Evolution in mathematics
Text written by Bojan Crnković and Vedrana Mikulić Crnković, Faculty of Mathematics, University of Rijeka
Mathematical optimisation is a branch of mathematics that studies methods for determining the maximum or minimum of real functions. Many practical problems in science and everyday life can be reduced to determining the minima of a function, which is a consequence of the mathematical model of the observed problem. It is precisely for this reason that optimisation methods are often used in applied mathematics. Problems that are solved using these methods can be found in various fields: technical sciences, economics, computer science, etc.
One of the most frequently used optimisation methods is the genetic algorithm, which was inspired by the process of natural evolution. Evolutionary computation is a family of heuristic algorithms for global optimisation inspired by biological evolution. Genetic algorithms are a subtype of evolutionary algorithms. The main idea of evolutionary algorithms is to use the trial-and-error method to simulate the evolutionary process and apply it to solving various optimisation problems (determining the minimum of an objective function).
Potential solutions to the problem form a population of artificial individuals living in a virtual environment. The function whose minimum we are looking for is used to evaluate how adapted a single individual is, and based on this evaluation the individual can have more or less influence on the creation of the future generation of solutions. Each individual is assigned an artificial DNA that fully describes that individual. The artificial population undergoes a simulated evolutionary process with crossovers, selection and mutations of artificial DNA. This process has proven to be very useful for many problems and has served as inspiration for the development of artificial intelligence.