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On Some Basic Concepts of Genetic Algorithms As a Meta-Heuristic Method for Solving of Optimization Problems

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On Some Basic Concepts of Genetic Algorithms As a Meta-Heuristic Method for Solving of Optimization Problems Journal of Software Engineering and Applications, 2011, 4, 482-486 doi:10.4236/jsea.2011.48055 Published Online August 2011 (http://www.SciRP.org/journal/jsea) On Some Basic Concepts of Genetic Algorithms as a Meta-Heuristic Method for Solving of Optimization Problems Milena Bogdanović Teacher Training Faculty, University in Niš, Vranje, Serbia. Email: [email protected], [email protected] Received June 27th, 2011, revised July 25th, 2011, accepted August 1st, 2011. ABSTRACT The genetic algorithms represent a family of algorithms using some of genetic principles being present in nature, in order to solve particular computational problems. These natural principles are: inheritance, crossover, mutation, sur- vival of the fittest, migrations and so on. The paper describes the most important aspects of a genetic algorithm as a stochastic method for solving various classes of optimization problems. It also describes the basic genetic operator se- lection, crossover and mutation, serving for a new generation of individuals to achieve an optimal or a good enough solution of an optimization problem being in question. Keywords: Genetic Algorithm, Individuals, Genetic Operator, Selection, Crossover, Mutation 1. Introduction similar principles, such as: evolutionary strategies, The word heuristic is derived from the Greek word simulated annealing, εύρίεσκω meaning I find. From here it can immediately genetic programming. that the heuristic algorithms incurred in fact from ex- Evolutionary strategies, developed in Germany in the perimentation in order to obtain a satisfactory solution. sixties of the last century, have a lot of common features An important feature of heuristic algorithms is that can with a genetic algorithm. It is difficult to determine the approximately, but still good enough to solve the prob border between the two approaches having in mind their lems of exponential complexity. However, it should be various variants. Both methods work with a population of stressed the problem heuristic algorithms may not lead to solutions over which are implemented defined operations a satisfactory solution, and for some of problems, heuris- which periodically repeat. The phases of this process tic algorithms give relatively poor results. having a model in the natural evolutionary flows are Genetic algorithms are robust and adaptive methods called generations. which in addition to other fields of application can be Simulated annealing is a process having found a basis used for solving combinatorial optimization problems. in the thermodynamic motion of matter to the energy- The central concept in the description of genetic algo- minimum in a gradual lowering of temperature as a pa- rithms is a population of individuals, which is usually rameter of the system. The method works with a single between 10 and 200; each individual represents a possi- solution from which in the each iteration is required a ble solution in the search space for a problem (the space “neighboring” solution. An old solution is always re- of all solutions). placed with a new if one if it came to satisfying of crite- These algorithms can be used for solving of various ria and it is possible a better solution to be replaced by a classes of problems because they are of general nature. worse one is better if certain of stochastic are satisfied By mode of action, genetic algorithms are among the regulating the “temperature” of the system. A higher methods of guided random search techniques of space temperature gives a higher probability that a new, even a solutions in looking for a global optimum. In the same worse solution, to replace the old one. The process starts group can be classified several other methods based on from a certain temperature, which allows a relatively Copyright © 2011 SciRes. JSEA On Some Basic Concepts of Genetic Algorithms as a Meta-Heuristic Method for Solving of Optimization Problems 483 high probability of acceptance (more than 50%), this defined so that individuals do not create new solutions parameter to decrease exponentially until the motion be- that are impossible, because in this way significantly comes almost deterministic. reduce the performance of genetic algorithm. Genetic programming is an automated optimization No matter what kind of genetic algorithm works, the process of developing computer programs, whose pur- algorithm has the following parameters: population size, pose is solving most complex problems in the field of number of generations or iterations and the probability of computing, but also the problems that we encounter mutation. For generations the genetic algorithm should every day. The concept is based on ideas drawn from the also be mentioned, and the likelihood of hybridization. In general theory of genetic algorithms and other evolution- eliminative genetic algorithm, instead of crossing prob- ary methods. Simply put, the ultimate goal of genetic