freetealAI and Robotics

Oct 23, 2013 (4 years and 8 months ago)


E. P. Zatsepin, post-graduate student,
National Mining University, Dnipropetrovs’k,
B. S. Busygin, Doctor of Science, Prof.
Language consltant: S. I. Kostrytska, Assoc. Prof.
Genetic algorithms as stochastic search methods based on concepts of evolution and natural selection have been used in
optimization of nonlinear problems in a wide variety of fields, including water resources and environmental analysis, due to their
robustness and general applicability to various problems. For example, genetic algorithms have been used in calibration of
hydrologic models, water quality models, optimization of water distribution systems, and water pollution control in environmental
systems, optimization of waste-water systems, and in desalination problems.
A genetic algorithms draw an analogy from the conceptual model of natural selection, in that it follows the notion of evolution
and survival of the fittest. Briefly, a genetic algorithm is a random search method that mimics the natural processes of reproduction,
crossover, and mutation. These three operations enable a genetic algorithm to more effectively sample different parts of the search
space associated with potential global minima.
Genetic algorithms have many advantages over the conventional gradient-based optimization and search methods. In the local
gradient-based methods and enumerative methods that have been traditionally used, there is a high chance of entrapment in local
minima when the error function of the searched space exhibits sharp gradients or complicated surface patterns. Unlike the
conventional methods, genetic algorithms are not local in scope and do not rely upon auxiliary information like the derivatives of the
error function of the searched space for solving the problems. The genetic search algorithm is solely driven by objective function
values. Genetic algorithm makes use of a population of points rather than a single point to search for the solution and therefore has
an advantage over other methods, which search one point at a time.
Estimation of the parameters by fitting a model to a measured breakthrough curve is an optimization problem aiming to
minimize an optional norm of the difference between measured and modeled data. Genetic algorithms have proven to be effective
and robust tools for finding the solutions to optimization problems. A genetic algorithm is a stochastic search method which works
with a population of points instead of a single point continuously moved. In a genetic algorithm, first a population of points is
generated randomly. A “fitness” is associated with each point (or individual as is called in genetic terminology) based on a measure
of optimality of the objective function evaluated at the point it represents. The probability that an individual can survive or reproduce
in the next generation is proportional to the fitness value associated with it. The reproduction of new individuals from their parents
in the previous generation takes place using an operator called cross-over. In order to perform cross-over on two individuals they are
decoded into binary values so that strings of binary values represent all decimal input values of the model. There are a few different
methods for performing cross-over. The simplest method is the one-point cross-over in which a random position is selected over the
binary strings with an equal chance given to each location and then the coded information associated with that location is swapped
with its counterpart in the mating individual and two new offspring is produced. In two-point cross-over, two randomly selected
points are selected and the strings between them are swapped. In uniform cross-over, each bit on the string have a 50 % chance of
being chosen and be swapped with its counterpart in the mating individual. Mutation is an operator which is used to maintain the
diversity in the population and allows the algorithm to avoid local minima by preventing the individuals in a population from
becoming too similar. Mutation randomly changes some bit in a binary sequence representing an individual according to the
mutation probability. The mutation probability is often chosen between 0.001 and 0.01.