Fitness proportionate selection

Fitness proportionate selection example

Fitness proportionate selection, also known as roulette wheel selection, is a technique used in genetic algorithms for selecting potentially useful solutions for recombination. In a genetic algorithm, a population of candidate solutions to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genome) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.

Overview

Fitness proportionate selection works by giving each individual in the population a probability of being selected that is directly proportional to its fitness. The fitness of a solution is typically defined as the value of the objective function in the optimization problem being solved. The higher the fitness, the higher the probability of being selected for reproduction. This method mimics the process of natural selection, where the fittest individuals are more likely to be the ones that reproduce.

Mechanism

The basic mechanism of fitness proportionate selection can be compared to a roulette wheel where each slice is sized proportionally to the fitness of the individual. Imagine a wheel where each individual in the population occupies a slice of the wheel; the size of the slice is proportional to the individual's fitness. When the wheel is spun, the probability of the wheel stopping on a particular slice is proportional to the size of the slice, thus giving higher fitness individuals a greater chance of selection.

Mathematical Representation

The probability \(P(i)\) of selecting an individual \(i\) is calculated as: \[ P(i) = \frac{f_i}{\sum_{j=1}^{N} f_j} \] where \(f_i\) is the fitness of individual \(i\) and \(N\) is the total number of individuals in the population. The denominator represents the sum of fitness values of all individuals in the population, ensuring that the probabilities sum up to 1.

Advantages and Disadvantages

One of the main advantages of fitness proportionate selection is its simplicity and direct analogy to natural selection. However, it has several disadvantages. For instance, when there are individuals with very high fitness compared to the rest of the population, they can dominate the selection process, leading to a loss of genetic diversity and premature convergence on suboptimal solutions. This problem is known as "selection pressure."

Variants

To address some of the issues associated with basic fitness proportionate selection, several variants have been proposed:

• Stochastic universal sampling (SUS) is a method that provides a more even spread of selections when there are small numbers of individuals with high fitness.
• Rank-based selection involves ranking individuals by fitness and then selecting based on this ranking, rather than directly on fitness values, to help maintain diversity.
• Tournament selection selects a number of individuals randomly and then chooses the best out of these to reproduce, which can control the selection pressure more effectively.

Applications

Fitness proportionate selection is widely used in genetic algorithms for solving a variety of optimization problems, including those in artificial intelligence, machine learning, and engineering design. Its application spans across many fields such as economics, biology, and computer science, where optimization of complex systems is required.

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