Genetic algorithms for mathematical optimization

Abstract

The inability to find the solution in engineering problems has led to a large part of the scientific community developing indirect and alternative techniques to find optimization problem-solving. Genetic algorithms are looking for models based on the natural and genetic selection process, which optimizes a population or set of possible solutions to deliver one that is optimal or at least very close to it in the sense of a fitting function. In this work, we derive and evaluate a method based on genetic algorithms to find the relative maximum of differentiable functions that are difficult to find by analytical methods. We build a library in Python that includes different components from genetic algorithms. The test problems include finding the maximum or minimum of functions in one and two dimensions.

Utilizing the Genetic Algorithm to Pruning the C4.5 Decision Tree Algorithm

“…Genetic algorithm [22][23][24] is an algorithm explained by American psychologist and computer scientist John Holland to solve optimization problems. The algorithm is based on the evolution of nature as a model.…”

Personalized Clinical Treatment Selection Using Genetic Algorithm and Analytic Hierarchy Process

“…The "selection" [53][54][55] of individuals from the current population is carried out. This procedure aims to select individuals for the next generation creation, and the chance of selecting each individual directly depends on the value of his fitness function.…”

“…3.2.2. The usage of "crossover" (one of the genetic operators) [53][54][55] for crossing the resulting pairs of individuals. A mixing of "genes" (parameters of I-vector) occurs between a pair of individuals, thus forming a new individual that stores the information about his "ancestors".…”

“…In the general case, randomly the "crossover point" is determined, which allows mixing a pair of "parents": the genes of the first parent are before the crossover point, and after itthe genes of the second parent: That creates a new individual. To ensure the diversity of the population during the entire algorithm's operation, another genetic operator called "mutation" [53][54][55] is also used. This operator can be triggered with low probability instead of crossover, and its main purpose is to replace randomly selected genes of individuals with completely new ones.…”

Using particle swarm optimization to solve test functions problems

“…They proposed particle swarm optimization in order to estimate the better site and the size of distributed generation. Garcia et al [8] estimated a technique utilizing genetic algorithm (GA) to evaluate the relation maximum of differentiable functions. The authors introduced Python library contains components from the algorithm.…”