optimal, or at least feasible, solution is found.
Simulation of natural evolution
ļ® On 1 July 1858, Charles Darwin presented his theory of evolution before the Linnean Society of London. This day marks the beginning of a revolution in biology.
ļ® Darwinās classical theory of evolution , together with Weismannās theory of natural selection and Mendelās concept of genetics , now represent the neo-Darwinian paradigm.
ļ® Neo-Darwinism is based on processes of reproduction, mutation, competition and selection. The power to reproduce appears to be an essential property of life. The power to mutate is also guaranteed in any living organism that reproduces itself in a continuously changing environment. Processes of competition and selection normally take place in the natural world, where expanding populations of different species are limited by a finite space.
ļ® Let us consider a population of rabbits. Some rabbits are faster than others, and we may say that these rabbits possess superior fitness, because they have a greater chance of avoiding foxes, surviving and then breeding.
ļ® 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 environmental challenges in the face of foxes.
How is a population with increasing fitness generated?
Simulation of natural evolution
ļ® All methods of evolutionary computation simulate natural evolution by creating a population of individuals, evaluating their fitness, generating a new population through genetic operations, and repeating this process a number of times.
ļ® We will start with Genetic Algorithms (GAs) as most of the other evolutionary algorithms can be viewed as variations of genetic algorithms.
ļ® Nature has an ability to adapt and learn without being told what to do. In other words, nature finds good chromosomes blindly. GAs do the same. Two mechanisms link a GA to the problem it is solving: encoding and evaluation.
ļ® 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 pc and the mutation probability pm.
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.
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.
Step 8: Repeat Step 5 until the size of the 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.
Genetic algorithms
ļ® GA represents an iterative process. Each iteration is called a generation. A typical number of generations for a simple GA can range from 50 to over 500. The entire set of generations is called a run.
ļ® A common practice is to terminate a GA after a specified number of generations and then examine the best chromosomes in the population. If no satisfactory solution is found, the GA is restarted.
ļ® Because GAs use a stochastic search method, the fitness of a population may remain stable for a number of generations before a superior chromosome appears.
Suppose that the size of the chromosome population N is 6, the crossover probability pc equals 0.7, and the mutation probability pm equals 0.001. The fitness function in our example is defined by
f ( x ) = 15 x ā x^2
Chromosome label
Chromosome string
Decoded integer
Chromosome fitness
Fitness ratio, % X1 1 1 0 0 12 36 16. X2 0 1 0 0 4 44 20. X3 0 0 0 1 1 14 6. X4 1 1 1 0 14 14 6. X5 0 1 1 1 7 56 25. X6 1 0 0 1 9 54 24.
x
50 40 30 20
60
10 (^00 5 10 )
f ( x )
( a ) Chromosome initial locations.
x
50 40 30 20
60
10 (^00 5 10 ) ( b ) Chromosome final locations.
Roulette wheel selection The most commonly used chromosome selection techniques is the roulette wheel selection.
100 0
49.5 43.
X1: 16.5% X2: 20.2% X3: 6.4% X4: 6.4% X5: 25.3% X6: 24.8%
Crossover operator
ļ® In our example, we have an initial population of 6 chromosomes. Thus, to establish the same population in the next generation, the roulette wheel would be spun six times.
ļ® Once a pair of parent chromosomes is selected, the crossover operator is applied.