ability, specifies the number of individuals for elimina- programming (as product) is a universal computer pro- tion. gram that finds solutions to problems as input data. 2. Coding and Fitness Functions The genetic programming can be accessed in several different ways and from different perspectives, such as As the most important aspects of a genetic algorithm, from linear—most of them are universal access to a point out the encryption functions (coding) and adapta- computer program as a formal tree in the context of bility (fitness), which is very important to be well graph theory. In fact, any computer program can be adapted to the nature of a particular problem. It has been viewed as a tree or forest trees (in the broad sense), said that the usual binary encoding or of a higher cardi- where the internal tree nodes have the role of the opera- nality alphabet. Preferably the connection between the tor (or function of a number of variables), and leaves the genetic codes and solutions to the problem is an injective role of operands. In this case, a set of operators (function and onto mapping. Then it is possible that the application set, F) and operands (terminal set, T) are predefined sets of genetic operators in a certain generation get called of the final. incorrect individual, or the individuals whose genetic In accordance with the general theory of evolutionary code does not correspond to any solution. Overcoming algorithms, we can say that the role of chromosomal ge- this problem is possible in several ways. One possibility netic programming with non-linear structures play graphs is to allocate any such individuals as the adaptation of the and trees. It is the properties of trees as the strict mathe- function is zero, so that operators are already using such matical objects, such as a simple recursive tour, sealed selection to eliminate individuals. This approach proved the developmental course of genetic programming in a suitable only when the ratio of the number of incorrect pronounced direction. and correct individuals in the population is too large, Genetic algorithms simulate the natural evolutionary which in practice often not the case. It is possible, how- process. For the evolutionary process can be determined ever, the incorrect inclusion of individuals in the popula- as follows: tion, so that any unfair individuals assigned the value of • there is a population of individuals; penalty function. The goal is that individuals and unfair • some individuals are better (better adapted to the given a chance to participate in the crossing, but to be environment); discriminated against in relation to the correct individual. • better individuals have a higher probability of sur- Should take into account that the value of penalty func- vival and reproduction; tion balance, because too small values can lead to the fact • properties of individuals are written in the chromo- that some of the genetic algorithm codes incorrect decal- somes using the genetic code; rations of the solution, while, on the other hand, exces- • children inherit the properties (characteristics) of sive punishment can cause loss of useful information parents; from the incorrect individuals. There is another way to • Mutation can affect the individual. solve this problem—and it is unfair to individual repair The individuals represent potential solutions for ge- to make them correct or incorrect that each individual is netic algorithm, while the environment is the objective the correct replacement. function. Calculating the function of adaptation is possible in All data having indicates an individual, are written in a several ways. Some of these methods are direct down- single chromosome. In the most general case, the chromo- load, linear scaling, interval scaling, sigma clipping, etc. some can be any data structure who describes the char- The simplest way of measuring the function of adap- acteristics of one individual. The chromosome represents tation is a direct download, which means that the value a possible solution to a given problem for the genetic function for the adaptation of a specimen is taken, its algorithm. It is necessary to define the genetic operators value of objective function. However, in practice this for each data structure. These genetic operators should be approach gives poor results. Copyright © 2011 SciRes. JSEA 484 On Some Basic Concepts of Genetic Algorithms as a Meta-Heuristic Method for Solving of Optimization Problems The fitness for some individuals is calculated as a lin- 4. Crossover ear function of the objective function values and indi- viduals in the case of linear scaling. For this, there are Process of exchanging genetic material between indi- different approaches to choosing coefficients that accu- viduals of parents, in order to form new offspring indi- rately determine the linear function. viduals is performed by the operator crossover. The most scaling functions in the unit interval adaptation looks common type of operators are crossing one-position, at the interval [0, 1], with the best individual has the two-position, multi-position, and uniform crossover, and adaptability which is equal to 1, and the lowest adjusted 0.
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