Genetic algorithms (GA) are an adaptation procedure based on the mechanics of natural genetics and natural selection. They are designed to perform search procedures of an artificial system by emulating the evolution process (Darwin’s evolution principle) observed in nature and biological organisms. The evolution process is based on the preferential survival and reproduction of the fittest member of a population with direct inheritance of genetic information from parents to offspring and the occasional mutation of genes. The principal advantages of genetic algorithms are their ability to converge expeditiously on an optimal or near-optimal solution without having to analyze all possible solutions available and without requiring derivatives or other auxiliary knowledge.

OVERVIEW OF GENETIC ALGORITHMS

Genetic algorithms are fundamentally different from traditional optimization methods in terms of the search process. While traditional routines track only a single pathway to the optimal solution, genetic algorithms search from an entire population of possible solutions (individuals). In addition, genetic algorithms use randomized and localized operators as opposed to deterministic rules. Each individual in the population is represented by either a string or a set of real numbers encoding one possible solution. The performance of each individual in the population is measured by its fitness (goodness), which quantifies the degree of optimality of the solution. Based on their fitness values, individuals are selected for reproduction of the next generation. Each new generation maintains its original size. The selected individuals reproduce their offspring by mimicking gene operations of crossover and mutation. After a number of generations, the population is expected to evolve artificially, and the optimal or near optimal solution is ultimately reached.

COMPONENTS OF GENETIC ALGORITHMS

Standard genetic algorithms involve three basic functions: selection, crossover, and mutation. Each function is briefly described below.

Selection – Individuals in a population are selected for reproduction according to their fitness values. In biology, fitness is the number of offspring that survive to reproduction. Given a population consisting of individuals identified by their chromosomes, selecting two chromosomes to represent parents to reproduce offspring is guided by a probability rule that the higher the fitness an individual has, the more likely the individual will survive. There are many selection methods available including weighted roulette wheel, sorting schemes, proportionate reproduction, and tournament selection.

Crossover - Selected parents reproduce the offspring by performing a crossover operation on the chromosomes (cut and splice pieces of one parent to those of another). In nature, crossover implies two parents exchange parts of their corresponding chromosomes. In genetic algorithms, a crossover operation makes two strings swap their partial strings. Since more fit individuals have a higher probability of producing offspring than less fit ones, the new population will possess, on average, an improved fitness level. The basic crossover is a one-point crossover. Two selected strings create two offspring strings by swapping the partial strings, which is cut by one randomly sampled breakpoint along the chromosome. The one-point crossover can easily be extended to k-point crossover. It randomly samples k breakpoints on chromosomes and then exchanges every second corresponding segments of two parent strings.

Mutation - Mutation is an insurance policy against lost bits. It works on the level of string bits by randomly altering a bit value. With small probability, it randomly selects one bit on a chromosome then inverts the bit from 0 to 1 or vice versa. The operation is designed to prevent GA from premature termination namely converging to a solution too early.

Elitism - The selection and crossover operators will tend to ensure that the best genetic material and the components of the fittest chromosomes will be carried forward to the next generation. However, the probabilistic nature of these operators implies that this will not always be the case. An elitist strategy is therefore required to ensure that the best genetic material will not be lost by chance. This is accomplished by always carrying forward the best chromosome from one generation to the next.