## Overview: GA Procedure

Genetic algorithms are a family of local search algorithms that seek optimal solutions to problems by applying the principles of natural selection and evolution. Genetic algorithms can be applied to almost any optimization problem and are especially useful for problems where other calculus-based techniques do not work, such as when the objective function has many local optima, when it is not differentiable or continuous, or when solution elements are constrained to be integers or sequences. In most cases genetic algorithms require more computation than specialized techniques that take advantage of specific problem structures or characteristics. However, for optimization problems with no such techniques available, genetic algorithms provide a robust general method of solution.

In general, genetic algorithms use some variation of the following procedure to search for an optimal solution:

 initialization: An initial population of solutions is randomly generated, and the objective function is evaluated for each member of this initial generation. selection: Individual members of the current generation are chosen stochastically either to parent the next generation or to be passed on to it, such that those members who are the fittest are more likely to be selected. A solution’s fitness is based on its objective value, with better objective values reflecting higher fitness. crossover: Some of the selected solutions are passed to a crossover operator. The crossover operator combines two or more parents to produce new offspring solutions for the next generation. The crossover operator tends to produce new offspring that retain the common characteristics of the parent solutions, while combining the other traits in new ways. In this way new areas of the search space are explored, hopefully while retaining optimal solution characteristics. mutation: Some of the next-generation solutions are passed to a mutation operator, which introduces random variations in the solutions. The purpose of the mutation operator is to ensure that the solution space is adequately searched to prevent premature convergence to a local optimum. repeat: The current generation of solutions is replaced by the new generation. If the stopping criterion is not satisfied, the process returns to the selection phase.

The crossover and mutation operators are commonly called genetic operators. Selection and crossover distinguish genetic algorithms from a purely random search and direct the algorithm toward finding an optimum. Mutation is designed to ensure diversity in the search to prevent premature convergence to a local optimum.

There are many ways to implement the general strategy just outlined, and it is also possible to combine the genetic algorithm approach with other heuristic solution improvement techniques. In the traditional genetic algorithm, the solutions space is composed of bit strings, mapped to an objective function, and the genetic operators are modeled after biological processes. Although there is a theoretical foundation for the convergence of genetic algorithms formulated in this way, in practice most problems do not fit naturally into this paradigm. Modern research has shown that optimizations can be set up by using the natural solution domain (for example, a real vector or integer sequence) and applying crossover and mutation operators analogous to the traditional genetic operators, but more appropriate to the natural formulation of the problem. This is the approach, sometimes called evolutionary computing, taken in the GA procedure. It enables you to model your problem by using a variety of solution forms including sequences, integer or real vectors, Boolean encodings, and combinations of these. The GA procedure also provides you with a choice of genetic operators appropriate for these encodings, while permitting you to write your own.

The GA procedure enables you to implement the basic genetic algorithm by default, and to employ other advanced techniques to handle constraints, accelerate convergence, and perform multiobjective optimizations. These advanced techniques are discussed in the section Details: GA Procedure.

Although genetic algorithms have been demonstrated to work well for a variety of problems, there is no guarantee of convergence to a global optimum. Also, the convergence of genetic algorithms can be sensitive to the choice of genetic operators, mutation probability, and selection criteria, so that some initial experimentation and fine-tuning of these parameters is often required.